Moving static to its own directory
This commit is contained in:
Piotr Mitros
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@@ -1,568 +0,0 @@
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/*
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||||
* jQuery UI CSS Framework 1.8.16
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*
|
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* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
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* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Theming/API
|
||||
*/
|
||||
|
||||
/* Layout helpers
|
||||
----------------------------------*/
|
||||
.ui-helper-hidden { display: none; }
|
||||
.ui-helper-hidden-accessible { position: absolute !important; clip: rect(1px 1px 1px 1px); clip: rect(1px,1px,1px,1px); }
|
||||
.ui-helper-reset { margin: 0; padding: 0; border: 0; outline: 0; line-height: 1.3; text-decoration: none; font-size: 100%; list-style: none; }
|
||||
.ui-helper-clearfix:after { content: "."; display: block; height: 0; clear: both; visibility: hidden; }
|
||||
.ui-helper-clearfix { display: inline-block; }
|
||||
/* required comment for clearfix to work in Opera \*/
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* html .ui-helper-clearfix { height:1%; }
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||||
.ui-helper-clearfix { display:block; }
|
||||
/* end clearfix */
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||||
.ui-helper-zfix { width: 100%; height: 100%; top: 0; left: 0; position: absolute; opacity: 0; filter:Alpha(Opacity=0); }
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||||
|
||||
|
||||
/* Interaction Cues
|
||||
----------------------------------*/
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.ui-state-disabled { cursor: default !important; }
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|
||||
|
||||
/* Icons
|
||||
----------------------------------*/
|
||||
|
||||
/* states and images */
|
||||
.ui-icon { display: block; text-indent: -99999px; overflow: hidden; background-repeat: no-repeat; }
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|
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|
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/* Misc visuals
|
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----------------------------------*/
|
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|
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/* Overlays */
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.ui-widget-overlay { position: absolute; top: 0; left: 0; width: 100%; height: 100%; }
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|
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|
||||
/*
|
||||
* jQuery UI CSS Framework 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Theming/API
|
||||
*
|
||||
* To view and modify this theme, visit http://jqueryui.com/themeroller/?ffDefault=Lucida%20Grande,%20Lucida%20Sans,%20Arial,%20sans-serif&fwDefault=bold&fsDefault=1.1em&cornerRadius=6px&bgColorHeader=deedf7&bgTextureHeader=03_highlight_soft.png&bgImgOpacityHeader=100&borderColorHeader=aed0ea&fcHeader=222222&iconColorHeader=72a7cf&bgColorContent=f2f5f7&bgTextureContent=04_highlight_hard.png&bgImgOpacityContent=100&borderColorContent=dddddd&fcContent=362b36&iconColorContent=72a7cf&bgColorDefault=d7ebf9&bgTextureDefault=02_glass.png&bgImgOpacityDefault=80&borderColorDefault=aed0ea&fcDefault=2779aa&iconColorDefault=3d80b3&bgColorHover=e4f1fb&bgTextureHover=02_glass.png&bgImgOpacityHover=100&borderColorHover=74b2e2&fcHover=0070a3&iconColorHover=2694e8&bgColorActive=3baae3&bgTextureActive=02_glass.png&bgImgOpacityActive=50&borderColorActive=2694e8&fcActive=ffffff&iconColorActive=ffffff&bgColorHighlight=ffef8f&bgTextureHighlight=03_highlight_soft.png&bgImgOpacityHighlight=25&borderColorHighlight=f9dd34&fcHighlight=363636&iconColorHighlight=2e83ff&bgColorError=cd0a0a&bgTextureError=01_flat.png&bgImgOpacityError=15&borderColorError=cd0a0a&fcError=ffffff&iconColorError=ffffff&bgColorOverlay=eeeeee&bgTextureOverlay=08_diagonals_thick.png&bgImgOpacityOverlay=90&opacityOverlay=80&bgColorShadow=000000&bgTextureShadow=04_highlight_hard.png&bgImgOpacityShadow=70&opacityShadow=30&thicknessShadow=7px&offsetTopShadow=-7px&offsetLeftShadow=-7px&cornerRadiusShadow=8px
|
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*/
|
||||
|
||||
|
||||
/* Component containers
|
||||
----------------------------------*/
|
||||
.ui-widget { font-family: Lucida Grande, Lucida Sans, Arial, sans-serif; font-size: 1.1em; }
|
||||
.ui-widget .ui-widget { font-size: 1em; }
|
||||
.ui-widget input, .ui-widget select, .ui-widget textarea, .ui-widget button { font-family: Lucida Grande, Lucida Sans, Arial, sans-serif; font-size: 1em; }
|
||||
.ui-widget-content { border: 1px solid #dddddd; background: #f2f5f7 url(images/ui-bg_highlight-hard_100_f2f5f7_1x100.png) 50% top repeat-x; color: #362b36; }
|
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.ui-widget-content a { color: #362b36; }
|
||||
.ui-widget-header { border: 1px solid #aed0ea; background: #deedf7 url(images/ui-bg_highlight-soft_100_deedf7_1x100.png) 50% 50% repeat-x; color: #222222; font-weight: bold; }
|
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.ui-widget-header a { color: #222222; }
|
||||
|
||||
/* Interaction states
|
||||
----------------------------------*/
|
||||
.ui-state-default, .ui-widget-content .ui-state-default, .ui-widget-header .ui-state-default { border: 1px solid #aed0ea; background: #d7ebf9 url(images/ui-bg_glass_80_d7ebf9_1x400.png) 50% 50% repeat-x; font-weight: bold; color: #2779aa; }
|
||||
.ui-state-default a, .ui-state-default a:link, .ui-state-default a:visited { color: #2779aa; text-decoration: none; }
|
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.ui-state-hover, .ui-widget-content .ui-state-hover, .ui-widget-header .ui-state-hover, .ui-state-focus, .ui-widget-content .ui-state-focus, .ui-widget-header .ui-state-focus { border: 1px solid #74b2e2; background: #e4f1fb url(images/ui-bg_glass_100_e4f1fb_1x400.png) 50% 50% repeat-x; font-weight: bold; color: #0070a3; }
|
||||
.ui-state-hover a, .ui-state-hover a:hover { color: #0070a3; text-decoration: none; }
|
||||
.ui-state-active, .ui-widget-content .ui-state-active, .ui-widget-header .ui-state-active { border: 1px solid #2694e8; background: #3baae3 url(images/ui-bg_glass_50_3baae3_1x400.png) 50% 50% repeat-x; font-weight: bold; color: #ffffff; }
|
||||
.ui-state-active a, .ui-state-active a:link, .ui-state-active a:visited { color: #ffffff; text-decoration: none; }
|
||||
.ui-widget :active { outline: none; }
|
||||
|
||||
/* Interaction Cues
|
||||
----------------------------------*/
|
||||
.ui-state-highlight, .ui-widget-content .ui-state-highlight, .ui-widget-header .ui-state-highlight {border: 1px solid #f9dd34; background: #ffef8f url(images/ui-bg_highlight-soft_25_ffef8f_1x100.png) 50% top repeat-x; color: #363636; }
|
||||
.ui-state-highlight a, .ui-widget-content .ui-state-highlight a,.ui-widget-header .ui-state-highlight a { color: #363636; }
|
||||
.ui-state-error, .ui-widget-content .ui-state-error, .ui-widget-header .ui-state-error {border: 1px solid #cd0a0a; background: #cd0a0a url(images/ui-bg_flat_15_cd0a0a_40x100.png) 50% 50% repeat-x; color: #ffffff; }
|
||||
.ui-state-error a, .ui-widget-content .ui-state-error a, .ui-widget-header .ui-state-error a { color: #ffffff; }
|
||||
.ui-state-error-text, .ui-widget-content .ui-state-error-text, .ui-widget-header .ui-state-error-text { color: #ffffff; }
|
||||
.ui-priority-primary, .ui-widget-content .ui-priority-primary, .ui-widget-header .ui-priority-primary { font-weight: bold; }
|
||||
.ui-priority-secondary, .ui-widget-content .ui-priority-secondary, .ui-widget-header .ui-priority-secondary { opacity: .7; filter:Alpha(Opacity=70); font-weight: normal; }
|
||||
.ui-state-disabled, .ui-widget-content .ui-state-disabled, .ui-widget-header .ui-state-disabled { opacity: .35; filter:Alpha(Opacity=35); background-image: none; }
|
||||
|
||||
/* Icons
|
||||
----------------------------------*/
|
||||
|
||||
/* states and images */
|
||||
.ui-icon { width: 16px; height: 16px; background-image: url(images/ui-icons_72a7cf_256x240.png); }
|
||||
.ui-widget-content .ui-icon {background-image: url(images/ui-icons_72a7cf_256x240.png); }
|
||||
.ui-widget-header .ui-icon {background-image: url(images/ui-icons_72a7cf_256x240.png); }
|
||||
.ui-state-default .ui-icon { background-image: url(images/ui-icons_3d80b3_256x240.png); }
|
||||
.ui-state-hover .ui-icon, .ui-state-focus .ui-icon {background-image: url(images/ui-icons_2694e8_256x240.png); }
|
||||
.ui-state-active .ui-icon {background-image: url(images/ui-icons_ffffff_256x240.png); }
|
||||
.ui-state-highlight .ui-icon {background-image: url(images/ui-icons_2e83ff_256x240.png); }
|
||||
.ui-state-error .ui-icon, .ui-state-error-text .ui-icon {background-image: url(images/ui-icons_ffffff_256x240.png); }
|
||||
|
||||
/* positioning */
|
||||
.ui-icon-carat-1-n { background-position: 0 0; }
|
||||
.ui-icon-carat-1-ne { background-position: -16px 0; }
|
||||
.ui-icon-carat-1-e { background-position: -32px 0; }
|
||||
.ui-icon-carat-1-se { background-position: -48px 0; }
|
||||
.ui-icon-carat-1-s { background-position: -64px 0; }
|
||||
.ui-icon-carat-1-sw { background-position: -80px 0; }
|
||||
.ui-icon-carat-1-w { background-position: -96px 0; }
|
||||
.ui-icon-carat-1-nw { background-position: -112px 0; }
|
||||
.ui-icon-carat-2-n-s { background-position: -128px 0; }
|
||||
.ui-icon-carat-2-e-w { background-position: -144px 0; }
|
||||
.ui-icon-triangle-1-n { background-position: 0 -16px; }
|
||||
.ui-icon-triangle-1-ne { background-position: -16px -16px; }
|
||||
.ui-icon-triangle-1-e { background-position: -32px -16px; }
|
||||
.ui-icon-triangle-1-se { background-position: -48px -16px; }
|
||||
.ui-icon-triangle-1-s { background-position: -64px -16px; }
|
||||
.ui-icon-triangle-1-sw { background-position: -80px -16px; }
|
||||
.ui-icon-triangle-1-w { background-position: -96px -16px; }
|
||||
.ui-icon-triangle-1-nw { background-position: -112px -16px; }
|
||||
.ui-icon-triangle-2-n-s { background-position: -128px -16px; }
|
||||
.ui-icon-triangle-2-e-w { background-position: -144px -16px; }
|
||||
.ui-icon-arrow-1-n { background-position: 0 -32px; }
|
||||
.ui-icon-arrow-1-ne { background-position: -16px -32px; }
|
||||
.ui-icon-arrow-1-e { background-position: -32px -32px; }
|
||||
.ui-icon-arrow-1-se { background-position: -48px -32px; }
|
||||
.ui-icon-arrow-1-s { background-position: -64px -32px; }
|
||||
.ui-icon-arrow-1-sw { background-position: -80px -32px; }
|
||||
.ui-icon-arrow-1-w { background-position: -96px -32px; }
|
||||
.ui-icon-arrow-1-nw { background-position: -112px -32px; }
|
||||
.ui-icon-arrow-2-n-s { background-position: -128px -32px; }
|
||||
.ui-icon-arrow-2-ne-sw { background-position: -144px -32px; }
|
||||
.ui-icon-arrow-2-e-w { background-position: -160px -32px; }
|
||||
.ui-icon-arrow-2-se-nw { background-position: -176px -32px; }
|
||||
.ui-icon-arrowstop-1-n { background-position: -192px -32px; }
|
||||
.ui-icon-arrowstop-1-e { background-position: -208px -32px; }
|
||||
.ui-icon-arrowstop-1-s { background-position: -224px -32px; }
|
||||
.ui-icon-arrowstop-1-w { background-position: -240px -32px; }
|
||||
.ui-icon-arrowthick-1-n { background-position: 0 -48px; }
|
||||
.ui-icon-arrowthick-1-ne { background-position: -16px -48px; }
|
||||
.ui-icon-arrowthick-1-e { background-position: -32px -48px; }
|
||||
.ui-icon-arrowthick-1-se { background-position: -48px -48px; }
|
||||
.ui-icon-arrowthick-1-s { background-position: -64px -48px; }
|
||||
.ui-icon-arrowthick-1-sw { background-position: -80px -48px; }
|
||||
.ui-icon-arrowthick-1-w { background-position: -96px -48px; }
|
||||
.ui-icon-arrowthick-1-nw { background-position: -112px -48px; }
|
||||
.ui-icon-arrowthick-2-n-s { background-position: -128px -48px; }
|
||||
.ui-icon-arrowthick-2-ne-sw { background-position: -144px -48px; }
|
||||
.ui-icon-arrowthick-2-e-w { background-position: -160px -48px; }
|
||||
.ui-icon-arrowthick-2-se-nw { background-position: -176px -48px; }
|
||||
.ui-icon-arrowthickstop-1-n { background-position: -192px -48px; }
|
||||
.ui-icon-arrowthickstop-1-e { background-position: -208px -48px; }
|
||||
.ui-icon-arrowthickstop-1-s { background-position: -224px -48px; }
|
||||
.ui-icon-arrowthickstop-1-w { background-position: -240px -48px; }
|
||||
.ui-icon-arrowreturnthick-1-w { background-position: 0 -64px; }
|
||||
.ui-icon-arrowreturnthick-1-n { background-position: -16px -64px; }
|
||||
.ui-icon-arrowreturnthick-1-e { background-position: -32px -64px; }
|
||||
.ui-icon-arrowreturnthick-1-s { background-position: -48px -64px; }
|
||||
.ui-icon-arrowreturn-1-w { background-position: -64px -64px; }
|
||||
.ui-icon-arrowreturn-1-n { background-position: -80px -64px; }
|
||||
.ui-icon-arrowreturn-1-e { background-position: -96px -64px; }
|
||||
.ui-icon-arrowreturn-1-s { background-position: -112px -64px; }
|
||||
.ui-icon-arrowrefresh-1-w { background-position: -128px -64px; }
|
||||
.ui-icon-arrowrefresh-1-n { background-position: -144px -64px; }
|
||||
.ui-icon-arrowrefresh-1-e { background-position: -160px -64px; }
|
||||
.ui-icon-arrowrefresh-1-s { background-position: -176px -64px; }
|
||||
.ui-icon-arrow-4 { background-position: 0 -80px; }
|
||||
.ui-icon-arrow-4-diag { background-position: -16px -80px; }
|
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.ui-icon-extlink { background-position: -32px -80px; }
|
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.ui-icon-newwin { background-position: -48px -80px; }
|
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.ui-icon-refresh { background-position: -64px -80px; }
|
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.ui-icon-shuffle { background-position: -80px -80px; }
|
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.ui-icon-transfer-e-w { background-position: -96px -80px; }
|
||||
.ui-icon-transferthick-e-w { background-position: -112px -80px; }
|
||||
.ui-icon-folder-collapsed { background-position: 0 -96px; }
|
||||
.ui-icon-folder-open { background-position: -16px -96px; }
|
||||
.ui-icon-document { background-position: -32px -96px; }
|
||||
.ui-icon-document-b { background-position: -48px -96px; }
|
||||
.ui-icon-note { background-position: -64px -96px; }
|
||||
.ui-icon-mail-closed { background-position: -80px -96px; }
|
||||
.ui-icon-mail-open { background-position: -96px -96px; }
|
||||
.ui-icon-suitcase { background-position: -112px -96px; }
|
||||
.ui-icon-comment { background-position: -128px -96px; }
|
||||
.ui-icon-person { background-position: -144px -96px; }
|
||||
.ui-icon-print { background-position: -160px -96px; }
|
||||
.ui-icon-trash { background-position: -176px -96px; }
|
||||
.ui-icon-locked { background-position: -192px -96px; }
|
||||
.ui-icon-unlocked { background-position: -208px -96px; }
|
||||
.ui-icon-bookmark { background-position: -224px -96px; }
|
||||
.ui-icon-tag { background-position: -240px -96px; }
|
||||
.ui-icon-home { background-position: 0 -112px; }
|
||||
.ui-icon-flag { background-position: -16px -112px; }
|
||||
.ui-icon-calendar { background-position: -32px -112px; }
|
||||
.ui-icon-cart { background-position: -48px -112px; }
|
||||
.ui-icon-pencil { background-position: -64px -112px; }
|
||||
.ui-icon-clock { background-position: -80px -112px; }
|
||||
.ui-icon-disk { background-position: -96px -112px; }
|
||||
.ui-icon-calculator { background-position: -112px -112px; }
|
||||
.ui-icon-zoomin { background-position: -128px -112px; }
|
||||
.ui-icon-zoomout { background-position: -144px -112px; }
|
||||
.ui-icon-search { background-position: -160px -112px; }
|
||||
.ui-icon-wrench { background-position: -176px -112px; }
|
||||
.ui-icon-gear { background-position: -192px -112px; }
|
||||
.ui-icon-heart { background-position: -208px -112px; }
|
||||
.ui-icon-star { background-position: -224px -112px; }
|
||||
.ui-icon-link { background-position: -240px -112px; }
|
||||
.ui-icon-cancel { background-position: 0 -128px; }
|
||||
.ui-icon-plus { background-position: -16px -128px; }
|
||||
.ui-icon-plusthick { background-position: -32px -128px; }
|
||||
.ui-icon-minus { background-position: -48px -128px; }
|
||||
.ui-icon-minusthick { background-position: -64px -128px; }
|
||||
.ui-icon-close { background-position: -80px -128px; }
|
||||
.ui-icon-closethick { background-position: -96px -128px; }
|
||||
.ui-icon-key { background-position: -112px -128px; }
|
||||
.ui-icon-lightbulb { background-position: -128px -128px; }
|
||||
.ui-icon-scissors { background-position: -144px -128px; }
|
||||
.ui-icon-clipboard { background-position: -160px -128px; }
|
||||
.ui-icon-copy { background-position: -176px -128px; }
|
||||
.ui-icon-contact { background-position: -192px -128px; }
|
||||
.ui-icon-image { background-position: -208px -128px; }
|
||||
.ui-icon-video { background-position: -224px -128px; }
|
||||
.ui-icon-script { background-position: -240px -128px; }
|
||||
.ui-icon-alert { background-position: 0 -144px; }
|
||||
.ui-icon-info { background-position: -16px -144px; }
|
||||
.ui-icon-notice { background-position: -32px -144px; }
|
||||
.ui-icon-help { background-position: -48px -144px; }
|
||||
.ui-icon-check { background-position: -64px -144px; }
|
||||
.ui-icon-bullet { background-position: -80px -144px; }
|
||||
.ui-icon-radio-off { background-position: -96px -144px; }
|
||||
.ui-icon-radio-on { background-position: -112px -144px; }
|
||||
.ui-icon-pin-w { background-position: -128px -144px; }
|
||||
.ui-icon-pin-s { background-position: -144px -144px; }
|
||||
.ui-icon-play { background-position: 0 -160px; }
|
||||
.ui-icon-pause { background-position: -16px -160px; }
|
||||
.ui-icon-seek-next { background-position: -32px -160px; }
|
||||
.ui-icon-seek-prev { background-position: -48px -160px; }
|
||||
.ui-icon-seek-end { background-position: -64px -160px; }
|
||||
.ui-icon-seek-start { background-position: -80px -160px; }
|
||||
/* ui-icon-seek-first is deprecated, use ui-icon-seek-start instead */
|
||||
.ui-icon-seek-first { background-position: -80px -160px; }
|
||||
.ui-icon-stop { background-position: -96px -160px; }
|
||||
.ui-icon-eject { background-position: -112px -160px; }
|
||||
.ui-icon-volume-off { background-position: -128px -160px; }
|
||||
.ui-icon-volume-on { background-position: -144px -160px; }
|
||||
.ui-icon-power { background-position: 0 -176px; }
|
||||
.ui-icon-signal-diag { background-position: -16px -176px; }
|
||||
.ui-icon-signal { background-position: -32px -176px; }
|
||||
.ui-icon-battery-0 { background-position: -48px -176px; }
|
||||
.ui-icon-battery-1 { background-position: -64px -176px; }
|
||||
.ui-icon-battery-2 { background-position: -80px -176px; }
|
||||
.ui-icon-battery-3 { background-position: -96px -176px; }
|
||||
.ui-icon-circle-plus { background-position: 0 -192px; }
|
||||
.ui-icon-circle-minus { background-position: -16px -192px; }
|
||||
.ui-icon-circle-close { background-position: -32px -192px; }
|
||||
.ui-icon-circle-triangle-e { background-position: -48px -192px; }
|
||||
.ui-icon-circle-triangle-s { background-position: -64px -192px; }
|
||||
.ui-icon-circle-triangle-w { background-position: -80px -192px; }
|
||||
.ui-icon-circle-triangle-n { background-position: -96px -192px; }
|
||||
.ui-icon-circle-arrow-e { background-position: -112px -192px; }
|
||||
.ui-icon-circle-arrow-s { background-position: -128px -192px; }
|
||||
.ui-icon-circle-arrow-w { background-position: -144px -192px; }
|
||||
.ui-icon-circle-arrow-n { background-position: -160px -192px; }
|
||||
.ui-icon-circle-zoomin { background-position: -176px -192px; }
|
||||
.ui-icon-circle-zoomout { background-position: -192px -192px; }
|
||||
.ui-icon-circle-check { background-position: -208px -192px; }
|
||||
.ui-icon-circlesmall-plus { background-position: 0 -208px; }
|
||||
.ui-icon-circlesmall-minus { background-position: -16px -208px; }
|
||||
.ui-icon-circlesmall-close { background-position: -32px -208px; }
|
||||
.ui-icon-squaresmall-plus { background-position: -48px -208px; }
|
||||
.ui-icon-squaresmall-minus { background-position: -64px -208px; }
|
||||
.ui-icon-squaresmall-close { background-position: -80px -208px; }
|
||||
.ui-icon-grip-dotted-vertical { background-position: 0 -224px; }
|
||||
.ui-icon-grip-dotted-horizontal { background-position: -16px -224px; }
|
||||
.ui-icon-grip-solid-vertical { background-position: -32px -224px; }
|
||||
.ui-icon-grip-solid-horizontal { background-position: -48px -224px; }
|
||||
.ui-icon-gripsmall-diagonal-se { background-position: -64px -224px; }
|
||||
.ui-icon-grip-diagonal-se { background-position: -80px -224px; }
|
||||
|
||||
|
||||
/* Misc visuals
|
||||
----------------------------------*/
|
||||
|
||||
/* Corner radius */
|
||||
.ui-corner-all, .ui-corner-top, .ui-corner-left, .ui-corner-tl { -moz-border-radius-topleft: 6px; -webkit-border-top-left-radius: 6px; -khtml-border-top-left-radius: 6px; border-top-left-radius: 6px; }
|
||||
.ui-corner-all, .ui-corner-top, .ui-corner-right, .ui-corner-tr { -moz-border-radius-topright: 6px; -webkit-border-top-right-radius: 6px; -khtml-border-top-right-radius: 6px; border-top-right-radius: 6px; }
|
||||
.ui-corner-all, .ui-corner-bottom, .ui-corner-left, .ui-corner-bl { -moz-border-radius-bottomleft: 6px; -webkit-border-bottom-left-radius: 6px; -khtml-border-bottom-left-radius: 6px; border-bottom-left-radius: 6px; }
|
||||
.ui-corner-all, .ui-corner-bottom, .ui-corner-right, .ui-corner-br { -moz-border-radius-bottomright: 6px; -webkit-border-bottom-right-radius: 6px; -khtml-border-bottom-right-radius: 6px; border-bottom-right-radius: 6px; }
|
||||
|
||||
/* Overlays */
|
||||
.ui-widget-overlay { background: #eeeeee url(images/ui-bg_diagonals-thick_90_eeeeee_40x40.png) 50% 50% repeat; opacity: .80;filter:Alpha(Opacity=80); }
|
||||
.ui-widget-shadow { margin: -7px 0 0 -7px; padding: 7px; background: #000000 url(images/ui-bg_highlight-hard_70_000000_1x100.png) 50% top repeat-x; opacity: .30;filter:Alpha(Opacity=30); -moz-border-radius: 8px; -khtml-border-radius: 8px; -webkit-border-radius: 8px; border-radius: 8px; }/*
|
||||
* jQuery UI Resizable 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Resizable#theming
|
||||
*/
|
||||
.ui-resizable { position: relative;}
|
||||
.ui-resizable-handle { position: absolute;font-size: 0.1px;z-index: 99999; display: block; }
|
||||
.ui-resizable-disabled .ui-resizable-handle, .ui-resizable-autohide .ui-resizable-handle { display: none; }
|
||||
.ui-resizable-n { cursor: n-resize; height: 7px; width: 100%; top: -5px; left: 0; }
|
||||
.ui-resizable-s { cursor: s-resize; height: 7px; width: 100%; bottom: -5px; left: 0; }
|
||||
.ui-resizable-e { cursor: e-resize; width: 7px; right: -5px; top: 0; height: 100%; }
|
||||
.ui-resizable-w { cursor: w-resize; width: 7px; left: -5px; top: 0; height: 100%; }
|
||||
.ui-resizable-se { cursor: se-resize; width: 12px; height: 12px; right: 1px; bottom: 1px; }
|
||||
.ui-resizable-sw { cursor: sw-resize; width: 9px; height: 9px; left: -5px; bottom: -5px; }
|
||||
.ui-resizable-nw { cursor: nw-resize; width: 9px; height: 9px; left: -5px; top: -5px; }
|
||||
.ui-resizable-ne { cursor: ne-resize; width: 9px; height: 9px; right: -5px; top: -5px;}/*
|
||||
* jQuery UI Selectable 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Selectable#theming
|
||||
*/
|
||||
.ui-selectable-helper { position: absolute; z-index: 100; border:1px dotted black; }
|
||||
/*
|
||||
* jQuery UI Accordion 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Accordion#theming
|
||||
*/
|
||||
/* IE/Win - Fix animation bug - #4615 */
|
||||
.ui-accordion { width: 100%; }
|
||||
.ui-accordion .ui-accordion-header { cursor: pointer; position: relative; margin-top: 1px; zoom: 1; }
|
||||
.ui-accordion .ui-accordion-li-fix { display: inline; }
|
||||
.ui-accordion .ui-accordion-header-active { border-bottom: 0 !important; }
|
||||
.ui-accordion .ui-accordion-header a { display: block; font-size: 1em; padding: .5em .5em .5em .7em; }
|
||||
.ui-accordion-icons .ui-accordion-header a { padding-left: 2.2em; }
|
||||
.ui-accordion .ui-accordion-header .ui-icon { position: absolute; left: .5em; top: 50%; margin-top: -8px; }
|
||||
.ui-accordion .ui-accordion-content { padding: 1em 2.2em; border-top: 0; margin-top: -2px; position: relative; top: 1px; margin-bottom: 2px; overflow: auto; display: none; zoom: 1; }
|
||||
.ui-accordion .ui-accordion-content-active { display: block; }
|
||||
/*
|
||||
* jQuery UI Autocomplete 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Autocomplete#theming
|
||||
*/
|
||||
.ui-autocomplete { position: absolute; cursor: default; }
|
||||
|
||||
/* workarounds */
|
||||
* html .ui-autocomplete { width:1px; } /* without this, the menu expands to 100% in IE6 */
|
||||
|
||||
/*
|
||||
* jQuery UI Menu 1.8.16
|
||||
*
|
||||
* Copyright 2010, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Menu#theming
|
||||
*/
|
||||
.ui-menu {
|
||||
list-style:none;
|
||||
padding: 2px;
|
||||
margin: 0;
|
||||
display:block;
|
||||
float: left;
|
||||
}
|
||||
.ui-menu .ui-menu {
|
||||
margin-top: -3px;
|
||||
}
|
||||
.ui-menu .ui-menu-item {
|
||||
margin:0;
|
||||
padding: 0;
|
||||
zoom: 1;
|
||||
float: left;
|
||||
clear: left;
|
||||
width: 100%;
|
||||
}
|
||||
.ui-menu .ui-menu-item a {
|
||||
text-decoration:none;
|
||||
display:block;
|
||||
padding:.2em .4em;
|
||||
line-height:1.5;
|
||||
zoom:1;
|
||||
}
|
||||
.ui-menu .ui-menu-item a.ui-state-hover,
|
||||
.ui-menu .ui-menu-item a.ui-state-active {
|
||||
font-weight: normal;
|
||||
margin: -1px;
|
||||
}
|
||||
/*
|
||||
* jQuery UI Button 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Button#theming
|
||||
*/
|
||||
.ui-button { display: inline-block; position: relative; padding: 0; margin-right: .1em; text-decoration: none !important; cursor: pointer; text-align: center; zoom: 1; overflow: visible; } /* the overflow property removes extra width in IE */
|
||||
.ui-button-icon-only { width: 2.2em; } /* to make room for the icon, a width needs to be set here */
|
||||
button.ui-button-icon-only { width: 2.4em; } /* button elements seem to need a little more width */
|
||||
.ui-button-icons-only { width: 3.4em; }
|
||||
button.ui-button-icons-only { width: 3.7em; }
|
||||
|
||||
/*button text element */
|
||||
.ui-button .ui-button-text { display: block; line-height: 1.4; }
|
||||
.ui-button-text-only .ui-button-text { padding: .4em 1em; }
|
||||
.ui-button-icon-only .ui-button-text, .ui-button-icons-only .ui-button-text { padding: .4em; text-indent: -9999999px; }
|
||||
.ui-button-text-icon-primary .ui-button-text, .ui-button-text-icons .ui-button-text { padding: .4em 1em .4em 2.1em; }
|
||||
.ui-button-text-icon-secondary .ui-button-text, .ui-button-text-icons .ui-button-text { padding: .4em 2.1em .4em 1em; }
|
||||
.ui-button-text-icons .ui-button-text { padding-left: 2.1em; padding-right: 2.1em; }
|
||||
/* no icon support for input elements, provide padding by default */
|
||||
input.ui-button { padding: .4em 1em; }
|
||||
|
||||
/*button icon element(s) */
|
||||
.ui-button-icon-only .ui-icon, .ui-button-text-icon-primary .ui-icon, .ui-button-text-icon-secondary .ui-icon, .ui-button-text-icons .ui-icon, .ui-button-icons-only .ui-icon { position: absolute; top: 50%; margin-top: -8px; }
|
||||
.ui-button-icon-only .ui-icon { left: 50%; margin-left: -8px; }
|
||||
.ui-button-text-icon-primary .ui-button-icon-primary, .ui-button-text-icons .ui-button-icon-primary, .ui-button-icons-only .ui-button-icon-primary { left: .5em; }
|
||||
.ui-button-text-icon-secondary .ui-button-icon-secondary, .ui-button-text-icons .ui-button-icon-secondary, .ui-button-icons-only .ui-button-icon-secondary { right: .5em; }
|
||||
.ui-button-text-icons .ui-button-icon-secondary, .ui-button-icons-only .ui-button-icon-secondary { right: .5em; }
|
||||
|
||||
/*button sets*/
|
||||
.ui-buttonset { margin-right: 7px; }
|
||||
.ui-buttonset .ui-button { margin-left: 0; margin-right: -.3em; }
|
||||
|
||||
/* workarounds */
|
||||
button.ui-button::-moz-focus-inner { border: 0; padding: 0; } /* reset extra padding in Firefox */
|
||||
/*
|
||||
* jQuery UI Dialog 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Dialog#theming
|
||||
*/
|
||||
.ui-dialog { position: absolute; padding: .2em; width: 300px; overflow: hidden; }
|
||||
.ui-dialog .ui-dialog-titlebar { padding: .4em 1em; position: relative; }
|
||||
.ui-dialog .ui-dialog-title { float: left; margin: .1em 16px .1em 0; }
|
||||
.ui-dialog .ui-dialog-titlebar-close { position: absolute; right: .3em; top: 50%; width: 19px; margin: -10px 0 0 0; padding: 1px; height: 18px; }
|
||||
.ui-dialog .ui-dialog-titlebar-close span { display: block; margin: 1px; }
|
||||
.ui-dialog .ui-dialog-titlebar-close:hover, .ui-dialog .ui-dialog-titlebar-close:focus { padding: 0; }
|
||||
.ui-dialog .ui-dialog-content { position: relative; border: 0; padding: .5em 1em; background: none; overflow: auto; zoom: 1; }
|
||||
.ui-dialog .ui-dialog-buttonpane { text-align: left; border-width: 1px 0 0 0; background-image: none; margin: .5em 0 0 0; padding: .3em 1em .5em .4em; }
|
||||
.ui-dialog .ui-dialog-buttonpane .ui-dialog-buttonset { float: right; }
|
||||
.ui-dialog .ui-dialog-buttonpane button { margin: .5em .4em .5em 0; cursor: pointer; }
|
||||
.ui-dialog .ui-resizable-se { width: 14px; height: 14px; right: 3px; bottom: 3px; }
|
||||
.ui-draggable .ui-dialog-titlebar { cursor: move; }
|
||||
/*
|
||||
* jQuery UI Slider 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Slider#theming
|
||||
*/
|
||||
.ui-slider { position: relative; text-align: left; }
|
||||
.ui-slider .ui-slider-handle { position: absolute; z-index: 2; width: 1.2em; height: 1.2em; cursor: default; }
|
||||
.ui-slider .ui-slider-range { position: absolute; z-index: 1; font-size: .7em; display: block; border: 0; background-position: 0 0; }
|
||||
|
||||
.ui-slider-horizontal { height: .8em; }
|
||||
.ui-slider-horizontal .ui-slider-handle { top: -.3em; margin-left: -.6em; }
|
||||
.ui-slider-horizontal .ui-slider-range { top: 0; height: 100%; }
|
||||
.ui-slider-horizontal .ui-slider-range-min { left: 0; }
|
||||
.ui-slider-horizontal .ui-slider-range-max { right: 0; }
|
||||
|
||||
.ui-slider-vertical { width: .8em; height: 100px; }
|
||||
.ui-slider-vertical .ui-slider-handle { left: -.3em; margin-left: 0; margin-bottom: -.6em; }
|
||||
.ui-slider-vertical .ui-slider-range { left: 0; width: 100%; }
|
||||
.ui-slider-vertical .ui-slider-range-min { bottom: 0; }
|
||||
.ui-slider-vertical .ui-slider-range-max { top: 0; }/*
|
||||
* jQuery UI Tabs 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Tabs#theming
|
||||
*/
|
||||
.ui-tabs { position: relative; padding: .2em; zoom: 1; } /* position: relative prevents IE scroll bug (element with position: relative inside container with overflow: auto appear as "fixed") */
|
||||
.ui-tabs .ui-tabs-nav { margin: 0; padding: .2em .2em 0; }
|
||||
.ui-tabs .ui-tabs-nav li { list-style: none; float: left; position: relative; top: 1px; margin: 0 .2em 1px 0; border-bottom: 0 !important; padding: 0; white-space: nowrap; }
|
||||
.ui-tabs .ui-tabs-nav li a { float: left; padding: .5em 1em; text-decoration: none; }
|
||||
.ui-tabs .ui-tabs-nav li.ui-tabs-selected { margin-bottom: 0; padding-bottom: 1px; }
|
||||
.ui-tabs .ui-tabs-nav li.ui-tabs-selected a, .ui-tabs .ui-tabs-nav li.ui-state-disabled a, .ui-tabs .ui-tabs-nav li.ui-state-processing a { cursor: text; }
|
||||
.ui-tabs .ui-tabs-nav li a, .ui-tabs.ui-tabs-collapsible .ui-tabs-nav li.ui-tabs-selected a { cursor: pointer; } /* first selector in group seems obsolete, but required to overcome bug in Opera applying cursor: text overall if defined elsewhere... */
|
||||
.ui-tabs .ui-tabs-panel { display: block; border-width: 0; padding: 1em 1.4em; background: none; }
|
||||
.ui-tabs .ui-tabs-hide { display: none !important; }
|
||||
/*
|
||||
* jQuery UI Datepicker 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Datepicker#theming
|
||||
*/
|
||||
.ui-datepicker { width: 17em; padding: .2em .2em 0; display: none; }
|
||||
.ui-datepicker .ui-datepicker-header { position:relative; padding:.2em 0; }
|
||||
.ui-datepicker .ui-datepicker-prev, .ui-datepicker .ui-datepicker-next { position:absolute; top: 2px; width: 1.8em; height: 1.8em; }
|
||||
.ui-datepicker .ui-datepicker-prev-hover, .ui-datepicker .ui-datepicker-next-hover { top: 1px; }
|
||||
.ui-datepicker .ui-datepicker-prev { left:2px; }
|
||||
.ui-datepicker .ui-datepicker-next { right:2px; }
|
||||
.ui-datepicker .ui-datepicker-prev-hover { left:1px; }
|
||||
.ui-datepicker .ui-datepicker-next-hover { right:1px; }
|
||||
.ui-datepicker .ui-datepicker-prev span, .ui-datepicker .ui-datepicker-next span { display: block; position: absolute; left: 50%; margin-left: -8px; top: 50%; margin-top: -8px; }
|
||||
.ui-datepicker .ui-datepicker-title { margin: 0 2.3em; line-height: 1.8em; text-align: center; }
|
||||
.ui-datepicker .ui-datepicker-title select { font-size:1em; margin:1px 0; }
|
||||
.ui-datepicker select.ui-datepicker-month-year {width: 100%;}
|
||||
.ui-datepicker select.ui-datepicker-month,
|
||||
.ui-datepicker select.ui-datepicker-year { width: 49%;}
|
||||
.ui-datepicker table {width: 100%; font-size: .9em; border-collapse: collapse; margin:0 0 .4em; }
|
||||
.ui-datepicker th { padding: .7em .3em; text-align: center; font-weight: bold; border: 0; }
|
||||
.ui-datepicker td { border: 0; padding: 1px; }
|
||||
.ui-datepicker td span, .ui-datepicker td a { display: block; padding: .2em; text-align: right; text-decoration: none; }
|
||||
.ui-datepicker .ui-datepicker-buttonpane { background-image: none; margin: .7em 0 0 0; padding:0 .2em; border-left: 0; border-right: 0; border-bottom: 0; }
|
||||
.ui-datepicker .ui-datepicker-buttonpane button { float: right; margin: .5em .2em .4em; cursor: pointer; padding: .2em .6em .3em .6em; width:auto; overflow:visible; }
|
||||
.ui-datepicker .ui-datepicker-buttonpane button.ui-datepicker-current { float:left; }
|
||||
|
||||
/* with multiple calendars */
|
||||
.ui-datepicker.ui-datepicker-multi { width:auto; }
|
||||
.ui-datepicker-multi .ui-datepicker-group { float:left; }
|
||||
.ui-datepicker-multi .ui-datepicker-group table { width:95%; margin:0 auto .4em; }
|
||||
.ui-datepicker-multi-2 .ui-datepicker-group { width:50%; }
|
||||
.ui-datepicker-multi-3 .ui-datepicker-group { width:33.3%; }
|
||||
.ui-datepicker-multi-4 .ui-datepicker-group { width:25%; }
|
||||
.ui-datepicker-multi .ui-datepicker-group-last .ui-datepicker-header { border-left-width:0; }
|
||||
.ui-datepicker-multi .ui-datepicker-group-middle .ui-datepicker-header { border-left-width:0; }
|
||||
.ui-datepicker-multi .ui-datepicker-buttonpane { clear:left; }
|
||||
.ui-datepicker-row-break { clear:both; width:100%; font-size:0em; }
|
||||
|
||||
/* RTL support */
|
||||
.ui-datepicker-rtl { direction: rtl; }
|
||||
.ui-datepicker-rtl .ui-datepicker-prev { right: 2px; left: auto; }
|
||||
.ui-datepicker-rtl .ui-datepicker-next { left: 2px; right: auto; }
|
||||
.ui-datepicker-rtl .ui-datepicker-prev:hover { right: 1px; left: auto; }
|
||||
.ui-datepicker-rtl .ui-datepicker-next:hover { left: 1px; right: auto; }
|
||||
.ui-datepicker-rtl .ui-datepicker-buttonpane { clear:right; }
|
||||
.ui-datepicker-rtl .ui-datepicker-buttonpane button { float: left; }
|
||||
.ui-datepicker-rtl .ui-datepicker-buttonpane button.ui-datepicker-current { float:right; }
|
||||
.ui-datepicker-rtl .ui-datepicker-group { float:right; }
|
||||
.ui-datepicker-rtl .ui-datepicker-group-last .ui-datepicker-header { border-right-width:0; border-left-width:1px; }
|
||||
.ui-datepicker-rtl .ui-datepicker-group-middle .ui-datepicker-header { border-right-width:0; border-left-width:1px; }
|
||||
|
||||
/* IE6 IFRAME FIX (taken from datepicker 1.5.3 */
|
||||
.ui-datepicker-cover {
|
||||
display: none; /*sorry for IE5*/
|
||||
display/**/: block; /*sorry for IE5*/
|
||||
position: absolute; /*must have*/
|
||||
z-index: -1; /*must have*/
|
||||
filter: mask(); /*must have*/
|
||||
top: -4px; /*must have*/
|
||||
left: -4px; /*must have*/
|
||||
width: 200px; /*must have*/
|
||||
height: 200px; /*must have*/
|
||||
}/*
|
||||
* jQuery UI Progressbar 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Progressbar#theming
|
||||
*/
|
||||
.ui-progressbar { height:2em; text-align: left; }
|
||||
.ui-progressbar .ui-progressbar-value {margin: -1px; height:100%; }
|
||||
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|
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568
courseware/static/css/jquery-ui-1.8.16.custom.css
vendored
568
courseware/static/css/jquery-ui-1.8.16.custom.css
vendored
@@ -1,568 +0,0 @@
|
||||
/*
|
||||
* jQuery UI CSS Framework 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Theming/API
|
||||
*/
|
||||
|
||||
/* Layout helpers
|
||||
----------------------------------*/
|
||||
.ui-helper-hidden { display: none; }
|
||||
.ui-helper-hidden-accessible { position: absolute !important; clip: rect(1px 1px 1px 1px); clip: rect(1px,1px,1px,1px); }
|
||||
.ui-helper-reset { margin: 0; padding: 0; border: 0; outline: 0; line-height: 1.3; text-decoration: none; font-size: 100%; list-style: none; }
|
||||
.ui-helper-clearfix:after { content: "."; display: block; height: 0; clear: both; visibility: hidden; }
|
||||
.ui-helper-clearfix { display: inline-block; }
|
||||
/* required comment for clearfix to work in Opera \*/
|
||||
* html .ui-helper-clearfix { height:1%; }
|
||||
.ui-helper-clearfix { display:block; }
|
||||
/* end clearfix */
|
||||
.ui-helper-zfix { width: 100%; height: 100%; top: 0; left: 0; position: absolute; opacity: 0; filter:Alpha(Opacity=0); }
|
||||
|
||||
|
||||
/* Interaction Cues
|
||||
----------------------------------*/
|
||||
.ui-state-disabled { cursor: default !important; }
|
||||
|
||||
|
||||
/* Icons
|
||||
----------------------------------*/
|
||||
|
||||
/* states and images */
|
||||
.ui-icon { display: block; text-indent: -99999px; overflow: hidden; background-repeat: no-repeat; }
|
||||
|
||||
|
||||
/* Misc visuals
|
||||
----------------------------------*/
|
||||
|
||||
/* Overlays */
|
||||
.ui-widget-overlay { position: absolute; top: 0; left: 0; width: 100%; height: 100%; }
|
||||
|
||||
|
||||
/*
|
||||
* jQuery UI CSS Framework 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Theming/API
|
||||
*
|
||||
* To view and modify this theme, visit http://jqueryui.com/themeroller/?ffDefault=Helvetica,%20Arial,%20sans-serif&fwDefault=bold&fsDefault=1.1em&cornerRadius=2px&bgColorHeader=7fbcfd&bgTextureHeader=03_highlight_soft.png&bgImgOpacityHeader=50&borderColorHeader=dae5c9&fcHeader=031634&iconColorHeader=031634&bgColorContent=ffffff&bgTextureContent=01_flat.png&bgImgOpacityContent=75&borderColorContent=dae5c9&fcContent=031634&iconColorContent=adcc80&bgColorDefault=7fbcdf&bgTextureDefault=03_highlight_soft.png&bgImgOpacityDefault=100&borderColorDefault=dae5c9&fcDefault=7a994c&iconColorDefault=adcc80&bgColorHover=bddeff&bgTextureHover=03_highlight_soft.png&bgImgOpacityHover=25&borderColorHover=7fbcdf&fcHover=7a994c&iconColorHover=adcc80&bgColorActive=023063&bgTextureActive=02_glass.png&bgImgOpacityActive=65&borderColorActive=dae5c9&fcActive=dae5c9&iconColorActive=454545&bgColorHighlight=ffffff&bgTextureHighlight=01_flat.png&bgImgOpacityHighlight=55&borderColorHighlight=cccccc&fcHighlight=444444&iconColorHighlight=adcc80&bgColorError=ffffff&bgTextureError=01_flat.png&bgImgOpacityError=55&borderColorError=fa720a&fcError=222222&iconColorError=fa720a&bgColorOverlay=eeeeee&bgTextureOverlay=01_flat.png&bgImgOpacityOverlay=0&opacityOverlay=80&bgColorShadow=aaaaaa&bgTextureShadow=01_flat.png&bgImgOpacityShadow=0&opacityShadow=60&thicknessShadow=4px&offsetTopShadow=-4px&offsetLeftShadow=-4px&cornerRadiusShadow=0px
|
||||
*/
|
||||
|
||||
|
||||
/* Component containers
|
||||
----------------------------------*/
|
||||
.ui-widget { font-family: Helvetica, Arial, sans-serif; font-size: 1.1em; }
|
||||
.ui-widget .ui-widget { font-size: 1em; }
|
||||
.ui-widget input, .ui-widget select, .ui-widget textarea, .ui-widget button { font-family: Helvetica, Arial, sans-serif; font-size: 1em; }
|
||||
.ui-widget-content { border: 1px solid #dae5c9; background: #ffffff url(images/ui-bg_flat_75_ffffff_40x100.png) 50% 50% repeat-x; color: #031634; }
|
||||
.ui-widget-content a { color: #031634; }
|
||||
.ui-widget-header { border: 1px solid #dae5c9; background: #7fbcfd url(images/ui-bg_highlight-soft_50_7fbcfd_1x100.png) 50% 50% repeat-x; color: #031634; font-weight: bold; }
|
||||
.ui-widget-header a { color: #031634; }
|
||||
|
||||
/* Interaction states
|
||||
----------------------------------*/
|
||||
.ui-state-default, .ui-widget-content .ui-state-default, .ui-widget-header .ui-state-default { border: 1px solid #dae5c9; background: #7fbcdf url(images/ui-bg_highlight-soft_100_7fbcdf_1x100.png) 50% 50% repeat-x; font-weight: bold; color: #7a994c; }
|
||||
.ui-state-default a, .ui-state-default a:link, .ui-state-default a:visited { color: #7a994c; text-decoration: none; }
|
||||
.ui-state-hover, .ui-widget-content .ui-state-hover, .ui-widget-header .ui-state-hover, .ui-state-focus, .ui-widget-content .ui-state-focus, .ui-widget-header .ui-state-focus { border: 1px solid #7fbcdf; background: #bddeff url(images/ui-bg_highlight-soft_25_bddeff_1x100.png) 50% 50% repeat-x; font-weight: bold; color: #7a994c; }
|
||||
.ui-state-hover a, .ui-state-hover a:hover { color: #7a994c; text-decoration: none; }
|
||||
.ui-state-active, .ui-widget-content .ui-state-active, .ui-widget-header .ui-state-active { border: 1px solid #dae5c9; background: #023063 url(images/ui-bg_glass_65_023063_1x400.png) 50% 50% repeat-x; font-weight: bold; color: #dae5c9; }
|
||||
.ui-state-active a, .ui-state-active a:link, .ui-state-active a:visited { color: #dae5c9; text-decoration: none; }
|
||||
.ui-widget :active { outline: none; }
|
||||
|
||||
/* Interaction Cues
|
||||
----------------------------------*/
|
||||
.ui-state-highlight, .ui-widget-content .ui-state-highlight, .ui-widget-header .ui-state-highlight {border: 1px solid #cccccc; background: #ffffff url(images/ui-bg_flat_55_ffffff_40x100.png) 50% 50% repeat-x; color: #444444; }
|
||||
.ui-state-highlight a, .ui-widget-content .ui-state-highlight a,.ui-widget-header .ui-state-highlight a { color: #444444; }
|
||||
.ui-state-error, .ui-widget-content .ui-state-error, .ui-widget-header .ui-state-error {border: 1px solid #fa720a; background: #ffffff url(images/ui-bg_flat_55_ffffff_40x100.png) 50% 50% repeat-x; color: #222222; }
|
||||
.ui-state-error a, .ui-widget-content .ui-state-error a, .ui-widget-header .ui-state-error a { color: #222222; }
|
||||
.ui-state-error-text, .ui-widget-content .ui-state-error-text, .ui-widget-header .ui-state-error-text { color: #222222; }
|
||||
.ui-priority-primary, .ui-widget-content .ui-priority-primary, .ui-widget-header .ui-priority-primary { font-weight: bold; }
|
||||
.ui-priority-secondary, .ui-widget-content .ui-priority-secondary, .ui-widget-header .ui-priority-secondary { opacity: .7; filter:Alpha(Opacity=70); font-weight: normal; }
|
||||
.ui-state-disabled, .ui-widget-content .ui-state-disabled, .ui-widget-header .ui-state-disabled { opacity: .35; filter:Alpha(Opacity=35); background-image: none; }
|
||||
|
||||
/* Icons
|
||||
----------------------------------*/
|
||||
|
||||
/* states and images */
|
||||
.ui-icon { width: 16px; height: 16px; background-image: url(images/ui-icons_adcc80_256x240.png); }
|
||||
.ui-widget-content .ui-icon {background-image: url(images/ui-icons_adcc80_256x240.png); }
|
||||
.ui-widget-header .ui-icon {background-image: url(images/ui-icons_031634_256x240.png); }
|
||||
.ui-state-default .ui-icon { background-image: url(images/ui-icons_adcc80_256x240.png); }
|
||||
.ui-state-hover .ui-icon, .ui-state-focus .ui-icon {background-image: url(images/ui-icons_adcc80_256x240.png); }
|
||||
.ui-state-active .ui-icon {background-image: url(images/ui-icons_454545_256x240.png); }
|
||||
.ui-state-highlight .ui-icon {background-image: url(images/ui-icons_adcc80_256x240.png); }
|
||||
.ui-state-error .ui-icon, .ui-state-error-text .ui-icon {background-image: url(images/ui-icons_fa720a_256x240.png); }
|
||||
|
||||
/* positioning */
|
||||
.ui-icon-carat-1-n { background-position: 0 0; }
|
||||
.ui-icon-carat-1-ne { background-position: -16px 0; }
|
||||
.ui-icon-carat-1-e { background-position: -32px 0; }
|
||||
.ui-icon-carat-1-se { background-position: -48px 0; }
|
||||
.ui-icon-carat-1-s { background-position: -64px 0; }
|
||||
.ui-icon-carat-1-sw { background-position: -80px 0; }
|
||||
.ui-icon-carat-1-w { background-position: -96px 0; }
|
||||
.ui-icon-carat-1-nw { background-position: -112px 0; }
|
||||
.ui-icon-carat-2-n-s { background-position: -128px 0; }
|
||||
.ui-icon-carat-2-e-w { background-position: -144px 0; }
|
||||
.ui-icon-triangle-1-n { background-position: 0 -16px; }
|
||||
.ui-icon-triangle-1-ne { background-position: -16px -16px; }
|
||||
.ui-icon-triangle-1-e { background-position: -32px -16px; }
|
||||
.ui-icon-triangle-1-se { background-position: -48px -16px; }
|
||||
.ui-icon-triangle-1-s { background-position: -64px -16px; }
|
||||
.ui-icon-triangle-1-sw { background-position: -80px -16px; }
|
||||
.ui-icon-triangle-1-w { background-position: -96px -16px; }
|
||||
.ui-icon-triangle-1-nw { background-position: -112px -16px; }
|
||||
.ui-icon-triangle-2-n-s { background-position: -128px -16px; }
|
||||
.ui-icon-triangle-2-e-w { background-position: -144px -16px; }
|
||||
.ui-icon-arrow-1-n { background-position: 0 -32px; }
|
||||
.ui-icon-arrow-1-ne { background-position: -16px -32px; }
|
||||
.ui-icon-arrow-1-e { background-position: -32px -32px; }
|
||||
.ui-icon-arrow-1-se { background-position: -48px -32px; }
|
||||
.ui-icon-arrow-1-s { background-position: -64px -32px; }
|
||||
.ui-icon-arrow-1-sw { background-position: -80px -32px; }
|
||||
.ui-icon-arrow-1-w { background-position: -96px -32px; }
|
||||
.ui-icon-arrow-1-nw { background-position: -112px -32px; }
|
||||
.ui-icon-arrow-2-n-s { background-position: -128px -32px; }
|
||||
.ui-icon-arrow-2-ne-sw { background-position: -144px -32px; }
|
||||
.ui-icon-arrow-2-e-w { background-position: -160px -32px; }
|
||||
.ui-icon-arrow-2-se-nw { background-position: -176px -32px; }
|
||||
.ui-icon-arrowstop-1-n { background-position: -192px -32px; }
|
||||
.ui-icon-arrowstop-1-e { background-position: -208px -32px; }
|
||||
.ui-icon-arrowstop-1-s { background-position: -224px -32px; }
|
||||
.ui-icon-arrowstop-1-w { background-position: -240px -32px; }
|
||||
.ui-icon-arrowthick-1-n { background-position: 0 -48px; }
|
||||
.ui-icon-arrowthick-1-ne { background-position: -16px -48px; }
|
||||
.ui-icon-arrowthick-1-e { background-position: -32px -48px; }
|
||||
.ui-icon-arrowthick-1-se { background-position: -48px -48px; }
|
||||
.ui-icon-arrowthick-1-s { background-position: -64px -48px; }
|
||||
.ui-icon-arrowthick-1-sw { background-position: -80px -48px; }
|
||||
.ui-icon-arrowthick-1-w { background-position: -96px -48px; }
|
||||
.ui-icon-arrowthick-1-nw { background-position: -112px -48px; }
|
||||
.ui-icon-arrowthick-2-n-s { background-position: -128px -48px; }
|
||||
.ui-icon-arrowthick-2-ne-sw { background-position: -144px -48px; }
|
||||
.ui-icon-arrowthick-2-e-w { background-position: -160px -48px; }
|
||||
.ui-icon-arrowthick-2-se-nw { background-position: -176px -48px; }
|
||||
.ui-icon-arrowthickstop-1-n { background-position: -192px -48px; }
|
||||
.ui-icon-arrowthickstop-1-e { background-position: -208px -48px; }
|
||||
.ui-icon-arrowthickstop-1-s { background-position: -224px -48px; }
|
||||
.ui-icon-arrowthickstop-1-w { background-position: -240px -48px; }
|
||||
.ui-icon-arrowreturnthick-1-w { background-position: 0 -64px; }
|
||||
.ui-icon-arrowreturnthick-1-n { background-position: -16px -64px; }
|
||||
.ui-icon-arrowreturnthick-1-e { background-position: -32px -64px; }
|
||||
.ui-icon-arrowreturnthick-1-s { background-position: -48px -64px; }
|
||||
.ui-icon-arrowreturn-1-w { background-position: -64px -64px; }
|
||||
.ui-icon-arrowreturn-1-n { background-position: -80px -64px; }
|
||||
.ui-icon-arrowreturn-1-e { background-position: -96px -64px; }
|
||||
.ui-icon-arrowreturn-1-s { background-position: -112px -64px; }
|
||||
.ui-icon-arrowrefresh-1-w { background-position: -128px -64px; }
|
||||
.ui-icon-arrowrefresh-1-n { background-position: -144px -64px; }
|
||||
.ui-icon-arrowrefresh-1-e { background-position: -160px -64px; }
|
||||
.ui-icon-arrowrefresh-1-s { background-position: -176px -64px; }
|
||||
.ui-icon-arrow-4 { background-position: 0 -80px; }
|
||||
.ui-icon-arrow-4-diag { background-position: -16px -80px; }
|
||||
.ui-icon-extlink { background-position: -32px -80px; }
|
||||
.ui-icon-newwin { background-position: -48px -80px; }
|
||||
.ui-icon-refresh { background-position: -64px -80px; }
|
||||
.ui-icon-shuffle { background-position: -80px -80px; }
|
||||
.ui-icon-transfer-e-w { background-position: -96px -80px; }
|
||||
.ui-icon-transferthick-e-w { background-position: -112px -80px; }
|
||||
.ui-icon-folder-collapsed { background-position: 0 -96px; }
|
||||
.ui-icon-folder-open { background-position: -16px -96px; }
|
||||
.ui-icon-document { background-position: -32px -96px; }
|
||||
.ui-icon-document-b { background-position: -48px -96px; }
|
||||
.ui-icon-note { background-position: -64px -96px; }
|
||||
.ui-icon-mail-closed { background-position: -80px -96px; }
|
||||
.ui-icon-mail-open { background-position: -96px -96px; }
|
||||
.ui-icon-suitcase { background-position: -112px -96px; }
|
||||
.ui-icon-comment { background-position: -128px -96px; }
|
||||
.ui-icon-person { background-position: -144px -96px; }
|
||||
.ui-icon-print { background-position: -160px -96px; }
|
||||
.ui-icon-trash { background-position: -176px -96px; }
|
||||
.ui-icon-locked { background-position: -192px -96px; }
|
||||
.ui-icon-unlocked { background-position: -208px -96px; }
|
||||
.ui-icon-bookmark { background-position: -224px -96px; }
|
||||
.ui-icon-tag { background-position: -240px -96px; }
|
||||
.ui-icon-home { background-position: 0 -112px; }
|
||||
.ui-icon-flag { background-position: -16px -112px; }
|
||||
.ui-icon-calendar { background-position: -32px -112px; }
|
||||
.ui-icon-cart { background-position: -48px -112px; }
|
||||
.ui-icon-pencil { background-position: -64px -112px; }
|
||||
.ui-icon-clock { background-position: -80px -112px; }
|
||||
.ui-icon-disk { background-position: -96px -112px; }
|
||||
.ui-icon-calculator { background-position: -112px -112px; }
|
||||
.ui-icon-zoomin { background-position: -128px -112px; }
|
||||
.ui-icon-zoomout { background-position: -144px -112px; }
|
||||
.ui-icon-search { background-position: -160px -112px; }
|
||||
.ui-icon-wrench { background-position: -176px -112px; }
|
||||
.ui-icon-gear { background-position: -192px -112px; }
|
||||
.ui-icon-heart { background-position: -208px -112px; }
|
||||
.ui-icon-star { background-position: -224px -112px; }
|
||||
.ui-icon-link { background-position: -240px -112px; }
|
||||
.ui-icon-cancel { background-position: 0 -128px; }
|
||||
.ui-icon-plus { background-position: -16px -128px; }
|
||||
.ui-icon-plusthick { background-position: -32px -128px; }
|
||||
.ui-icon-minus { background-position: -48px -128px; }
|
||||
.ui-icon-minusthick { background-position: -64px -128px; }
|
||||
.ui-icon-close { background-position: -80px -128px; }
|
||||
.ui-icon-closethick { background-position: -96px -128px; }
|
||||
.ui-icon-key { background-position: -112px -128px; }
|
||||
.ui-icon-lightbulb { background-position: -128px -128px; }
|
||||
.ui-icon-scissors { background-position: -144px -128px; }
|
||||
.ui-icon-clipboard { background-position: -160px -128px; }
|
||||
.ui-icon-copy { background-position: -176px -128px; }
|
||||
.ui-icon-contact { background-position: -192px -128px; }
|
||||
.ui-icon-image { background-position: -208px -128px; }
|
||||
.ui-icon-video { background-position: -224px -128px; }
|
||||
.ui-icon-script { background-position: -240px -128px; }
|
||||
.ui-icon-alert { background-position: 0 -144px; }
|
||||
.ui-icon-info { background-position: -16px -144px; }
|
||||
.ui-icon-notice { background-position: -32px -144px; }
|
||||
.ui-icon-help { background-position: -48px -144px; }
|
||||
.ui-icon-check { background-position: -64px -144px; }
|
||||
.ui-icon-bullet { background-position: -80px -144px; }
|
||||
.ui-icon-radio-off { background-position: -96px -144px; }
|
||||
.ui-icon-radio-on { background-position: -112px -144px; }
|
||||
.ui-icon-pin-w { background-position: -128px -144px; }
|
||||
.ui-icon-pin-s { background-position: -144px -144px; }
|
||||
.ui-icon-play { background-position: 0 -160px; }
|
||||
.ui-icon-pause { background-position: -16px -160px; }
|
||||
.ui-icon-seek-next { background-position: -32px -160px; }
|
||||
.ui-icon-seek-prev { background-position: -48px -160px; }
|
||||
.ui-icon-seek-end { background-position: -64px -160px; }
|
||||
.ui-icon-seek-start { background-position: -80px -160px; }
|
||||
/* ui-icon-seek-first is deprecated, use ui-icon-seek-start instead */
|
||||
.ui-icon-seek-first { background-position: -80px -160px; }
|
||||
.ui-icon-stop { background-position: -96px -160px; }
|
||||
.ui-icon-eject { background-position: -112px -160px; }
|
||||
.ui-icon-volume-off { background-position: -128px -160px; }
|
||||
.ui-icon-volume-on { background-position: -144px -160px; }
|
||||
.ui-icon-power { background-position: 0 -176px; }
|
||||
.ui-icon-signal-diag { background-position: -16px -176px; }
|
||||
.ui-icon-signal { background-position: -32px -176px; }
|
||||
.ui-icon-battery-0 { background-position: -48px -176px; }
|
||||
.ui-icon-battery-1 { background-position: -64px -176px; }
|
||||
.ui-icon-battery-2 { background-position: -80px -176px; }
|
||||
.ui-icon-battery-3 { background-position: -96px -176px; }
|
||||
.ui-icon-circle-plus { background-position: 0 -192px; }
|
||||
.ui-icon-circle-minus { background-position: -16px -192px; }
|
||||
.ui-icon-circle-close { background-position: -32px -192px; }
|
||||
.ui-icon-circle-triangle-e { background-position: -48px -192px; }
|
||||
.ui-icon-circle-triangle-s { background-position: -64px -192px; }
|
||||
.ui-icon-circle-triangle-w { background-position: -80px -192px; }
|
||||
.ui-icon-circle-triangle-n { background-position: -96px -192px; }
|
||||
.ui-icon-circle-arrow-e { background-position: -112px -192px; }
|
||||
.ui-icon-circle-arrow-s { background-position: -128px -192px; }
|
||||
.ui-icon-circle-arrow-w { background-position: -144px -192px; }
|
||||
.ui-icon-circle-arrow-n { background-position: -160px -192px; }
|
||||
.ui-icon-circle-zoomin { background-position: -176px -192px; }
|
||||
.ui-icon-circle-zoomout { background-position: -192px -192px; }
|
||||
.ui-icon-circle-check { background-position: -208px -192px; }
|
||||
.ui-icon-circlesmall-plus { background-position: 0 -208px; }
|
||||
.ui-icon-circlesmall-minus { background-position: -16px -208px; }
|
||||
.ui-icon-circlesmall-close { background-position: -32px -208px; }
|
||||
.ui-icon-squaresmall-plus { background-position: -48px -208px; }
|
||||
.ui-icon-squaresmall-minus { background-position: -64px -208px; }
|
||||
.ui-icon-squaresmall-close { background-position: -80px -208px; }
|
||||
.ui-icon-grip-dotted-vertical { background-position: 0 -224px; }
|
||||
.ui-icon-grip-dotted-horizontal { background-position: -16px -224px; }
|
||||
.ui-icon-grip-solid-vertical { background-position: -32px -224px; }
|
||||
.ui-icon-grip-solid-horizontal { background-position: -48px -224px; }
|
||||
.ui-icon-gripsmall-diagonal-se { background-position: -64px -224px; }
|
||||
.ui-icon-grip-diagonal-se { background-position: -80px -224px; }
|
||||
|
||||
|
||||
/* Misc visuals
|
||||
----------------------------------*/
|
||||
|
||||
/* Corner radius */
|
||||
.ui-corner-all, .ui-corner-top, .ui-corner-left, .ui-corner-tl { -moz-border-radius-topleft: 2px; -webkit-border-top-left-radius: 2px; -khtml-border-top-left-radius: 2px; border-top-left-radius: 2px; }
|
||||
.ui-corner-all, .ui-corner-top, .ui-corner-right, .ui-corner-tr { -moz-border-radius-topright: 2px; -webkit-border-top-right-radius: 2px; -khtml-border-top-right-radius: 2px; border-top-right-radius: 2px; }
|
||||
.ui-corner-all, .ui-corner-bottom, .ui-corner-left, .ui-corner-bl { -moz-border-radius-bottomleft: 2px; -webkit-border-bottom-left-radius: 2px; -khtml-border-bottom-left-radius: 2px; border-bottom-left-radius: 2px; }
|
||||
.ui-corner-all, .ui-corner-bottom, .ui-corner-right, .ui-corner-br { -moz-border-radius-bottomright: 2px; -webkit-border-bottom-right-radius: 2px; -khtml-border-bottom-right-radius: 2px; border-bottom-right-radius: 2px; }
|
||||
|
||||
/* Overlays */
|
||||
.ui-widget-overlay { background: #eeeeee url(images/ui-bg_flat_0_eeeeee_40x100.png) 50% 50% repeat-x; opacity: .80;filter:Alpha(Opacity=80); }
|
||||
.ui-widget-shadow { margin: -4px 0 0 -4px; padding: 4px; background: #aaaaaa url(images/ui-bg_flat_0_aaaaaa_40x100.png) 50% 50% repeat-x; opacity: .60;filter:Alpha(Opacity=60); -moz-border-radius: 0px; -khtml-border-radius: 0px; -webkit-border-radius: 0px; border-radius: 0px; }/*
|
||||
* jQuery UI Resizable 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Resizable#theming
|
||||
*/
|
||||
.ui-resizable { position: relative;}
|
||||
.ui-resizable-handle { position: absolute;font-size: 0.1px;z-index: 99999; display: block; }
|
||||
.ui-resizable-disabled .ui-resizable-handle, .ui-resizable-autohide .ui-resizable-handle { display: none; }
|
||||
.ui-resizable-n { cursor: n-resize; height: 7px; width: 100%; top: -5px; left: 0; }
|
||||
.ui-resizable-s { cursor: s-resize; height: 7px; width: 100%; bottom: -5px; left: 0; }
|
||||
.ui-resizable-e { cursor: e-resize; width: 7px; right: -5px; top: 0; height: 100%; }
|
||||
.ui-resizable-w { cursor: w-resize; width: 7px; left: -5px; top: 0; height: 100%; }
|
||||
.ui-resizable-se { cursor: se-resize; width: 12px; height: 12px; right: 1px; bottom: 1px; }
|
||||
.ui-resizable-sw { cursor: sw-resize; width: 9px; height: 9px; left: -5px; bottom: -5px; }
|
||||
.ui-resizable-nw { cursor: nw-resize; width: 9px; height: 9px; left: -5px; top: -5px; }
|
||||
.ui-resizable-ne { cursor: ne-resize; width: 9px; height: 9px; right: -5px; top: -5px;}/*
|
||||
* jQuery UI Selectable 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Selectable#theming
|
||||
*/
|
||||
.ui-selectable-helper { position: absolute; z-index: 100; border:1px dotted black; }
|
||||
/*
|
||||
* jQuery UI Accordion 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Accordion#theming
|
||||
*/
|
||||
/* IE/Win - Fix animation bug - #4615 */
|
||||
.ui-accordion { width: 100%; }
|
||||
.ui-accordion .ui-accordion-header { cursor: pointer; position: relative; margin-top: 1px; zoom: 1; }
|
||||
.ui-accordion .ui-accordion-li-fix { display: inline; }
|
||||
.ui-accordion .ui-accordion-header-active { border-bottom: 0 !important; }
|
||||
.ui-accordion .ui-accordion-header a { display: block; font-size: 1em; padding: .5em .5em .5em .7em; }
|
||||
.ui-accordion-icons .ui-accordion-header a { padding-left: 2.2em; }
|
||||
.ui-accordion .ui-accordion-header .ui-icon { position: absolute; left: .5em; top: 50%; margin-top: -8px; }
|
||||
.ui-accordion .ui-accordion-content { padding: 1em 2.2em; border-top: 0; margin-top: -2px; position: relative; top: 1px; margin-bottom: 2px; overflow: auto; display: none; zoom: 1; }
|
||||
.ui-accordion .ui-accordion-content-active { display: block; }
|
||||
/*
|
||||
* jQuery UI Autocomplete 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Autocomplete#theming
|
||||
*/
|
||||
.ui-autocomplete { position: absolute; cursor: default; }
|
||||
|
||||
/* workarounds */
|
||||
* html .ui-autocomplete { width:1px; } /* without this, the menu expands to 100% in IE6 */
|
||||
|
||||
/*
|
||||
* jQuery UI Menu 1.8.16
|
||||
*
|
||||
* Copyright 2010, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Menu#theming
|
||||
*/
|
||||
.ui-menu {
|
||||
list-style:none;
|
||||
padding: 2px;
|
||||
margin: 0;
|
||||
display:block;
|
||||
float: left;
|
||||
}
|
||||
.ui-menu .ui-menu {
|
||||
margin-top: -3px;
|
||||
}
|
||||
.ui-menu .ui-menu-item {
|
||||
margin:0;
|
||||
padding: 0;
|
||||
zoom: 1;
|
||||
float: left;
|
||||
clear: left;
|
||||
width: 100%;
|
||||
}
|
||||
.ui-menu .ui-menu-item a {
|
||||
text-decoration:none;
|
||||
display:block;
|
||||
padding:.2em .4em;
|
||||
line-height:1.5;
|
||||
zoom:1;
|
||||
}
|
||||
.ui-menu .ui-menu-item a.ui-state-hover,
|
||||
.ui-menu .ui-menu-item a.ui-state-active {
|
||||
font-weight: normal;
|
||||
margin: -1px;
|
||||
}
|
||||
/*
|
||||
* jQuery UI Button 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Button#theming
|
||||
*/
|
||||
.ui-button { display: inline-block; position: relative; padding: 0; margin-right: .1em; text-decoration: none !important; cursor: pointer; text-align: center; zoom: 1; overflow: visible; } /* the overflow property removes extra width in IE */
|
||||
.ui-button-icon-only { width: 2.2em; } /* to make room for the icon, a width needs to be set here */
|
||||
button.ui-button-icon-only { width: 2.4em; } /* button elements seem to need a little more width */
|
||||
.ui-button-icons-only { width: 3.4em; }
|
||||
button.ui-button-icons-only { width: 3.7em; }
|
||||
|
||||
/*button text element */
|
||||
.ui-button .ui-button-text { display: block; line-height: 1.4; }
|
||||
.ui-button-text-only .ui-button-text { padding: .4em 1em; }
|
||||
.ui-button-icon-only .ui-button-text, .ui-button-icons-only .ui-button-text { padding: .4em; text-indent: -9999999px; }
|
||||
.ui-button-text-icon-primary .ui-button-text, .ui-button-text-icons .ui-button-text { padding: .4em 1em .4em 2.1em; }
|
||||
.ui-button-text-icon-secondary .ui-button-text, .ui-button-text-icons .ui-button-text { padding: .4em 2.1em .4em 1em; }
|
||||
.ui-button-text-icons .ui-button-text { padding-left: 2.1em; padding-right: 2.1em; }
|
||||
/* no icon support for input elements, provide padding by default */
|
||||
input.ui-button { padding: .4em 1em; }
|
||||
|
||||
/*button icon element(s) */
|
||||
.ui-button-icon-only .ui-icon, .ui-button-text-icon-primary .ui-icon, .ui-button-text-icon-secondary .ui-icon, .ui-button-text-icons .ui-icon, .ui-button-icons-only .ui-icon { position: absolute; top: 50%; margin-top: -8px; }
|
||||
.ui-button-icon-only .ui-icon { left: 50%; margin-left: -8px; }
|
||||
.ui-button-text-icon-primary .ui-button-icon-primary, .ui-button-text-icons .ui-button-icon-primary, .ui-button-icons-only .ui-button-icon-primary { left: .5em; }
|
||||
.ui-button-text-icon-secondary .ui-button-icon-secondary, .ui-button-text-icons .ui-button-icon-secondary, .ui-button-icons-only .ui-button-icon-secondary { right: .5em; }
|
||||
.ui-button-text-icons .ui-button-icon-secondary, .ui-button-icons-only .ui-button-icon-secondary { right: .5em; }
|
||||
|
||||
/*button sets*/
|
||||
.ui-buttonset { margin-right: 7px; }
|
||||
.ui-buttonset .ui-button { margin-left: 0; margin-right: -.3em; }
|
||||
|
||||
/* workarounds */
|
||||
button.ui-button::-moz-focus-inner { border: 0; padding: 0; } /* reset extra padding in Firefox */
|
||||
/*
|
||||
* jQuery UI Dialog 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Dialog#theming
|
||||
*/
|
||||
.ui-dialog { position: absolute; padding: .2em; width: 300px; overflow: hidden; }
|
||||
.ui-dialog .ui-dialog-titlebar { padding: .4em 1em; position: relative; }
|
||||
.ui-dialog .ui-dialog-title { float: left; margin: .1em 16px .1em 0; }
|
||||
.ui-dialog .ui-dialog-titlebar-close { position: absolute; right: .3em; top: 50%; width: 19px; margin: -10px 0 0 0; padding: 1px; height: 18px; }
|
||||
.ui-dialog .ui-dialog-titlebar-close span { display: block; margin: 1px; }
|
||||
.ui-dialog .ui-dialog-titlebar-close:hover, .ui-dialog .ui-dialog-titlebar-close:focus { padding: 0; }
|
||||
.ui-dialog .ui-dialog-content { position: relative; border: 0; padding: .5em 1em; background: none; overflow: auto; zoom: 1; }
|
||||
.ui-dialog .ui-dialog-buttonpane { text-align: left; border-width: 1px 0 0 0; background-image: none; margin: .5em 0 0 0; padding: .3em 1em .5em .4em; }
|
||||
.ui-dialog .ui-dialog-buttonpane .ui-dialog-buttonset { float: right; }
|
||||
.ui-dialog .ui-dialog-buttonpane button { margin: .5em .4em .5em 0; cursor: pointer; }
|
||||
.ui-dialog .ui-resizable-se { width: 14px; height: 14px; right: 3px; bottom: 3px; }
|
||||
.ui-draggable .ui-dialog-titlebar { cursor: move; }
|
||||
/*
|
||||
* jQuery UI Slider 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Slider#theming
|
||||
*/
|
||||
.ui-slider { position: relative; text-align: left; }
|
||||
.ui-slider .ui-slider-handle { position: absolute; z-index: 2; width: 1.2em; height: 1.2em; cursor: default; }
|
||||
.ui-slider .ui-slider-range { position: absolute; z-index: 1; font-size: .7em; display: block; border: 0; background-position: 0 0; }
|
||||
|
||||
.ui-slider-horizontal { height: .8em; }
|
||||
.ui-slider-horizontal .ui-slider-handle { top: -.3em; margin-left: -.6em; }
|
||||
.ui-slider-horizontal .ui-slider-range { top: 0; height: 100%; }
|
||||
.ui-slider-horizontal .ui-slider-range-min { left: 0; }
|
||||
.ui-slider-horizontal .ui-slider-range-max { right: 0; }
|
||||
|
||||
.ui-slider-vertical { width: .8em; height: 100px; }
|
||||
.ui-slider-vertical .ui-slider-handle { left: -.3em; margin-left: 0; margin-bottom: -.6em; }
|
||||
.ui-slider-vertical .ui-slider-range { left: 0; width: 100%; }
|
||||
.ui-slider-vertical .ui-slider-range-min { bottom: 0; }
|
||||
.ui-slider-vertical .ui-slider-range-max { top: 0; }/*
|
||||
* jQuery UI Tabs 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Tabs#theming
|
||||
*/
|
||||
.ui-tabs { position: relative; padding: .2em; zoom: 1; } /* position: relative prevents IE scroll bug (element with position: relative inside container with overflow: auto appear as "fixed") */
|
||||
.ui-tabs .ui-tabs-nav { margin: 0; padding: .2em .2em 0; }
|
||||
.ui-tabs .ui-tabs-nav li { list-style: none; float: left; position: relative; top: 1px; margin: 0 .2em 1px 0; border-bottom: 0 !important; padding: 0; white-space: nowrap; }
|
||||
.ui-tabs .ui-tabs-nav li a { float: left; padding: .5em 1em; text-decoration: none; }
|
||||
.ui-tabs .ui-tabs-nav li.ui-tabs-selected { margin-bottom: 0; padding-bottom: 1px; }
|
||||
.ui-tabs .ui-tabs-nav li.ui-tabs-selected a, .ui-tabs .ui-tabs-nav li.ui-state-disabled a, .ui-tabs .ui-tabs-nav li.ui-state-processing a { cursor: text; }
|
||||
.ui-tabs .ui-tabs-nav li a, .ui-tabs.ui-tabs-collapsible .ui-tabs-nav li.ui-tabs-selected a { cursor: pointer; } /* first selector in group seems obsolete, but required to overcome bug in Opera applying cursor: text overall if defined elsewhere... */
|
||||
.ui-tabs .ui-tabs-panel { display: block; border-width: 0; padding: 1em 1.4em; background: none; }
|
||||
.ui-tabs .ui-tabs-hide { display: none !important; }
|
||||
/*
|
||||
* jQuery UI Datepicker 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Datepicker#theming
|
||||
*/
|
||||
.ui-datepicker { width: 17em; padding: .2em .2em 0; display: none; }
|
||||
.ui-datepicker .ui-datepicker-header { position:relative; padding:.2em 0; }
|
||||
.ui-datepicker .ui-datepicker-prev, .ui-datepicker .ui-datepicker-next { position:absolute; top: 2px; width: 1.8em; height: 1.8em; }
|
||||
.ui-datepicker .ui-datepicker-prev-hover, .ui-datepicker .ui-datepicker-next-hover { top: 1px; }
|
||||
.ui-datepicker .ui-datepicker-prev { left:2px; }
|
||||
.ui-datepicker .ui-datepicker-next { right:2px; }
|
||||
.ui-datepicker .ui-datepicker-prev-hover { left:1px; }
|
||||
.ui-datepicker .ui-datepicker-next-hover { right:1px; }
|
||||
.ui-datepicker .ui-datepicker-prev span, .ui-datepicker .ui-datepicker-next span { display: block; position: absolute; left: 50%; margin-left: -8px; top: 50%; margin-top: -8px; }
|
||||
.ui-datepicker .ui-datepicker-title { margin: 0 2.3em; line-height: 1.8em; text-align: center; }
|
||||
.ui-datepicker .ui-datepicker-title select { font-size:1em; margin:1px 0; }
|
||||
.ui-datepicker select.ui-datepicker-month-year {width: 100%;}
|
||||
.ui-datepicker select.ui-datepicker-month,
|
||||
.ui-datepicker select.ui-datepicker-year { width: 49%;}
|
||||
.ui-datepicker table {width: 100%; font-size: .9em; border-collapse: collapse; margin:0 0 .4em; }
|
||||
.ui-datepicker th { padding: .7em .3em; text-align: center; font-weight: bold; border: 0; }
|
||||
.ui-datepicker td { border: 0; padding: 1px; }
|
||||
.ui-datepicker td span, .ui-datepicker td a { display: block; padding: .2em; text-align: right; text-decoration: none; }
|
||||
.ui-datepicker .ui-datepicker-buttonpane { background-image: none; margin: .7em 0 0 0; padding:0 .2em; border-left: 0; border-right: 0; border-bottom: 0; }
|
||||
.ui-datepicker .ui-datepicker-buttonpane button { float: right; margin: .5em .2em .4em; cursor: pointer; padding: .2em .6em .3em .6em; width:auto; overflow:visible; }
|
||||
.ui-datepicker .ui-datepicker-buttonpane button.ui-datepicker-current { float:left; }
|
||||
|
||||
/* with multiple calendars */
|
||||
.ui-datepicker.ui-datepicker-multi { width:auto; }
|
||||
.ui-datepicker-multi .ui-datepicker-group { float:left; }
|
||||
.ui-datepicker-multi .ui-datepicker-group table { width:95%; margin:0 auto .4em; }
|
||||
.ui-datepicker-multi-2 .ui-datepicker-group { width:50%; }
|
||||
.ui-datepicker-multi-3 .ui-datepicker-group { width:33.3%; }
|
||||
.ui-datepicker-multi-4 .ui-datepicker-group { width:25%; }
|
||||
.ui-datepicker-multi .ui-datepicker-group-last .ui-datepicker-header { border-left-width:0; }
|
||||
.ui-datepicker-multi .ui-datepicker-group-middle .ui-datepicker-header { border-left-width:0; }
|
||||
.ui-datepicker-multi .ui-datepicker-buttonpane { clear:left; }
|
||||
.ui-datepicker-row-break { clear:both; width:100%; font-size:0em; }
|
||||
|
||||
/* RTL support */
|
||||
.ui-datepicker-rtl { direction: rtl; }
|
||||
.ui-datepicker-rtl .ui-datepicker-prev { right: 2px; left: auto; }
|
||||
.ui-datepicker-rtl .ui-datepicker-next { left: 2px; right: auto; }
|
||||
.ui-datepicker-rtl .ui-datepicker-prev:hover { right: 1px; left: auto; }
|
||||
.ui-datepicker-rtl .ui-datepicker-next:hover { left: 1px; right: auto; }
|
||||
.ui-datepicker-rtl .ui-datepicker-buttonpane { clear:right; }
|
||||
.ui-datepicker-rtl .ui-datepicker-buttonpane button { float: left; }
|
||||
.ui-datepicker-rtl .ui-datepicker-buttonpane button.ui-datepicker-current { float:right; }
|
||||
.ui-datepicker-rtl .ui-datepicker-group { float:right; }
|
||||
.ui-datepicker-rtl .ui-datepicker-group-last .ui-datepicker-header { border-right-width:0; border-left-width:1px; }
|
||||
.ui-datepicker-rtl .ui-datepicker-group-middle .ui-datepicker-header { border-right-width:0; border-left-width:1px; }
|
||||
|
||||
/* IE6 IFRAME FIX (taken from datepicker 1.5.3 */
|
||||
.ui-datepicker-cover {
|
||||
display: none; /*sorry for IE5*/
|
||||
display/**/: block; /*sorry for IE5*/
|
||||
position: absolute; /*must have*/
|
||||
z-index: -1; /*must have*/
|
||||
filter: mask(); /*must have*/
|
||||
top: -4px; /*must have*/
|
||||
left: -4px; /*must have*/
|
||||
width: 200px; /*must have*/
|
||||
height: 200px; /*must have*/
|
||||
}/*
|
||||
* jQuery UI Progressbar 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Progressbar#theming
|
||||
*/
|
||||
.ui-progressbar { height:2em; text-align: left; }
|
||||
.ui-progressbar .ui-progressbar-value {margin: -1px; height:100%; }
|
||||
@@ -1,58 +0,0 @@
|
||||
#coursenav {
|
||||
background-color:#031634;
|
||||
padding: 4px 8px 8px 0px;
|
||||
margin: 4px 8px 8px 0px;
|
||||
width: 100%;
|
||||
text-align: right;
|
||||
}
|
||||
|
||||
#left_nav {
|
||||
border: 0;
|
||||
padding: 0;
|
||||
margin: 0;
|
||||
float: left;
|
||||
width: 276;
|
||||
}
|
||||
|
||||
#hide_acc {
|
||||
min-height:600;
|
||||
}
|
||||
|
||||
#mainblock {
|
||||
border: 0;
|
||||
padding: 0;
|
||||
margin: 0;
|
||||
width: 200;
|
||||
min-height:600px;
|
||||
margin-left: 276px;
|
||||
margin-right: 0px;
|
||||
}
|
||||
|
||||
|
||||
#bodyContent {
|
||||
width: 100%;
|
||||
}
|
||||
|
||||
.bordered { border: 1px solid #AAAAAA; border-style : dotted; }
|
||||
|
||||
.seq_problem_visited { background-color: #ccccaa;}
|
||||
.seq_video_visited { background-color: #ccaacc;}
|
||||
.seq_video_visited { background-color: #cccaac;}
|
||||
.seq_html_visited { background-color: #caaccc;}
|
||||
.seq_tab_visited { background-color: #aacccc;}
|
||||
.seq_vertical_visited { background-color: #acaccc;}
|
||||
.seq_sequential_visited { background-color: #cacacc;}
|
||||
.seq_problem_visited { background-color: #ccacac;}
|
||||
.seq_schematic_visited { background-color: #cccaca;}
|
||||
|
||||
.seq_problem_inactive { background-color: #aaaa99;}
|
||||
.seq_video_inactive { background-color: #aa99aa;}
|
||||
.seq_video_inactive { background-color: #aaa99a;}
|
||||
.seq_html_inactive { background-color: #a99aaa;}
|
||||
.seq_tab_inactive { background-color: #99aaaa;}
|
||||
.seq_vertical_inactive { background-color: #9a9aab;}
|
||||
.seq_sequential_inactive { background-color: #a9a9aa;}
|
||||
.seq_problem_inactive { background-color: #aa9a9a;}
|
||||
.seq_schematic_inactive { background-color: #aaa9a9;}
|
||||
|
||||
.seq_active { background-color: red;}
|
||||
@@ -1,363 +0,0 @@
|
||||
|
||||
/*
|
||||
----------------------------------------------------------------------------------------
|
||||
|
||||
Copyright 2010 - Thierry Ruiz - www.dotemplate.com - All rights reserved.
|
||||
|
||||
THIS TEMPLATE IS FREE AS LONG AS YOU KEEP THE LINK TO WWW.DOTEMPLATE.COM IN THE FOOTER
|
||||
TO REMOVE THE LINK, PLEASE MAKE A 10 DOLLARS DONATION at www.dotemplate.com/#donate
|
||||
|
||||
pmitros donated $10
|
||||
|
||||
Colors:
|
||||
Light blue: bddeff
|
||||
Blue: 7fbcfd
|
||||
Very dark blue: #031634
|
||||
|
||||
Dark blue: #023063;
|
||||
Dark Greenish: #7a994c;
|
||||
Greenish: #adcc80;
|
||||
Very light greenish: #dae5c9;
|
||||
Bright orange: #fa720a;
|
||||
|
||||
|
||||
----------------------------------------------------------------------------------------
|
||||
*/
|
||||
|
||||
|
||||
html {
|
||||
background: $bottomWrapper.bg.color;
|
||||
margin:0 0 0 -1px;
|
||||
padding:0;
|
||||
overflow-Y: scroll;
|
||||
}
|
||||
|
||||
|
||||
body {
|
||||
padding:0;
|
||||
margin :0;
|
||||
display:table;
|
||||
width:100%;
|
||||
}
|
||||
|
||||
|
||||
body {
|
||||
color:#023063;
|
||||
font-family: Helvetica, Arial, sans-serif;
|
||||
font-size: 0.8em;
|
||||
font-style: normal;
|
||||
font-weight: normal;
|
||||
text-transform: normal;
|
||||
}
|
||||
|
||||
p {
|
||||
letter-spacing: normal;
|
||||
line-height: 20px;
|
||||
}
|
||||
|
||||
h1 {
|
||||
color:#adcc80;
|
||||
font-size:1.6em;
|
||||
margin:25px 0 10px 0;
|
||||
clear:both;
|
||||
}
|
||||
|
||||
|
||||
h2 {
|
||||
color:#adcc80;
|
||||
font-size:1.1em;
|
||||
margin:20px 0 10px 0;
|
||||
clear:both;
|
||||
}
|
||||
|
||||
|
||||
h3 {
|
||||
color:#adcc80;
|
||||
font-size:1em;
|
||||
margin:20px 0 5px 0;
|
||||
clear:both;
|
||||
}
|
||||
|
||||
|
||||
|
||||
a:link, a:visited {
|
||||
color:#adcc80;
|
||||
text-decoration:none;
|
||||
}
|
||||
|
||||
|
||||
a:hover {
|
||||
color:#fa720a;
|
||||
text-decoration:underline;
|
||||
}
|
||||
|
||||
#sectiondesc {
|
||||
font-size:8px;
|
||||
}
|
||||
|
||||
#wrapper {
|
||||
background: transparent url( images/css/page-vbg.jpg ) repeat-y scroll 50% 0px;
|
||||
margin:0 auto ;
|
||||
width:100%;
|
||||
}
|
||||
|
||||
body {
|
||||
background-color:#FFFFFF;
|
||||
}
|
||||
|
||||
#wrapper {
|
||||
border-top: 1px solid #ffffff;
|
||||
}
|
||||
|
||||
|
||||
|
||||
#topWrapper {
|
||||
width:100%;
|
||||
height:100px;
|
||||
background-color:${topWrapper.bg.color};
|
||||
background-image:url(images/css/topWrapper-bg.jpg);
|
||||
background-position:center top ;
|
||||
background-repeat:repeat-x;
|
||||
}
|
||||
|
||||
|
||||
|
||||
#topBanner {
|
||||
width:800px;
|
||||
margin:0 auto;
|
||||
height:100px;
|
||||
background-image:url(images/css/topBanner.jpg);
|
||||
background-repeat:no-repeat;
|
||||
}
|
||||
|
||||
|
||||
|
||||
#topnav {
|
||||
background:transparent url('images/css/hmenu.jpg') repeat-x top left;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
#topnav {
|
||||
height:20px;
|
||||
margin:0 auto ;
|
||||
text-align:center;
|
||||
}
|
||||
|
||||
#topnav ul {
|
||||
display:table;
|
||||
margin:0 auto;
|
||||
padding:0;
|
||||
list-style-type:none;
|
||||
position:relative;
|
||||
height:20px;
|
||||
text-transform:uppercase;
|
||||
font-size:0.9em;
|
||||
font-family:Arial,sans-serif;
|
||||
}
|
||||
|
||||
|
||||
#topnav ul li {
|
||||
display:block;
|
||||
float:left;
|
||||
margin:0;
|
||||
padding:0;
|
||||
background:transparent url('images/css/hmenu.jpg') repeat-x top left;
|
||||
|
||||
}
|
||||
|
||||
|
||||
#topnav ul li a {
|
||||
display:block;
|
||||
float:left;
|
||||
color:#031634;
|
||||
text-decoration:none;
|
||||
padding:0px 50px ;
|
||||
line-height:20px;
|
||||
font-weight:bold;
|
||||
}
|
||||
|
||||
|
||||
#topnav ul li a:hover, #topnav li#current a {
|
||||
color:#7a994c;
|
||||
background:transparent url('images/css/hmenu-sel.jpg') repeat-x top left;
|
||||
}
|
||||
|
||||
|
||||
|
||||
#topnav ul {
|
||||
width:800px;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
body {
|
||||
background-position : center 120px;
|
||||
}
|
||||
|
||||
|
||||
|
||||
#bg {
|
||||
margin:0 auto;
|
||||
padding:0;
|
||||
background:transparent ;
|
||||
background-image:url(images/css/hat.jpg);
|
||||
background-repeat:no-repeat;
|
||||
background-position: center top ;
|
||||
}
|
||||
|
||||
|
||||
|
||||
#header {
|
||||
margin: 0 auto;
|
||||
min-height:0px;
|
||||
height: 0px;
|
||||
width: 800px;
|
||||
}
|
||||
|
||||
|
||||
#page {
|
||||
background: transparent url( images/css/page-bg.jpg ) no-repeat center top;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
#container {
|
||||
margin:0 auto;
|
||||
width:800px;
|
||||
}
|
||||
|
||||
|
||||
#content {
|
||||
width:780px;
|
||||
margin:0 auto ;
|
||||
text-align:left;
|
||||
min-height:800px;
|
||||
}
|
||||
|
||||
|
||||
#content p {
|
||||
text-align:justify;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
#footerWrapper {
|
||||
margin:0 auto;
|
||||
height:10px;
|
||||
padding:0;
|
||||
background:transparent url( images/css/footerWrapper-bg.jpg ) no-repeat scroll center top;
|
||||
}
|
||||
|
||||
|
||||
#footer {
|
||||
margin:0 auto;
|
||||
padding:0;
|
||||
width:800px;
|
||||
height:10px;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
#right {
|
||||
width:200px;
|
||||
padding:10px 20px 20px 20px;
|
||||
float:left;
|
||||
}
|
||||
|
||||
|
||||
#center {
|
||||
width:500px;
|
||||
padding:10px 20px 20px 20px;
|
||||
float:left;
|
||||
}
|
||||
|
||||
|
||||
#content p {
|
||||
margin-top:10px;
|
||||
text-align:justify;
|
||||
}
|
||||
|
||||
|
||||
|
||||
#sidebar ul.vmenu {
|
||||
list-style: none;
|
||||
text-align: left;
|
||||
margin: 7px 0px 8px 0px;
|
||||
padding: 0;
|
||||
text-decoration: none;
|
||||
border-top: 1px solid #eeeeee;
|
||||
}
|
||||
|
||||
|
||||
#sidebar ul.vmenu li {
|
||||
list-style: none;
|
||||
padding: 4px 0 4px 0px;
|
||||
margin: 0 2px;
|
||||
border-bottom: 1px solid #eeeeee;
|
||||
}
|
||||
|
||||
|
||||
|
||||
#sidebar ul.vmenu li a {
|
||||
text-decoration: none;
|
||||
color:#023063;
|
||||
}
|
||||
|
||||
|
||||
#sidebar ul.vmenu li a:hover {
|
||||
color:#adcc80;
|
||||
}
|
||||
|
||||
|
||||
#sidebar ul.vmenu ul { margin: 0 0 0 5px; padding: 0; }
|
||||
#sidebar ul.vmenu ul li { border: none; }
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
#bottomWrapper {
|
||||
height:140px;
|
||||
background-color:#031634;
|
||||
background-image:url(images/css/bottomWrapper-bg.jpg);
|
||||
background-position:center top ;
|
||||
background-repeat:repeat-x;
|
||||
text-align:center;
|
||||
color:#adcc80;
|
||||
text-align:center;
|
||||
}
|
||||
|
||||
#bottomWrapper a:link, #footer a:visited {
|
||||
color:#dae5c9;
|
||||
}
|
||||
|
||||
|
||||
#bottomWrapper a:hover{
|
||||
color:#adcc80;
|
||||
text-decoration:none;
|
||||
}
|
||||
|
||||
|
||||
|
||||
a img {
|
||||
border:none;
|
||||
}
|
||||
|
||||
|
||||
.clear {
|
||||
clear: both;
|
||||
display: block;
|
||||
overflow: hidden;
|
||||
visibility: hidden;
|
||||
width: 0;
|
||||
height: 0;
|
||||
}
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 260 B |
Binary file not shown.
|
Before Width: | Height: | Size: 251 B |
Binary file not shown.
|
Before Width: | Height: | Size: 178 B |
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|
Before Width: | Height: | Size: 104 B |
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|
Before Width: | Height: | Size: 125 B |
Binary file not shown.
|
Before Width: | Height: | Size: 105 B |
Binary file not shown.
|
Before Width: | Height: | Size: 3.7 KiB |
Binary file not shown.
|
Before Width: | Height: | Size: 90 B |
Binary file not shown.
|
Before Width: | Height: | Size: 129 B |
Binary file not shown.
|
Before Width: | Height: | Size: 4.3 KiB |
Binary file not shown.
|
Before Width: | Height: | Size: 4.3 KiB |
Binary file not shown.
|
Before Width: | Height: | Size: 4.3 KiB |
Binary file not shown.
|
Before Width: | Height: | Size: 4.3 KiB |
Binary file not shown.
|
Before Width: | Height: | Size: 4.3 KiB |
@@ -1,568 +0,0 @@
|
||||
/*
|
||||
* jQuery UI CSS Framework 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Theming/API
|
||||
*/
|
||||
|
||||
/* Layout helpers
|
||||
----------------------------------*/
|
||||
.ui-helper-hidden { display: none; }
|
||||
.ui-helper-hidden-accessible { position: absolute !important; clip: rect(1px 1px 1px 1px); clip: rect(1px,1px,1px,1px); }
|
||||
.ui-helper-reset { margin: 0; padding: 0; border: 0; outline: 0; line-height: 1.3; text-decoration: none; font-size: 100%; list-style: none; }
|
||||
.ui-helper-clearfix:after { content: "."; display: block; height: 0; clear: both; visibility: hidden; }
|
||||
.ui-helper-clearfix { display: inline-block; }
|
||||
/* required comment for clearfix to work in Opera \*/
|
||||
* html .ui-helper-clearfix { height:1%; }
|
||||
.ui-helper-clearfix { display:block; }
|
||||
/* end clearfix */
|
||||
.ui-helper-zfix { width: 100%; height: 100%; top: 0; left: 0; position: absolute; opacity: 0; filter:Alpha(Opacity=0); }
|
||||
|
||||
|
||||
/* Interaction Cues
|
||||
----------------------------------*/
|
||||
.ui-state-disabled { cursor: default !important; }
|
||||
|
||||
|
||||
/* Icons
|
||||
----------------------------------*/
|
||||
|
||||
/* states and images */
|
||||
.ui-icon { display: block; text-indent: -99999px; overflow: hidden; background-repeat: no-repeat; }
|
||||
|
||||
|
||||
/* Misc visuals
|
||||
----------------------------------*/
|
||||
|
||||
/* Overlays */
|
||||
.ui-widget-overlay { position: absolute; top: 0; left: 0; width: 100%; height: 100%; }
|
||||
|
||||
|
||||
/*
|
||||
* jQuery UI CSS Framework 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Theming/API
|
||||
*
|
||||
* To view and modify this theme, visit http://jqueryui.com/themeroller/?ffDefault=Trebuchet%20MS,%20Tahoma,%20Verdana,%20Arial,%20sans-serif&fwDefault=bold&fsDefault=1.1em&cornerRadius=4px&bgColorHeader=f6a828&bgTextureHeader=12_gloss_wave.png&bgImgOpacityHeader=35&borderColorHeader=e78f08&fcHeader=ffffff&iconColorHeader=ffffff&bgColorContent=eeeeee&bgTextureContent=03_highlight_soft.png&bgImgOpacityContent=100&borderColorContent=dddddd&fcContent=333333&iconColorContent=222222&bgColorDefault=f6f6f6&bgTextureDefault=02_glass.png&bgImgOpacityDefault=100&borderColorDefault=cccccc&fcDefault=1c94c4&iconColorDefault=ef8c08&bgColorHover=fdf5ce&bgTextureHover=02_glass.png&bgImgOpacityHover=100&borderColorHover=fbcb09&fcHover=c77405&iconColorHover=ef8c08&bgColorActive=ffffff&bgTextureActive=02_glass.png&bgImgOpacityActive=65&borderColorActive=fbd850&fcActive=eb8f00&iconColorActive=ef8c08&bgColorHighlight=ffe45c&bgTextureHighlight=03_highlight_soft.png&bgImgOpacityHighlight=75&borderColorHighlight=fed22f&fcHighlight=363636&iconColorHighlight=228ef1&bgColorError=b81900&bgTextureError=08_diagonals_thick.png&bgImgOpacityError=18&borderColorError=cd0a0a&fcError=ffffff&iconColorError=ffd27a&bgColorOverlay=666666&bgTextureOverlay=08_diagonals_thick.png&bgImgOpacityOverlay=20&opacityOverlay=50&bgColorShadow=000000&bgTextureShadow=01_flat.png&bgImgOpacityShadow=10&opacityShadow=20&thicknessShadow=5px&offsetTopShadow=-5px&offsetLeftShadow=-5px&cornerRadiusShadow=5px
|
||||
*/
|
||||
|
||||
|
||||
/* Component containers
|
||||
----------------------------------*/
|
||||
.ui-widget { font-family: Trebuchet MS, Tahoma, Verdana, Arial, sans-serif; font-size: 1.1em; }
|
||||
.ui-widget .ui-widget { font-size: 1em; }
|
||||
.ui-widget input, .ui-widget select, .ui-widget textarea, .ui-widget button { font-family: Trebuchet MS, Tahoma, Verdana, Arial, sans-serif; font-size: 1em; }
|
||||
.ui-widget-content { border: 1px solid #dddddd; background: #eeeeee url(images/ui-bg_highlight-soft_100_eeeeee_1x100.png) 50% top repeat-x; color: #333333; }
|
||||
.ui-widget-content a { color: #333333; }
|
||||
.ui-widget-header { border: 1px solid #e78f08; background: #f6a828 url(images/ui-bg_gloss-wave_35_f6a828_500x100.png) 50% 50% repeat-x; color: #ffffff; font-weight: bold; }
|
||||
.ui-widget-header a { color: #ffffff; }
|
||||
|
||||
/* Interaction states
|
||||
----------------------------------*/
|
||||
.ui-state-default, .ui-widget-content .ui-state-default, .ui-widget-header .ui-state-default { border: 1px solid #cccccc; background: #f6f6f6 url(images/ui-bg_glass_100_f6f6f6_1x400.png) 50% 50% repeat-x; font-weight: bold; color: #1c94c4; }
|
||||
.ui-state-default a, .ui-state-default a:link, .ui-state-default a:visited { color: #1c94c4; text-decoration: none; }
|
||||
.ui-state-hover, .ui-widget-content .ui-state-hover, .ui-widget-header .ui-state-hover, .ui-state-focus, .ui-widget-content .ui-state-focus, .ui-widget-header .ui-state-focus { border: 1px solid #fbcb09; background: #fdf5ce url(images/ui-bg_glass_100_fdf5ce_1x400.png) 50% 50% repeat-x; font-weight: bold; color: #c77405; }
|
||||
.ui-state-hover a, .ui-state-hover a:hover { color: #c77405; text-decoration: none; }
|
||||
.ui-state-active, .ui-widget-content .ui-state-active, .ui-widget-header .ui-state-active { border: 1px solid #fbd850; background: #ffffff url(images/ui-bg_glass_65_ffffff_1x400.png) 50% 50% repeat-x; font-weight: bold; color: #eb8f00; }
|
||||
.ui-state-active a, .ui-state-active a:link, .ui-state-active a:visited { color: #eb8f00; text-decoration: none; }
|
||||
.ui-widget :active { outline: none; }
|
||||
|
||||
/* Interaction Cues
|
||||
----------------------------------*/
|
||||
.ui-state-highlight, .ui-widget-content .ui-state-highlight, .ui-widget-header .ui-state-highlight {border: 1px solid #fed22f; background: #ffe45c url(images/ui-bg_highlight-soft_75_ffe45c_1x100.png) 50% top repeat-x; color: #363636; }
|
||||
.ui-state-highlight a, .ui-widget-content .ui-state-highlight a,.ui-widget-header .ui-state-highlight a { color: #363636; }
|
||||
.ui-state-error, .ui-widget-content .ui-state-error, .ui-widget-header .ui-state-error {border: 1px solid #cd0a0a; background: #b81900 url(images/ui-bg_diagonals-thick_18_b81900_40x40.png) 50% 50% repeat; color: #ffffff; }
|
||||
.ui-state-error a, .ui-widget-content .ui-state-error a, .ui-widget-header .ui-state-error a { color: #ffffff; }
|
||||
.ui-state-error-text, .ui-widget-content .ui-state-error-text, .ui-widget-header .ui-state-error-text { color: #ffffff; }
|
||||
.ui-priority-primary, .ui-widget-content .ui-priority-primary, .ui-widget-header .ui-priority-primary { font-weight: bold; }
|
||||
.ui-priority-secondary, .ui-widget-content .ui-priority-secondary, .ui-widget-header .ui-priority-secondary { opacity: .7; filter:Alpha(Opacity=70); font-weight: normal; }
|
||||
.ui-state-disabled, .ui-widget-content .ui-state-disabled, .ui-widget-header .ui-state-disabled { opacity: .35; filter:Alpha(Opacity=35); background-image: none; }
|
||||
|
||||
/* Icons
|
||||
----------------------------------*/
|
||||
|
||||
/* states and images */
|
||||
.ui-icon { width: 16px; height: 16px; background-image: url(images/ui-icons_222222_256x240.png); }
|
||||
.ui-widget-content .ui-icon {background-image: url(images/ui-icons_222222_256x240.png); }
|
||||
.ui-widget-header .ui-icon {background-image: url(images/ui-icons_ffffff_256x240.png); }
|
||||
.ui-state-default .ui-icon { background-image: url(images/ui-icons_ef8c08_256x240.png); }
|
||||
.ui-state-hover .ui-icon, .ui-state-focus .ui-icon {background-image: url(images/ui-icons_ef8c08_256x240.png); }
|
||||
.ui-state-active .ui-icon {background-image: url(images/ui-icons_ef8c08_256x240.png); }
|
||||
.ui-state-highlight .ui-icon {background-image: url(images/ui-icons_228ef1_256x240.png); }
|
||||
.ui-state-error .ui-icon, .ui-state-error-text .ui-icon {background-image: url(images/ui-icons_ffd27a_256x240.png); }
|
||||
|
||||
/* positioning */
|
||||
.ui-icon-carat-1-n { background-position: 0 0; }
|
||||
.ui-icon-carat-1-ne { background-position: -16px 0; }
|
||||
.ui-icon-carat-1-e { background-position: -32px 0; }
|
||||
.ui-icon-carat-1-se { background-position: -48px 0; }
|
||||
.ui-icon-carat-1-s { background-position: -64px 0; }
|
||||
.ui-icon-carat-1-sw { background-position: -80px 0; }
|
||||
.ui-icon-carat-1-w { background-position: -96px 0; }
|
||||
.ui-icon-carat-1-nw { background-position: -112px 0; }
|
||||
.ui-icon-carat-2-n-s { background-position: -128px 0; }
|
||||
.ui-icon-carat-2-e-w { background-position: -144px 0; }
|
||||
.ui-icon-triangle-1-n { background-position: 0 -16px; }
|
||||
.ui-icon-triangle-1-ne { background-position: -16px -16px; }
|
||||
.ui-icon-triangle-1-e { background-position: -32px -16px; }
|
||||
.ui-icon-triangle-1-se { background-position: -48px -16px; }
|
||||
.ui-icon-triangle-1-s { background-position: -64px -16px; }
|
||||
.ui-icon-triangle-1-sw { background-position: -80px -16px; }
|
||||
.ui-icon-triangle-1-w { background-position: -96px -16px; }
|
||||
.ui-icon-triangle-1-nw { background-position: -112px -16px; }
|
||||
.ui-icon-triangle-2-n-s { background-position: -128px -16px; }
|
||||
.ui-icon-triangle-2-e-w { background-position: -144px -16px; }
|
||||
.ui-icon-arrow-1-n { background-position: 0 -32px; }
|
||||
.ui-icon-arrow-1-ne { background-position: -16px -32px; }
|
||||
.ui-icon-arrow-1-e { background-position: -32px -32px; }
|
||||
.ui-icon-arrow-1-se { background-position: -48px -32px; }
|
||||
.ui-icon-arrow-1-s { background-position: -64px -32px; }
|
||||
.ui-icon-arrow-1-sw { background-position: -80px -32px; }
|
||||
.ui-icon-arrow-1-w { background-position: -96px -32px; }
|
||||
.ui-icon-arrow-1-nw { background-position: -112px -32px; }
|
||||
.ui-icon-arrow-2-n-s { background-position: -128px -32px; }
|
||||
.ui-icon-arrow-2-ne-sw { background-position: -144px -32px; }
|
||||
.ui-icon-arrow-2-e-w { background-position: -160px -32px; }
|
||||
.ui-icon-arrow-2-se-nw { background-position: -176px -32px; }
|
||||
.ui-icon-arrowstop-1-n { background-position: -192px -32px; }
|
||||
.ui-icon-arrowstop-1-e { background-position: -208px -32px; }
|
||||
.ui-icon-arrowstop-1-s { background-position: -224px -32px; }
|
||||
.ui-icon-arrowstop-1-w { background-position: -240px -32px; }
|
||||
.ui-icon-arrowthick-1-n { background-position: 0 -48px; }
|
||||
.ui-icon-arrowthick-1-ne { background-position: -16px -48px; }
|
||||
.ui-icon-arrowthick-1-e { background-position: -32px -48px; }
|
||||
.ui-icon-arrowthick-1-se { background-position: -48px -48px; }
|
||||
.ui-icon-arrowthick-1-s { background-position: -64px -48px; }
|
||||
.ui-icon-arrowthick-1-sw { background-position: -80px -48px; }
|
||||
.ui-icon-arrowthick-1-w { background-position: -96px -48px; }
|
||||
.ui-icon-arrowthick-1-nw { background-position: -112px -48px; }
|
||||
.ui-icon-arrowthick-2-n-s { background-position: -128px -48px; }
|
||||
.ui-icon-arrowthick-2-ne-sw { background-position: -144px -48px; }
|
||||
.ui-icon-arrowthick-2-e-w { background-position: -160px -48px; }
|
||||
.ui-icon-arrowthick-2-se-nw { background-position: -176px -48px; }
|
||||
.ui-icon-arrowthickstop-1-n { background-position: -192px -48px; }
|
||||
.ui-icon-arrowthickstop-1-e { background-position: -208px -48px; }
|
||||
.ui-icon-arrowthickstop-1-s { background-position: -224px -48px; }
|
||||
.ui-icon-arrowthickstop-1-w { background-position: -240px -48px; }
|
||||
.ui-icon-arrowreturnthick-1-w { background-position: 0 -64px; }
|
||||
.ui-icon-arrowreturnthick-1-n { background-position: -16px -64px; }
|
||||
.ui-icon-arrowreturnthick-1-e { background-position: -32px -64px; }
|
||||
.ui-icon-arrowreturnthick-1-s { background-position: -48px -64px; }
|
||||
.ui-icon-arrowreturn-1-w { background-position: -64px -64px; }
|
||||
.ui-icon-arrowreturn-1-n { background-position: -80px -64px; }
|
||||
.ui-icon-arrowreturn-1-e { background-position: -96px -64px; }
|
||||
.ui-icon-arrowreturn-1-s { background-position: -112px -64px; }
|
||||
.ui-icon-arrowrefresh-1-w { background-position: -128px -64px; }
|
||||
.ui-icon-arrowrefresh-1-n { background-position: -144px -64px; }
|
||||
.ui-icon-arrowrefresh-1-e { background-position: -160px -64px; }
|
||||
.ui-icon-arrowrefresh-1-s { background-position: -176px -64px; }
|
||||
.ui-icon-arrow-4 { background-position: 0 -80px; }
|
||||
.ui-icon-arrow-4-diag { background-position: -16px -80px; }
|
||||
.ui-icon-extlink { background-position: -32px -80px; }
|
||||
.ui-icon-newwin { background-position: -48px -80px; }
|
||||
.ui-icon-refresh { background-position: -64px -80px; }
|
||||
.ui-icon-shuffle { background-position: -80px -80px; }
|
||||
.ui-icon-transfer-e-w { background-position: -96px -80px; }
|
||||
.ui-icon-transferthick-e-w { background-position: -112px -80px; }
|
||||
.ui-icon-folder-collapsed { background-position: 0 -96px; }
|
||||
.ui-icon-folder-open { background-position: -16px -96px; }
|
||||
.ui-icon-document { background-position: -32px -96px; }
|
||||
.ui-icon-document-b { background-position: -48px -96px; }
|
||||
.ui-icon-note { background-position: -64px -96px; }
|
||||
.ui-icon-mail-closed { background-position: -80px -96px; }
|
||||
.ui-icon-mail-open { background-position: -96px -96px; }
|
||||
.ui-icon-suitcase { background-position: -112px -96px; }
|
||||
.ui-icon-comment { background-position: -128px -96px; }
|
||||
.ui-icon-person { background-position: -144px -96px; }
|
||||
.ui-icon-print { background-position: -160px -96px; }
|
||||
.ui-icon-trash { background-position: -176px -96px; }
|
||||
.ui-icon-locked { background-position: -192px -96px; }
|
||||
.ui-icon-unlocked { background-position: -208px -96px; }
|
||||
.ui-icon-bookmark { background-position: -224px -96px; }
|
||||
.ui-icon-tag { background-position: -240px -96px; }
|
||||
.ui-icon-home { background-position: 0 -112px; }
|
||||
.ui-icon-flag { background-position: -16px -112px; }
|
||||
.ui-icon-calendar { background-position: -32px -112px; }
|
||||
.ui-icon-cart { background-position: -48px -112px; }
|
||||
.ui-icon-pencil { background-position: -64px -112px; }
|
||||
.ui-icon-clock { background-position: -80px -112px; }
|
||||
.ui-icon-disk { background-position: -96px -112px; }
|
||||
.ui-icon-calculator { background-position: -112px -112px; }
|
||||
.ui-icon-zoomin { background-position: -128px -112px; }
|
||||
.ui-icon-zoomout { background-position: -144px -112px; }
|
||||
.ui-icon-search { background-position: -160px -112px; }
|
||||
.ui-icon-wrench { background-position: -176px -112px; }
|
||||
.ui-icon-gear { background-position: -192px -112px; }
|
||||
.ui-icon-heart { background-position: -208px -112px; }
|
||||
.ui-icon-star { background-position: -224px -112px; }
|
||||
.ui-icon-link { background-position: -240px -112px; }
|
||||
.ui-icon-cancel { background-position: 0 -128px; }
|
||||
.ui-icon-plus { background-position: -16px -128px; }
|
||||
.ui-icon-plusthick { background-position: -32px -128px; }
|
||||
.ui-icon-minus { background-position: -48px -128px; }
|
||||
.ui-icon-minusthick { background-position: -64px -128px; }
|
||||
.ui-icon-close { background-position: -80px -128px; }
|
||||
.ui-icon-closethick { background-position: -96px -128px; }
|
||||
.ui-icon-key { background-position: -112px -128px; }
|
||||
.ui-icon-lightbulb { background-position: -128px -128px; }
|
||||
.ui-icon-scissors { background-position: -144px -128px; }
|
||||
.ui-icon-clipboard { background-position: -160px -128px; }
|
||||
.ui-icon-copy { background-position: -176px -128px; }
|
||||
.ui-icon-contact { background-position: -192px -128px; }
|
||||
.ui-icon-image { background-position: -208px -128px; }
|
||||
.ui-icon-video { background-position: -224px -128px; }
|
||||
.ui-icon-script { background-position: -240px -128px; }
|
||||
.ui-icon-alert { background-position: 0 -144px; }
|
||||
.ui-icon-info { background-position: -16px -144px; }
|
||||
.ui-icon-notice { background-position: -32px -144px; }
|
||||
.ui-icon-help { background-position: -48px -144px; }
|
||||
.ui-icon-check { background-position: -64px -144px; }
|
||||
.ui-icon-bullet { background-position: -80px -144px; }
|
||||
.ui-icon-radio-off { background-position: -96px -144px; }
|
||||
.ui-icon-radio-on { background-position: -112px -144px; }
|
||||
.ui-icon-pin-w { background-position: -128px -144px; }
|
||||
.ui-icon-pin-s { background-position: -144px -144px; }
|
||||
.ui-icon-play { background-position: 0 -160px; }
|
||||
.ui-icon-pause { background-position: -16px -160px; }
|
||||
.ui-icon-seek-next { background-position: -32px -160px; }
|
||||
.ui-icon-seek-prev { background-position: -48px -160px; }
|
||||
.ui-icon-seek-end { background-position: -64px -160px; }
|
||||
.ui-icon-seek-start { background-position: -80px -160px; }
|
||||
/* ui-icon-seek-first is deprecated, use ui-icon-seek-start instead */
|
||||
.ui-icon-seek-first { background-position: -80px -160px; }
|
||||
.ui-icon-stop { background-position: -96px -160px; }
|
||||
.ui-icon-eject { background-position: -112px -160px; }
|
||||
.ui-icon-volume-off { background-position: -128px -160px; }
|
||||
.ui-icon-volume-on { background-position: -144px -160px; }
|
||||
.ui-icon-power { background-position: 0 -176px; }
|
||||
.ui-icon-signal-diag { background-position: -16px -176px; }
|
||||
.ui-icon-signal { background-position: -32px -176px; }
|
||||
.ui-icon-battery-0 { background-position: -48px -176px; }
|
||||
.ui-icon-battery-1 { background-position: -64px -176px; }
|
||||
.ui-icon-battery-2 { background-position: -80px -176px; }
|
||||
.ui-icon-battery-3 { background-position: -96px -176px; }
|
||||
.ui-icon-circle-plus { background-position: 0 -192px; }
|
||||
.ui-icon-circle-minus { background-position: -16px -192px; }
|
||||
.ui-icon-circle-close { background-position: -32px -192px; }
|
||||
.ui-icon-circle-triangle-e { background-position: -48px -192px; }
|
||||
.ui-icon-circle-triangle-s { background-position: -64px -192px; }
|
||||
.ui-icon-circle-triangle-w { background-position: -80px -192px; }
|
||||
.ui-icon-circle-triangle-n { background-position: -96px -192px; }
|
||||
.ui-icon-circle-arrow-e { background-position: -112px -192px; }
|
||||
.ui-icon-circle-arrow-s { background-position: -128px -192px; }
|
||||
.ui-icon-circle-arrow-w { background-position: -144px -192px; }
|
||||
.ui-icon-circle-arrow-n { background-position: -160px -192px; }
|
||||
.ui-icon-circle-zoomin { background-position: -176px -192px; }
|
||||
.ui-icon-circle-zoomout { background-position: -192px -192px; }
|
||||
.ui-icon-circle-check { background-position: -208px -192px; }
|
||||
.ui-icon-circlesmall-plus { background-position: 0 -208px; }
|
||||
.ui-icon-circlesmall-minus { background-position: -16px -208px; }
|
||||
.ui-icon-circlesmall-close { background-position: -32px -208px; }
|
||||
.ui-icon-squaresmall-plus { background-position: -48px -208px; }
|
||||
.ui-icon-squaresmall-minus { background-position: -64px -208px; }
|
||||
.ui-icon-squaresmall-close { background-position: -80px -208px; }
|
||||
.ui-icon-grip-dotted-vertical { background-position: 0 -224px; }
|
||||
.ui-icon-grip-dotted-horizontal { background-position: -16px -224px; }
|
||||
.ui-icon-grip-solid-vertical { background-position: -32px -224px; }
|
||||
.ui-icon-grip-solid-horizontal { background-position: -48px -224px; }
|
||||
.ui-icon-gripsmall-diagonal-se { background-position: -64px -224px; }
|
||||
.ui-icon-grip-diagonal-se { background-position: -80px -224px; }
|
||||
|
||||
|
||||
/* Misc visuals
|
||||
----------------------------------*/
|
||||
|
||||
/* Corner radius */
|
||||
.ui-corner-all, .ui-corner-top, .ui-corner-left, .ui-corner-tl { -moz-border-radius-topleft: 4px; -webkit-border-top-left-radius: 4px; -khtml-border-top-left-radius: 4px; border-top-left-radius: 4px; }
|
||||
.ui-corner-all, .ui-corner-top, .ui-corner-right, .ui-corner-tr { -moz-border-radius-topright: 4px; -webkit-border-top-right-radius: 4px; -khtml-border-top-right-radius: 4px; border-top-right-radius: 4px; }
|
||||
.ui-corner-all, .ui-corner-bottom, .ui-corner-left, .ui-corner-bl { -moz-border-radius-bottomleft: 4px; -webkit-border-bottom-left-radius: 4px; -khtml-border-bottom-left-radius: 4px; border-bottom-left-radius: 4px; }
|
||||
.ui-corner-all, .ui-corner-bottom, .ui-corner-right, .ui-corner-br { -moz-border-radius-bottomright: 4px; -webkit-border-bottom-right-radius: 4px; -khtml-border-bottom-right-radius: 4px; border-bottom-right-radius: 4px; }
|
||||
|
||||
/* Overlays */
|
||||
.ui-widget-overlay { background: #666666 url(images/ui-bg_diagonals-thick_20_666666_40x40.png) 50% 50% repeat; opacity: .50;filter:Alpha(Opacity=50); }
|
||||
.ui-widget-shadow { margin: -5px 0 0 -5px; padding: 5px; background: #000000 url(images/ui-bg_flat_10_000000_40x100.png) 50% 50% repeat-x; opacity: .20;filter:Alpha(Opacity=20); -moz-border-radius: 5px; -khtml-border-radius: 5px; -webkit-border-radius: 5px; border-radius: 5px; }/*
|
||||
* jQuery UI Resizable 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Resizable#theming
|
||||
*/
|
||||
.ui-resizable { position: relative;}
|
||||
.ui-resizable-handle { position: absolute;font-size: 0.1px;z-index: 99999; display: block; }
|
||||
.ui-resizable-disabled .ui-resizable-handle, .ui-resizable-autohide .ui-resizable-handle { display: none; }
|
||||
.ui-resizable-n { cursor: n-resize; height: 7px; width: 100%; top: -5px; left: 0; }
|
||||
.ui-resizable-s { cursor: s-resize; height: 7px; width: 100%; bottom: -5px; left: 0; }
|
||||
.ui-resizable-e { cursor: e-resize; width: 7px; right: -5px; top: 0; height: 100%; }
|
||||
.ui-resizable-w { cursor: w-resize; width: 7px; left: -5px; top: 0; height: 100%; }
|
||||
.ui-resizable-se { cursor: se-resize; width: 12px; height: 12px; right: 1px; bottom: 1px; }
|
||||
.ui-resizable-sw { cursor: sw-resize; width: 9px; height: 9px; left: -5px; bottom: -5px; }
|
||||
.ui-resizable-nw { cursor: nw-resize; width: 9px; height: 9px; left: -5px; top: -5px; }
|
||||
.ui-resizable-ne { cursor: ne-resize; width: 9px; height: 9px; right: -5px; top: -5px;}/*
|
||||
* jQuery UI Selectable 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Selectable#theming
|
||||
*/
|
||||
.ui-selectable-helper { position: absolute; z-index: 100; border:1px dotted black; }
|
||||
/*
|
||||
* jQuery UI Accordion 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Accordion#theming
|
||||
*/
|
||||
/* IE/Win - Fix animation bug - #4615 */
|
||||
.ui-accordion { width: 100%; }
|
||||
.ui-accordion .ui-accordion-header { cursor: pointer; position: relative; margin-top: 1px; zoom: 1; }
|
||||
.ui-accordion .ui-accordion-li-fix { display: inline; }
|
||||
.ui-accordion .ui-accordion-header-active { border-bottom: 0 !important; }
|
||||
.ui-accordion .ui-accordion-header a { display: block; font-size: 1em; padding: .5em .5em .5em .7em; }
|
||||
.ui-accordion-icons .ui-accordion-header a { padding-left: 2.2em; }
|
||||
.ui-accordion .ui-accordion-header .ui-icon { position: absolute; left: .5em; top: 50%; margin-top: -8px; }
|
||||
.ui-accordion .ui-accordion-content { padding: 1em 2.2em; border-top: 0; margin-top: -2px; position: relative; top: 1px; margin-bottom: 2px; overflow: auto; display: none; zoom: 1; }
|
||||
.ui-accordion .ui-accordion-content-active { display: block; }
|
||||
/*
|
||||
* jQuery UI Autocomplete 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Autocomplete#theming
|
||||
*/
|
||||
.ui-autocomplete { position: absolute; cursor: default; }
|
||||
|
||||
/* workarounds */
|
||||
* html .ui-autocomplete { width:1px; } /* without this, the menu expands to 100% in IE6 */
|
||||
|
||||
/*
|
||||
* jQuery UI Menu 1.8.16
|
||||
*
|
||||
* Copyright 2010, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Menu#theming
|
||||
*/
|
||||
.ui-menu {
|
||||
list-style:none;
|
||||
padding: 2px;
|
||||
margin: 0;
|
||||
display:block;
|
||||
float: left;
|
||||
}
|
||||
.ui-menu .ui-menu {
|
||||
margin-top: -3px;
|
||||
}
|
||||
.ui-menu .ui-menu-item {
|
||||
margin:0;
|
||||
padding: 0;
|
||||
zoom: 1;
|
||||
float: left;
|
||||
clear: left;
|
||||
width: 100%;
|
||||
}
|
||||
.ui-menu .ui-menu-item a {
|
||||
text-decoration:none;
|
||||
display:block;
|
||||
padding:.2em .4em;
|
||||
line-height:1.5;
|
||||
zoom:1;
|
||||
}
|
||||
.ui-menu .ui-menu-item a.ui-state-hover,
|
||||
.ui-menu .ui-menu-item a.ui-state-active {
|
||||
font-weight: normal;
|
||||
margin: -1px;
|
||||
}
|
||||
/*
|
||||
* jQuery UI Button 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Button#theming
|
||||
*/
|
||||
.ui-button { display: inline-block; position: relative; padding: 0; margin-right: .1em; text-decoration: none !important; cursor: pointer; text-align: center; zoom: 1; overflow: visible; } /* the overflow property removes extra width in IE */
|
||||
.ui-button-icon-only { width: 2.2em; } /* to make room for the icon, a width needs to be set here */
|
||||
button.ui-button-icon-only { width: 2.4em; } /* button elements seem to need a little more width */
|
||||
.ui-button-icons-only { width: 3.4em; }
|
||||
button.ui-button-icons-only { width: 3.7em; }
|
||||
|
||||
/*button text element */
|
||||
.ui-button .ui-button-text { display: block; line-height: 1.4; }
|
||||
.ui-button-text-only .ui-button-text { padding: .4em 1em; }
|
||||
.ui-button-icon-only .ui-button-text, .ui-button-icons-only .ui-button-text { padding: .4em; text-indent: -9999999px; }
|
||||
.ui-button-text-icon-primary .ui-button-text, .ui-button-text-icons .ui-button-text { padding: .4em 1em .4em 2.1em; }
|
||||
.ui-button-text-icon-secondary .ui-button-text, .ui-button-text-icons .ui-button-text { padding: .4em 2.1em .4em 1em; }
|
||||
.ui-button-text-icons .ui-button-text { padding-left: 2.1em; padding-right: 2.1em; }
|
||||
/* no icon support for input elements, provide padding by default */
|
||||
input.ui-button { padding: .4em 1em; }
|
||||
|
||||
/*button icon element(s) */
|
||||
.ui-button-icon-only .ui-icon, .ui-button-text-icon-primary .ui-icon, .ui-button-text-icon-secondary .ui-icon, .ui-button-text-icons .ui-icon, .ui-button-icons-only .ui-icon { position: absolute; top: 50%; margin-top: -8px; }
|
||||
.ui-button-icon-only .ui-icon { left: 50%; margin-left: -8px; }
|
||||
.ui-button-text-icon-primary .ui-button-icon-primary, .ui-button-text-icons .ui-button-icon-primary, .ui-button-icons-only .ui-button-icon-primary { left: .5em; }
|
||||
.ui-button-text-icon-secondary .ui-button-icon-secondary, .ui-button-text-icons .ui-button-icon-secondary, .ui-button-icons-only .ui-button-icon-secondary { right: .5em; }
|
||||
.ui-button-text-icons .ui-button-icon-secondary, .ui-button-icons-only .ui-button-icon-secondary { right: .5em; }
|
||||
|
||||
/*button sets*/
|
||||
.ui-buttonset { margin-right: 7px; }
|
||||
.ui-buttonset .ui-button { margin-left: 0; margin-right: -.3em; }
|
||||
|
||||
/* workarounds */
|
||||
button.ui-button::-moz-focus-inner { border: 0; padding: 0; } /* reset extra padding in Firefox */
|
||||
/*
|
||||
* jQuery UI Dialog 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Dialog#theming
|
||||
*/
|
||||
.ui-dialog { position: absolute; padding: .2em; width: 300px; overflow: hidden; }
|
||||
.ui-dialog .ui-dialog-titlebar { padding: .4em 1em; position: relative; }
|
||||
.ui-dialog .ui-dialog-title { float: left; margin: .1em 16px .1em 0; }
|
||||
.ui-dialog .ui-dialog-titlebar-close { position: absolute; right: .3em; top: 50%; width: 19px; margin: -10px 0 0 0; padding: 1px; height: 18px; }
|
||||
.ui-dialog .ui-dialog-titlebar-close span { display: block; margin: 1px; }
|
||||
.ui-dialog .ui-dialog-titlebar-close:hover, .ui-dialog .ui-dialog-titlebar-close:focus { padding: 0; }
|
||||
.ui-dialog .ui-dialog-content { position: relative; border: 0; padding: .5em 1em; background: none; overflow: auto; zoom: 1; }
|
||||
.ui-dialog .ui-dialog-buttonpane { text-align: left; border-width: 1px 0 0 0; background-image: none; margin: .5em 0 0 0; padding: .3em 1em .5em .4em; }
|
||||
.ui-dialog .ui-dialog-buttonpane .ui-dialog-buttonset { float: right; }
|
||||
.ui-dialog .ui-dialog-buttonpane button { margin: .5em .4em .5em 0; cursor: pointer; }
|
||||
.ui-dialog .ui-resizable-se { width: 14px; height: 14px; right: 3px; bottom: 3px; }
|
||||
.ui-draggable .ui-dialog-titlebar { cursor: move; }
|
||||
/*
|
||||
* jQuery UI Slider 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Slider#theming
|
||||
*/
|
||||
.ui-slider { position: relative; text-align: left; }
|
||||
.ui-slider .ui-slider-handle { position: absolute; z-index: 2; width: 1.2em; height: 1.2em; cursor: default; }
|
||||
.ui-slider .ui-slider-range { position: absolute; z-index: 1; font-size: .7em; display: block; border: 0; background-position: 0 0; }
|
||||
|
||||
.ui-slider-horizontal { height: .8em; }
|
||||
.ui-slider-horizontal .ui-slider-handle { top: -.3em; margin-left: -.6em; }
|
||||
.ui-slider-horizontal .ui-slider-range { top: 0; height: 100%; }
|
||||
.ui-slider-horizontal .ui-slider-range-min { left: 0; }
|
||||
.ui-slider-horizontal .ui-slider-range-max { right: 0; }
|
||||
|
||||
.ui-slider-vertical { width: .8em; height: 100px; }
|
||||
.ui-slider-vertical .ui-slider-handle { left: -.3em; margin-left: 0; margin-bottom: -.6em; }
|
||||
.ui-slider-vertical .ui-slider-range { left: 0; width: 100%; }
|
||||
.ui-slider-vertical .ui-slider-range-min { bottom: 0; }
|
||||
.ui-slider-vertical .ui-slider-range-max { top: 0; }/*
|
||||
* jQuery UI Tabs 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Tabs#theming
|
||||
*/
|
||||
.ui-tabs { position: relative; padding: .2em; zoom: 1; } /* position: relative prevents IE scroll bug (element with position: relative inside container with overflow: auto appear as "fixed") */
|
||||
.ui-tabs .ui-tabs-nav { margin: 0; padding: .2em .2em 0; }
|
||||
.ui-tabs .ui-tabs-nav li { list-style: none; float: left; position: relative; top: 1px; margin: 0 .2em 1px 0; border-bottom: 0 !important; padding: 0; white-space: nowrap; }
|
||||
.ui-tabs .ui-tabs-nav li a { float: left; padding: .5em 1em; text-decoration: none; }
|
||||
.ui-tabs .ui-tabs-nav li.ui-tabs-selected { margin-bottom: 0; padding-bottom: 1px; }
|
||||
.ui-tabs .ui-tabs-nav li.ui-tabs-selected a, .ui-tabs .ui-tabs-nav li.ui-state-disabled a, .ui-tabs .ui-tabs-nav li.ui-state-processing a { cursor: text; }
|
||||
.ui-tabs .ui-tabs-nav li a, .ui-tabs.ui-tabs-collapsible .ui-tabs-nav li.ui-tabs-selected a { cursor: pointer; } /* first selector in group seems obsolete, but required to overcome bug in Opera applying cursor: text overall if defined elsewhere... */
|
||||
.ui-tabs .ui-tabs-panel { display: block; border-width: 0; padding: 1em 1.4em; background: none; }
|
||||
.ui-tabs .ui-tabs-hide { display: none !important; }
|
||||
/*
|
||||
* jQuery UI Datepicker 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Datepicker#theming
|
||||
*/
|
||||
.ui-datepicker { width: 17em; padding: .2em .2em 0; display: none; }
|
||||
.ui-datepicker .ui-datepicker-header { position:relative; padding:.2em 0; }
|
||||
.ui-datepicker .ui-datepicker-prev, .ui-datepicker .ui-datepicker-next { position:absolute; top: 2px; width: 1.8em; height: 1.8em; }
|
||||
.ui-datepicker .ui-datepicker-prev-hover, .ui-datepicker .ui-datepicker-next-hover { top: 1px; }
|
||||
.ui-datepicker .ui-datepicker-prev { left:2px; }
|
||||
.ui-datepicker .ui-datepicker-next { right:2px; }
|
||||
.ui-datepicker .ui-datepicker-prev-hover { left:1px; }
|
||||
.ui-datepicker .ui-datepicker-next-hover { right:1px; }
|
||||
.ui-datepicker .ui-datepicker-prev span, .ui-datepicker .ui-datepicker-next span { display: block; position: absolute; left: 50%; margin-left: -8px; top: 50%; margin-top: -8px; }
|
||||
.ui-datepicker .ui-datepicker-title { margin: 0 2.3em; line-height: 1.8em; text-align: center; }
|
||||
.ui-datepicker .ui-datepicker-title select { font-size:1em; margin:1px 0; }
|
||||
.ui-datepicker select.ui-datepicker-month-year {width: 100%;}
|
||||
.ui-datepicker select.ui-datepicker-month,
|
||||
.ui-datepicker select.ui-datepicker-year { width: 49%;}
|
||||
.ui-datepicker table {width: 100%; font-size: .9em; border-collapse: collapse; margin:0 0 .4em; }
|
||||
.ui-datepicker th { padding: .7em .3em; text-align: center; font-weight: bold; border: 0; }
|
||||
.ui-datepicker td { border: 0; padding: 1px; }
|
||||
.ui-datepicker td span, .ui-datepicker td a { display: block; padding: .2em; text-align: right; text-decoration: none; }
|
||||
.ui-datepicker .ui-datepicker-buttonpane { background-image: none; margin: .7em 0 0 0; padding:0 .2em; border-left: 0; border-right: 0; border-bottom: 0; }
|
||||
.ui-datepicker .ui-datepicker-buttonpane button { float: right; margin: .5em .2em .4em; cursor: pointer; padding: .2em .6em .3em .6em; width:auto; overflow:visible; }
|
||||
.ui-datepicker .ui-datepicker-buttonpane button.ui-datepicker-current { float:left; }
|
||||
|
||||
/* with multiple calendars */
|
||||
.ui-datepicker.ui-datepicker-multi { width:auto; }
|
||||
.ui-datepicker-multi .ui-datepicker-group { float:left; }
|
||||
.ui-datepicker-multi .ui-datepicker-group table { width:95%; margin:0 auto .4em; }
|
||||
.ui-datepicker-multi-2 .ui-datepicker-group { width:50%; }
|
||||
.ui-datepicker-multi-3 .ui-datepicker-group { width:33.3%; }
|
||||
.ui-datepicker-multi-4 .ui-datepicker-group { width:25%; }
|
||||
.ui-datepicker-multi .ui-datepicker-group-last .ui-datepicker-header { border-left-width:0; }
|
||||
.ui-datepicker-multi .ui-datepicker-group-middle .ui-datepicker-header { border-left-width:0; }
|
||||
.ui-datepicker-multi .ui-datepicker-buttonpane { clear:left; }
|
||||
.ui-datepicker-row-break { clear:both; width:100%; font-size:0em; }
|
||||
|
||||
/* RTL support */
|
||||
.ui-datepicker-rtl { direction: rtl; }
|
||||
.ui-datepicker-rtl .ui-datepicker-prev { right: 2px; left: auto; }
|
||||
.ui-datepicker-rtl .ui-datepicker-next { left: 2px; right: auto; }
|
||||
.ui-datepicker-rtl .ui-datepicker-prev:hover { right: 1px; left: auto; }
|
||||
.ui-datepicker-rtl .ui-datepicker-next:hover { left: 1px; right: auto; }
|
||||
.ui-datepicker-rtl .ui-datepicker-buttonpane { clear:right; }
|
||||
.ui-datepicker-rtl .ui-datepicker-buttonpane button { float: left; }
|
||||
.ui-datepicker-rtl .ui-datepicker-buttonpane button.ui-datepicker-current { float:right; }
|
||||
.ui-datepicker-rtl .ui-datepicker-group { float:right; }
|
||||
.ui-datepicker-rtl .ui-datepicker-group-last .ui-datepicker-header { border-right-width:0; border-left-width:1px; }
|
||||
.ui-datepicker-rtl .ui-datepicker-group-middle .ui-datepicker-header { border-right-width:0; border-left-width:1px; }
|
||||
|
||||
/* IE6 IFRAME FIX (taken from datepicker 1.5.3 */
|
||||
.ui-datepicker-cover {
|
||||
display: none; /*sorry for IE5*/
|
||||
display/**/: block; /*sorry for IE5*/
|
||||
position: absolute; /*must have*/
|
||||
z-index: -1; /*must have*/
|
||||
filter: mask(); /*must have*/
|
||||
top: -4px; /*must have*/
|
||||
left: -4px; /*must have*/
|
||||
width: 200px; /*must have*/
|
||||
height: 200px; /*must have*/
|
||||
}/*
|
||||
* jQuery UI Progressbar 1.8.16
|
||||
*
|
||||
* Copyright 2011, AUTHORS.txt (http://jqueryui.com/about)
|
||||
* Dual licensed under the MIT or GPL Version 2 licenses.
|
||||
* http://jquery.org/license
|
||||
*
|
||||
* http://docs.jquery.com/UI/Progressbar#theming
|
||||
*/
|
||||
.ui-progressbar { height:2em; text-align: left; }
|
||||
.ui-progressbar .ui-progressbar-value {margin: -1px; height:100%; }
|
||||
@@ -1,2016 +0,0 @@
|
||||
//////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Simple schematic capture
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
// Chris Terman, Nov. 2011
|
||||
|
||||
// add schematics to a document with
|
||||
//
|
||||
// <input type="hidden" class="schematic" name="unique_form_id" value="...schematic/netlist info..." .../>
|
||||
//
|
||||
// other attributes you can add to the input tag:
|
||||
// width -- width in pixels of diagram
|
||||
// height -- height in pixels of diagram
|
||||
// parts -- comma-separated list of parts for parts bin (see parts_map)
|
||||
|
||||
// JSON schematic representation:
|
||||
// sch := [part, part, ...]
|
||||
// part := [type, coords, properties, connections]
|
||||
// type := string (see parts_map)
|
||||
// coords := [number, ...] // (x,y,rot) or (x1,y1,x2,y2)
|
||||
// properties := {name: value, ...}
|
||||
// connections := [node, ...] // one per connection point in canoncial order
|
||||
// node := string
|
||||
|
||||
// TO DO:
|
||||
|
||||
// - draggable overlay window base class (dialogs, scope, ...)
|
||||
// - wire labels?
|
||||
// - devices: diode, nfet, pfet, opamp, scope probe
|
||||
// - icons for test equipment? (scope, sig gen, counter, ...)
|
||||
|
||||
// - zoom/scroll canvas
|
||||
// - freeze_diagram, freeze_properties attributes (freeze certain components/properties?)
|
||||
// - rotate multiple objects around their center of mass
|
||||
// - rubber band wires when moving components
|
||||
|
||||
// - simulation: operating points, trans, ac analysis, sweeps?
|
||||
|
||||
// set up each schematic entry widget
|
||||
function update_schematics() {
|
||||
// set up each schematic on the page
|
||||
var schematics = document.getElementsByClassName('schematic');
|
||||
for (var i = schematics.length - 1; i >= 0; i--)
|
||||
if (schematics[i].getAttribute("loaded") != "true") {
|
||||
new Schematic(schematics[i]);
|
||||
schematics[i].setAttribute("loaded","true");
|
||||
}
|
||||
}
|
||||
|
||||
// add ourselves to the tasks that get performed when window is loaded
|
||||
function add_schematic_handler(other_onload) {
|
||||
return function() {
|
||||
// execute othe onload functions first
|
||||
if (other_onload) other_onload();
|
||||
|
||||
update_schematics();
|
||||
}
|
||||
}
|
||||
window.onload = add_schematic_handler(window.onload);
|
||||
|
||||
background_style = 'rgb(220,220,220)';
|
||||
element_style = 'rgb(255,255,255)';
|
||||
thumb_style = 'rgb(128,128,128)';
|
||||
normal_style = 'rgb(0,0,0)'; // color for unselected components
|
||||
selected_style = 'rgb(64,255,64)'; // highlight color for selected components
|
||||
grid_style = "rgb(128,128,128)";
|
||||
|
||||
// list of all the defined parts
|
||||
parts_map = {
|
||||
'g': [Ground, 'Ground connection'],
|
||||
'v': [VSource, 'Voltage source'],
|
||||
'i': [ISource, 'Current source'],
|
||||
'r': [Resistor, 'Resistor'],
|
||||
'c': [Capacitor, 'Capacitor'],
|
||||
'l': [Inductor, 'Inductor'],
|
||||
};
|
||||
|
||||
// fix cursor bug in Chrome (default behavior: change to text cursor
|
||||
// whenever a drag is initiated).
|
||||
document.onselectstart = function() { return false; };
|
||||
|
||||
///////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Schematic = diagram + parts bin + status area
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
// setup a schematic by populating the <div> with the appropriate children
|
||||
function Schematic(input) {
|
||||
this.div = document.createElement('div');
|
||||
// set up div so we can position elements inside of it
|
||||
this.div.style.position = 'relative';
|
||||
this.div.style.cursor = 'default';
|
||||
|
||||
this.grid = 8;
|
||||
this.scale = 2;
|
||||
this.origin_x = 0;
|
||||
this.origin_y = 0;
|
||||
this.clipboard = null;
|
||||
|
||||
// start with a background element with normal positioning
|
||||
this.background = document.createElement('canvas');
|
||||
this.background.style.backgroundColor = background_style;
|
||||
this.background.style.borderStyle = 'solid';
|
||||
this.background.style.borderWidth = '2px';
|
||||
|
||||
this.status_div = document.createElement('div');
|
||||
//this.status_div.style.borderStyle = 'solid';
|
||||
//this.status_div.style.borderWidth = '1px';
|
||||
this.status_div.style.position = 'absolute';
|
||||
this.status_div.style.padding = '2px';
|
||||
//this.status_div.style.backgroundColor = element_style;
|
||||
this.status = document.createTextNode('');
|
||||
this.status_div.appendChild(this.status);
|
||||
|
||||
this.connection_points = new Array(); // location string => list of cp's
|
||||
this.components = [];
|
||||
|
||||
// this is where schematic is rendered
|
||||
this.canvas = document.createElement('canvas');
|
||||
this.canvas.tabIndex = 1; // so we get keystrokes
|
||||
this.canvas.style.borderStyle = 'solid';
|
||||
this.canvas.style.borderWidth = '1px';
|
||||
this.canvas.style.borderColor = grid_style;
|
||||
this.canvas.style.position = 'absolute';
|
||||
this.canvas.style.outline = 'none';
|
||||
|
||||
this.canvas.schematic = this;
|
||||
this.canvas.addEventListener('mousemove',schematic_mouse_move,false);
|
||||
this.canvas.addEventListener('mouseover',schematic_mouse_enter,false);
|
||||
this.canvas.addEventListener('mouseout',schematic_mouse_leave,false);
|
||||
this.canvas.addEventListener('mousedown',schematic_mouse_down,false);
|
||||
this.canvas.addEventListener('mouseup',schematic_mouse_up,false);
|
||||
this.canvas.addEventListener('dblclick',schematic_double_click,false);
|
||||
this.canvas.addEventListener('keydown',schematic_key_down,false);
|
||||
this.canvas.addEventListener('keypress',schematic_key_press,false);
|
||||
|
||||
// toolbar
|
||||
this.tools = new Array();
|
||||
this.toolbar = [];
|
||||
this.tools['cut'] = this.add_tool(cut_icon,'Cut: move selected components from diagram to the clipboard',this.cut);
|
||||
this.tools['copy'] = this.add_tool(copy_icon,'Copy: copy selected components into the clipboard',this.copy);
|
||||
this.tools['paste'] = this.add_tool(paste_icon,'Paste: copy clipboard into the diagram',this.paste);
|
||||
|
||||
// make the canvas "clickable" by registering a dummy click handler
|
||||
// this should make things work on the iPad
|
||||
this.canvas.addEventListener('click',function(){},false);
|
||||
|
||||
this.dragging = false;
|
||||
this.drawCursor = false;
|
||||
this.cursor_x = 0;
|
||||
this.cursor_y = 0;
|
||||
this.draw_cursor = null;
|
||||
this.select_rect = null;
|
||||
this.wire = null;
|
||||
|
||||
// repaint simply draws this buffer and then adds selected elements on top
|
||||
this.bg_image = document.createElement('canvas');
|
||||
|
||||
// use user-supplied list of parts if supplied
|
||||
// else just populate parts bin with all the parts
|
||||
var parts = input.getAttribute('parts');
|
||||
if (parts) parts = parts.split(',');
|
||||
else {
|
||||
parts = new Array();
|
||||
for (var p in parts_map) parts.push(p);
|
||||
}
|
||||
|
||||
// now add the parts to the parts bin
|
||||
var parts_left = this.width + 3 + background_margin;
|
||||
var parts_top = background_margin;
|
||||
this.parts_bin = [];
|
||||
for (var i = 0; i < parts.length; i++) {
|
||||
var part = new Part(this);
|
||||
var pm = parts_map[parts[i]];
|
||||
part.set_component(new pm[0](part,0,0,0),pm[1]);
|
||||
this.parts_bin.push(part);
|
||||
}
|
||||
|
||||
// add all elements to the DOM
|
||||
this.div.appendChild(this.background);
|
||||
for (var i = 0; i < this.toolbar.length; i++)
|
||||
this.div.appendChild(this.toolbar[i]);
|
||||
this.div.appendChild(this.canvas);
|
||||
this.div.appendChild(this.status_div);
|
||||
for (var i = 0; i < this.parts_bin.length; i++)
|
||||
this.div.appendChild(this.parts_bin[i].canvas);
|
||||
input.parentNode.insertBefore(this.div,input.nextSibling);
|
||||
|
||||
// make sure other code can find us!
|
||||
input.schematic = this;
|
||||
this.input = input;
|
||||
|
||||
// set locations of all the elements in the editor
|
||||
var w = parseInt(input.getAttribute('width'));
|
||||
var h = parseInt(input.getAttribute('height'));
|
||||
this.set_locations(w,h);
|
||||
|
||||
// process initial contents of diagram
|
||||
this.load_schematic(this.input.value);
|
||||
}
|
||||
|
||||
|
||||
Schematic.prototype.load_schematic = function(value) {
|
||||
if (value) {
|
||||
// convert string value into data structure
|
||||
var json = JSON.parse(value);
|
||||
|
||||
// top level is a list of components
|
||||
for (var i = json.length - 1; i >= 0; --i) {
|
||||
var c = json[i];
|
||||
if (c[0] == 'view') {
|
||||
// special hack: view component lets us recreate view
|
||||
this.origin_x = c[1];
|
||||
this.origin_y = c[2];
|
||||
this.scale = c[3];
|
||||
} else if (c[0] == 'w') {
|
||||
// wire
|
||||
this.add_wire(c[1][0],c[1][1],c[1][2],c[1][3]);
|
||||
} else {
|
||||
// ordinary component
|
||||
// c := [type, coords, properties, connections]
|
||||
var type = c[0];
|
||||
var coords = c[1];
|
||||
var properties = c[2];
|
||||
|
||||
// make the part
|
||||
var part = new parts_map[type][0](this,coords[0],coords[1],coords[2]);
|
||||
|
||||
// give it its properties
|
||||
for (var name in properties)
|
||||
part.properties[name] = properties[name];
|
||||
|
||||
// add component to the diagram
|
||||
this.add_component(part);
|
||||
}
|
||||
}
|
||||
|
||||
// see what we've got!
|
||||
this.redraw_background();
|
||||
}
|
||||
}
|
||||
|
||||
background_margin = 5;
|
||||
part_w = 42; // size of a parts bin compartment
|
||||
part_h = 42;
|
||||
status_height = 18;
|
||||
|
||||
// w,h are the dimensions of the canvas, everyone else is positioned accordingly
|
||||
Schematic.prototype.set_locations = function(w,h) {
|
||||
// limit the shrinkage factor
|
||||
w = Math.max(w,120);
|
||||
h = Math.max(h,120);
|
||||
|
||||
this.width = w;
|
||||
this.height = h;
|
||||
this.bg_image.width = w;
|
||||
this.bg_image.height = h;
|
||||
|
||||
this.min_x = 0;
|
||||
this.min_y = 0;
|
||||
this.max_x = w/this.scale;
|
||||
this.max_y = h/this.scale;
|
||||
|
||||
var left = 2*background_margin; // space to the left
|
||||
|
||||
// start with tool bar
|
||||
var top = background_margin;
|
||||
if (this.toolbar.length > 0) {
|
||||
tool_left = left;
|
||||
for (var i = 0; i < this.toolbar.length; i++) {
|
||||
var img = this.toolbar[i];
|
||||
img.style.left = tool_left + 'px';
|
||||
img.style.top = top + 'px';
|
||||
tool_left += 24; // width + 2*padding + 2*border + gap
|
||||
}
|
||||
top += 27; // height + 2*padding + 2*border + gap;
|
||||
}
|
||||
|
||||
// configure canvas
|
||||
this.canvas.style.left = left + 'px';
|
||||
this.canvas.style.top = top + 'px';
|
||||
this.canvas.width = w;
|
||||
this.canvas.height = h;
|
||||
this.redraw_background(); // redraw diagram
|
||||
|
||||
// configure status bar
|
||||
this.status_div.style.left = left + 'px';
|
||||
this.status_div.style.top = this.canvas.offsetTop + this.canvas.offsetHeight + 3 + 'px';
|
||||
this.status_div.style.width = (w - 4) + 'px'; // subtract interior padding
|
||||
this.status_div.style.height = status_height + 'px';
|
||||
|
||||
// configure parts bin
|
||||
var total_w = this.canvas.offsetLeft + this.canvas.offsetWidth;
|
||||
var parts_left = total_w + 5;
|
||||
var parts_top = top;
|
||||
var parts_h_limit = this.canvas.offsetTop + this.canvas.offsetHeight;
|
||||
for (var i = 0; i < this.parts_bin.length; i++) {
|
||||
var part = this.parts_bin[i];
|
||||
part.set_location(parts_left,parts_top);
|
||||
|
||||
total_w = part.right();
|
||||
parts_top = part.bottom() + 2;
|
||||
if (parts_top + part_h > parts_h_limit) {
|
||||
parts_left = total_w - 1;
|
||||
parts_top = top;
|
||||
}
|
||||
}
|
||||
|
||||
// configure background
|
||||
var total_h = this.status_div.offsetTop + this.status_div.offsetHeight + background_margin;
|
||||
total_w += background_margin;
|
||||
this.background.height = total_h;
|
||||
this.background.width = total_w;
|
||||
|
||||
/* enable when there's support for resizing schematic
|
||||
// redraw thumb
|
||||
var c = this.background.getContext('2d');
|
||||
c.clearRect(0,0,w,h);
|
||||
c.strokeStyle = thumb_style;
|
||||
c.lineWidth = 1;
|
||||
c.beginPath();
|
||||
w = total_w - 1;
|
||||
h = total_h - 1;
|
||||
c.moveTo(w,h-4); c.lineTo(w-4,h);
|
||||
c.moveTo(w,h-8); c.lineTo(w-8,h);
|
||||
c.moveTo(w,h-12); c.lineTo(w-12,h);
|
||||
c.stroke();
|
||||
*/
|
||||
}
|
||||
|
||||
// label all the nodes in the circuit
|
||||
Schematic.prototype.label_connection_points = function() {
|
||||
// start by clearing all the connection point labels
|
||||
for (var i = this.components.length - 1; i >=0; --i)
|
||||
this.components[i].clear_labels();
|
||||
|
||||
// components are in charge of labeling their unlabeled connections.
|
||||
// labels given to connection points will propagate to coincident connection
|
||||
// points and across Wires.
|
||||
|
||||
// let special components like GND label their connection(s)
|
||||
for (var i = this.components.length - 1; i >=0; --i)
|
||||
this.components[i].add_default_labels();
|
||||
|
||||
// now have components generate labels for unlabeled connections
|
||||
this.next_label = 0;
|
||||
for (var i = this.components.length - 1; i >=0; --i)
|
||||
this.components[i].label_connections();
|
||||
}
|
||||
|
||||
// generate a new label
|
||||
Schematic.prototype.get_next_label = function() {
|
||||
// generate next label in sequence
|
||||
this.next_label += 1;
|
||||
return this.next_label.toString();
|
||||
}
|
||||
|
||||
// propagate label to coincident connection points
|
||||
Schematic.prototype.propagate_label = function(label,location) {
|
||||
var cplist = this.connection_points[location];
|
||||
for (var i = cplist.length - 1; i >= 0; --i)
|
||||
cplist[i].propagate_label(label);
|
||||
}
|
||||
|
||||
// update the value field of our corresponding input field with JSON
|
||||
// representation of schematic
|
||||
Schematic.prototype.update_value = function() {
|
||||
// label connection points
|
||||
this.label_connection_points();
|
||||
|
||||
// build JSON data structure, convert to string value for
|
||||
// input field
|
||||
this.input.value = JSON.stringify(this.json());
|
||||
}
|
||||
|
||||
// produce a JSON representation of the diagram
|
||||
Schematic.prototype.json = function() {
|
||||
var json = [];
|
||||
|
||||
// output all the components/wires in the diagram
|
||||
for (var i = this.components.length - 1; i >=0; --i)
|
||||
json.push(this.components[i].json());
|
||||
|
||||
// capture the current view parameters
|
||||
json.push(['view',this.origin_x,this.origin_y,this.scale]);
|
||||
|
||||
return json;
|
||||
}
|
||||
|
||||
Schematic.prototype.add_component = function(new_c) {
|
||||
this.components.push(new_c);
|
||||
|
||||
// create undoable edit record here
|
||||
}
|
||||
|
||||
Schematic.prototype.remove_component = function(c) {
|
||||
var index = this.components.indexOf(c);
|
||||
if (index != -1) this.components.splice(index,1);
|
||||
}
|
||||
|
||||
// add connection point to list of connection points at that location
|
||||
Schematic.prototype.add_connection_point = function(cp) {
|
||||
var cplist = this.connection_points[cp.location];
|
||||
if (cplist) cplist.push(cp);
|
||||
else {
|
||||
cplist = [cp];
|
||||
this.connection_points[cp.location] = cplist;
|
||||
}
|
||||
|
||||
// return list of conincident connection points
|
||||
return cplist;
|
||||
}
|
||||
|
||||
// remove connection point from the list points at the old location
|
||||
Schematic.prototype.remove_connection_point = function(cp,old_location) {
|
||||
// remove cp from list at old location
|
||||
var cplist = this.connection_points[old_location];
|
||||
if (cplist) {
|
||||
var index = cplist.indexOf(cp);
|
||||
if (index != -1) {
|
||||
cplist.splice(index,1);
|
||||
// if no more connections at this location, remove
|
||||
// entry from array to keep our search time short
|
||||
if (cplist.length == 0)
|
||||
delete this.connection_points[old_location];
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// connection point has changed location: remove, then add
|
||||
Schematic.prototype.update_connection_point = function(cp,old_location) {
|
||||
this.remove_connection_point(cp,old_location);
|
||||
return this.add_connection_point(cp);
|
||||
}
|
||||
|
||||
// add a wire to the schematic
|
||||
Schematic.prototype.add_wire = function(x1,y1,x2,y2) {
|
||||
var new_wire = new Wire(this,x1,y1,x2,y2);
|
||||
this.add_component(new_wire);
|
||||
new_wire.move_end();
|
||||
return new_wire;
|
||||
}
|
||||
|
||||
// see if connection points of component c split any wires
|
||||
Schematic.prototype.check_wires = function(c) {
|
||||
for (var i = this.components.length - 1; i >=0; --i) {
|
||||
var cc = this.components[i];
|
||||
if (cc != c) { // don't check a component against itself
|
||||
// only wires will do return non-null from a bisect call
|
||||
var cp = cc.bisect(c);
|
||||
if (cp) {
|
||||
// cc is a wire bisected by connection point cp
|
||||
|
||||
// remove biscted wire
|
||||
cc.delete();
|
||||
|
||||
// add two new wires with cp in the middle
|
||||
this.add_wire(cc.x,cc.y,cp.x,cp.y);
|
||||
this.add_wire(cc.x+cc.dx,cc.y+cc.dy,cp.x,cp.y);
|
||||
this.redraw_background();
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
Schematic.prototype.unselect_all = function(which) {
|
||||
for (var i = this.components.length - 1; i >= 0; --i)
|
||||
if (i != which) this.components[i].set_select(false);
|
||||
}
|
||||
|
||||
Schematic.prototype.drag_begin = function() {
|
||||
// let components know they're about to move
|
||||
for (var i = this.components.length - 1; i >= 0; --i) {
|
||||
var component = this.components[i];
|
||||
if (component.selected) component.move_begin();
|
||||
}
|
||||
|
||||
// remember where drag started
|
||||
this.drag_x = this.cursor_x;
|
||||
this.drag_y = this.cursor_y;
|
||||
this.dragging = true;
|
||||
}
|
||||
|
||||
Schematic.prototype.drag_end = function() {
|
||||
// let components know they're done moving
|
||||
for (var i = this.components.length - 1; i >= 0; --i) {
|
||||
var component = this.components[i];
|
||||
if (component.selected) component.move_end();
|
||||
}
|
||||
this.dragging = false;
|
||||
}
|
||||
|
||||
Schematic.prototype.cut = function() {
|
||||
// clear previous contents
|
||||
this.clipboard = [];
|
||||
|
||||
// look for selected components, move them to clipboard.
|
||||
for (var i = this.components.length - 1; i >=0; --i) {
|
||||
var c = this.components[i];
|
||||
if (c.selected) {
|
||||
c.delete();
|
||||
this.clipboard.push(c);
|
||||
}
|
||||
}
|
||||
|
||||
// update diagram view
|
||||
this.redraw();
|
||||
}
|
||||
|
||||
Schematic.prototype.copy = function() {
|
||||
// clear previous contents
|
||||
this.clipboard = [];
|
||||
|
||||
// look for selected components, copy them to clipboard.
|
||||
for (var i = this.components.length - 1; i >=0; --i) {
|
||||
var c = this.components[i];
|
||||
if (c.selected)
|
||||
this.clipboard.push(c.clone(this,c.x,c.y));
|
||||
}
|
||||
}
|
||||
|
||||
Schematic.prototype.paste = function() {
|
||||
// compute left,top of bounding box for origins of
|
||||
// components in the clipboard
|
||||
var left = null;
|
||||
var top = null;
|
||||
for (var i = this.clipboard.length - 1; i >= 0; --i) {
|
||||
var c = this.clipboard[i];
|
||||
left = left ? Math.min(left,c.x) : left;
|
||||
top = top ? Math.min(top,c.y) : top;
|
||||
}
|
||||
|
||||
// clear current selections
|
||||
this.unselect_all(-1);
|
||||
this.redraw_background(); // so we see any components that got unselected
|
||||
|
||||
// make clones of components on the clipboard, positioning
|
||||
// them relative to the cursor
|
||||
for (var i = this.clipboard.length - 1; i >= 0; --i) {
|
||||
var c = this.clipboard[i];
|
||||
var new_c = c.clone(this,this.cursor_x + (c.x - left),this.cursor_y + (c.y - top));
|
||||
this.add_component(new_c);
|
||||
new_c.set_select(true);
|
||||
}
|
||||
|
||||
// see what we've wrought
|
||||
this.redraw();
|
||||
}
|
||||
|
||||
///////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Drawing support -- deals with scaling and scrolling of diagrama
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
// here to redraw background image containing static portions of the schematic.
|
||||
// Also redraws dynamic portion.
|
||||
Schematic.prototype.redraw_background = function() {
|
||||
var c = this.bg_image.getContext('2d');
|
||||
var w = this.bg_image.width;
|
||||
var h = this.bg_imageheight;
|
||||
|
||||
// paint background color
|
||||
c.fillStyle = element_style;
|
||||
c.fillRect(0,0,this.width,this.height);
|
||||
|
||||
// border
|
||||
//c.strokeStyle = "rgb(0,0,0)";
|
||||
//c.strokeRect(0,0,this.width,this.height);
|
||||
|
||||
// grid
|
||||
c.strokeStyle = grid_style;
|
||||
var first_x = this.min_x;
|
||||
var last_x = this.max_x;
|
||||
var first_y = this.min_y;
|
||||
var last_y = this.max_y;
|
||||
for (var i = first_x; i < last_x; i += this.grid)
|
||||
this.draw_line(c,i,first_y,i,last_y,0.1);
|
||||
for (var i = first_y; i < last_y; i += this.grid)
|
||||
this.draw_line(c,first_x,i,last_x,i,0.1);
|
||||
|
||||
// unselected components
|
||||
for (var i = this.components.length - 1; i >= 0; --i) {
|
||||
var component = this.components[i];
|
||||
if (!component.selected) component.draw(c);
|
||||
}
|
||||
|
||||
this.redraw(); // background changed, redraw on screen
|
||||
}
|
||||
|
||||
// redraw what user sees = static image + dynamic parts
|
||||
Schematic.prototype.redraw = function() {
|
||||
var c = this.canvas.getContext('2d');
|
||||
|
||||
// put static image in the background
|
||||
c.drawImage(this.bg_image, 0, 0);
|
||||
|
||||
// selected components
|
||||
var selections = false;
|
||||
for (var i = this.components.length - 1; i >= 0; --i) {
|
||||
var component = this.components[i];
|
||||
if (component.selected) {
|
||||
component.draw(c);
|
||||
selections = true;
|
||||
}
|
||||
}
|
||||
this.enable_tool('cut',selections);
|
||||
this.enable_tool('copy',selections);
|
||||
this.enable_tool('paste',this.clipboard);
|
||||
|
||||
// connection points: draw one at each location
|
||||
for (var location in this.connection_points) {
|
||||
var cplist = this.connection_points[location];
|
||||
cplist[0].draw(c,cplist.length);
|
||||
}
|
||||
|
||||
// draw new wire
|
||||
if (this.wire) {
|
||||
var r = this.wire;
|
||||
c.strokeStyle = selected_style;
|
||||
this.draw_line(c,r[0],r[1],r[2],r[3],1);
|
||||
}
|
||||
|
||||
// draw selection rectangle
|
||||
if (this.select_rect) {
|
||||
var r = this.select_rect;
|
||||
c.lineWidth = 1;
|
||||
c.strokeStyle = selected_style;
|
||||
c.beginPath();
|
||||
c.moveTo(r[0],r[1]);
|
||||
c.lineTo(r[0],r[3]);
|
||||
c.lineTo(r[2],r[3]);
|
||||
c.lineTo(r[2],r[1]);
|
||||
c.lineTo(r[0],r[1]);
|
||||
c.stroke();
|
||||
}
|
||||
|
||||
// finally overlay cursor
|
||||
if (this.drawCursor && this.draw_cursor) {
|
||||
//var x = this.cursor_x;
|
||||
//var y = this.cursor_y;
|
||||
//this.draw_text(c,'('+x+','+y+')',x+this.grid,y-this.grid,10);
|
||||
this.draw_cursor(c,this.cursor_x,this.cursor_y);
|
||||
}
|
||||
}
|
||||
|
||||
// draws a cross cursor
|
||||
Schematic.prototype.cross_cursor = function(c,x,y) {
|
||||
this.draw_line(c,x-this.grid,y,x+this.grid,y,1);
|
||||
this.draw_line(c,x,y-this.grid,x,y+this.grid,1);
|
||||
}
|
||||
|
||||
Schematic.prototype.draw_line = function(c,x1,y1,x2,y2,width) {
|
||||
c.lineWidth = width*this.scale;
|
||||
c.beginPath();
|
||||
c.moveTo((x1 - this.origin_x) * this.scale,(y1 - this.origin_y) * this.scale);
|
||||
c.lineTo((x2 - this.origin_x) * this.scale,(y2 - this.origin_y) * this.scale);
|
||||
c.stroke();
|
||||
}
|
||||
|
||||
Schematic.prototype.draw_arc = function(c,x,y,radius,start_radians,end_radians,anticlockwise,width,filled) {
|
||||
c.lineWidth = width*this.scale;
|
||||
c.beginPath();
|
||||
c.arc((x - this.origin_x)*this.scale,(y - this.origin_y)*this.scale,radius*this.scale,
|
||||
start_radians,end_radians,anticlockwise);
|
||||
if (filled) c.fill();
|
||||
else c.stroke();
|
||||
}
|
||||
|
||||
Schematic.prototype.draw_text = function(c,text,x,y,size) {
|
||||
c.font = size*this.scale+'pt sans-serif'
|
||||
c.fillText(text,(x - this.origin_x) * this.scale,(y - this.origin_y) * this.scale);
|
||||
}
|
||||
|
||||
// add method to canvas to compute relative coords for event
|
||||
HTMLCanvasElement.prototype.relMouseCoords = function(event){
|
||||
// run up the DOM tree to figure out coords for top,left of canvas
|
||||
var totalOffsetX = 0;
|
||||
var totalOffsetY = 0;
|
||||
var canvasY = 0;
|
||||
var currentElement = this;
|
||||
do {
|
||||
totalOffsetX += currentElement.offsetLeft;
|
||||
totalOffsetY += currentElement.offsetTop;
|
||||
}
|
||||
while(currentElement = currentElement.offsetParent);
|
||||
|
||||
// now compute relative position of click within the canvas
|
||||
this.mouse_x = event.pageX - totalOffsetX;
|
||||
this.mouse_y = event.pageY - totalOffsetY;
|
||||
}
|
||||
|
||||
///////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Event handling
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
// process special keys here since they don't get delivered correctly on keypress
|
||||
function schematic_key_down(event) {
|
||||
if (!event) event = window.event;
|
||||
var sch = (window.event) ? event.srcElement.schematic : event.target.schematic;
|
||||
var code = event.keyCode;
|
||||
|
||||
if (code == 8 || code == 46) {
|
||||
// delete selected components
|
||||
for (var i = sch.components.length - 1; i >= 0; --i) {
|
||||
var component = sch.components[i];
|
||||
if (component.selected) component.delete(1);
|
||||
}
|
||||
sch.redraw();
|
||||
event.preventDefault();
|
||||
return false;
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
// process normal characters
|
||||
function schematic_key_press(event) {
|
||||
if (!event) event = window.event;
|
||||
var sch = (window.event) ? event.srcElement.schematic : event.target.schematic;
|
||||
var code = window.event ? event.keyCode : event.charCode;
|
||||
var char = String.fromCharCode(code);
|
||||
|
||||
// rotate
|
||||
if (!event.control && !event.altKey && (char == 'r' || char == 'R')) {
|
||||
// rotate
|
||||
for (var i = sch.components.length - 1; i >= 0; --i) {
|
||||
var component = sch.components[i];
|
||||
if (component.selected) component.rotate(1);
|
||||
}
|
||||
sch.redraw();
|
||||
event.preventDefault();
|
||||
return false;
|
||||
}
|
||||
|
||||
// cut
|
||||
if ((event.ctrlKey || event.altKey) && char == 'x') {
|
||||
sch.cut();
|
||||
event.preventDefault();
|
||||
return false;
|
||||
}
|
||||
|
||||
// copy
|
||||
if ((event.ctrlKey || event.altKey) && char == 'c') {
|
||||
sch.copy();
|
||||
event.preventDefault();
|
||||
return false;
|
||||
}
|
||||
|
||||
// paste
|
||||
if ((event.ctrlKey || event.altKey) && char == 'v') {
|
||||
sch.paste();
|
||||
event.preventDefault();
|
||||
return false;
|
||||
}
|
||||
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
function schematic_mouse_enter(event) {
|
||||
if (!event) event = window.event;
|
||||
var sch = (window.event) ? event.srcElement.schematic : event.target.schematic;
|
||||
|
||||
// see if user has selected a new part
|
||||
if (sch.new_part) {
|
||||
// grab incoming part, turn off selection of parts bin
|
||||
var part = sch.new_part;
|
||||
sch.new_part = null;
|
||||
part.select(false);
|
||||
|
||||
// make a clone of the component in the parts bin
|
||||
part = part.component.clone(sch,sch.cursor_x,sch.cursor_y);
|
||||
|
||||
// unselect everything else in the schematic, add part and select it
|
||||
sch.unselect_all(-1);
|
||||
sch.redraw_background(); // so we see any components that got unselected
|
||||
sch.add_component(part);
|
||||
part.set_select(true);
|
||||
|
||||
// and start dragging it
|
||||
sch.drag_begin();
|
||||
}
|
||||
|
||||
sch.drawCursor = true;
|
||||
sch.redraw();
|
||||
sch.canvas.focus(); // capture key strokes
|
||||
return false;
|
||||
}
|
||||
|
||||
function schematic_mouse_leave(event) {
|
||||
if (!event) event = window.event;
|
||||
var sch = (window.event) ? event.srcElement.schematic : event.target.schematic;
|
||||
sch.drawCursor = false;
|
||||
sch.redraw();
|
||||
return false;
|
||||
}
|
||||
|
||||
function schematic_mouse_down(event) {
|
||||
if (!event) event = window.event;
|
||||
else event.preventDefault();
|
||||
var sch = (window.event) ? event.srcElement.schematic : event.target.schematic;
|
||||
|
||||
// determine where event happened in schematic coordinates
|
||||
sch.canvas.relMouseCoords(event);
|
||||
var x = sch.canvas.mouse_x/sch.scale + sch.origin_x;
|
||||
var y = sch.canvas.mouse_y/sch.scale + sch.origin_y;
|
||||
sch.cursor_x = Math.round(x/sch.grid) * sch.grid;
|
||||
sch.cursor_y = Math.round(y/sch.grid) * sch.grid;
|
||||
|
||||
/*
|
||||
// for debugging... triggered by clicks in upper left corner
|
||||
if (sch.cursor_x < 10 && sch.cursor_y < 10) {
|
||||
sch.label_connection_points();
|
||||
sch.append_message(JSON.stringify(sch.json()));
|
||||
}
|
||||
*/
|
||||
|
||||
// is mouse over a connection point? If so, start dragging a wire
|
||||
var cplist = sch.connection_points[sch.cursor_x + ',' + sch.cursor_y];
|
||||
if (cplist && !event.shiftKey) {
|
||||
sch.unselect_all(-1);
|
||||
sch.wire = [sch.cursor_x,sch.cursor_y,sch.cursor_x,sch.cursor_y];
|
||||
} else {
|
||||
// give all components a shot at processing the selection event
|
||||
var which = -1;
|
||||
for (var i = sch.components.length - 1; i >= 0; --i)
|
||||
if (sch.components[i].select(x,y,event.shiftKey)) {
|
||||
if (sch.components[i].selected) {
|
||||
sch.drag_begin();
|
||||
which = i; // keep track of component we found
|
||||
}
|
||||
break;
|
||||
}
|
||||
// did we just click on a previously selected component?
|
||||
var reselect = which!=-1 && sch.components[which].was_previously_selected;
|
||||
|
||||
if (!event.shiftKey) {
|
||||
// if shift key isn't pressed and we didn't click on component
|
||||
// that was already selected, unselect everyone except component
|
||||
// we just clicked on
|
||||
if (!reselect) sch.unselect_all(which);
|
||||
|
||||
// if there's nothing to drag, set up a selection rectangle
|
||||
if (!sch.dragging) sch.select_rect = [sch.canvas.mouse_x,sch.canvas.mouse_y,
|
||||
sch.canvas.mouse_x,sch.canvas.mouse_y];
|
||||
}
|
||||
}
|
||||
|
||||
sch.redraw_background();
|
||||
return false;
|
||||
}
|
||||
|
||||
function schematic_mouse_move(event) {
|
||||
if (!event) event = window.event;
|
||||
var sch = (window.event) ? event.srcElement.schematic : event.target.schematic;
|
||||
|
||||
sch.canvas.relMouseCoords(event);
|
||||
var x = sch.canvas.mouse_x/sch.scale + sch.origin_x;
|
||||
var y = sch.canvas.mouse_y/sch.scale + sch.origin_y;
|
||||
sch.cursor_x = Math.round(x/sch.grid) * sch.grid;
|
||||
sch.cursor_y = Math.round(y/sch.grid) * sch.grid;
|
||||
|
||||
if (sch.wire) {
|
||||
// update new wire end point
|
||||
sch.wire[2] = sch.cursor_x;
|
||||
sch.wire[3] = sch.cursor_y;
|
||||
} else if (sch.dragging) {
|
||||
// see how far we moved
|
||||
var dx = sch.cursor_x - sch.drag_x;
|
||||
var dy = sch.cursor_y - sch.drag_y;
|
||||
if (dx != 0 || dy != 0) {
|
||||
// update position for next time
|
||||
sch.drag_x = sch.cursor_x;
|
||||
sch.drag_y = sch.cursor_y;
|
||||
|
||||
// give all components a shot at processing the event
|
||||
for (var i = sch.components.length - 1; i >= 0; --i) {
|
||||
var component = sch.components[i];
|
||||
if (component.selected) component.move(dx,dy);
|
||||
}
|
||||
}
|
||||
} else if (sch.select_rect) {
|
||||
// update moving corner of selection rectangle
|
||||
sch.select_rect[2] = sch.canvas.mouse_x;
|
||||
sch.select_rect[3] = sch.canvas.mouse_y;
|
||||
//sch.message(sch.select_rect.toString());
|
||||
}
|
||||
|
||||
// just redraw dynamic components
|
||||
sch.redraw();
|
||||
|
||||
return false;
|
||||
}
|
||||
|
||||
function schematic_mouse_up(event) {
|
||||
if (!event) event = window.event;
|
||||
else event.preventDefault();
|
||||
var sch = (window.event) ? event.srcElement.schematic : event.target.schematic;
|
||||
|
||||
// drawing a new wire
|
||||
if (sch.wire) {
|
||||
var r = sch.wire;
|
||||
sch.wire = null;
|
||||
|
||||
if (r[0]!=r[2] || r[1]!=r[3]) {
|
||||
// insert wire component
|
||||
sch.add_wire(r[0],r[1],r[2],r[3]);
|
||||
sch.redraw_background();
|
||||
} else sch.redraw();
|
||||
}
|
||||
|
||||
// dragging
|
||||
if (sch.dragging) sch.drag_end();
|
||||
|
||||
// selection rectangle
|
||||
if (sch.select_rect) {
|
||||
var r = sch.select_rect;
|
||||
|
||||
// if select_rect is a point, we've already dealt with selection
|
||||
// in mouse_down handler
|
||||
if (r[0]!=r[2] || r[1]!=r[3]) {
|
||||
// convert to schematic coordinates
|
||||
var s = [r[0]/sch.scale + sch.origin_x, r[1]/sch.scale + sch.origin_y,
|
||||
r[2]/sch.scale + sch.origin_x, r[3]/sch.scale + sch.origin_y];
|
||||
canonicalize(s);
|
||||
|
||||
if (!event.shiftKey) sch.unselect_all();
|
||||
|
||||
// select components that intersect selection rectangle
|
||||
for (var i = sch.components.length - 1; i >= 0; --i)
|
||||
sch.components[i].select_rect(s,event.shiftKey);
|
||||
}
|
||||
|
||||
sch.select_rect = null;
|
||||
sch.redraw_background();
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
function schematic_double_click(event) {
|
||||
if (!event) event = window.event;
|
||||
else event.preventDefault();
|
||||
var sch = (window.event) ? event.srcElement.schematic : event.target.schematic;
|
||||
|
||||
// determine where event happened in schematic coordinates
|
||||
sch.canvas.relMouseCoords(event);
|
||||
var x = sch.canvas.mouse_x/sch.scale + sch.origin_x;
|
||||
var y = sch.canvas.mouse_y/sch.scale + sch.origin_y;
|
||||
sch.cursor_x = Math.round(x/sch.grid) * sch.grid;
|
||||
sch.cursor_y = Math.round(y/sch.grid) * sch.grid;
|
||||
|
||||
// see if we double-clicked a component. If so, edit it's properties
|
||||
for (var i = sch.components.length - 1; i >= 0; --i)
|
||||
if (sch.components[i].edit_properties(x,y)) break;
|
||||
|
||||
return false;
|
||||
}
|
||||
|
||||
///////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Status message and dialogs
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
Schematic.prototype.message = function(message) {
|
||||
this.status.nodeValue = message;
|
||||
}
|
||||
|
||||
Schematic.prototype.append_message = function(message) {
|
||||
this.status.nodeValue += ' / '+message;
|
||||
}
|
||||
|
||||
// set up a dialog with specified title, content and two buttons at
|
||||
// the bottom: OK and Cancel. If Cancel is clicked, dialog goes away
|
||||
// and we're done. If OK is clicked, dialog goes away and the
|
||||
// callback function is called with the content as an argument (so
|
||||
// that the values of any fields can be captured).
|
||||
Schematic.prototype.dialog = function(title,content,callback) {
|
||||
// create the div for the top level of the dialog, add to DOM
|
||||
var dialog = document.createElement('div');
|
||||
dialog.sch = this;
|
||||
dialog.content = content;
|
||||
|
||||
// div to hold the title
|
||||
var head = document.createElement('div');
|
||||
head.style.backgroundColor = 'black';
|
||||
head.style.color = 'white';
|
||||
head.style.textAlign = 'center';
|
||||
head.style.padding = '5px';
|
||||
head.appendChild(document.createTextNode(title));
|
||||
dialog.appendChild(head);
|
||||
|
||||
// div to hold the content
|
||||
var body = document.createElement('div');
|
||||
body.appendChild(content);
|
||||
body.style.padding = '5px';
|
||||
dialog.appendChild(body);
|
||||
|
||||
// OK button
|
||||
var ok_button = document.createElement('span');
|
||||
ok_button.appendChild(document.createTextNode('OK'));
|
||||
ok_button.dialog = dialog; // for the handler to use
|
||||
ok_button.addEventListener('click',dialog_okay,false);
|
||||
ok_button.style.border = '1px solid';
|
||||
ok_button.style.padding = '5px';
|
||||
ok_button.style.margin = '10px';
|
||||
|
||||
// cancel button
|
||||
var cancel_button = document.createElement('span');
|
||||
cancel_button.appendChild(document.createTextNode('Cancel'));
|
||||
cancel_button.dialog = dialog; // for the handler to use
|
||||
cancel_button.addEventListener('click',dialog_cancel,false);
|
||||
cancel_button.style.border = '1px solid';
|
||||
cancel_button.style.padding = '5px';
|
||||
cancel_button.style.margin = '10px';
|
||||
|
||||
// div to hold the two buttons
|
||||
var buttons = document.createElement('div');
|
||||
buttons.appendChild(ok_button);
|
||||
buttons.appendChild(cancel_button);
|
||||
buttons.style.padding = '5px';
|
||||
buttons.style.margin = '10px';
|
||||
dialog.appendChild(buttons);
|
||||
|
||||
// add to DOM
|
||||
dialog.style.background = 'white';
|
||||
dialog.style.zindex = '1000';
|
||||
dialog.style.position = 'absolute';
|
||||
dialog.style.left = this.canvas.mouse_x+'px';
|
||||
dialog.style.top = this.canvas.mouse_y+'px';
|
||||
dialog.style.border = '2px solid';
|
||||
dialog.callback = callback;
|
||||
this.div.appendChild(dialog);
|
||||
}
|
||||
|
||||
// callback when user click "Cancel" in a dialog
|
||||
function dialog_cancel(event) {
|
||||
if (!event) event = window.event;
|
||||
var dialog = (window.event) ? event.srcElement.dialog : event.target.dialog;
|
||||
|
||||
// remove the dialog from the top-level div of the schematic
|
||||
dialog.parentNode.removeChild(dialog);
|
||||
}
|
||||
|
||||
// callback when user click "OK" in a dialog
|
||||
function dialog_okay(event) {
|
||||
if (!event) event = window.event;
|
||||
var dialog = (window.event) ? event.srcElement.dialog : event.target.dialog;
|
||||
|
||||
// remove the dialog from the top-level div of the schematic
|
||||
dialog.parentNode.removeChild(dialog);
|
||||
|
||||
// invoke the callback with the dialog contents as the argument
|
||||
if (dialog.callback) dialog.callback(dialog.content);
|
||||
}
|
||||
|
||||
///////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Toolbar
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
Schematic.prototype.add_tool = function(icon,tip,callback) {
|
||||
var img = document.createElement('img');
|
||||
img.src = icon;
|
||||
img.style.borderWidth = '1px';
|
||||
img.style.borderStyle = 'solid';
|
||||
img.style.borderColor = background_style;
|
||||
img.style.position = 'absolute';
|
||||
img.style.padding = '2px';
|
||||
|
||||
img.addEventListener('mouseover',tool_enter,false);
|
||||
img.addEventListener('mouseout',tool_leave,false);
|
||||
img.addEventListener('click',tool_click,false);
|
||||
|
||||
img.sch = this;
|
||||
img.tip = tip;
|
||||
img.callback = callback;
|
||||
this.toolbar.push(img);
|
||||
|
||||
img.enabled = false;
|
||||
img.style.opacity = 0.2;
|
||||
|
||||
return img;
|
||||
}
|
||||
|
||||
Schematic.prototype.enable_tool = function(tname,which) {
|
||||
var img = this.tools[tname];
|
||||
img.style.opacity = which ? 1.0 : 0.2;
|
||||
img.enabled = which;
|
||||
|
||||
// if disabling tool, remove border and tip
|
||||
if (!which) {
|
||||
img.style.borderColor = background_style;
|
||||
img.sch.message('');
|
||||
}
|
||||
}
|
||||
|
||||
// highlight tool button by turning on border, changing background
|
||||
function tool_enter(event) {
|
||||
if (!event) event = window.event;
|
||||
var img = (window.event) ? event.srcElement : event.target;
|
||||
|
||||
if (img.enabled) {
|
||||
img.style.borderColor = normal_style;
|
||||
img.sch.message(img.tip);
|
||||
img.opacity = 1.0;
|
||||
}
|
||||
}
|
||||
|
||||
// unhighlight tool button by turning off border, reverting to normal background
|
||||
function tool_leave(event) {
|
||||
if (!event) event = window.event;
|
||||
var img = (window.event) ? event.srcElement : event.target;
|
||||
|
||||
if (img.enabled) {
|
||||
img.style.borderColor = background_style;
|
||||
img.sch.message('');
|
||||
}
|
||||
}
|
||||
|
||||
// handle click on a tool
|
||||
function tool_click(event) {
|
||||
if (!event) event = window.event;
|
||||
var img = (window.event) ? event.srcElement : event.target;
|
||||
|
||||
if (img.enabled) img.callback.call(img.sch);
|
||||
}
|
||||
|
||||
cut_icon = 'data:image/gif;base64,R0lGODlhEAAQALMAAAAAAIAAAACAAICAAAAAgIAAgACAgMDAwICAgP8AAAD/AP//AAAA//8A/wD//////yH5BAEAAAcALAAAAAAQABAAAAQu8MhJqz1g5qs7lxv2gRkQfuWomarXEgDRHjJhf3YtyRav0xcfcFgR0nhB5OwTAQA7';
|
||||
|
||||
copy_icon = 'data:image/gif;base64,R0lGODlhEAAQALMAAAAAAIAAAACAAICAAAAAgIAAgACAgMDAwICAgP8AAAD/AP//AAAA//8A/wD//////yH5BAEAAAcALAAAAAAQABAAAAQ+8MhJ6wE4Wwqef9gmdV8HiKZJrCz3ecS7TikWfzExvk+M9a0a4MbTkXCgTMeoHPJgG5+yF31SLazsTMTtViIAOw==';
|
||||
|
||||
paste_icon = 'data:image/gif;base64,R0lGODlhEAAQALMAAAAAAIAAAACAAICAAAAAgIAAgACAgMDAwICAgP8AAAD/AP//AAAA//8A/wD//////yH5BAEAAAcALAAAAAAQABAAAARL8MhJqwUYWJnxWp3GDcgAgCdQIqLKXmVLhhnyHiqpr7rME8AgocVDEB5IJHD0SyofBFzxGIQGAbvB0ZkcTq1CKK6z5YorwnR0w44AADs=';
|
||||
|
||||
///////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Parts bin
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
// one instance will be created for each part in the parts bin
|
||||
function Part(sch) {
|
||||
this.sch = sch;
|
||||
this.component = null;
|
||||
this.selected = false;
|
||||
|
||||
// set up canvas
|
||||
this.canvas = document.createElement('canvas');
|
||||
this.canvas.style.borderStyle = 'solid';
|
||||
this.canvas.style.borderWidth = '1px';
|
||||
this.canvas.style.borderColor = background_style;
|
||||
this.canvas.style.position = 'absolute';
|
||||
this.canvas.style.cursor = 'default';
|
||||
this.canvas.height = part_w;
|
||||
this.canvas.width = part_h;
|
||||
this.canvas.part = this;
|
||||
|
||||
this.canvas.addEventListener('mouseover',part_enter,false);
|
||||
this.canvas.addEventListener('mouseout',part_leave,false);
|
||||
this.canvas.addEventListener('mousedown',part_mouse_down,false);
|
||||
this.canvas.addEventListener('mouseup',part_mouse_up,false);
|
||||
|
||||
// make the part "clickable" by registering a dummy click handler
|
||||
// this should make things work on the iPad
|
||||
this.canvas.addEventListener('click',function(){},false);
|
||||
}
|
||||
|
||||
Part.prototype.set_location = function(left,top) {
|
||||
this.canvas.style.left = left + 'px';
|
||||
this.canvas.style.top = top + 'px';
|
||||
}
|
||||
|
||||
Part.prototype.right = function() {
|
||||
return this.canvas.offsetLeft + this.canvas.offsetWidth;
|
||||
}
|
||||
|
||||
Part.prototype.bottom = function() {
|
||||
return this.canvas.offsetTop + this.canvas.offsetHeight;
|
||||
}
|
||||
|
||||
Part.prototype.set_component = function(component,tip) {
|
||||
this.component = component;
|
||||
this.tip = tip;
|
||||
|
||||
// figure out scaling and centering of parts icon
|
||||
var b = component.bounding_box;
|
||||
var dx = b[2] - b[0];
|
||||
var dy = b[3] - b[1];
|
||||
this.scale = 0.8; //Math.min(part_w/(1.2*dx),part_h/(1.2*dy));
|
||||
this.origin_x = b[0] + dx/2.0 - part_w/(2.0*this.scale);
|
||||
this.origin_y = b[1] + dy/2.0 - part_h/(2.0*this.scale);
|
||||
|
||||
this.redraw();
|
||||
}
|
||||
|
||||
Part.prototype.redraw = function(part) {
|
||||
var c = this.canvas.getContext('2d');
|
||||
|
||||
// paint background color
|
||||
c.fillStyle = this.selected ? selected_style : background_style;
|
||||
c.fillRect(0,0,part_w,part_h);
|
||||
|
||||
if (this.component) this.component.draw(c);
|
||||
}
|
||||
|
||||
Part.prototype.select = function(which) {
|
||||
this.selected = which;
|
||||
this.redraw();
|
||||
}
|
||||
|
||||
Part.prototype.update_connection_point = function(cp,old_location) {
|
||||
// no connection points in the parts bin
|
||||
}
|
||||
|
||||
Part.prototype.draw_line = function(c,x1,y1,x2,y2,width) {
|
||||
c.lineWidth = width*this.scale;
|
||||
c.beginPath();
|
||||
c.moveTo((x1 - this.origin_x) * this.scale,(y1 - this.origin_y) * this.scale);
|
||||
c.lineTo((x2 - this.origin_x) * this.scale,(y2 - this.origin_y) * this.scale);
|
||||
c.stroke();
|
||||
}
|
||||
|
||||
Part.prototype.draw_arc = function(c,x,y,radius,start_radians,end_radians,anticlockwise,width,filled) {
|
||||
c.lineWidth = width*this.scale;
|
||||
c.beginPath();
|
||||
c.arc((x - this.origin_x)*this.scale,(y - this.origin_y)*this.scale,radius*this.scale,
|
||||
start_radians,end_radians,anticlockwise);
|
||||
if (filled) c.fill();
|
||||
else c.stroke();
|
||||
}
|
||||
|
||||
Part.prototype.draw_text = function(c,text,x,y,size) {
|
||||
// no text displayed for the parts icon
|
||||
}
|
||||
|
||||
function part_enter(event) {
|
||||
if (!event) event = window.event;
|
||||
var canvas = (window.event) ? event.srcElement : event.target;
|
||||
var part = canvas.part;
|
||||
|
||||
canvas.style.borderColor = normal_style;
|
||||
part.sch.message(part.tip+': drag onto diagram to insert');
|
||||
return false;
|
||||
}
|
||||
|
||||
function part_leave(event) {
|
||||
if (!event) event = window.event;
|
||||
var canvas = (window.event) ? event.srcElement : event.target;
|
||||
var part = canvas.part;
|
||||
|
||||
canvas.style.borderColor = background_style;
|
||||
part.sch.message('');
|
||||
return false;
|
||||
}
|
||||
|
||||
function part_mouse_down(event) {
|
||||
if (!event) event = window.event;
|
||||
var part = (window.event) ? event.srcElement.part : event.target.part;
|
||||
|
||||
part.select(true);
|
||||
part.sch.new_part = part;
|
||||
return false;
|
||||
}
|
||||
|
||||
function part_mouse_up(event) {
|
||||
if (!event) event = window.event;
|
||||
var part = (window.event) ? event.srcElement.part : event.target.part;
|
||||
|
||||
part.select(false);
|
||||
part.sch.new_part = null;
|
||||
return false;
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Rectangle helper functions
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
// rect is an array of the form [left,top,right,bottom]
|
||||
|
||||
// ensure left < right, top < bottom
|
||||
function canonicalize(r) {
|
||||
var temp;
|
||||
|
||||
// canonicalize bounding box
|
||||
if (r[0] > r[2]) {
|
||||
temp = r[0];
|
||||
r[0] = r[2];
|
||||
r[2] = temp;
|
||||
}
|
||||
if (r[1] > r[3]) {
|
||||
temp = r[1];
|
||||
r[1] = r[3];
|
||||
r[3] = temp;
|
||||
}
|
||||
}
|
||||
|
||||
function between(x,x1,x2) {
|
||||
return x1 <= x && x <= x2;
|
||||
}
|
||||
|
||||
function inside(rect,x,y) {
|
||||
return between(x,rect[0],rect[2]) && between(y,rect[1],rect[3]);
|
||||
}
|
||||
|
||||
// only works for manhattan rectangles
|
||||
function intersect(r1,r2) {
|
||||
// look for non-intersection, negate result
|
||||
var result = !(r2[0] > r1[2] ||
|
||||
r2[2] < r1[0] ||
|
||||
r2[1] > r1[3] ||
|
||||
r2[3] < r1[1]);
|
||||
|
||||
// if I try to return the above expression, javascript returns undefined!!!
|
||||
return result;
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Component base class
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
property_size = 5; // point size for Component property text
|
||||
|
||||
function Component(sch,x,y,rotation) {
|
||||
this.sch = sch;
|
||||
this.x = x;
|
||||
this.y = y;
|
||||
this.rotation = rotation;
|
||||
this.selected = false;
|
||||
this.properties = new Array();
|
||||
this.bounding_box = [0,0,0,0]; // in device coords [left,top,right,bottom]
|
||||
this.bbox = this.bounding_box; // in absolute coords
|
||||
this.connections = [];
|
||||
}
|
||||
|
||||
Component.prototype.json = function() {
|
||||
var props = {};
|
||||
for (var p in this.properties) props[p] = this.properties[p];
|
||||
|
||||
var conns = [];
|
||||
for (var i = 0; i < this.connections.length; i++)
|
||||
conns.push(this.connections[i].json());
|
||||
|
||||
var json = [this.type,[this.x, this.y, this.rotation],props,conns];
|
||||
return json;
|
||||
}
|
||||
|
||||
Component.prototype.add_connection = function(offset_x,offset_y) {
|
||||
this.connections.push(new ConnectionPoint(this,offset_x,offset_y));
|
||||
}
|
||||
|
||||
Component.prototype.update_coords = function() {
|
||||
var x = this.x;
|
||||
var y = this.y;
|
||||
|
||||
// update bbox
|
||||
var b = this.bounding_box;
|
||||
this.bbox[0] = this.transform_x(b[0],b[1]) + x;
|
||||
this.bbox[1] = this.transform_y(b[0],b[1]) + y;
|
||||
this.bbox[2] = this.transform_x(b[2],b[3]) + x;
|
||||
this.bbox[3] = this.transform_y(b[2],b[3]) + y;
|
||||
canonicalize(this.bbox);
|
||||
|
||||
// update connections
|
||||
for (var i = this.connections.length - 1; i >= 0; --i)
|
||||
this.connections[i].update_location();
|
||||
}
|
||||
|
||||
Component.prototype.rotate = function(amount) {
|
||||
var old_rotation = this.rotation;
|
||||
this.rotation = (this.rotation + amount) % 8;
|
||||
this.update_coords();
|
||||
|
||||
// create an undoable edit record here
|
||||
// using old_rotation
|
||||
}
|
||||
|
||||
Component.prototype.move_begin = function() {
|
||||
// remember where we started this move
|
||||
this.move_x = this.x;
|
||||
this.move_y = this.y;
|
||||
}
|
||||
|
||||
Component.prototype.move = function(dx,dy) {
|
||||
// update coordinates
|
||||
this.x += dx;
|
||||
this.y += dy;
|
||||
this.update_coords();
|
||||
}
|
||||
|
||||
Component.prototype.move_end = function() {
|
||||
var dx = this.x - this.move_x;
|
||||
var dy = this.y - this.move_y;
|
||||
|
||||
if (dx != 0 || dy != 0) {
|
||||
// create an undoable edit record here
|
||||
|
||||
this.sch.check_wires(this);
|
||||
}
|
||||
}
|
||||
|
||||
Component.prototype.delete = function() {
|
||||
// remove connection points from schematic
|
||||
for (var i = this.connections.length - 1; i >= 0; --i) {
|
||||
var cp = this.connections[i];
|
||||
this.sch.remove_connection_point(cp,cp.location);
|
||||
}
|
||||
|
||||
// remove component from schematic
|
||||
this.sch.remove_component(this);
|
||||
|
||||
// create an undoable edit record here
|
||||
}
|
||||
|
||||
Component.prototype.transform_x = function(x,y) {
|
||||
var rot = this.rotation;
|
||||
if (rot == 0 || rot == 6) return x;
|
||||
else if (rot == 1 || rot == 5) return -y;
|
||||
else if (rot == 2 || rot == 4) return -x;
|
||||
else return y;
|
||||
}
|
||||
|
||||
Component.prototype.transform_y = function(x,y) {
|
||||
var rot = this.rotation;
|
||||
if (rot == 1 || rot == 7) return x;
|
||||
else if (rot == 2 || rot == 6) return -y;
|
||||
else if (rot == 3 || rot == 5) return -x;
|
||||
else return y;
|
||||
}
|
||||
|
||||
Component.prototype.draw_line = function(c,x1,y1,x2,y2) {
|
||||
c.strokeStyle = this.selected ? selected_style : normal_style;
|
||||
var nx1 = this.transform_x(x1,y1) + this.x;
|
||||
var ny1 = this.transform_y(x1,y1) + this.y;
|
||||
var nx2 = this.transform_x(x2,y2) + this.x;
|
||||
var ny2 = this.transform_y(x2,y2) + this.y;
|
||||
this.sch.draw_line(c,nx1,ny1,nx2,ny2,1);
|
||||
}
|
||||
|
||||
Component.prototype.draw_circle = function(c,x,y,radius,filled) {
|
||||
if (filled) c.fillStyle = this.selected ? selected_style : normal_style;
|
||||
else c.strokeStyle = this.selected ? selected_style : normal_style;
|
||||
var nx = this.transform_x(x,y) + this.x;
|
||||
var ny = this.transform_y(x,y) + this.y;
|
||||
|
||||
this.sch.draw_arc(c,nx,ny,radius,0,2*Math.PI,false,1,filled);
|
||||
}
|
||||
|
||||
rot_angle = [
|
||||
0.0, // NORTH (identity)
|
||||
Math.PI/2, // EAST (rot270)
|
||||
Math.PI, // SOUTH (rot180)
|
||||
3*Math.PI/2, // WEST (rot90)
|
||||
0.0, // RNORTH (negy)
|
||||
Math.PI/2, // REAST (int-neg)
|
||||
Math.PI, // RSOUTH (negx)
|
||||
3*Math.PI/2, // RWEST (int-pos)
|
||||
];
|
||||
|
||||
Component.prototype.draw_arc = function(c,x,y,radius,start_radians,end_radians) {
|
||||
c.strokeStyle = this.selected ? selected_style : normal_style;
|
||||
var nx = this.transform_x(x,y) + this.x;
|
||||
var ny = this.transform_y(x,y) + this.y;
|
||||
this.sch.draw_arc(c,nx,ny,radius,
|
||||
start_radians+rot_angle[this.rotation],end_radians+rot_angle[this.rotation],
|
||||
false,1,false);
|
||||
}
|
||||
|
||||
Component.prototype.draw = function(c) {
|
||||
}
|
||||
|
||||
// result of rotating an alignment [rot*9 + align]
|
||||
aOrient = [
|
||||
0, 1, 2, 3, 4, 5, 6, 7, 8, // NORTH (identity)
|
||||
2, 5, 8, 1, 4, 7, 0, 3, 6, // EAST (rot270)
|
||||
8, 7, 6, 5, 4, 3, 2, 1, 0, // SOUTH (rot180)
|
||||
6, 3, 0, 7, 4, 1, 8, 5, 3, // WEST (rot90)
|
||||
2, 1, 0, 5, 4, 3, 8, 7, 6, // RNORTH (negy)
|
||||
8, 5, 2, 7, 4, 1, 6, 3, 0, // REAST (int-neg)
|
||||
6, 7, 8, 3, 4, 5, 0, 1, 2, // RSOUTH (negx)
|
||||
0, 3, 6, 1, 4, 7, 2, 5, 8 // RWEST (int-pos)
|
||||
];
|
||||
|
||||
textAlign = [
|
||||
'left', 'center', 'right',
|
||||
'left', 'center', 'right',
|
||||
'left', 'center', 'right'
|
||||
];
|
||||
|
||||
textBaseline = [
|
||||
'top', 'top', 'top',
|
||||
'middle', 'middle', 'middle',
|
||||
'bottom', 'bottom', 'bottom'
|
||||
];
|
||||
|
||||
Component.prototype.draw_text = function(c,text,x,y,alignment,size) {
|
||||
var a = aOrient[this.rotation*9 + alignment];
|
||||
c.textAlign = textAlign[a];
|
||||
c.textBaseline = textBaseline[a];
|
||||
c.fillStyle = this.selected ? selected_style : normal_style;
|
||||
this.sch.draw_text(c,text,
|
||||
this.transform_x(x,y) + this.x,
|
||||
this.transform_y(x,y) + this.y,
|
||||
size);
|
||||
}
|
||||
|
||||
Component.prototype.set_select = function(which) {
|
||||
if (which != this.selected) {
|
||||
this.selected = which;
|
||||
// create an undoable edit record here
|
||||
}
|
||||
}
|
||||
|
||||
Component.prototype.select = function(x,y,shiftKey) {
|
||||
this.was_previously_selected = this.selected;
|
||||
if (inside(this.bbox,x,y)) {
|
||||
this.set_select(shiftKey ? !this.selected : true);
|
||||
return true;
|
||||
} else return false;
|
||||
}
|
||||
|
||||
Component.prototype.select_rect = function(s) {
|
||||
this.was_previously_selected = this.selected;
|
||||
if (intersect(this.bbox,s))
|
||||
this.set_select(true);
|
||||
}
|
||||
|
||||
// if connection point of component c bisects the
|
||||
// wire represented by this compononent, return that
|
||||
// connection point. Otherwise return null.
|
||||
Component.prototype.bisect = function(c) {
|
||||
return null;
|
||||
}
|
||||
|
||||
Component.prototype.edit_properties = function(x,y) {
|
||||
if (inside(this.bbox,x,y)) {
|
||||
var content = document.createElement('table');
|
||||
content.style.marginBotton = '5px';
|
||||
content.fields = [];
|
||||
|
||||
// add an <input> field for each property
|
||||
for (var i in this.properties) {
|
||||
var label = document.createTextNode(i + ': ');
|
||||
var field = document.createElement('input');
|
||||
field.type = 'text';
|
||||
field.value = this.properties[i];
|
||||
field.size = 10;
|
||||
content.fields.push([i,field]);
|
||||
|
||||
var col1 = document.createElement('td');
|
||||
col1.appendChild(label);
|
||||
var col2 = document.createElement('td');
|
||||
col2.appendChild(field);
|
||||
var row = document.createElement('tr');
|
||||
row.appendChild(col1);
|
||||
row.appendChild(col2);
|
||||
row.style.verticalAlign = 'center';
|
||||
|
||||
content.appendChild(row);
|
||||
}
|
||||
|
||||
var component = this; // capture in closure below
|
||||
this.sch.dialog('Edit Properties',content,function(content) {
|
||||
var fields = content.fields;
|
||||
for (var i = fields.length - 1; i >= 0; i--)
|
||||
component.properties[fields[i][0]] = fields[i][1].value;
|
||||
component.sch.redraw(); // component is selected, so this will redraw it
|
||||
});
|
||||
return true;
|
||||
} else return false;
|
||||
}
|
||||
|
||||
// clear the labels on all connections
|
||||
Component.prototype.clear_labels = function() {
|
||||
for (var i = this.connections.length - 1; i >=0; --i) {
|
||||
this.connections[i].clear_label();
|
||||
}
|
||||
}
|
||||
|
||||
// default action: don't propagate label
|
||||
Component.prototype.propagate_label = function(label) {
|
||||
}
|
||||
|
||||
// give components a chance to generate default labels for their connection(s)
|
||||
// default action: do nothing
|
||||
Component.prototype.add_default_labels = function() {
|
||||
}
|
||||
|
||||
// component should generate labels for all unlabeled connections
|
||||
Component.prototype.label_connections = function() {
|
||||
for (var i = this.connections.length - 1; i >=0; --i) {
|
||||
var cp = this.connections[i];
|
||||
if (!cp.label)
|
||||
cp.propagate_label(this.sch.get_next_label());
|
||||
}
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Connection point
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
connection_point_radius = 2;
|
||||
|
||||
function ConnectionPoint(parent,x,y) {
|
||||
this.parent = parent;
|
||||
this.offset_x = x;
|
||||
this.offset_y = y;
|
||||
this.location = '';
|
||||
this.update_location();
|
||||
this.label = null;
|
||||
}
|
||||
|
||||
ConnectionPoint.prototype.toString = function() {
|
||||
return '<ConnectionPoint ('+this.offset_x+','+this.offset_y+') '+this.parent.toString()+'>';
|
||||
}
|
||||
|
||||
ConnectionPoint.prototype.json = function() {
|
||||
return this.label;
|
||||
}
|
||||
|
||||
ConnectionPoint.prototype.clear_label = function() {
|
||||
this.label = null;
|
||||
}
|
||||
|
||||
ConnectionPoint.prototype.propagate_label = function(label) {
|
||||
// should we check if existing label is the same? it should be...
|
||||
|
||||
if (this.label == null) {
|
||||
// label this connection point
|
||||
this.label = label;
|
||||
|
||||
// propagate label to coincident connection points
|
||||
this.parent.sch.propagate_label(label,this.location);
|
||||
|
||||
// possibly label other cp's for this device?
|
||||
this.parent.propagate_label(label);
|
||||
}
|
||||
}
|
||||
|
||||
ConnectionPoint.prototype.update_location = function() {
|
||||
// update location string which we use as a key to find coincident connection points
|
||||
var old_location = this.location;
|
||||
var parent = this.parent;
|
||||
var nx = parent.transform_x(this.offset_x,this.offset_y) + parent.x;
|
||||
var ny = parent.transform_y(this.offset_x,this.offset_y) + parent.y;
|
||||
this.x = nx;
|
||||
this.y = ny;
|
||||
this.location = nx + ',' + ny;
|
||||
|
||||
// add ourselves to the connection list for the new location
|
||||
parent.sch.update_connection_point(this,old_location);
|
||||
}
|
||||
|
||||
ConnectionPoint.prototype.coincident = function(x,y) {
|
||||
return this.x==x && this.y==y;
|
||||
}
|
||||
|
||||
ConnectionPoint.prototype.draw = function(c,n) {
|
||||
if (n != 2)
|
||||
this.parent.draw_circle(c,this.offset_x,this.offset_y,connection_point_radius,n > 2);
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Wire
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
near_distance = 2; // how close to wire counts as "near by"
|
||||
|
||||
function Wire(sch,x1,y1,x2,y2) {
|
||||
// arbitrarily call x1,y1 the origin
|
||||
Component.call(this,sch,x1,y1,0);
|
||||
this.dx = x2 - x1;
|
||||
this.dy = y2 - y1;
|
||||
this.add_connection(0,0);
|
||||
this.add_connection(this.dx,this.dy);
|
||||
|
||||
// compute bounding box (expanded slightly)
|
||||
var r = [0,0,this.dx,this.dy];
|
||||
canonicalize(r);
|
||||
r[0] -= near_distance;
|
||||
r[1] -= near_distance;
|
||||
r[2] += near_distance;
|
||||
r[3] += near_distance;
|
||||
this.bounding_box = r;
|
||||
this.update_coords(); // update bbox
|
||||
|
||||
// used in selection calculations
|
||||
this.len = Math.sqrt(this.dx*this.dx + this.dy*this.dy);
|
||||
}
|
||||
Wire.prototype = new Component();
|
||||
Wire.prototype.constructor = Wire;
|
||||
|
||||
Wire.prototype.toString = function() {
|
||||
return '<Wire ('+this.x+','+this.y+') ('+(this.x+this.dx)+','+(this.y+this.dy)+')>';
|
||||
}
|
||||
|
||||
Wire.prototype.json = function() {
|
||||
var json = ['w',[this.x, this.y, this.x+this.dx, this.y+this.dy]];
|
||||
return json;
|
||||
}
|
||||
|
||||
Wire.prototype.draw = function(c) {
|
||||
this.draw_line(c,0,0,this.dx,this.dy);
|
||||
}
|
||||
|
||||
Wire.prototype.clone = function(sch,x,y) {
|
||||
return new Wire(sch,x,y,x+this.dx,y+this.dy);
|
||||
}
|
||||
|
||||
Wire.prototype.near = function(x,y) {
|
||||
// crude check: (x,y) within expanded bounding box of wire
|
||||
if (inside(this.bbox,x,y)) {
|
||||
// compute distance between x,y and nearst point on line
|
||||
// http://www.allegro.cc/forums/thread/589720
|
||||
var D = Math.abs((x - this.x)*this.dy - (y - this.y)*this.dx)/this.len;
|
||||
if (D <= near_distance) return true;
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
Wire.prototype.select = function(x,y,shiftKey) {
|
||||
this.was_previously_selected = this.selected;
|
||||
if (this.near(x,y)) {
|
||||
this.set_select(shiftKey ? !this.selected : true);
|
||||
return true;
|
||||
} else return false;
|
||||
}
|
||||
|
||||
// selection rectangle selects wire only if it includes
|
||||
// one of the end points
|
||||
Wire.prototype.select_rect = function(s) {
|
||||
this.was_previously_selected = this.selected;
|
||||
if (inside(s,this.x,this.y) || inside(s,this.x+this.dx,this.y+this.dy))
|
||||
this.set_select(true);
|
||||
}
|
||||
|
||||
// if connection point of component c bisects the
|
||||
// wire represented by this compononent, return that
|
||||
// connection point. Otherwise return null.
|
||||
Wire.prototype.bisect = function(c) {
|
||||
for (var i = c.connections.length - 1; i >= 0; --i) {
|
||||
var cp = c.connections[i];
|
||||
var x = cp.x;
|
||||
var y = cp.y;
|
||||
|
||||
// crude check: (x,y) within expanded bounding box of wire
|
||||
if (inside(this.bbox,x,y)) {
|
||||
// compute distance between x,y and nearst point on line
|
||||
// http://www.allegro.cc/forums/thread/589720
|
||||
var D = Math.abs((x - this.x)*this.dy - (y - this.y)*this.dx)/this.len;
|
||||
// final check: ensure point isn't an end point of the wire
|
||||
if (D < 1 && !this.connections[0].coincident(x,y) && !this.connections[1].coincident(x,y))
|
||||
return cp;
|
||||
}
|
||||
}
|
||||
return null;
|
||||
}
|
||||
|
||||
Wire.prototype.move_end = function() {
|
||||
this.sch.check_wires(this);
|
||||
}
|
||||
|
||||
// wires "conduct" their label to the other end
|
||||
Wire.prototype.propagate_label = function(label) {
|
||||
// don't worry about relabeling a cp, it won't recurse!
|
||||
this.connections[0].propagate_label(label);
|
||||
this.connections[1].propagate_label(label);
|
||||
}
|
||||
|
||||
// some actual component will start the labeling of electrical nodes,
|
||||
// so do nothing here
|
||||
Wire.prototype.label_connections = function() {
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Ground
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
function Ground(sch,x,y,rotation) {
|
||||
Component.call(this,sch,x,y,rotation);
|
||||
this.add_connection(0,0);
|
||||
this.bounding_box = [-6,0,6,8];
|
||||
this.update_coords();
|
||||
this.type = 'g';
|
||||
}
|
||||
Ground.prototype = new Component();
|
||||
Ground.prototype.constructor = Ground;
|
||||
|
||||
Ground.prototype.toString = function() {
|
||||
return '<Ground ('+this.x+','+this.y+')>';
|
||||
}
|
||||
|
||||
Ground.prototype.draw = function(c) {
|
||||
this.draw_line(c,0,0,0,8);
|
||||
this.draw_line(c,-6,8,6,8);
|
||||
}
|
||||
|
||||
Ground.prototype.clone = function(sch,x,y) {
|
||||
return new Ground(sch,x,y,this.rotation);
|
||||
}
|
||||
|
||||
// give components a chance to generate a label for their connection(s)
|
||||
// default action: do nothing
|
||||
Ground.prototype.add_default_labels = function() {
|
||||
this.connections[0].propagate_label('0'); // canonical label for GND node
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Resistor
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
function Resistor(sch,x,y,rotation,name,r) {
|
||||
Component.call(this,sch,x,y,rotation);
|
||||
this.properties['name'] = name;
|
||||
this.properties['r'] = r ? r : '1';
|
||||
this.add_connection(0,0);
|
||||
this.add_connection(0,48);
|
||||
this.bounding_box = [-4,0,4,48];
|
||||
this.update_coords();
|
||||
this.type = 'r';
|
||||
}
|
||||
Resistor.prototype = new Component();
|
||||
Resistor.prototype.constructor = Resistor;
|
||||
|
||||
Resistor.prototype.toString = function() {
|
||||
return '<Resistor '+this.properties['r']+' ('+this.x+','+this.y+')>';
|
||||
}
|
||||
|
||||
Resistor.prototype.draw = function(c) {
|
||||
this.draw_line(c,0,0,0,12);
|
||||
this.draw_line(c,0,12,4,14);
|
||||
this.draw_line(c,4,14,-4,18);
|
||||
this.draw_line(c,-4,18,4,22);
|
||||
this.draw_line(c,4,22,-4,26);
|
||||
this.draw_line(c,-4,26,4,30);
|
||||
this.draw_line(c,4,30,-4,34);
|
||||
this.draw_line(c,-4,34,0,36);
|
||||
this.draw_line(c,0,36,0,48);
|
||||
if (this.properties['r'])
|
||||
this.draw_text(c,this.properties['r']+'\u03A9',5,24,3,property_size);
|
||||
if (this.properties['name'])
|
||||
this.draw_text(c,this.properties['name'],-5,24,5,property_size);
|
||||
}
|
||||
|
||||
Resistor.prototype.clone = function(sch,x,y) {
|
||||
return new Resistor(sch,x,y,this.rotation,'',this.properties['r']);
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Capacitor
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
function Capacitor(sch,x,y,rotation,name,c) {
|
||||
Component.call(this,sch,x,y,rotation);
|
||||
this.properties['name'] = name;
|
||||
this.properties['c'] = c ? c : '1p';
|
||||
this.add_connection(0,0);
|
||||
this.add_connection(0,48);
|
||||
this.bounding_box = [-8,0,8,48];
|
||||
this.update_coords();
|
||||
this.type = 'c';
|
||||
}
|
||||
Capacitor.prototype = new Component();
|
||||
Capacitor.prototype.constructor = Capacitor;
|
||||
|
||||
Capacitor.prototype.toString = function() {
|
||||
return '<Capacitor '+this.properties['r']+' ('+this.x+','+this.y+')>';
|
||||
}
|
||||
|
||||
Capacitor.prototype.draw = function(c) {
|
||||
this.draw_line(c,0,0,0,22);
|
||||
this.draw_line(c,-8,22,8,22);
|
||||
this.draw_line(c,-8,26,8,26);
|
||||
this.draw_line(c,0,26,0,48);
|
||||
if (this.properties['c'])
|
||||
this.draw_text(c,this.properties['c']+'F',9,24,3,property_size);
|
||||
if (this.properties['name'])
|
||||
this.draw_text(c,this.properties['name'],-9,24,5,property_size);
|
||||
}
|
||||
|
||||
Capacitor.prototype.clone = function(sch,x,y) {
|
||||
return new Capacitor(sch,x,y,this.rotation,'',this.properties['c']);
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Inductor
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
function Inductor(sch,x,y,rotation,name,l) {
|
||||
Component.call(this,sch,x,y,rotation);
|
||||
this.properties['name'] = name;
|
||||
this.properties['l'] = l ? l : '1n';
|
||||
this.add_connection(0,0);
|
||||
this.add_connection(0,48);
|
||||
this.bounding_box = [-4,0,5,48];
|
||||
this.update_coords();
|
||||
this.type = 'l';
|
||||
}
|
||||
Inductor.prototype = new Component();
|
||||
Inductor.prototype.constructor = Inductor;
|
||||
|
||||
Inductor.prototype.toString = function() {
|
||||
return '<Inductor '+this.properties['l']+' ('+this.x+','+this.y+')>';
|
||||
}
|
||||
|
||||
Inductor.prototype.draw = function(c) {
|
||||
this.draw_line(c,0,0,0,14);
|
||||
this.draw_arc(c,0,18,4,6*Math.PI/4,3*Math.PI/4);
|
||||
this.draw_arc(c,0,24,4,5*Math.PI/4,3*Math.PI/4);
|
||||
this.draw_arc(c,0,30,4,5*Math.PI/4,2*Math.PI/4);
|
||||
this.draw_line(c,0,34,0,48);
|
||||
|
||||
if (this.properties['l'])
|
||||
this.draw_text(c,this.properties['l']+'H',6,24,3,property_size);
|
||||
if (this.properties['name'])
|
||||
this.draw_text(c,this.properties['name'],-3,24,5,property_size);
|
||||
}
|
||||
|
||||
Inductor.prototype.clone = function(sch,x,y) {
|
||||
return new Inductor(sch,x,y,this.rotation,'',this.properties['l']);
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Source
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
function Source(sch,x,y,rotation,name,type,value) {
|
||||
Component.call(this,sch,x,y,rotation);
|
||||
this.type = type;
|
||||
this.properties['name'] = name;
|
||||
this.properties['value'] = value ? value : '1';
|
||||
this.add_connection(0,0);
|
||||
this.add_connection(0,48);
|
||||
this.bounding_box = [-12,0,12,48];
|
||||
this.update_coords();
|
||||
}
|
||||
Source.prototype = new Component();
|
||||
Source.prototype.constructor = Source;
|
||||
|
||||
Source.prototype.toString = function() {
|
||||
return '<'+this.type+'source '+this.properties['params']+' ('+this.x+','+this.y+')>';
|
||||
}
|
||||
|
||||
Source.prototype.draw = function(c) {
|
||||
this.draw_line(c,0,0,0,12);
|
||||
this.draw_circle(c,0,24,12,false);
|
||||
this.draw_line(c,0,36,0,48);
|
||||
|
||||
if (this.type == 'v') { // voltage source
|
||||
// draw + and -
|
||||
this.draw_line(c,8,5,8,11);
|
||||
this.draw_line(c,5,8,11,8);
|
||||
this.draw_line(c,5,40,11,40);
|
||||
// draw V
|
||||
this.draw_line(c,-3,20,0,28);
|
||||
this.draw_line(c,3,20,0,28);
|
||||
} else if (this.type == 'i') { // current source
|
||||
// draw arrow: pos to neg
|
||||
this.draw_line(c,0,16,0,32);
|
||||
this.draw_line(c,-3,24,0,32);
|
||||
this.draw_line(c,3,24,0,32);
|
||||
}
|
||||
|
||||
if (this.properties['name'])
|
||||
this.draw_text(c,this.properties['name'],-13,24,5,property_size);
|
||||
if (this.properties['value'])
|
||||
this.draw_text(c,this.properties['value']+(this.type=='v'?'V':'A'),13,24,3,property_size);
|
||||
}
|
||||
|
||||
Source.prototype.clone = function(sch,x,y) {
|
||||
return new Source(sch,x,y,this.rotation,'',this.type,this.properties['value']);
|
||||
}
|
||||
|
||||
function VSource(sch,x,y,rotation,name,value) {
|
||||
Source.call(this,sch,x,y,rotation,name,'v',value);
|
||||
this.type = 'v';
|
||||
}
|
||||
VSource.prototype = new Component();
|
||||
VSource.prototype.constructor = VSource;
|
||||
VSource.prototype.toString = Source.prototype.toString;
|
||||
VSource.prototype.draw = Source.prototype.draw;
|
||||
VSource.prototype.clone = Source.prototype.clone;
|
||||
|
||||
function ISource(sch,x,y,rotation,name,value) {
|
||||
Source.call(this,sch,x,y,rotation,name,'i',value);
|
||||
this.type = 'i';
|
||||
}
|
||||
ISource.prototype = new Component();
|
||||
ISource.prototype.constructor = ISource;
|
||||
ISource.prototype.toString = Source.prototype.toString;
|
||||
ISource.prototype.draw = Source.prototype.draw;
|
||||
ISource.prototype.clone = Source.prototype.clone;
|
||||
@@ -1,317 +0,0 @@
|
||||
// Things to abstract out to another file
|
||||
|
||||
function postJSON(url, data, callback, csrf) {
|
||||
$.ajax({
|
||||
url: url,
|
||||
dataType: 'json',
|
||||
data: data,
|
||||
success: callback
|
||||
});
|
||||
}
|
||||
|
||||
var global=5;
|
||||
|
||||
// Video player
|
||||
|
||||
var load_id = 0;
|
||||
|
||||
var video_speed = 1.0;
|
||||
|
||||
function change_video_speed(speed, youtube_id) {
|
||||
new_position = ytplayer.getCurrentTime() * video_speed / speed;
|
||||
video_speed = speed;
|
||||
ytplayer.loadVideoById(youtube_id, new_position);
|
||||
}
|
||||
|
||||
function caption_at(index) {
|
||||
if (captions==0)
|
||||
return " ";
|
||||
|
||||
text_array=captions.text
|
||||
|
||||
if ((index>=text_array.length) || (index < 0))
|
||||
return " ";
|
||||
return text_array[index];
|
||||
}
|
||||
|
||||
function caption_time_at(index) {
|
||||
if (captions==0)
|
||||
return 0;
|
||||
|
||||
time_array=captions.start;
|
||||
|
||||
if (index < 0)
|
||||
return 0;
|
||||
if (index>=time_array.length)
|
||||
return ytplayer.getDuration();
|
||||
|
||||
return time_array[index] / 1000.0 / video_speed;
|
||||
}
|
||||
|
||||
function caption_index(now) {
|
||||
// Returns the index of the current caption, given a time
|
||||
now = now * video_speed;
|
||||
|
||||
if (captions==0)
|
||||
return 0;
|
||||
|
||||
time_array=captions.start
|
||||
|
||||
// TODO: Bisection would be better, or something incremental
|
||||
var i;
|
||||
for(i=0;i<captions.start.length; i++) {
|
||||
if(time_array[i]>(now*1000)) {
|
||||
return i-1;
|
||||
}
|
||||
}
|
||||
return i-1;
|
||||
}
|
||||
|
||||
function update_captions(t) {
|
||||
var i=caption_index(t);
|
||||
$("#std_n5").html(caption_at(i-5));
|
||||
$("#std_n4").html(caption_at(i-4));
|
||||
$("#std_n3").html(caption_at(i-3));
|
||||
$("#std_n2").html(caption_at(i-2));
|
||||
$("#std_n1").html(caption_at(i-1));
|
||||
$("#std_0").html(caption_at(i));
|
||||
$("#std_p1").html(caption_at(i+1));
|
||||
$("#std_p2").html(caption_at(i+2));
|
||||
$("#std_p3").html(caption_at(i+3));
|
||||
$("#std_p4").html(caption_at(i+4));
|
||||
$("#std_p5").html(caption_at(i+5));
|
||||
$("#std_p6").html(caption_at(i+6));
|
||||
}
|
||||
|
||||
function title_seek(i) {
|
||||
// Seek video forwards or backwards by i subtitles
|
||||
current=caption_index(getCurrentTime());
|
||||
new_time=caption_time_at(current+i);
|
||||
|
||||
ytplayer.seekTo(new_time, true);
|
||||
}
|
||||
|
||||
function updateHTML(elmId, value) {
|
||||
document.getElementById(elmId).innerHTML = value;
|
||||
}
|
||||
|
||||
function setytplayerState(newState) {
|
||||
// updateHTML("playerstate", newState);
|
||||
}
|
||||
|
||||
// Updates server with location in video so we can resume from the same place
|
||||
// IMPORTANT TODO: Load test
|
||||
// POSSIBLE FIX: Move to unload() event and similar
|
||||
var ajax_video=function(){};
|
||||
|
||||
function onYouTubePlayerReady(playerId) {
|
||||
ytplayer = document.getElementById("myytplayer");
|
||||
setInterval(updateytplayerInfo, 1000);
|
||||
setInterval(ajax_video,1000);
|
||||
ytplayer.addEventListener("onStateChange", "onytplayerStateChange");
|
||||
ytplayer.addEventListener("onError", "onPlayerError");
|
||||
if((typeof load_id != "undefined") && (load_id != 0)) {
|
||||
var id=load_id;
|
||||
loadNewVideo(id, 0);
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
function videoDestroy() {
|
||||
load_id = 0;
|
||||
// TODO/BUG: Figure out why removeEventListener doesn't work
|
||||
ytplayer.removeEventListener("onStateChange", "onytplayerStateChange");
|
||||
ytplayer.removeEventListener("onError", "onPlayerError");
|
||||
ytplayer = false;
|
||||
}
|
||||
|
||||
function log_event(e, d) {
|
||||
// CRITICAL TODO: Change to AJAX
|
||||
//$("#eventlog").append("<br>");
|
||||
//$("#eventlog").append(JSON.stringify(e));
|
||||
|
||||
// TODO: Figure out
|
||||
// XMLHttpRequest cannot load http://localhost:7000/userlog. Origin http://localhost:8000 is not allowed by Access-Control-Allow-Origin.
|
||||
|
||||
/*window['console'].log(JSON.stringify(e));
|
||||
$.get("http://localhost:7000/userlog",
|
||||
{'user':'pmitros',
|
||||
'key':'key',
|
||||
'event_type':'unknown',
|
||||
'data':'e'},
|
||||
function(data) {
|
||||
});*/
|
||||
}
|
||||
|
||||
function seek_slide(type,oe,value) {
|
||||
//log_event('video', [type, value]);
|
||||
if(type=='slide') {
|
||||
// HACK/TODO: Youtube recommends this be false for slide and true for stop.
|
||||
// Works better on my system with true/true.
|
||||
// We should test both configurations on low/high bandwidth
|
||||
// connections, and different browsers
|
||||
// One issue is that we query the Youtube window every 250ms for position/state
|
||||
// With false, it returns the old one (ignoring the new seek), and moves the
|
||||
// scroll bar to the wrong spot.
|
||||
ytplayer.seekTo(value, true);
|
||||
} else if (type=='stop') {
|
||||
ytplayer.seekTo(value, true);
|
||||
log_event('video', [type, value]);
|
||||
}
|
||||
|
||||
update_captions(value);
|
||||
}
|
||||
|
||||
function get_state() {
|
||||
if (ytplayer)
|
||||
return [ytplayer.getPlayerState(),
|
||||
ytplayer.getVideoUrl(),
|
||||
ytplayer.getDuration(), ytplayer.getCurrentTime(),
|
||||
ytplayer.getVideoBytesLoaded(), ytplayer.getVideoBytesTotal(),
|
||||
ytplayer.getVideoStartBytes(),
|
||||
ytplayer.getVolume(),ytplayer.isMuted(),
|
||||
ytplayer.getPlaybackQuality(),
|
||||
ytplayer.getAvailableQualityLevels()];
|
||||
return [];
|
||||
}
|
||||
|
||||
function onytplayerStateChange(newState) {
|
||||
setytplayerState(newState);
|
||||
log_event('video', ['State Change',newState, get_state()]);
|
||||
}
|
||||
|
||||
function onPlayerError(errorCode) {
|
||||
alert("An error occured: " + errorCode);
|
||||
}
|
||||
|
||||
function updateytplayerInfo() {
|
||||
if(ytplayer.getPlayerState()!=3) {
|
||||
$("#slider").slider("option","max",ytplayer.getDuration());
|
||||
$("#slider").slider("option","value",ytplayer.getCurrentTime());
|
||||
}
|
||||
if (getPlayerState() == 1){
|
||||
update_captions(getCurrentTime());
|
||||
}
|
||||
|
||||
// updateHTML("videoduration", getDuration());
|
||||
// updateHTML("videotime", getCurrentTime());
|
||||
// updateHTML("startbytes", getStartBytes());
|
||||
// updateHTML("volume", getVolume());
|
||||
}
|
||||
|
||||
// functions for the api calls
|
||||
function loadNewVideo(id, startSeconds) {
|
||||
captions={"start":[0],"end":[0],"text":["Attempting to load captions..."]};
|
||||
$.getJSON("/static/subs/"+id+".srt.sjson", function(data) {
|
||||
captions=data;
|
||||
});
|
||||
load_id = id;
|
||||
//if ((typeof ytplayer != "undefined") && (ytplayer.type=="application/x-shockwave-flash")) {
|
||||
// Try it every time. If we fail, we want the error message for now.
|
||||
// TODO: Add try/catch
|
||||
try {
|
||||
ytplayer.loadVideoById(id, parseInt(startSeconds));
|
||||
load_id=0;
|
||||
}
|
||||
catch(e) {
|
||||
window['console'].log(JSON.stringify(e));
|
||||
}
|
||||
}
|
||||
|
||||
function cueNewVideo(id, startSeconds) {
|
||||
if (ytplayer) {
|
||||
ytplayer.cueVideoById(id, startSeconds);
|
||||
}
|
||||
}
|
||||
|
||||
function play() {
|
||||
if (ytplayer) {
|
||||
ytplayer.playVideo();
|
||||
}
|
||||
}
|
||||
|
||||
function pause() {
|
||||
if (ytplayer) {
|
||||
ytplayer.pauseVideo();
|
||||
}
|
||||
}
|
||||
|
||||
function stop() {
|
||||
if (ytplayer) {
|
||||
ytplayer.stopVideo();
|
||||
}
|
||||
}
|
||||
|
||||
function getPlayerState() {
|
||||
if (ytplayer) {
|
||||
return ytplayer.getPlayerState();
|
||||
}
|
||||
}
|
||||
|
||||
function seekTo(seconds) {
|
||||
if (ytplayer) {
|
||||
ytplayer.seekTo(seconds, true);
|
||||
}
|
||||
}
|
||||
|
||||
function getBytesTotal() {
|
||||
if (ytplayer) {
|
||||
return ytplayer.getVideoBytesTotal();
|
||||
}
|
||||
}
|
||||
|
||||
function getCurrentTime() {
|
||||
if (ytplayer) {
|
||||
return ytplayer.getCurrentTime();
|
||||
}
|
||||
}
|
||||
|
||||
function getDuration() {
|
||||
if (ytplayer) {
|
||||
return ytplayer.getDuration();
|
||||
}
|
||||
}
|
||||
|
||||
function getStartBytes() {
|
||||
if (ytplayer) {
|
||||
return ytplayer.getVideoStartBytes();
|
||||
}
|
||||
}
|
||||
|
||||
function mute() {
|
||||
if (ytplayer) {
|
||||
ytplayer.mute();
|
||||
}
|
||||
}
|
||||
|
||||
function unMute() {
|
||||
if (ytplayer) {
|
||||
ytplayer.unMute();
|
||||
}
|
||||
}
|
||||
|
||||
function getEmbedCode() {
|
||||
alert(ytplayer.getVideoEmbedCode());
|
||||
}
|
||||
|
||||
function getVideoUrl() {
|
||||
alert(ytplayer.getVideoUrl());
|
||||
}
|
||||
|
||||
function setVolume(newVolume) {
|
||||
if (ytplayer) {
|
||||
ytplayer.setVolume(newVolume);
|
||||
}
|
||||
}
|
||||
|
||||
function getVolume() {
|
||||
if (ytplayer) {
|
||||
return ytplayer.getVolume();
|
||||
}
|
||||
}
|
||||
|
||||
function clearVideo() {
|
||||
if (ytplayer) {
|
||||
ytplayer.clearVideo();
|
||||
}
|
||||
}
|
||||
@@ -1,260 +0,0 @@
|
||||
var load_id;
|
||||
|
||||
function caption_at(index) {
|
||||
if (captions==0)
|
||||
return " ";
|
||||
|
||||
text_array=captions.text
|
||||
|
||||
if ((index>=text_array.length) || (index < 0))
|
||||
return " ";
|
||||
return text_array[index];
|
||||
}
|
||||
|
||||
function caption_time_at(index) {
|
||||
if (captions==0)
|
||||
return 0;
|
||||
|
||||
time_array=captions.start;
|
||||
|
||||
if (index < 0)
|
||||
return 0;
|
||||
if (index>=time_array.length)
|
||||
return ytplayer.getDuration();
|
||||
|
||||
return time_array[index]/1000.0;
|
||||
}
|
||||
|
||||
function caption_index(now) {
|
||||
// Returns the index of the current caption, given a time
|
||||
if (captions==0)
|
||||
return 0;
|
||||
|
||||
time_array=captions.start
|
||||
|
||||
// TODO: Bisection would be better, or something incremental
|
||||
var i;
|
||||
for(i=0;i<captions.start.length; i++) {
|
||||
if(time_array[i]>(now*1000)) {
|
||||
return i-1;
|
||||
}
|
||||
}
|
||||
return i-1;
|
||||
}
|
||||
|
||||
function update_captions(t) {
|
||||
var i=caption_index(t);
|
||||
$("#std_n5").html(caption_at(i-5));
|
||||
$("#std_n4").html(caption_at(i-4));
|
||||
$("#std_n3").html(caption_at(i-3));
|
||||
$("#std_n2").html(caption_at(i-2));
|
||||
$("#std_n1").html(caption_at(i-1));
|
||||
$("#std_0").html(caption_at(i));
|
||||
$("#std_p1").html(caption_at(i+1));
|
||||
$("#std_p2").html(caption_at(i+2));
|
||||
$("#std_p3").html(caption_at(i+3));
|
||||
$("#std_p4").html(caption_at(i+4));
|
||||
$("#std_p5").html(caption_at(i+5));
|
||||
$("#std_p6").html(caption_at(i+6));
|
||||
}
|
||||
|
||||
function title_seek(i) {
|
||||
// Seek video forwards or backwards by i subtitles
|
||||
current=caption_index(getCurrentTime());
|
||||
new_time=caption_time_at(current+i);
|
||||
|
||||
ytplayer.seekTo(new_time, true);
|
||||
}
|
||||
|
||||
function updateHTML(elmId, value) {
|
||||
document.getElementById(elmId).innerHTML = value;
|
||||
}
|
||||
|
||||
function setytplayerState(newState) {
|
||||
updateHTML("playerstate", newState);
|
||||
}
|
||||
|
||||
function onYouTubePlayerReady(playerId) {
|
||||
ytplayer = document.getElementById("myytplayer");
|
||||
setInterval(updateytplayerInfo, 250);
|
||||
ytplayer.addEventListener("onStateChange", "onytplayerStateChange");
|
||||
ytplayer.addEventListener("onError", "onPlayerError");
|
||||
if((typeof load_id != "undefined") && (load_id != null)) {
|
||||
var id=load_id;
|
||||
load_id = null;
|
||||
loadNewVideo(id);
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
function log_event(e) {
|
||||
//$("#eventlog").append("<br>");
|
||||
//$("#eventlog").append(JSON.stringify(e));
|
||||
window['console'].log(JSON.stringify(e));
|
||||
}
|
||||
|
||||
function seek_slide(type,oe,value) {
|
||||
//log_event([type, value]);
|
||||
if(type=='slide') {
|
||||
// HACK/TODO: Youtube recommends this be false for slide and true for stop.
|
||||
// Works better on my system with true/true.
|
||||
// We should test both configurations on low/high bandwidth
|
||||
// connections, and different browsers
|
||||
// One issue is that we query the Youtube window every 250ms for position/state
|
||||
// With false, it returns the old one (ignoring the new seek), and moves the
|
||||
// scroll bar to the wrong spot.
|
||||
ytplayer.seekTo(value, true);
|
||||
} else if (type=='stop') {
|
||||
ytplayer.seekTo(value, true);
|
||||
log_event([type, value]);
|
||||
}
|
||||
|
||||
update_captions(value);
|
||||
}
|
||||
|
||||
function get_state() {
|
||||
if (ytplayer)
|
||||
return [ytplayer.getPlayerState(),
|
||||
ytplayer.getVideoUrl(),
|
||||
ytplayer.getDuration(), ytplayer.getCurrentTime(),
|
||||
ytplayer.getVideoBytesLoaded(), ytplayer.getVideoBytesTotal(),
|
||||
ytplayer.getVideoStartBytes(),
|
||||
ytplayer.getVolume(),ytplayer.isMuted(),
|
||||
ytplayer.getPlaybackQuality(),
|
||||
ytplayer.getAvailableQualityLevels()];
|
||||
return [];
|
||||
}
|
||||
|
||||
function onytplayerStateChange(newState) {
|
||||
setytplayerState(newState);
|
||||
log_event(['State Change',newState, get_state()]);
|
||||
}
|
||||
|
||||
function onPlayerError(errorCode) {
|
||||
alert("An error occured: " + errorCode);
|
||||
}
|
||||
|
||||
function updateytplayerInfo() {
|
||||
if(ytplayer.getPlayerState()!=3) {
|
||||
$("#slider").slider("option","max",ytplayer.getDuration());
|
||||
$("#slider").slider("option","value",ytplayer.getCurrentTime());
|
||||
}
|
||||
update_captions(getCurrentTime());
|
||||
|
||||
updateHTML("videoduration", getDuration());
|
||||
updateHTML("videotime", getCurrentTime());
|
||||
updateHTML("startbytes", getStartBytes());
|
||||
updateHTML("volume", getVolume());
|
||||
}
|
||||
|
||||
// functions for the api calls
|
||||
function loadNewVideo(id, startSeconds) {
|
||||
if (typeof ytplayer != "undefined") {
|
||||
ytplayer.loadVideoById(id, parseInt(startSeconds));
|
||||
} else {
|
||||
load_id = id;
|
||||
}
|
||||
|
||||
$.getJSON("/static/subs/"+id+".srt.sjson", function(data) {
|
||||
captions=data;
|
||||
});
|
||||
|
||||
}
|
||||
|
||||
function cueNewVideo(id, startSeconds) {
|
||||
if (ytplayer) {
|
||||
ytplayer.cueVideoById(id, startSeconds);
|
||||
}
|
||||
}
|
||||
|
||||
function play() {
|
||||
if (ytplayer) {
|
||||
ytplayer.playVideo();
|
||||
}
|
||||
}
|
||||
|
||||
function pause() {
|
||||
if (ytplayer) {
|
||||
ytplayer.pauseVideo();
|
||||
}
|
||||
}
|
||||
|
||||
function stop() {
|
||||
if (ytplayer) {
|
||||
ytplayer.stopVideo();
|
||||
}
|
||||
}
|
||||
|
||||
function getPlayerState() {
|
||||
if (ytplayer) {
|
||||
return ytplayer.getPlayerState();
|
||||
}
|
||||
}
|
||||
|
||||
function seekTo(seconds) {
|
||||
if (ytplayer) {
|
||||
ytplayer.seekTo(seconds, true);
|
||||
}
|
||||
}
|
||||
|
||||
function getBytesTotal() {
|
||||
if (ytplayer) {
|
||||
return ytplayer.getVideoBytesTotal();
|
||||
}
|
||||
}
|
||||
|
||||
function getCurrentTime() {
|
||||
if (ytplayer) {
|
||||
return ytplayer.getCurrentTime();
|
||||
}
|
||||
}
|
||||
|
||||
function getDuration() {
|
||||
if (ytplayer) {
|
||||
return ytplayer.getDuration();
|
||||
}
|
||||
}
|
||||
|
||||
function getStartBytes() {
|
||||
if (ytplayer) {
|
||||
return ytplayer.getVideoStartBytes();
|
||||
}
|
||||
}
|
||||
|
||||
function mute() {
|
||||
if (ytplayer) {
|
||||
ytplayer.mute();
|
||||
}
|
||||
}
|
||||
|
||||
function unMute() {
|
||||
if (ytplayer) {
|
||||
ytplayer.unMute();
|
||||
}
|
||||
}
|
||||
|
||||
function getEmbedCode() {
|
||||
alert(ytplayer.getVideoEmbedCode());
|
||||
}
|
||||
|
||||
function getVideoUrl() {
|
||||
alert(ytplayer.getVideoUrl());
|
||||
}
|
||||
|
||||
function setVolume(newVolume) {
|
||||
if (ytplayer) {
|
||||
ytplayer.setVolume(newVolume);
|
||||
}
|
||||
}
|
||||
|
||||
function getVolume() {
|
||||
if (ytplayer) {
|
||||
return ytplayer.getVolume();
|
||||
}
|
||||
}
|
||||
|
||||
function clearVideo() {
|
||||
if (ytplayer) {
|
||||
ytplayer.clearVideo();
|
||||
}
|
||||
}
|
||||
Binary file not shown.
|
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Binary file not shown.
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Before Width: | Height: | Size: 10 KiB |
Binary file not shown.
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Before Width: | Height: | Size: 56 KiB |
Binary file not shown.
|
Before Width: | Height: | Size: 55 KiB |
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"text": [
|
||||
"",
|
||||
"All right. Good morning.",
|
||||
"Let's get going. In today's lecture we continue",
|
||||
"with the operational amplifier, \"op amp\" for short.",
|
||||
"And what we are going to do is just build up a bunch of fun",
|
||||
"building blocks using the op amp.",
|
||||
"As a quick review --",
|
||||
"",
|
||||
"To quickly review what we've seen about the op amp --",
|
||||
"",
|
||||
"We represented the op amp as a device that looked like this",
|
||||
"where the amplifier had an incredibly high gain.",
|
||||
"So, if I had a small voltage difference here --",
|
||||
"I call this v plus and this v minus with respect to ground.",
|
||||
"And if I had a small voltage difference then this gain here",
|
||||
"would multiply the difference by a large number and thereby",
|
||||
"giving me an output that was on the order of a million times",
|
||||
"greater than this difference. And because of that when I use",
|
||||
"the op amp in a mode like this without any negative feedback",
|
||||
"the output would usually crank up to the positive rail or the",
|
||||
"negative rail. We also saw that it had",
|
||||
"infinite input resistance so that the current flowing in here",
|
||||
"or here was zero and also had zero output resistance.",
|
||||
"This is my ideal op amp where irrespective of what load I",
|
||||
"connect here the op amp would supply pretty much any current.",
|
||||
"Now, in practical op amps that's not the case.",
|
||||
"But suffice it to say that when used as an ideal op amp the",
|
||||
"output impedance, the output resistance is going",
|
||||
"to be zero. The op amp is a huge workhorse",
|
||||
"of the analog industry. You will see based both on what",
|
||||
"you've done on Tuesday and Wednesday but also today that",
|
||||
"it's very, very simple to build circuits using the op amp.",
|
||||
"When you use the amplifier, you don't have to worry about",
|
||||
"things like nonlinear analysis. You don't have to worry about",
|
||||
"am I really meeting the criteria for saturation limits and so on?",
|
||||
"To some extent you have to think about that with the op",
|
||||
"amp, too, because if the output hits the positive rail or",
|
||||
"negative rail it isn't going to behave like you expect it to.",
|
||||
"But fundamentally with this primitive model,",
|
||||
"this idea model it becomes really simple to build circuits",
|
||||
"with the op amp. Therefore it has become a key",
|
||||
"building block for circuits. When circuit designers build",
|
||||
"analog circuits very often their primitive building blocks are",
|
||||
"really an amplifier of this sort, an op amp,",
|
||||
"resistors, capacitors and some of our other primitive building",
|
||||
"elements. If you look at the course notes",
|
||||
"the readings are -- There are a bunch of examples",
|
||||
"solved in Chapter 16. And you will see that using the",
|
||||
"op amp it is indeed possible to build current sources that look",
|
||||
"like more or less ideal current sources.",
|
||||
"It is also possible to build voltage sources and so on.",
|
||||
"It is an incredibly neat building block using which you",
|
||||
"can do all kinds of cool stuff.",
|
||||
"",
|
||||
"In this course you will see a whole bunch of example circuits",
|
||||
"using the op amp. In today's lecture you will see",
|
||||
"things like a subtractor. You will also see integrators",
|
||||
"and a differentiator. And then in your lab,",
|
||||
"lab four, you will build a really fun mixed signal circuit",
|
||||
"involving both digital and analog components.",
|
||||
"And you will build what is called a digital to an analog",
|
||||
"converter using the op amp. And of course I can build all",
|
||||
"our good-old amplifiers and circuits of that sort.",
|
||||
"In a later lecture you will also see how we can build",
|
||||
"filters using an op amp. This is going to be using the",
|
||||
"knowledge you learn in terms of connecting resistors,",
|
||||
"capacitors and inductors together and doing a frequency",
|
||||
"domain analysis, well we can throw the op amp in",
|
||||
"there and build filters, too.",
|
||||
"This is just to give you a preview of upcoming attractions.",
|
||||
"For today I am going to focus on these circuits.",
|
||||
"I won't be covering any new theory or any new set of",
|
||||
"foundations but pretty much take the simple properties that I",
|
||||
"have explained to you about the op amp.",
|
||||
"And using those simple properties very quickly build up",
|
||||
"a bunch of circuits that you can use to analyze signals in a",
|
||||
"variety of ways. Let's start with the following",
|
||||
"circuit. With op amps I start with this",
|
||||
"little guy. And what I am going to do is",
|
||||
"use two voltage sources, v1, and this is a resistor,",
|
||||
"not an inductor. And value R1,",
|
||||
"value R2. So, I have a voltage connected",
|
||||
"by a divider, voltage divider to the plus",
|
||||
"input. And I am going to provide some",
|
||||
"negative feedback in the following way.",
|
||||
"This is going to be R2, the same as this one here,",
|
||||
"a resistor R1. And then a voltage source v2",
|
||||
"that I connect out here. So notice that- Oh,",
|
||||
"and I take the output vOUT out here.",
|
||||
"And that vOUT of course is with respect to ground,",
|
||||
"and R2, v1 and v2 are also connected to ground.",
|
||||
"What I am going to do is analyze the circuit it two",
|
||||
"different ways, and as I analyze it describe",
|
||||
"some other interesting properties to you.",
|
||||
"In the last lecture the technique I used to analyze op",
|
||||
"amps was one in which I replaced the op amp with its ideal model",
|
||||
"involving a dependent source and so on with a large gain A and",
|
||||
"showed that. I wrote the expression and then",
|
||||
"I let A increase to infinity to the limits and got an expression",
|
||||
"that was independent of A. And then in recitation",
|
||||
"yesterday you would have covered another technique which makes it",
|
||||
"much simpler to analyze op amps. Let me very quickly review that",
|
||||
"method. We fondly call that technique,",
|
||||
"there is no formal name for it, but we fondly call that v plus",
|
||||
"more or less equal to v minus method.",
|
||||
"This is also variously called the virtual ground method and so",
|
||||
"on, but we shall call it the v plus more or less equal to v",
|
||||
"minus method. The insight here is that",
|
||||
"whenever I use the op amp in a way in which I am giving it",
|
||||
"negative feedback, so I am feeding some portion of",
|
||||
"the output to its negative input.",
|
||||
"I am giving it negative feedback.",
|
||||
"That's one property. Second property is that my",
|
||||
"inputs, v1 and v2, and my resistance values are",
|
||||
"chosen such that the output is not in saturation.",
|
||||
"So, the op amp is not at the plus VS rail or minus VS rail.",
|
||||
"Rather it's somewhere in the middle in its active region.",
|
||||
"When that happens we claim that the v minus and v plus for the",
|
||||
"op amp are more or less equal. And to give you some intuition",
|
||||
"as to why that is so, let's say the output is 6 volts",
|
||||
"and my supply is plus/minus 12. This is 6 volts and the",
|
||||
"amplifier is a gain of a million, ten to the six.",
|
||||
"To sustain 6 volts at the output all I need is a",
|
||||
"difference of 6 microvolts here. Six divided by ten to the six",
|
||||
"is the difference between v plus and v minus.",
|
||||
"It's very, very, very small.",
|
||||
"It's so small as to make v plus more or less equal to v minus.",
|
||||
"All it takes is a very small differential voltage here to",
|
||||
"give you 6 volts at the output. The key thing to observe is",
|
||||
"under negative feedback, when the op amp is not in",
|
||||
"saturation the property that v plus equals v minus holds.",
|
||||
"And the way it works is that it's not that it's a magical",
|
||||
"property. It is simply that when I apply",
|
||||
"negative feedback the negative feedback is such that it will",
|
||||
"force this v minus node here to be at more or less the same",
|
||||
"voltage as v plus. Remember the when in doubt",
|
||||
"simply go back and think about the anti lock brakes example we",
|
||||
"did last time. For example if v plus increases",
|
||||
"the output will increase and so will the voltage here and tend",
|
||||
"to make these two equal. What we can do,",
|
||||
"being rather tricky here, what we'll do is say look,",
|
||||
"if we know for a fact that under negative feedback the op",
|
||||
"amp is going to engineer these two node voltages to be more or",
|
||||
"less equal then why don't I just use that fact to begin with and",
|
||||
"analyze my circuit assuming that it's true.",
|
||||
"This is just a bit of inverted logic here that says look,",
|
||||
"the circuit is going to make that happen.",
|
||||
"If the circuit is going to make that happen to analyze the",
|
||||
"circuit in its steady state, why don't I just go ahead and",
|
||||
"assume that to begin with? This again goes back to us",
|
||||
"wanting to be engineers here and do whatever is simply and find",
|
||||
"the simplest possible way of getting some place.",
|
||||
"I want to use that method, the v plus equals v minus",
|
||||
"method. Let me just first write down",
|
||||
"some values that I know about. I know that v plus is simply a",
|
||||
"voltage divider relation here. That's v1 times R2 divided by",
|
||||
"R1 plus R2. And by the v plus equals v",
|
||||
"minus method I know that this is going to be equal to v minus.",
|
||||
"And this is going to be true because I am giving you negative",
|
||||
"feedback here. And we are going to engineer",
|
||||
"the values of R1, R2, v1 and v2 such that the op",
|
||||
"amp is not in saturation. So, we know that.",
|
||||
"The next thing that we know, let's say this is a current i.",
|
||||
"This current i flows here. Know that there is no current",
|
||||
"going in here. Op amp has an infinite input",
|
||||
"resistance so there is nothing going in there.",
|
||||
"There is no current going in there.",
|
||||
"If there is no current going in here, what must happen to i?",
|
||||
"Remember, from the foundations of the universe Maxwell's",
|
||||
"equations and therefore KVL and KCL hold.",
|
||||
"KVL and KCL simply come straight from nature.",
|
||||
"You and I cannot mess with that.",
|
||||
"Bad things happen to you if you do.",
|
||||
"So, nature, Maxwell's equations, KVL,",
|
||||
"KCL. It's simply nature.",
|
||||
"So, KCL applies here. Current comes in here.",
|
||||
"Nothing goes there. Don't argue.",
|
||||
"The current has to go here, period.",
|
||||
"No if, ands or buts. There is i coming in here,",
|
||||
"nothing goes there, so that current must flow here.",
|
||||
"It has no choice. It's from basic nature.",
|
||||
"I can write down what my current i is going to look like.",
|
||||
"What is i going to look like? Well, I know v2,",
|
||||
"I know v minus. v minus is the same as v plus.",
|
||||
"And v plus is the i expression given here.",
|
||||
"So, I can write i as v2 minus v minus divided by R1.",
|
||||
"Let me keep track of those two and then go ahead and compute",
|
||||
"vOUT. So, my goal in life is compute",
|
||||
"vOUT as a function of the two input voltages v1 and v2.",
|
||||
"And just for kicks I have gone ahead and computed some of the",
|
||||
"intermediate node voltages and currents.",
|
||||
"How do I write vOUT? What is vOUT?",
|
||||
"vOUT is simply v minus from KVL.",
|
||||
"vOUT is simply v minus minus the drop across this resistor.",
|
||||
"So, the drop across that resistor is simply iR2.",
|
||||
"From good-old KVL from the first lecture,",
|
||||
"a voltage minus the drop across the resistor is equal to vOUT.",
|
||||
"Therefore it's simply v minus minus iR2.",
|
||||
"One thing to be very cautious about, I will tell you right",
|
||||
"now, is that the output here relates to the inversion of the",
|
||||
"voltage across this resistor R2. Be very, very careful in that",
|
||||
"if I have a voltage across this resistor here that impacts vOUT",
|
||||
"with a minus sign attached to it.",
|
||||
"Notice that iR2 is the voltage across R2 and vOUT relates to",
|
||||
"the negative of that. Be very cautious.",
|
||||
"That's one of the commonest silly mistakes I have seen",
|
||||
"people make in solving problems like this.",
|
||||
"Let's go ahead. I know v minus and I don't know",
|
||||
"i. Let me substitute for i for",
|
||||
"now, and that is v2 minus v minus divided by R1 times R2.",
|
||||
"Let me go ahead and collect all the v minuses.",
|
||||
"v minus, I get a one here, minus minus becomes a plus,",
|
||||
"and so I get R2 divided by R1 out there.",
|
||||
"And then I minus v2 R2 divided by R1.",
|
||||
"That is vOUT. Now let me go ahead and",
|
||||
"substitute for v minus. And that is simply v1 R2",
|
||||
"divided by R1 plus R2. That is v minus.",
|
||||
"And this character here is simplified to be R1,",
|
||||
"R1 plus R2 minus v2 R2 divided by R1.",
|
||||
"What do we get? I cancel these two suckers out",
|
||||
"and what I end up with is v1 R2 divided by R1 minus v2 R2",
|
||||
"divided by R1, which is simply R2/R1(v1-v2).",
|
||||
"What is interesting here is that what I have ended up",
|
||||
"building is a very primitive subtractor.",
|
||||
"So, my output relates to v1 minus v2 multiplied by the",
|
||||
"constant factor given by R2 divided by R1.",
|
||||
"",
|
||||
"Again, as I pointed out to you at the beginning of this",
|
||||
"lecture, no knew foundations today, no new theories,",
|
||||
"no new disciplines, no new laws.",
|
||||
"We are just going to take what you have learned --",
|
||||
"Three simple things, infinite gain,",
|
||||
"infinite input resistance, zero output resistance,",
|
||||
"plus this new thing v plus equals v minus.",
|
||||
"And just being armed with those four principles we are just",
|
||||
"going to charge ahead and analyze a bunch of circuits.",
|
||||
"It is purely intellectual and pure applications today.",
|
||||
"This is one way of doing it. There is another way of solving",
|
||||
"it. We can solve the circuit.",
|
||||
"Remember, whenever you see a linear circuit and you see two",
|
||||
"sources or three sources, just think superposition,",
|
||||
"right? You see a linear circuit and",
|
||||
"two or three sources, think superposition.",
|
||||
"We should be able to apply superposition to this.",
|
||||
"The op amp is simply another building block.",
|
||||
"It's a linear circuit. So, let's see if we get the",
|
||||
"same answer. Let's try to solve the circuit",
|
||||
"using superposition and see if we get the same answer.",
|
||||
"To do superposition what I am going to do is build two",
|
||||
"subcircuits. One subcircuit in which v1 is",
|
||||
"zero, and that subcircuit looks like this.",
|
||||
"If I set v1 to be zero then I get R1 parallel R2 going to",
|
||||
"ground. So, if v1 is set to zero then",
|
||||
"R1 goes to ground. And I get R1 parallel R2 here.",
|
||||
"And of course I have v2 as before.",
|
||||
"And this was R1, this was R2,",
|
||||
"and let me call that vOUT1. Oh, I'm sorry.",
|
||||
"Let me call it vOUT2 corresponding to that component",
|
||||
"of the output that relates to v2 acting alone.",
|
||||
"Remember superposition? Build two subcircuits,",
|
||||
"one that depends on v2 and another one that depends on v1.",
|
||||
"Let's do the second one, too.",
|
||||
"Second one is v2 going to zero. Here is my little op amp.",
|
||||
"And what I will do is simply flip the op amp just to see if",
|
||||
"you can identify some interesting patterns.",
|
||||
"Just flip the op amp around. And this is v1 as before.",
|
||||
"And recall that v1 was going to the plus node through a resistor",
|
||||
"R1. And then I had a R2 to ground.",
|
||||
"And then let me short v2 to ground.",
|
||||
"And when I short v2 to ground what happens?",
|
||||
"When I short v2 to ground what happens is that the tail of R1",
|
||||
"here goes to ground. And so it is as if the output",
|
||||
"is connected to the node v minus through a resistor,",
|
||||
"so it as if the output v R2 is connected to the minus input",
|
||||
"through a resistor. We will draw it like this.",
|
||||
"And the minus input goes through a resistor R1,",
|
||||
"to ground. If you thought that patterns",
|
||||
"were important in the earlier part of the course doing voltage",
|
||||
"divider patterns and current divider patterns and amplifier",
|
||||
"pattern, the source follower pattern, op amps is all about",
|
||||
"patterns. You should remember two or",
|
||||
"three simple patterns and be able to write down the",
|
||||
"expression for those just by observation.",
|
||||
"So, this is one common pattern that you have seen before in the",
|
||||
"very first lecture. And I just wrote it down in",
|
||||
"that manner. Let me go ahead and solve this",
|
||||
"circuit. It turns out that this is also",
|
||||
"a pattern. I will analyze it today but in",
|
||||
"the future v2 going to this node through R1 and then R2 to the",
|
||||
"output. You have probably also seen",
|
||||
"this in your recitation. This one is called an inverting",
|
||||
"connection and this one here is called a non-inverting",
|
||||
"connection. Let's go ahead and do vOUT2.",
|
||||
"vOUT2 is simply given by, notice that since this is",
|
||||
"ground, no current flowing here, this voltage is zero.",
|
||||
"If this voltage is zero, this voltage is zero by the v",
|
||||
"plus equals v minus method. If this is zero,",
|
||||
"the current that goes through here is v2 divided by R1.",
|
||||
"And that same current must flow through the resistance R2 as",
|
||||
"well. If the current v2 divided by R1",
|
||||
"flows through this resistor, the drop across this resistor",
|
||||
"is simply given by, let me hide this for a second,",
|
||||
"is simply given by v2. So, v2 divided by R1 is the",
|
||||
"current here. This is zero.",
|
||||
"So, the drop across this resistor is v2 R1 multiplied by",
|
||||
"R2. That's a drop across this",
|
||||
"resistor. This voltage is simply zero",
|
||||
"minus a drop across the resistor.",
|
||||
"So, it's zero minus the drop across the resistor and that",
|
||||
"gives me v2. Again, remember this minus sign",
|
||||
"comes in when I want to convert this to get the output voltage",
|
||||
"from that. This is a very common pattern.",
|
||||
"It's called an inverting connection where the output is",
|
||||
"some factor of the input voltage and the factor is given by R2",
|
||||
"divided by R1. Let's go ahead and analyze this",
|
||||
"guy now. What is vOUT1 equal to?",
|
||||
"I should have called this vOUT1 because it relates to v1.",
|
||||
"vOUT1. There is a v plus here.",
|
||||
"From our first lecture I know that vOUT1 relates to v plus in",
|
||||
"the following way. I know that it is v plus times",
|
||||
"the sum of the resistances divided by R1.",
|
||||
"Based on the first lecture this is true.",
|
||||
"vOUT1 is simply an amplified version of v plus where the",
|
||||
"amplification factor is given by R1 plus R2 divided by R1.",
|
||||
"And I know v plus is simply a voltage divider action here.",
|
||||
"And I can take a simple voltage divider action here because the",
|
||||
"current going in is zero. Looking in here this is as if",
|
||||
"it's an infinite resistance, so it is as if the element",
|
||||
"simply does not exist. The voltage here is simply v1",
|
||||
"divided by R1 plus R2 multiplied by R2, our voltage divider",
|
||||
"pattern. So, I get v1 times R2 divided",
|
||||
"by R1 plus R2 times R1 plus R2 divided by R1.",
|
||||
"These two cancel out which gives me vOUT1 is simply v1 R2",
|
||||
"divided by R1. To get vOUT I add up the two.",
|
||||
"vOUT is vOUT1 plus vOUT2, which is my goal.",
|
||||
"And that is simply v1 R2 by R1 minus v2 R2 by R1.",
|
||||
"Thankfully what we have here is the same as here.",
|
||||
"Again, there is really nothing new that I am going to cover",
|
||||
"today. Simply apply,",
|
||||
"apply, apply, four simple principles.",
|
||||
"Here I have used superposition and I am showing you a circuit.",
|
||||
"So, it turns out with op amps you should really remember that",
|
||||
"pattern. You will see it again and again",
|
||||
"and again. And each time you see it,",
|
||||
"it will save you six minutes of having to solve the circuit",
|
||||
"without knowing the pattern. So, remember this pattern.",
|
||||
"You can pick up another three or four minutes by remembering",
|
||||
"this pattern here. This pattern is simply v2 R2",
|
||||
"divided by R1. Imprint those two patterns into",
|
||||
"your brains. OK, so those are a couple of",
|
||||
"simple circuits using the op amp.",
|
||||
"We built a subtractor. The next step,",
|
||||
"let's go ahead and try to build an integrator.",
|
||||
"Using this little building block we can go ahead and try to",
|
||||
"build a bunch of circuits. We can build filters,",
|
||||
"A to D converters and so on. Let's build an integrator.",
|
||||
"Abstractly I need to build this box.",
|
||||
"Which when fed a vI, I want that box to integrate",
|
||||
"and give me a vO which is vI integrated over time.",
|
||||
"That is what I want to build. How do I go about building it?",
|
||||
"What I would like to do next is give you some flavor for design.",
|
||||
"How do you go about designing things with an op amp?",
|
||||
"Knowing that you do not know the pattern for this yet,",
|
||||
"how do you go about designing things?",
|
||||
"Well, let's start with the following intuition.",
|
||||
"The intuition that I begin with is that if I have a current i,",
|
||||
"and remember that capacitors and inductors related to,",
|
||||
"you saw differentiation and integration happening when we",
|
||||
"dealt with capacitors and inductors.",
|
||||
"So, I think we have to invoke a capacitor here or an inductor.",
|
||||
"In this example I invoke a capacitor.",
|
||||
"Notice that if I stick a capacitor in here this current",
|
||||
"is i, capacitance C, then my voltage vO is given by",
|
||||
"what? Voltage is simply the integral",
|
||||
"of the current flowing through it or vice versa i is C dv/dt.",
|
||||
"If i is C dv/dt then v is simply one by C integral.",
|
||||
"If I can pass the current through a capacitor then the",
|
||||
"voltage across the capacitor must be a current.",
|
||||
"Notice then that vO is related to i dt.",
|
||||
"I have some multiplying constants and so on,",
|
||||
"but fundamentally what I have found is if I can stick a",
|
||||
"current through a capacitor then the voltage across the capacitor",
|
||||
"relates to the integral of the current.",
|
||||
"OK, that's interesting. So, I have an integral in",
|
||||
"there. But I have a current.",
|
||||
"Notice my goal was to integrate a voltage.",
|
||||
"What I figured out how to do was if I can turn that voltage",
|
||||
"into a current -- If I can turn that voltage into",
|
||||
"a proportional current and then pump that current through a",
|
||||
"capacitor I will get the integration that I want.",
|
||||
"How do I convert my vI to i? How do I do that?",
|
||||
"Well, let's take a stab at it. Here is my vI.",
|
||||
"Let's take the resistor R. And remember I need to stick",
|
||||
"the capacitor here. I have some current I here.",
|
||||
"I don't know what the current is yet.",
|
||||
"And I stick a voltage here. And what I am trying to do is",
|
||||
"trying to see if I stick a voltage and a resistance in",
|
||||
"series then there is some relationship between the current",
|
||||
"and this voltage. Recall that I am trying to make",
|
||||
"this current be directly proportional to the voltage vI.",
|
||||
"But it turns out that i here is not equal to vI divided by R.",
|
||||
"If i was vI divided by R somehow, I am done.",
|
||||
"If i was vI divided by R, by some magic,",
|
||||
"then I have converted my voltage to a current,",
|
||||
"I feed that current through my capacitor and vO is my integral",
|
||||
"that I am looking for. But unfortunately i is not",
|
||||
"equal to vI divided by R. You know that.",
|
||||
"i relates to vI minus the capacitor voltage divided by R.",
|
||||
"So, i is not simply vI divided by R for all time but i is",
|
||||
"really vI minus the capacitor voltage divided by R.",
|
||||
"And, in fact, when we did RC circuits you",
|
||||
"wrote this equation to represent the dynamics of the circuit,",
|
||||
"RC dvO by dt plus vO equals vI. We wrote down this circuit for",
|
||||
"a first order RC, wrote this equation for a first",
|
||||
"order RC circuit. Now, it does turn out,",
|
||||
"to wrap up on this wild goose chase that we went on,",
|
||||
"it does turn out that if this term here is much bigger than",
|
||||
"that term. If this term is much bigger",
|
||||
"than that term then I can ignore that term and write down RC dvO",
|
||||
"by dt more or less equal to vI. If that were true,",
|
||||
"this would be true, and then vO would be more or",
|
||||
"less equal to one by RC integral of vI dt.",
|
||||
"Again, if this were true. If this were true for all time",
|
||||
"then vO would be integral of vI dt.",
|
||||
"Again, remember this is all a wild goose chase.",
|
||||
"Just write down WGC there just so you don't get confused.",
|
||||
"I am on this wild goose hunt here trying to find a way to get",
|
||||
"a current from a voltage which I can then feed into a capacitor.",
|
||||
"This was one thing I knew, but this was not what I want.",
|
||||
"But it does turn out to be what I want when vO is very,",
|
||||
"very small. So, I see some glimmer of hope",
|
||||
"but not quite. It turns that in R and C,",
|
||||
"if I make R and C very, very big, if I have a huge time",
|
||||
"constant, with a huge time constant the voltage vO looks",
|
||||
"like an integral of vI, but only when I have a very",
|
||||
"huge time constant. So, I give up on that track.",
|
||||
"Instead I try something else.",
|
||||
"",
|
||||
"Another try. I would like you to notice if",
|
||||
"you take your op amp, here is your op amp,",
|
||||
"if you take this op amp and you stick the positive terminal to",
|
||||
"ground, under reasonable feedback, under reasonable",
|
||||
"negative feedback what do you notice about the current?",
|
||||
"If I had a current i flowing here what did you notice?",
|
||||
"Look at this picture. I had a current i flowing in",
|
||||
"here, v2 divided by R1. And because this resistance was",
|
||||
"infinite all the current went through the upper terminal.",
|
||||
"So, this is zero volts. And by the v plus equals v",
|
||||
"minus method this is also more or less equal to zero.",
|
||||
"And I have a current i flowing in here, nothing goes here,",
|
||||
"so then the i must flow up there.",
|
||||
"So, all I am doing here is causing a reflection of the",
|
||||
"current from this grounded node. My current is being reflected",
|
||||
"into, or deflected if you feel like it, the upper edge here",
|
||||
"after coming in through this edge.",
|
||||
"That is interesting. We are just one step away from",
|
||||
"the key insight.",
|
||||
"",
|
||||
"I have an i coming in here, an i going out there.",
|
||||
"Notice that, as I said before,",
|
||||
"this is zero volts. How do I get my voltage vI to",
|
||||
"look like a current, to become proportional to a",
|
||||
"current? It is simple now.",
|
||||
"All I do is put a voltage vI and put a resistor R out there.",
|
||||
"If I do that, and since this is zero,",
|
||||
"the current i is given by vI divided by R.",
|
||||
"I have gotten to where I want to be.",
|
||||
"So, by using an op amp and using the fact that the minus",
|
||||
"node here, v minus is at the same potential as v plus when",
|
||||
"there is negative feedback then I can stick a resistor here.",
|
||||
"And because this is zero the current here is simply vI",
|
||||
"divided by R. I have gotten to the first",
|
||||
"place. Now all I need to do is simply",
|
||||
"pump this current through a capacitor and I get the integral",
|
||||
"of the, the voltage becomes an integral of the current.",
|
||||
"That is easy. I stick my capacitor here and I",
|
||||
"get my answer out there as vO. Notice that when I do this,",
|
||||
"let's say this is plus/minus VC.",
|
||||
"This is zero. So, vO is minus VC.",
|
||||
"Again, I will keep emphasizing it maybe 17 times throughout",
|
||||
"this course that if this is zero then the output here is related",
|
||||
"to the negative of this voltage, common, common,",
|
||||
"common mistake. I will be very upset after",
|
||||
"doing all this if I see this mistake happen in any of the",
|
||||
"future homeworks or finals or whatever.",
|
||||
"This should not happen. So, vO is a minus sign here VC.",
|
||||
"And I know that if I have a current i through a capacitor",
|
||||
"what is VC? If I have current i through a",
|
||||
"capacitor than this is simply t i dt.",
|
||||
"And i by design is -- So, I have my integrator.",
|
||||
"It is a two-step process. I stuck a resistor here,",
|
||||
"so the current became equal to vI divided by R.",
|
||||
"Then I took that current and pumped it through a capacitor",
|
||||
"through this terminal here, and the voltage across the",
|
||||
"capacitor for a current i is given by this expression.",
|
||||
"This is Capacitors 101. OK Capacitors 101 says that the",
|
||||
"voltage across the capacitor is simply one by C integral i dt.",
|
||||
"Another way of looking at it is the voltage across the capacitor",
|
||||
"is C, I'm sorry, the current through a capacitor",
|
||||
"is C dv/dt. This is simply the integral",
|
||||
"form of that equation. And I am done with my",
|
||||
"integrator. So, this is another very common",
|
||||
"building block. Remember this.",
|
||||
"Most of the circuits we will be seeing with op amps simply",
|
||||
"involve something here and some there.",
|
||||
"And the output in this inverting connection is the",
|
||||
"output times, if it is a resistance it is",
|
||||
"simply R2 divided by R1, if it's a capacitor I get the",
|
||||
"integral form looking like this. Yes.",
|
||||
"",
|
||||
"Can someone tell me where the negative sign went?",
|
||||
"The blackboard ate it up. Good catch.",
|
||||
"",
|
||||
"After all that lecture about watching the negative sign.",
|
||||
"After this little bit of faux pas here, now I will be doubly",
|
||||
"mad if you guys make that mistake.",
|
||||
"All right. Now that we have built the",
|
||||
"integrator, I could give this out as a homework problem.",
|
||||
"And you should be able to design a differentiator based on",
|
||||
"what you've learned here. You now have the tools to go",
|
||||
"and do some design like this, but we don't have any more",
|
||||
"homeworks left so I guess I will go ahead and solve this for you",
|
||||
"right here and do the design for you.",
|
||||
"The building block that we need looks like this,",
|
||||
"d/dt here. Let me take a vI and stick a vI",
|
||||
"in there. That's what I want to build.",
|
||||
"And what I built here is that different integrator box.",
|
||||
"And what I would like to do now is build a differentiator box.",
|
||||
"How do I go about doing it? I will go really slow here so",
|
||||
"you will have some time to think about it for yourselves and see",
|
||||
"if you folks are crack op amp circuit designers already,",
|
||||
"if you have the right instincts here.",
|
||||
"Again, when you see differentiation integration",
|
||||
"think capacitors or inductors, it doesn't matter.",
|
||||
"In fact, as a homework exercise, you may want to go",
|
||||
"back and see how you can get a similar effect using inductors.",
|
||||
"Can you play with inductors and get a similar effect?",
|
||||
"So, inductors are devices that are a dual of the capacitor.",
|
||||
"Whatever we will do with capacitors, there must be a",
|
||||
"corresponding way with inductors.",
|
||||
"You can try it out in your spare time.",
|
||||
"Let's go back to this one here. I will stick with the capacitor",
|
||||
"way of looking at things. I need a differentiation now.",
|
||||
"Remember this. If I have a vI and I stick this",
|
||||
"across a capacitor, I have a current C and some",
|
||||
"voltage vc across the capacitor, what does i relate to?",
|
||||
"i is simply C dv/dt and vc in this case is simply C dvI/dt.",
|
||||
"If I can stick a voltage across a capacitor, if my input voltage",
|
||||
"is stuck across a capacitor then the resulting current relates to",
|
||||
"dvI/dt. Here we have the opposite",
|
||||
"problem. By doing this simple trick,",
|
||||
"I can obtain a current that has the right form.",
|
||||
"Now what I need to do is somehow convert that current",
|
||||
"into a voltage because the abstraction that I need is a",
|
||||
"voltage to voltage. The next step,",
|
||||
"what I need to do is somehow convert a current to a voltage.",
|
||||
"How do I go about doing that? Again, remember for the op amp,",
|
||||
"if I have a current i flowing here then by the reflection",
|
||||
"property i gets pushed up into this edge, provided that the",
|
||||
"whole circuit is working with descent negative feedback.",
|
||||
"Given this trick what I can do is say look, suppose I did this.",
|
||||
"Remember, my goal here is how do I convert a current to a",
|
||||
"voltage? I have a current i coming in",
|
||||
"here, and I can turn that into a voltage because I know the",
|
||||
"current must come out here, I know this current must come",
|
||||
"out there. All I have to do is stick a",
|
||||
"resistor in there. If I stick a resistor in there",
|
||||
"what is vO equal to? vO is simply iR,",
|
||||
"right? That's right.",
|
||||
"vO, I get i here, so i pumps through here.",
|
||||
"Remember, what comes in here must get reflected up because",
|
||||
"the current going in here is zero.",
|
||||
"All the i must come out here. So, that i must pump through",
|
||||
"this resistor. The drop across this resistor",
|
||||
"is iR. That's the voltage drop across",
|
||||
"that resistor. And since this at a virtual",
|
||||
"ground the output here is simply zero minus this drop which is",
|
||||
"minus iR. So, I have gotten to where I",
|
||||
"want to be. I have my current i being",
|
||||
"converted to a voltage. I have taken my current,",
|
||||
"and I have been able to convert that into a voltage by sticking",
|
||||
"a resistor in here. As a final step,",
|
||||
"I simply need to produce the current.",
|
||||
"And that is pretty easy to do. Abstractly what I need to do,",
|
||||
"again, this is design here so we will talk about abstract",
|
||||
"stuff. If I had a voltage vI,",
|
||||
"I need to produce a current which relates to C dvI/dt.",
|
||||
"And I know I can do that by simply doing this.",
|
||||
"By doing this I know my i is C dvI, correct?",
|
||||
"If I can get this effect, I put this in quotes because",
|
||||
"that's my pattern. I am looking for a pattern,",
|
||||
"where a voltage vI is directly applied across a capacitor.",
|
||||
"And when that happens the current relates to C dv/dt.",
|
||||
"Let's go back to our op amp pattern here,",
|
||||
"op amp circuit. So far I have achieved --",
|
||||
"I just repeated this out there. And so somehow I need to take",
|
||||
"this pattern here and learn from that pattern and apply the",
|
||||
"pattern here. So, what I can do is,",
|
||||
"this is a ground node, correct?",
|
||||
"Now, the poor little capacitor, what does it care,",
|
||||
"whether it's a ground node or a virtual ground node?",
|
||||
"As long as it's a zero volt node down here what does it",
|
||||
"care? What I am going to do is stick",
|
||||
"this point, not here but into a virtual ground node.",
|
||||
"I am going to grab that point, take it here and stick it here.",
|
||||
"The poor little capacitor doesn't know the difference.",
|
||||
"I have really suckered the little beast.",
|
||||
"This is vI. Remember this.",
|
||||
"My i through the capacitor is proportional to C dv/dt.",
|
||||
"Instead what I have done is taken this guy and stuck it here",
|
||||
"to get something like this. Just remember these four or",
|
||||
"five little tricks. And you apply them in op amp",
|
||||
"circuits again and again and again and again.",
|
||||
"So, this is vI, this is my virtual ground.",
|
||||
"As far as this poor little capacitor is concerned,",
|
||||
"it is chugging along merrily thinking that it is connected to",
|
||||
"ground. Little does it know it is only",
|
||||
"a virtual ground, all right?",
|
||||
"But the current i here is simply C dvI/dt.",
|
||||
"And that current, the C dvI/dt,",
|
||||
"that current flows through here and gives me vO as iR.",
|
||||
"So, vO is simply minus R. Let me substitute for i there,",
|
||||
"C dvI/dt. OK, so notice then that my vO",
|
||||
"is now proportional to dvI/dt. So, vO is some RC time constant",
|
||||
"times dvI/dt. Therefore, I have my",
|
||||
"differentiator circuit. Remember this as a closing",
|
||||
"thought. Remember this v plus more or",
|
||||
"less equal to v minus trick. And to the extent possible",
|
||||
"simply use that trick to analyze op amp circuits under feedback",
|
||||
"and not in saturation. Just remember these two.",
|
||||
"Very quickly for the demo, I have a square wave input here",
|
||||
"to the op amp, that's my vI to the integrator.",
|
||||
"And this is the output vO. The integral of a square wave",
|
||||
"is a triangular wave, as you can see.",
|
||||
"And we will do the same thing for a differentiator.",
|
||||
"And for the differentiator, I input the square wave to this",
|
||||
"differentiator circuit. And I get this,",
|
||||
"wherever there is a sharp rise, I get this huge negative spike",
|
||||
"and a positive spike because of the minus sign.",
|
||||
"So, this is the differentiator circuit.",
|
||||
"Then I feed this into the op amp.",
|
||||
"OK. Thank you."
|
||||
]
|
||||
}
|
||||
@@ -1,1943 +0,0 @@
|
||||
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||||
"text": [
|
||||
"Good morning, OK.",
|
||||
"Let's get started. We have one handout today.",
|
||||
"That's your lecture notes. There's some copies still",
|
||||
"outside for those who haven't picked one up.",
|
||||
"In general, what I do is, in the lecture notes,",
|
||||
"I leave out large amounts of material.",
|
||||
"So, this will enable you to keep your hands busy while I'm",
|
||||
"lecturing and take down some notes and so on.",
|
||||
"So, don't assume that everything that I talk about is",
|
||||
"on here. Please follow along.",
|
||||
"OK, so as is my usual practice, let me start with a quick",
|
||||
"review of what we covered so far.",
|
||||
"So what we did primarily was looked at this discipline that",
|
||||
"we call the lump matter discipline, which was very",
|
||||
"similar, very reminiscent of the point mass simplification in",
|
||||
"physics. And this discipline,",
|
||||
"this set of constraints we imposed on ourselves,",
|
||||
"allowed us to move from Maxwell's equations to a very,",
|
||||
"very simple form of algebraic equations.",
|
||||
"And specifically, the discipline took two forms.",
|
||||
"One is, we said that we will deal with elements for whom the",
|
||||
"rate of change of magnetic flux is zero outside of the elements,",
|
||||
"and for whom the rate of change of charge I want to charge",
|
||||
"inside the element was zero. So, if I took any element,",
|
||||
"any element that I called a lump circuit element,",
|
||||
"like a resistor or a voltage source, and I put a black box",
|
||||
"around it, then what I'm saying is that the net charge inside",
|
||||
"that is going to be zero. And this is not true in",
|
||||
"general. We will see examples where,",
|
||||
"if you choose some piece of an element for example,",
|
||||
"there might be charge buildup, but net inside the,",
|
||||
"if I put a box around the entire element,",
|
||||
"I am going to assume that the rate of change of charge is",
|
||||
"going to be zero. So, what this did was it",
|
||||
"enabled us to create the lump circuit abstraction,",
|
||||
"where I could take elements, some element of the sort,",
|
||||
"this could be a resistor, a voltage source,",
|
||||
"or whatever, and I could now ascribe a",
|
||||
"voltage, some voltage across an element, and also some current,",
|
||||
"\"i,\" that was going into the element.",
|
||||
"And as I go forward, when I label the voltages and",
|
||||
"currents across and through elements, I'm going to be",
|
||||
"following a convention. OK, the convention is that I'm",
|
||||
"going to label, if I label V in the following",
|
||||
"manner, then I'm going to label \"i\" for that element as a",
|
||||
"current flowing into the positive terminal.",
|
||||
"It's just a convention. By doing this,",
|
||||
"it turns out that the power consumed by the element is \"vi\"",
|
||||
"is positive. OK, so by choosing I going in",
|
||||
"this way into the positive terminal, the power consumed by",
|
||||
"the element is going to be positive.",
|
||||
"OK, so in general of even simply following this",
|
||||
"convention, when I label voltages and currents,",
|
||||
"I'll be labeling the current into an element entering in",
|
||||
"through the plus terminal. Remember, of course,",
|
||||
"if the current is going this way, let's have one amp of",
|
||||
"current flowing this way, then when I compute the",
|
||||
"current, \"i\" will come out to be negative.",
|
||||
"OK, so by making these assumptions, the assumptions of",
|
||||
"the lumped matter discipline, I said I was able to simplify",
|
||||
"my life tremendously. And, in particular what it did",
|
||||
"was it allowed me to take Maxwell's equations,",
|
||||
"OK, and simplify them into a very simple algebraic form,",
|
||||
"which has both a voltage law and a current law that I call",
|
||||
"Kirchhoff's voltage law, and Kirchhoff's current law.",
|
||||
"KVL simply states that if I have some circuit,",
|
||||
"and if I measured the voltages in any loop in the circuit,",
|
||||
"so if I look at the voltages in any loop, then the voltages in",
|
||||
"the loop would sum to zero. OK, so I measure voltages in",
|
||||
"the loop, and they will sum to zero.",
|
||||
"Similarly, for the current, if I take a node of a circuit,",
|
||||
"if I build the circuit, a node is a point in the",
|
||||
"circuit where multiple edges connect.",
|
||||
"If I take a node, then the current coming into",
|
||||
"that node, the net current coming into a node is going to",
|
||||
"be zero. OK, so if I take any node of",
|
||||
"the circuit and sum up all the currents going into that node,",
|
||||
"they will all net sum to zero. So, notice what I've done is by",
|
||||
"this discipline, by this constraint I imposed on",
|
||||
"myself, I was able to make this incredible leap from Maxwell's",
|
||||
"equations to these really, really simple algebraic",
|
||||
"equations, KVL and KCL. And I promise you,",
|
||||
"going forward to the rest of 6.002, if this is all you know,",
|
||||
"you can pretty much solve any circuit using these two very",
|
||||
"simple relations. It's actually really,",
|
||||
"really simple. It's all very simple algebra,",
|
||||
"OK? So, just to show you an",
|
||||
"example, let me do a little demonstration.",
|
||||
"Let me build let me build a small circuit and measure some",
|
||||
"voltages for you, and show you that the voltages,",
|
||||
"indeed, add up to zero. So, here's my little circuit.",
|
||||
"",
|
||||
"So, I'm going to show you a simple circuit that looks like",
|
||||
"this, and let's go ahead and measure some voltages and",
|
||||
"currents. In terms of terminology to",
|
||||
"remember, this is called a loop. So if I start from the point C",
|
||||
"and I travel through the voltage source, come to the node A down",
|
||||
"through R1 and all the way down through R2 back to C,",
|
||||
"that's a loop. Similarly, this point A is a",
|
||||
"node where resistor R1 the voltage source V0,",
|
||||
"and R4 are connected. OK, just make sure your",
|
||||
"terminology is correct. So, what I'll do is I'll make",
|
||||
"some quick measurements for you, and show you that these KVL and",
|
||||
"KCL are indeed true. So, the circuits up there,",
|
||||
"could I have a volunteer? Any volunteer?",
|
||||
"All you have to do is write things on the board.",
|
||||
"Come on over. OK, so let me take some",
|
||||
"measurements, and why don't you write down",
|
||||
"what I measure on the board? What I'll do is,",
|
||||
"let me borrow another piece of chalk here.",
|
||||
"What I'll do is focus on this loop here, and focus on this",
|
||||
"node and make some measurements.",
|
||||
"",
|
||||
"All right, so you see the circuit up there.",
|
||||
"OK, so I get 3 volts for the voltage from C to A.",
|
||||
"so why don't you write down 3 volts?",
|
||||
"",
|
||||
"OK, so the next one is -1.6. And so that will be,",
|
||||
"I'm doing AB, V_AB.",
|
||||
"OK, and then let me do the last one.",
|
||||
"It is -1.37. The measurements,",
|
||||
"I guess, have been this way. So, what's written is V_AC.",
|
||||
"But it's OK for now. Don't worry about it.",
|
||||
"So, well, thank you. I appreciate your help here.",
|
||||
"OK, so within the bonds of experimental error,",
|
||||
"noticed that if I add up these three voltages,",
|
||||
"they nicely sum up to zero. OK, next let me focus on this",
|
||||
"node here. And at this node,",
|
||||
"let me go ahead and measure some currents.",
|
||||
"What I'll do now is change to an AC voltage so that I can go",
|
||||
"ahead and measure the current without breaking my circuit.",
|
||||
"OK, this time around, you'll get to see the",
|
||||
"measurements that I'm taking as well.",
|
||||
"So, what I have here, I guess you can see it this",
|
||||
"way. What I have here is three wires",
|
||||
"that I have pulled out from D. And this is the node D,",
|
||||
"OK? So, I have three wires coming",
|
||||
"into the node D just to make it a little bit easier for me to",
|
||||
"measure stuff. OK, so everybody keep your",
|
||||
"fingers crossed so I don't look like a fool here.",
|
||||
"I hope this works out. So, you roughly get,",
|
||||
"what's that, 10 mV.",
|
||||
"OK, so it's about 10 mV peak to peak out there,",
|
||||
"and let's say that if the waveform raises on the left-hand",
|
||||
"side, it's positive. So, it's positive 10 mV.",
|
||||
"And another positive 10 mV, so that's 20 mV.",
|
||||
"And this time, it's a negative,",
|
||||
"roughly 20, I guess, -20.",
|
||||
"So, I'm getting, in terms of currents,",
|
||||
"I have a -10, -10, I'm sorry,",
|
||||
"positive 10, positive 10,",
|
||||
"and a -20 that adds up to zero. But more interestingly,",
|
||||
"I can show you the same thing by holding this current",
|
||||
"measuring probe directly across the node.",
|
||||
"And, notice that the net current that is entering into",
|
||||
"this node here is zero. OK, so that should just show",
|
||||
"you that KCL does indeed hold in practice, and it is not just a",
|
||||
"figment of our imaginations. So, before I go on,",
|
||||
"I wanted to point one other thing out.",
|
||||
"Notice that I've written down two assumptions of the lumped",
|
||||
"matter discipline, OK?",
|
||||
"There is a total assumption of the lump matter discipline,",
|
||||
"and that assumption is, in spirit, at least,",
|
||||
"shared by the point mass simplification in physics as",
|
||||
"well. Can someone tell me what that",
|
||||
"assumption is? A total assumption,",
|
||||
"which I did not mention, which you can read in your",
|
||||
"notes in section 8.2 in the appendix, what's a total",
|
||||
"assumption that is shared in spirit with the point mass",
|
||||
"simplification? Anybody?",
|
||||
"A total assumption to be made here is that in all the signals",
|
||||
"that we will study in this course, we've made the",
|
||||
"assumption that the signal speeds of interest,",
|
||||
"transition speeds, and so on, are much slower than",
|
||||
"the speed of light. OK, that my signal transition",
|
||||
"speeds of interest are much slower than the speed of light.",
|
||||
"Remember, the laws of motion, the discrete laws of motion",
|
||||
"break down if your objects begin moving at the speed of light.",
|
||||
"OK, the same token here, our lump circuit abstraction",
|
||||
"breaks down if we approach the speed of light.",
|
||||
"And there are follow on courses that talk about waveguides and",
|
||||
"other distributed analysis techniques that deal with",
|
||||
"signals that travel close to speeds of light.",
|
||||
"OK, so with that, let me go on to talking about",
|
||||
"method one of circuit analysis. This is called the basic KVL",
|
||||
"KCL method. So just based on those two",
|
||||
"simple algebraic relations, I can analyze very interesting",
|
||||
"and complicated circuits. The method goes as follows.",
|
||||
"So, let's say our goal is, given a circuit like this,",
|
||||
"our goal is to solve it. OK, in this course,",
|
||||
"we will do two kinds of things: analysis and synthesis.",
|
||||
"Analysis says, given a circuit,",
|
||||
"OK, what can you tell me about the circuit?",
|
||||
"OK, so we'll solve existing circuits for all the voltages",
|
||||
"and currents, voltages across elements,",
|
||||
"and currents through those elements.",
|
||||
"Synthesis says, given a function,",
|
||||
"I may ask you to go and build circuits.",
|
||||
"OK, so for analysis here, we can apply this method that I",
|
||||
"want to show you. And the idea here is that,",
|
||||
"given a circuit like this, let us figure out all the",
|
||||
"voltages and currents that are a function of the way these",
|
||||
"elements are connected. So, the basic KVL and KCL",
|
||||
"method has the following steps. The first step is to write down",
|
||||
"the element VI relationships. OK, right down the element VI",
|
||||
"relationships for all the elements.",
|
||||
"The second step is write KCL for all the nodes,",
|
||||
"and the third step is to write KVL for all the loops in the",
|
||||
"circuit. That's it.",
|
||||
"Just go ahead and write down element rules,",
|
||||
"KVL, and KCL, and then go ahead and solve the",
|
||||
"circuit. So, what we'll do,",
|
||||
"we'll do an example, of course.",
|
||||
"But, just as a refresher, we've looked at a bunch of",
|
||||
"elements so far, and for the resistor,",
|
||||
"the element relation says that V is pi R, where R is the",
|
||||
"resistance of the element here. For a voltage source,",
|
||||
"V is equal to V nought. That's the element",
|
||||
"relationship. And for a current source,",
|
||||
"the element is the relation is, \"i\" is simply the current",
|
||||
"flowing through the element. OK, so these are some of the",
|
||||
"simple element rules for the devices that the current source,",
|
||||
"voltage source, and the resistor.",
|
||||
"So let's go ahead and solve this simple circuit.",
|
||||
"And what I'll do is go ahead and solve the circuit for you.",
|
||||
"OK, if you turn to page five of your notes, I'm going to go",
|
||||
"ahead and edit the circuit here. You can scribble the values on",
|
||||
"your notes on page five. OK, so as a first step of my",
|
||||
"KVL KCL method, I need to write down all my",
|
||||
"element VI relationships. So, before I do that,",
|
||||
"let me go ahead and label all the voltages and currents that",
|
||||
"are unknowns in the circuit. So, let me label the voltages",
|
||||
"and currents associated with the voltage source as here.",
|
||||
"Notice, I continue to follow this convention where whenever I",
|
||||
"label voltages and currents for an element, I will show the",
|
||||
"current going into the positive terminal of the element",
|
||||
"variable, OK, after element variable voltage.",
|
||||
"So here, I have V nought and I nought.",
|
||||
"Let me pause here for five seconds and show you a point of",
|
||||
"confusion that happens sometimes.",
|
||||
"Often times, people confuse between what is",
|
||||
"called the variable that is associated with the element",
|
||||
"versus the element value. OK, notice that here,",
|
||||
"capital V nought is the voltage that this voltage source",
|
||||
"provides, while this name here, v nought, is simply a variable",
|
||||
"that we've used to label the voltage across that element.",
|
||||
"So, similarly, I can label v1 as the voltage",
|
||||
"across the resistor, and i1 is the current flowing",
|
||||
"through the resistor. So this method of labeling,",
|
||||
"where I follow the convention, that the current flows into the",
|
||||
"positive terminal is called the associated variables discipline.",
|
||||
"I was trying to use the word discipline in situations where",
|
||||
"you have a choice, OK, and of a variety of",
|
||||
"possible choices, you pick one as the convention.",
|
||||
"OK, so here, as a convention,",
|
||||
"we use the associated variables discipline, and use that method",
|
||||
"to consistently label the unknown voltages and currents in",
|
||||
"our circuits. OK, so let me continue the",
|
||||
"labeling here, v4, i4, i3, v3 here,",
|
||||
"and v2 and i2, v5, and i5.",
|
||||
"I think that's it. So, I've gone ahead and labeled",
|
||||
"all my unknowns. So each of these voltages and",
|
||||
"currents are the voltages and currents associated with each of",
|
||||
"the elements. And my goal is to solve for",
|
||||
"these. OK, so in terms of our solution",
|
||||
"here, let's follow the method that I outlined for you.",
|
||||
"So, as the first step I am simply going to go ahead and",
|
||||
"write down all the element VI relationships.",
|
||||
"OK, so as a first step, I'm going to go ahead and write",
|
||||
"down all the VI relationships. So, can someone yell out for me",
|
||||
"the VI relationship for the voltage source?",
|
||||
"OK, good. So, v0 is capital V nought,",
|
||||
"that is that the variable V nought is simply equal to the",
|
||||
"voltage, v0. Similarly, I can write the",
|
||||
"others. v1 is i1, R1.",
|
||||
"v2 is i2, R2, and so on.",
|
||||
"OK, and I have one, two, three, four,",
|
||||
"five, six elements. So, I will get six such",
|
||||
"equations. Step two, I'm going to go ahead",
|
||||
"and write KCL for the nodes in my system.",
|
||||
"So, let me start with node A. So, for node A,",
|
||||
"let me take as positive the currents going out of the node.",
|
||||
"So, I get i nought flowing out, plus i1 flowing out,",
|
||||
"plus i4 flowing out, and they must sum to zero for",
|
||||
"node A. Then, I can go ahead and do the",
|
||||
"other nodes, let's say, for example,",
|
||||
"I do node B. For node B, I have i2 going",
|
||||
"out. That's positive,",
|
||||
"i3, and i1 is coming in, so I get -i1 equals zero.",
|
||||
"OK, so I have one, two, three, four,",
|
||||
"I have four nodes. OK, so I would get four",
|
||||
"equations. It turns out that the fourth",
|
||||
"equation is not independent. You can derive it from the",
|
||||
"others. So, I get three independent",
|
||||
"equations out of this. I can then write KVL.",
|
||||
"And for KVL, I just go down my loops here.",
|
||||
"And let me go through this first loop here in this manner.",
|
||||
"OK, and a simple trick that I use, you have to be incredibly",
|
||||
"careful when you go through this in keeping your minuses and",
|
||||
"pluses correct. Otherwise you can get",
|
||||
"hopelessly muddled. Once you label it,",
|
||||
"you need to be sure that you get all your minuses and pluses",
|
||||
"correct. So, for KVL,",
|
||||
"what I'd like to do is, let's say I start at C,",
|
||||
"and from C I'm going to go to A.",
|
||||
"For A I go to B, and from B I'm going to come",
|
||||
"back to C. OK, that's how I traverse my",
|
||||
"loop. And, the trick that I'm going",
|
||||
"to follow is, as my finger walks through that",
|
||||
"loop, I'm going to label the voltage as the first sign that I",
|
||||
"see for that voltage. OK, so I'm going to start with",
|
||||
"C, and I go up. I start by punching into the",
|
||||
"voltage source element, and then punch into it,",
|
||||
"I hit the minus sign for the V nought.",
|
||||
"OK, so I'm just going to write down minus V nought,",
|
||||
"plus then I go through and as I come up to A and go down to B,",
|
||||
"I punch to the plus sign of the V1.",
|
||||
"So, that's plus V1. And then I punch into the plus",
|
||||
"sign of the V2, and so I get plus V2,",
|
||||
"and that is zero. OK, good.",
|
||||
"So, that matches what you have in your notes as well.",
|
||||
"So, this is the first equation. Similarly, I can go through my",
|
||||
"other loops and write down equations for each of the loops.",
|
||||
"OK, and the convention that I like to follow is as I go",
|
||||
"through the loop, I write down as a sign for the",
|
||||
"voltage the first sign that I counter for that element.",
|
||||
"OK, you can do the exact opposite, if you want,",
|
||||
"just to be different. But, as long as you stay",
|
||||
"consistent, you'll be OK. All right, so in the same",
|
||||
"manner here, there are four loops that I can have,",
|
||||
"so four equations. Again, one of them turns out to",
|
||||
"be dependent on the others. So I end up getting three",
|
||||
"independent equations. So, I get a total of 12",
|
||||
"equations. I get 12 equations.",
|
||||
"There are six elements, OK, voltage source,",
|
||||
"and five resistors. So, there are six unknown",
|
||||
"voltages, and six unknown currents.",
|
||||
"So, I have 12 equations, and 12 unknowns.",
|
||||
"OK, I can take all of the equations and put them through a",
|
||||
"big crank, and sit there and grind.",
|
||||
"And if I was really cruel, I'd give this as a homework",
|
||||
"problem, and have you grind, and grind, and grind until you",
|
||||
"get your six voltages and six currents.",
|
||||
"OK, it works. OK, so you get 12 equations,",
|
||||
"and this method just works. However, notice that this is",
|
||||
"quite a grubby method. It's quite grungy.",
|
||||
"I get 12 equations, and it's quite a pain even for",
|
||||
"a simple circuit like this. However, suffice it to say that",
|
||||
"this fundamental method is one step away from Maxwell's",
|
||||
"equations, simply works. OK?",
|
||||
"So what you'll do is the rest of this lecture,",
|
||||
"I'll introduce you to a couple more methods.",
|
||||
"One is an intuitive method, and another one called the node",
|
||||
"method is a little bit more formal, but is much more,",
|
||||
"I guess, terse Than the KVL KCL method.",
|
||||
"Method 2. So the relevant section to read",
|
||||
"in the course notes is section 2.4.",
|
||||
"One of the things that I will be stressing this semester is",
|
||||
"intuition. What you'll find is that as you",
|
||||
"become EECS majors, and so on, and go on,",
|
||||
"or if you talk to your TAs or your professors and so on,",
|
||||
"you will find that very rarely do they actually go ahead and",
|
||||
"apply the formal methods of analysis.",
|
||||
"OK, by and large, engineers are able to look at a",
|
||||
"circuit and simply by observation write down an",
|
||||
"answer. And usually in the past,",
|
||||
"what we have tried to do is kind of ignore that process and",
|
||||
"told our students, look, we teach you all the",
|
||||
"formal methods, and you will develop your own",
|
||||
"intuition and be able to do it. What we'll try to do this term",
|
||||
"is try to stress the intuitive methods, and try to show you how",
|
||||
"the intuitive process goes, so you can very quickly solve",
|
||||
"many of these circuits simply by inspection.",
|
||||
"OK, so this method that I'm going to show you here is one",
|
||||
"such an intuitive method. And I'll call it element",
|
||||
"combination tools. OK, for many simple circuits,",
|
||||
"you can solve them very quickly by applying this method.",
|
||||
"The components of this method are these.",
|
||||
"I learned about how to compose a bunch of elements.",
|
||||
"So, let's say, for example,",
|
||||
"I have a set of resistors, R1 through RN,",
|
||||
"in series. OK, you can use KVL and KCL to",
|
||||
"show that this is equivalent to a single resistor whose value is",
|
||||
"given by the sum of the resistances.",
|
||||
"OK, so if I have resistors in series, then effectively it's",
|
||||
"the same as if there was a single resistor whose value is",
|
||||
"the sum of all the resistances. OK, you can look at the course",
|
||||
"notes for a proof for derivation of this fact.",
|
||||
"Similarly, if I have resistances in parallel,",
|
||||
"so let me call them conductances.",
|
||||
"A conductance is the reciprocal of a resistance.",
|
||||
"If resistance is measured in ohms, conductance is measured in",
|
||||
"mhos, M-H-O-S. OK, so that's the conductance",
|
||||
"is G1, G2, and G3. And effectively,",
|
||||
"this is the same as having a single conductance whose",
|
||||
"effective value is given by the sum of the conductances.",
|
||||
"OK, the conductances in parallel add,",
|
||||
"and resistances in series add. Similarly, for voltage sources,",
|
||||
"if I have voltage sources in series, then they are tantamount",
|
||||
"to the sum of the voltages. And similarly,",
|
||||
"for currents, if I have currents in parallel,",
|
||||
"then they can be viewed as a single current source,",
|
||||
"whose currents are the sum of the individual parallel",
|
||||
"currents. So, let's do a quick example.",
|
||||
"So let's do this example. So, let's say I have a circuit",
|
||||
"that looks like this, and three resistances.",
|
||||
"And let's say all I care about is the current,",
|
||||
"I, that flows through this wire.",
|
||||
"All I care about is that current.",
|
||||
"Of course, you can go ahead and write KVL and KCL.",
|
||||
"You will get four equations, and there are four unknowns.",
|
||||
"And you can solve it. But, I can apply my element",
|
||||
"combination rules, and very quickly figure out",
|
||||
"what the current I is, using the following technique.",
|
||||
"So, what I can do is, I can, first of all,",
|
||||
"take this circuit. And, I can compose these two",
|
||||
"resistances and show that the circuit is equivalent as far as",
|
||||
"this current, I, is concerned to the",
|
||||
"following circuit, R1.",
|
||||
"And I take the sum of the two conductances,",
|
||||
"OK, and that comes out to be R1, R2, R3, R2 plus R3.",
|
||||
"And then, I can further simplify it, and I get a single",
|
||||
"resistance, whose value is given by R1 plus R2,",
|
||||
"R3, R3. OK, I'm just simplifying the",
|
||||
"circuit. Now, from this circuit,",
|
||||
"I can get the answer that I need.",
|
||||
"I is simply the voltage, V, divided by R1 plus.",
|
||||
"OK, so in situations like this where I'm looking for a single",
|
||||
"current, I can very quickly get to the answer by applying some",
|
||||
"of these element combination rules.",
|
||||
"And, I can get rid of having to go through formal steps.",
|
||||
"So, in general, whenever you encounter a",
|
||||
"circuit, by and large attempt to use intuitive methods to solve",
|
||||
"it. And go to a formal method only",
|
||||
"if some intuitive method fails. Even in your homework,",
|
||||
"by and large, the homeworks are not meant to",
|
||||
"be grungy. OK, if you find a lot of grunge",
|
||||
"in your homework, just remember you're probably",
|
||||
"not using some intuitive method. OK, so just be cautious.",
|
||||
"All right, so let me go on to the third method of circuit",
|
||||
"analysis, and the third method is called the node method.",
|
||||
"So, the node method is simply a specific application of the KVL",
|
||||
"KCL method and results in a much, much more compact form of",
|
||||
"the final equations. If there's one method that you",
|
||||
"have to remember for life, then I would say just remember",
|
||||
"this method. OK, the node method is a",
|
||||
"workhorse of the easiest industry.",
|
||||
"OK, if there's one method that you want to consistently apply,",
|
||||
"then this is the one to remember.",
|
||||
"So, let me quickly outline for you to method,",
|
||||
"and then work out an example for you.",
|
||||
"The first step of the node method will be to select a",
|
||||
"reference or a ground node. This is the symbol for a ground",
|
||||
"node. The ground node simply says",
|
||||
"that I'm going to denote voltages at that point to be",
|
||||
"zero, and measure all my other voltages with reference to that",
|
||||
"point. So, I'm going to select a",
|
||||
"ground node in my circuit. Second, I want to label the",
|
||||
"remaining voltages with respect to the ground node.",
|
||||
"So, label voltages for all the other nodes with respect to the",
|
||||
"ground node. Next, write KCL for each of the",
|
||||
"nodes write KCL. OK, but don't write KCL for the",
|
||||
"ground node. Remember, if you have N nodes,",
|
||||
"the node equations will give you N-1 independent equations.",
|
||||
"So, write KCL for the nodes, but don't do so for the ground",
|
||||
"node. Then, solve for the node",
|
||||
"voltages. So, let's say when we label",
|
||||
"voltages. I want to be labeling them as E",
|
||||
"something or the other. So, solve for the unknown node",
|
||||
"voltages. And then, once I know all the",
|
||||
"voltages associated with the nodes, I can then back solve for",
|
||||
"all the branch voltages and currents.",
|
||||
"OK, once I know all the node voltages, I can then go ahead",
|
||||
"and figure out all the branch voltages and the branch",
|
||||
"currents. So, let's go ahead and apply",
|
||||
"this method, and work out an example.",
|
||||
"Again, remember, if there's one method that you",
|
||||
"should remember, it's the node method.",
|
||||
"OK, and when in doubt, consistently apply the node",
|
||||
"method and it will work whether your circuit is linear or",
|
||||
"nonlinear, if the resistors are built in the US or the USSR it",
|
||||
"doesn't matter. OK, the node method will simply",
|
||||
"work, linear or nonlinear, OK?",
|
||||
"So, what I'm going to do is I'm going to build a circuit that's",
|
||||
"my old faithful. It's our old faithful,",
|
||||
"plus I'll make it a little bit more complicated by adding in",
|
||||
"the current source. So, let's go have some fun.",
|
||||
"Let's do this. So here's my voltage source,",
|
||||
"as before. OK, what I'll do is for fun,",
|
||||
"add a current source out there. And, you can convince",
|
||||
"yourselves that if you go ahead and apply the KVL KCL method,",
|
||||
"it'll really be a mess of equations.",
|
||||
"OK, so R1, R3, R4, R2, R5.",
|
||||
"OK, so let's follow our method and just plug and chug here.",
|
||||
"So let's apply the first step. I select a ground node.",
|
||||
"It's a reference node from which I'll measure all my other",
|
||||
"voltages. OK, now without knowing",
|
||||
"anything about the node method, try to use intuition as to",
|
||||
"which node you should choose as a ground node.",
|
||||
"Remember, you want to label the ground node with the voltage",
|
||||
"zero, and measure all the other voltages with respect to that",
|
||||
"node. OK, a usual trick is to pick a",
|
||||
"node which has the largest number of elements connected to",
|
||||
"it as the ground node. OK, and in particular,",
|
||||
"you will find out later it's useful to pick a node in which",
|
||||
"all your voltage sources, the maximum number of your",
|
||||
"voltage sources are also connected.",
|
||||
"OK, so in this instance, I'm going to choose this as my",
|
||||
"ground node. OK, that's my first step.",
|
||||
"I chose that as my ground node. And I'm going to label that as",
|
||||
"having a voltage zero. Second step,",
|
||||
"I'll label voltages of the other branches with respect to",
|
||||
"the ground node. OK, so what I'll do is add this",
|
||||
"node here. So I'm going to label that",
|
||||
"voltage E1. These are my unknowns.",
|
||||
"Remember, node method, because my node voltages are my",
|
||||
"unknowns. So, I label this as E1.",
|
||||
"I label this one as my unknown voltage, E2.",
|
||||
"What about this one here? Is that voltage unknown?",
|
||||
"No. I know what the voltage is",
|
||||
"because I know that this node is at a voltage,",
|
||||
"V0, higher than the ground node.",
|
||||
"OK, notice that to go from here to here, I directly go through a",
|
||||
"voltage source. And so, this node has voltage",
|
||||
"V0. And I'll simply write down V0.",
|
||||
"OK, try to simplify the number of steps that you have to go",
|
||||
"through, so directly go ahead and write down the voltage,",
|
||||
"V0, for that node. What I will also do,",
|
||||
"is for convenience, I'm going to write down,",
|
||||
"I'm going to use conductances. So I'm going to use GI in the",
|
||||
"place of one by RI, and write down a bunch of node",
|
||||
"equations. OK, so step one,",
|
||||
"I've chosen my ground node. Step two, I've labeled my node",
|
||||
"voltages, E, OK? I've done that with two of my",
|
||||
"steps. Now, let me go ahead and --",
|
||||
"",
|
||||
"OK, so let me go ahead and apply step three.",
|
||||
"And, step three says go ahead and apply KCL for each of the",
|
||||
"nodes at which you have an unknown node voltage.",
|
||||
"And then that will give you your equations.",
|
||||
"So let me start by applying KCL at E1.",
|
||||
"So, let me write KCL at E1. I do one more thing.",
|
||||
"Notice, I don't have any currents there.",
|
||||
"OK, so how do I write KCL? KCL simply says the sum of",
|
||||
"currents into a node is zero again, remember,",
|
||||
"by the lump matter discipline. So, if I don't have currents in",
|
||||
"there, so the trick that I adopt is that to write KCL,",
|
||||
"I use the node voltages, and implicitly substitute for",
|
||||
"the node voltages, divide by the elemental the",
|
||||
"resistance, for instance, so I take the node voltages,",
|
||||
"and divide by the resistance, get the current.",
|
||||
"OK, so I implicitly apply element relationships to get the",
|
||||
"node currents. So, the example that make it",
|
||||
"clear, so I take node E1 and, again, for currents going out",
|
||||
"I'm going to assume to have, to be positive.",
|
||||
"So, the current going up is E1 minus V nought,",
|
||||
"divide by R1, so I multiplied by the G1.",
|
||||
"That's the current going up. Plus, the current going down is",
|
||||
"E1 minus zero where the ground node potential is zero,",
|
||||
"G2, OK, plus the current that is going to resistor R3,",
|
||||
"which is simply E1 minus E2, divide by R3.",
|
||||
"So, E1 minus E2, divide by R3,",
|
||||
"or multiplied by G3 is equal to zero.",
|
||||
"OK, see how I got this? This is simply KCL,",
|
||||
"but to get my currents, I simply take the differences",
|
||||
"of voltages across elements, and divide by the element of",
|
||||
"resistance, and I get the currents.",
|
||||
"OK, so I can similarly write KCL at E2.",
|
||||
"So, at KCL at E2, again, let me go outwards.",
|
||||
"So, the current going up is E2 minus V nought multiplied by G4.",
|
||||
"The current going left is E2 minus E1 divided by R3 or",
|
||||
"multiplied by G3. The current going down is E2",
|
||||
"minus zero multiplied by G5. And, the current going down is",
|
||||
"-I1. OK, you've got to be careful",
|
||||
"with your polarities here. So all the currents going out",
|
||||
"sum to zero. And here are the currents that",
|
||||
"are going out at this point. So what I do next is I can move",
|
||||
"the constant terms to the left-hand side and collect my",
|
||||
"unknowns. So, let me write them out here.",
|
||||
"So, let's say I get E1 here, OK, and from this equation,",
|
||||
"I have a V nought, G1, which comes out here.",
|
||||
"So, minus V nought G1 comes over to the other side.",
|
||||
"And, let me collect all the values that multiply E1.",
|
||||
"So I get, G1 is one example. I have G2, and I have G3.",
|
||||
"And then, for E2, I have minus G3.",
|
||||
"OK, so I'll simply express this as the element voltages",
|
||||
"multiplied by some terms in parentheses, and I put my",
|
||||
"external sources on the right hand side.",
|
||||
"Similarly, I go ahead and do the same thing here.",
|
||||
"In this instance, let me move my sources to the",
|
||||
"right. So, I get I1 coming out there,",
|
||||
"and I get V nought G4 coming out there.",
|
||||
"By the way, I just want to mention to you that if you're",
|
||||
"looking to fall asleep, this is a good time to do so",
|
||||
"because as soon as I write down these two equations,",
|
||||
"OK, from now on it's nap time. There's nothing new that you're",
|
||||
"going to learn from here on. It's just Anant Agarwal having",
|
||||
"fun at the blackboard, pushing symbols around.",
|
||||
"So, once you write down these two node equations,",
|
||||
"the rest of it is just grubby math.",
|
||||
"So, let me just have some fun. So let me just go ahead and do",
|
||||
"that. So, I moved my voltages and",
|
||||
"currents to the other side. And let me collect all the",
|
||||
"coefficients for E1 here. So, E1 minus G3,",
|
||||
"and that's it, I guess.",
|
||||
"OK, and then I'll do the same for E2.",
|
||||
"So, I get G4, and I get G3,",
|
||||
"and I get G5. OK, so notice here that I have",
|
||||
"two equations, and two unknowns.",
|
||||
"OK, the two equations are on the right hand side,",
|
||||
"I have some voltages and currents which are my dry",
|
||||
"voltages and dry currents. OK, so actually this is getting",
|
||||
"quite boring. I'm going to pause here,",
|
||||
"and talk about something else. So, you can take this and you",
|
||||
"can put it in matrix form, so I've done that for you on",
|
||||
"page ten. It's all matrix form.",
|
||||
"Yeah, I know that. You can use any technique to",
|
||||
"solve it, use algebraic techniques, use linear algebraic",
|
||||
"methods to solve it, use a computer,",
|
||||
"whatever you want. And, computers,",
|
||||
"when computers analyze circuits, they write down these",
|
||||
"equations, and deal with solving matrices.",
|
||||
"So, when you take the linear algebra across,",
|
||||
"how many people here have taken a linear algebra class?",
|
||||
"How many people here have heard of Gaussian elimination?",
|
||||
"How can more people have heard of Gaussian elimination than",
|
||||
"took a linear algebra class? Well anyway,",
|
||||
"so now you know why you took those linear algebra classes.",
|
||||
"And so, if I just collected these into matrix form --",
|
||||
"",
|
||||
"OK, so I just simply expressed those two equations in linear",
|
||||
"algebraic form, and here's my column vector of",
|
||||
"unknowns, and you can apply any of the techniques you've learned",
|
||||
"in linear algebra to solve for this.",
|
||||
"Gaussian elimination works. OK, and in computer,",
|
||||
"people doing research in computer techniques,",
|
||||
"or solving such equations simply deals with huge equations",
|
||||
"like this, building computer programs that,",
|
||||
"given equations like this, can go ahead and solve them.",
|
||||
"OK, so let me stop here and reemphasize that what you've",
|
||||
"done is made a huge leap from Maxwell's equations to using the",
|
||||
"lump matter discipline to KVL and KCL, which ended up giving a",
|
||||
"simple algebraic equation to solve, and not having to worry",
|
||||
"about partial differential equations that were the form of",
|
||||
"Maxwell's equations."
|
||||
]
|
||||
}
|
||||
@@ -1,2477 +0,0 @@
|
||||
{
|
||||
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|
||||
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|
||||
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||||
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||||
"text": [
|
||||
"",
|
||||
"OK. Good morning.",
|
||||
"Let's get going. As always, I will start with a",
|
||||
"review. And today we embark on another",
|
||||
"major milestone in our analysis of lumped circuits.",
|
||||
"And it is called the \"Sinusoidal Steady-state\".",
|
||||
"Again, I believe this will be the second and the last lecture",
|
||||
"for which I will be using view graphs.",
|
||||
"And the idea here is that, just like in the last lecture,",
|
||||
"there is a bunch of mathematical grunge that needs",
|
||||
"to be gone through. And I want to show you a",
|
||||
"sequence in a little chart today that talks about the effort",
|
||||
"level in doing some problems based on time domain",
|
||||
"differential equations, as in the last lecture,",
|
||||
"something slightly different today and something much better",
|
||||
"on Thursday. And so, in some sense,",
|
||||
"Thursday's lecture and today's lecture involve talking about",
|
||||
"the foundations of the behavior of certain types of circuits.",
|
||||
"And it is good for you to have this foundation as background,",
|
||||
"but when you actually go to solve circuits you don't quite",
|
||||
"use these methods. You use much easier techniques,",
|
||||
"which I will talk about next Thursday.",
|
||||
"Let's start with a quick review, and then we will go into",
|
||||
"sinusoidal steady state. The last lecture we talked",
|
||||
"about this circuit and we did the same two lectures ago on",
|
||||
"Tuesday. We had one inverter driving",
|
||||
"another inverter. And we said that the wire over",
|
||||
"ground had some inductance. CGS is the capacitor of the",
|
||||
"gate and R is the resistance at the drain of the first inverter.",
|
||||
"And if you look at this circuit, that circuit formed an",
|
||||
"RLC pattern. And what we did was we said",
|
||||
"let's drive this with a one to zero transition at the input.",
|
||||
"And the one to zero transition at the input would cause this",
|
||||
"transistor to switch off, and this node would then go",
|
||||
"from a very low value to a high value.",
|
||||
"So it as if a 5 volt step was applied at this input.",
|
||||
"We also saw that using time domain differential equations",
|
||||
"that by applying a step input here the output looked like",
|
||||
"this. The output would show some",
|
||||
"oscillatory behavior when we have a capacitor and inductor.",
|
||||
"I also gave you some insight as to why it oscillates like this.",
|
||||
"And you also heard in recitation that the reason for",
|
||||
"this oscillation was because of these two storage elements.",
|
||||
"Each of these storage elements tries to hold onto its state",
|
||||
"variable. For example,",
|
||||
"the capacitor tries to maintain its voltage while the inductor",
|
||||
"tries to maintain its current. And, much like a pendulum which",
|
||||
"oscillates back and forth, it swaps potential energy",
|
||||
"versus kinetic energy down here and swings back and forth.",
|
||||
"In the same way, in an LC circuit like this,",
|
||||
"energy swaps back and forth between a potential energy and a",
|
||||
"kinetic energy equivalent, which swaps back and forth",
|
||||
"between energy stored in the inductor and energy stored in",
|
||||
"the capacitor and sloshes back and forth.",
|
||||
"And because of this resistor the energy eventually dissipates",
|
||||
"and you end up getting a final value which corresponds to the 5",
|
||||
"volts appearing here. And why is that?",
|
||||
"That is because remember the capacitor is a long-term open",
|
||||
"for DC. It is a DC voltage.",
|
||||
"After a long time this capacitor looks like an open",
|
||||
"circuit and the inductor looks like a complete short circuit,",
|
||||
"an ideal inductor as a complete short circuit for DC.",
|
||||
"And so therefore in the long-term it is as if this guy",
|
||||
"is a short, this guy is an open, so 5 volts simply appears here.",
|
||||
"And this is the transient behavior.",
|
||||
"Then we just switch the first transistor off.",
|
||||
"In the last lecture, I left off with intuitive",
|
||||
"analysis. Let me quickly cover that and",
|
||||
"redo the intuitive analysis for you.",
|
||||
"I left it the last time by having you think about whether",
|
||||
"the transient response would begin by going down or begin by",
|
||||
"going up. And I will cover that today.",
|
||||
"This was the circuit that we analyzed.",
|
||||
"A VI input with a step and an RLC out here.",
|
||||
"And we were plotting the capacitor voltage.",
|
||||
"And intuitively we can plot this in the following way.",
|
||||
"I have also marked for you the section number in the course",
|
||||
"notes which has a discussion of this intuitive analysis,",
|
||||
"(Section 13.8). Let's do the easy stuff first.",
|
||||
"Notice that the capacitor wants to hold its voltage.",
|
||||
"And so given that we don't have any infinite impulse here,",
|
||||
"I am going to start out with the capacitor voltage being",
|
||||
"where it is. And the initial conditions are",
|
||||
"given to you. You are given that the",
|
||||
"capacitor voltage starts out being positive at v zero and the",
|
||||
"current starts out being negative at time zero.",
|
||||
"So I am telling you that there is a voltage v across the",
|
||||
"capacitor at time t=0 and there is a current that is flowing.",
|
||||
"Since i is negative there is a current initially that is",
|
||||
"flowing in the opposite direction to this arrow here.",
|
||||
"The i zero is negative. In light of that,",
|
||||
"I can start plotting my curve here by intuition.",
|
||||
"I start by saying at time t=0 I am told that the initial voltage",
|
||||
"of the capacitor is at zero. This is about as simple as it",
|
||||
"gets. Completely intuitive.",
|
||||
"I also know that after a long time, can someone tell me after",
|
||||
"a long time what the voltage will be at the end of the",
|
||||
"capacitor? You should be able to get his",
|
||||
"by observation? VI.",
|
||||
"And why is it VI? It is vI because this is a DC",
|
||||
"value VI. And after a long time this guy",
|
||||
"behaves like an open circuit to DC.",
|
||||
"This guy behaves like a short circuit to DC.",
|
||||
"So since this is an open circuit, VI will appear here",
|
||||
"after a long time. And so therefore,",
|
||||
"after a long time, the capacitor voltage is going",
|
||||
"to be at VI. And I just showed you that.",
|
||||
"There you go. You already have the two",
|
||||
"endpoints of your curve completely by observation,",
|
||||
"intuition. No DEs, no nothing.",
|
||||
"Just by staring at it and understanding the fundamentals",
|
||||
"of how simple primitive circuit elements work.",
|
||||
"Absolutely simple stuff. So you've nailed the two ends",
|
||||
"now and you cannot go wrong with the stuff in the middle.",
|
||||
"Let's see. As a next step what I do is I",
|
||||
"need to understand what the dynamics of the circuit looks",
|
||||
"like here. What I do is I develop the",
|
||||
"characteristic equation. And initially you will write",
|
||||
"the differential equation and then substitute e^st and get",
|
||||
"this characteristic equation. But you could also remember it",
|
||||
"as a pattern. For a series RLC circuit you",
|
||||
"always get an equation of this form, always.",
|
||||
"If this were R, L and C.",
|
||||
"And whether you are looking at L up here or C up here,",
|
||||
"as long as you're looking at the capacitor voltage,",
|
||||
"the capacitor voltage is going to behave the same.",
|
||||
"And for this circuit the characteristic equation remains",
|
||||
"the same as well for a series RLC.",
|
||||
"It is exactly this. And I write the standard",
|
||||
"canonic form as s squared plus two alpha s + omega nought",
|
||||
"squared. And omega nought is simply one",
|
||||
"by square root of LC and alpha is simply R divided by L and I",
|
||||
"have two in the denominator as well.",
|
||||
"And then I get omega d which is my damped frequency given by",
|
||||
"omega nought squared minus alpha squared.",
|
||||
"And Q is simply called the quality factor.",
|
||||
"And we will learn about Q in a lot more detail in about a",
|
||||
"couple of lectures from today. That is given where omega",
|
||||
"nought divided by two alpha. These parameters,",
|
||||
"alpha, omega nought, Q and omega d pretty much",
|
||||
"characterize everything else that I need to know about the",
|
||||
"circuit. First of all,",
|
||||
"omega d is the frequency of oscillation.",
|
||||
"And so since omega d is a frequency of oscillation then I",
|
||||
"know that the time period of oscillation is two pi by omega",
|
||||
"d. Omega is in radians.",
|
||||
"Notice that for typical values of circuits like this when R is",
|
||||
"pretty small, alpha squared is going to be",
|
||||
"very small. It's a common case for",
|
||||
"underdamped circuit that omega d will more or less be equal to",
|
||||
"omega nought. Commonly that is going to be",
|
||||
"the case. This frequency is governed by",
|
||||
"LC. And if R is large it is",
|
||||
"governed by this omega d here. So I have the frequency of",
|
||||
"oscillation. I also know that Q is related",
|
||||
"to the frequency of oscillation divided by alpha.",
|
||||
"It is a ratio of the frequency divided by how badly I am being",
|
||||
"damped. So it is a fight between the",
|
||||
"frequency of oscillation and now heavily I damp.",
|
||||
"And the ratio of that is an indication of how many cycles I",
|
||||
"ring. So Q tells me that the ringing",
|
||||
"stops approximately after Q cycles.",
|
||||
"These four values, omega d, Q, alpha and omega",
|
||||
"nought are telling me more and more now.",
|
||||
"So I have got these two factors.",
|
||||
"So I know now, based on omega d and Q,",
|
||||
"that it is going to look something like this.",
|
||||
"Some ringing here and then I stop at this point.",
|
||||
"The last thing that is left to do here for me for now is to",
|
||||
"figure out whether I start out going down or I start out going",
|
||||
"up. I start out going down or I",
|
||||
"start out going up? I don't know that yet.",
|
||||
"And I stopped at this point in the last lecture and let you",
|
||||
"think about how you can stare at the circuit and intuitively",
|
||||
"figure out whether this goes down or that goes up.",
|
||||
"So here is the insight. Let's stare at this for a",
|
||||
"minute purely through intuition. The capacitor has a voltage v",
|
||||
"across it, right? And that is because I am",
|
||||
"telling you that it has an initial voltage v.",
|
||||
"Now, I want to find out at prime t equals zero plus,",
|
||||
"in which direction does a capacitor voltage go?",
|
||||
"Increase or decrease? What do I do?",
|
||||
"Let me take a look at the inductor current.",
|
||||
"I am told that the inductor current is negative which means",
|
||||
"I am told that the inductor current is going in this",
|
||||
"direction initially. The inductor current is pushing",
|
||||
"in this direction. Now, remember,",
|
||||
"just as the capacitor is one stubborn nut trying to hold its",
|
||||
"voltage, the inductor is as stubborn.",
|
||||
"It is trying to hold its current.",
|
||||
"It is trying to maintain its current.",
|
||||
"And its initial current i(0) is in this direction.",
|
||||
"Capacitor has a voltage here, that is v(0),",
|
||||
"and the inductor is yanking the current in that direction.",
|
||||
"So what should happen to the capacitor voltage initially?",
|
||||
"If I am at v(0) and someone is yanking current out,",
|
||||
"at least initially in that direction, what should the",
|
||||
"initial dynamics of the capacitor voltage look like?",
|
||||
"Pardon? It should drop,",
|
||||
"which means that if the initial current is being pulled in that",
|
||||
"direction the capacitor voltage must droop to begin with.",
|
||||
"Completely through intuition. No math here.",
|
||||
"This means that i(0) is negative.",
|
||||
"It is as if i(0) is being pulled out in this manner,",
|
||||
"so the capacitor voltage must drop to begin life.",
|
||||
"Therefore, the dynamics look somewhat like this.",
|
||||
"Notice that this is very reminiscent of the ringing that",
|
||||
"we saw at the gate node of the second inverter.",
|
||||
"Let's stop here in terms of time domain analysis of RLC,",
|
||||
"and today let's take another big step forward.",
|
||||
"Today marks another transition in life here.",
|
||||
"This is actually a huge transition so I want to just",
|
||||
"pause and take like ten seconds of a breather just to clearly",
|
||||
"demarcate the fact that we have a huge transition coming up.",
|
||||
"The key to this transition is that I want to look at today the",
|
||||
"steady-state response of networks to a sinusoidal drive.",
|
||||
"We are going to do two things differently starting today on",
|
||||
"this new journey of ours. In the past,",
|
||||
"we looked at time domain behavior of circuits.",
|
||||
"For RLC, for example, we looked at the transient",
|
||||
"response. And what happened the instant I",
|
||||
"turn something on? The transient response.",
|
||||
"Today we are going to look at a steady-state response.",
|
||||
"Steady-state response says that if I wait long enough,",
|
||||
"for whatever the circuit wants to do in the beginning of life",
|
||||
"to die out. If I wait long enough,",
|
||||
"how is the circuit going to behave after a long time?",
|
||||
"I will tell you why that is important in a second.",
|
||||
"I look at the steady-state behavior.",
|
||||
"Second, I am going to look today at sinusoidal drive.",
|
||||
"Two things that are different from, say for example,",
|
||||
"what I covered in the past ten minutes.",
|
||||
"In the past ten minutes I covered two things which were",
|
||||
"different. One is that I looked at the",
|
||||
"transient response and then steady-state.",
|
||||
"And remember for a DC input, for a DC voltage the",
|
||||
"steady-state was a DC voltage across the capacitor,",
|
||||
"correct? So the steady-state was pretty",
|
||||
"boring, it was steady-state DC. But what we are going to do",
|
||||
"today is instead of having DC inputs or step inputs which",
|
||||
"settle to a DC value after some time, we are going to drive a",
|
||||
"circuit through the sinusoidal input.",
|
||||
"So you may ask me, Agarwal, are you nuts?",
|
||||
"Why do you want to drive something with a sinusoidal",
|
||||
"input? Why not just steps in DC and so",
|
||||
"on? That was painful enough.",
|
||||
"Why sinusoidal? Why not do triangular or why",
|
||||
"not do some other exponentially decaying stuff or something",
|
||||
"really cool like a whacko music signal?",
|
||||
"What is special about sinusoidal stuff?",
|
||||
"The key thing to realize is that, well, let me ask you a",
|
||||
"question first. How many people here know about",
|
||||
"Fourier series? Good.",
|
||||
"It looks like some of you have taken the prerequisites.",
|
||||
"Good. Need I say more as to why this",
|
||||
"is important? Just that question should give",
|
||||
"you the answer, right?",
|
||||
"You've learned about Fourier series.",
|
||||
"And when you learned about Fourier series you were",
|
||||
"wondering why on earth are we learning about Fourier series?",
|
||||
"Who cares that you can represent the periodic signals",
|
||||
"as a summation of a series of sine waves?",
|
||||
"Why is that interesting? Why are you telling me that I",
|
||||
"can take a square wave and represent that as a summation of",
|
||||
"periodic square waves and represent that as a summation of",
|
||||
"sines? Who cares that I can take a",
|
||||
"sequence of pulses with a fixed period and represent that as a",
|
||||
"sum of sines? Who cares that I can take a",
|
||||
"triangular wave and represent that as a sum of sines?",
|
||||
"I am not sure what answer your math professors gave you when",
|
||||
"they taught you Fourier series. But in math they are purists.",
|
||||
"They don't care about applications.",
|
||||
"The answer could well have been because it is aesthetically",
|
||||
"pleasing. I mean isn't it cool that you",
|
||||
"can represent a sequence of pulses as a sum of sines?",
|
||||
"That is good enough for mathematicians.",
|
||||
"But I am an engineer. If it I cannot see how it helps",
|
||||
"humanity in the short-term then I probably don't care too much",
|
||||
"about it. Let me give you some practical",
|
||||
"significance of this. So it turns out that,",
|
||||
"since we know that we can represent periodic signals with",
|
||||
"sums of sines. What this means is that if I",
|
||||
"can figure out the behavior of networks to a sinusoidal input,",
|
||||
"if I can understand how to analyze a network for a",
|
||||
"sinusoidal input that means that if the circuit is linear I can",
|
||||
"then compute the response of the circuit to any periodic",
|
||||
"waveform. Here is the argument.",
|
||||
"I can represent any periodic waveform as a sum of sines.",
|
||||
"The Fourier series, remember?",
|
||||
"If I just figure out the response of my network for a",
|
||||
"sine wave, then if this is a linear network,",
|
||||
"I can compute the response to any sequence of scaled sum of",
|
||||
"sines. A some sine,",
|
||||
"B sine two, omega whatever, C sine something or the other.",
|
||||
"I can simply take the response of the one sine.",
|
||||
"And from there I can go ahead, and knowing the response of a",
|
||||
"sine wave I can compute the response to a sum of sines.",
|
||||
"That is pretty cool. Therefore, doing it for",
|
||||
"sinusoidal drives is really important.",
|
||||
"Why steady-state now? Hopefully, I have convinced you",
|
||||
"that looking at the response of circuits to sinusoidal drive is",
|
||||
"important and interesting because we can long ways from",
|
||||
"there. What about steady-state?",
|
||||
"Well, it turns out that, and I am going to show you,",
|
||||
"when you listen to music, you have an amplifier and",
|
||||
"listen to music, what you are observing by and",
|
||||
"large is the steady-state behavior of the amplifier.",
|
||||
"You are listening to something over many seconds or many hours.",
|
||||
"And the transients used for most of our common circuits,",
|
||||
"the transients die out pretty quickly.",
|
||||
"And so the transients are quite complicated and they die out",
|
||||
"quickly. We say we are engineers.",
|
||||
"Let's focus on what is practically important.",
|
||||
"And we focus on the steady-state behavior as a large",
|
||||
"part of our analysis and just completely ignore the transient",
|
||||
"response when we care about the response to sinusoidal input.",
|
||||
"The transient response will die away, and I will show that",
|
||||
"mathematically to you in a few seconds.",
|
||||
"And let's focus on the steady-state because that what I",
|
||||
"am going to hear most of the time.",
|
||||
"I am going to listen to an average over long periods of",
|
||||
"time. That's the motivation behind",
|
||||
"this. And let me put this in",
|
||||
"perspective for you. By now this should bring",
|
||||
"memories to your mind. This is the playground that we",
|
||||
"are in. This is the lumped circuit",
|
||||
"playground here. Remember we came from the",
|
||||
"playground of nature to the playground of EECS where we made",
|
||||
"the big leap from Maxwell's equations to lumped circuits,",
|
||||
"that's lumped circuit abstraction.",
|
||||
"And within there we spent a large part of the last couple of",
|
||||
"months doing linear circuits. We also analyzed nonlinear",
|
||||
"circuits. Remember the amplifier circuit",
|
||||
"of the MOSFET large signal analysis was nonlinear?",
|
||||
"Well, there is linear and nonlinear.",
|
||||
"Within linear we also showed that if you take a digital",
|
||||
"circuit, at least as we understood them,",
|
||||
"and draw the subcircuit for a given set of switch settings,",
|
||||
"if I set the switches in a given way what I was left with",
|
||||
"was another linear circuit for a given value of all the switch",
|
||||
"settings. My small signal analysis was",
|
||||
"also linear. If I focused on small signals I",
|
||||
"also had linear analysis. Today what we are going to do",
|
||||
"is this. We are going to articulate a",
|
||||
"different part of the playground.",
|
||||
"This was a big linear playground.",
|
||||
"We've done this. We've done this.",
|
||||
"We are going to explore this territory.",
|
||||
"This is that territory of the playground in which we have",
|
||||
"sinusoidal inputs to circuits. Furthermore,",
|
||||
"we are going to look at a subcircuit of that region which",
|
||||
"is steady-state. We will look at sinusoidal",
|
||||
"input and in the steady-state. So that is going to be our",
|
||||
"focus for the next two or three lectures just to give you a",
|
||||
"perspective of where we are. To motivate this,",
|
||||
"what I would like to do is consider your amplifier.",
|
||||
"This is our friend the amplifier circuit,",
|
||||
"this part here. And remember,",
|
||||
"even though this is an amplifier, I am using a MOSFET",
|
||||
"here. And a MOSFET,",
|
||||
"as you know, has this gate capacitance CGS.",
|
||||
"I am explicitly drawing it out for you here.",
|
||||
"And I am going to drive this with a bias voltage plus some",
|
||||
"small signal vI, the usual template for",
|
||||
"amplifiers. And there is some Thevenin",
|
||||
"resistance attached to that source.",
|
||||
"I am going to model my source as a bias voltage,",
|
||||
"a small signal plus some source resistance.",
|
||||
"And I want to apply a sine wave here and I am going to look at",
|
||||
"what this looks like. You may think,",
|
||||
"look, this is a linear amplifier.",
|
||||
"And so if I apply a sine wave here I should see some response",
|
||||
"here, and that should be the same amplitude if I feed the",
|
||||
"same amplitude here over any frequency.",
|
||||
"But let's see what happens. Keep a look at,",
|
||||
"switch over to that view graph while I show you a little",
|
||||
"demonstration here. What you see here are three",
|
||||
"sine waves, a yellow sine wave which is the input here,",
|
||||
"you see a green sine wave which is the input vC at the gate of",
|
||||
"the MOSFET, and then you see the blue which is the output here.",
|
||||
"For now simply focus on the yellow and the blue.",
|
||||
"The yellow is the input and the blue is the output.",
|
||||
"So I apply some input and I get an output that looks more or",
|
||||
"less some linear function of this input here.",
|
||||
"It is a small signal. What I am going to do is I am",
|
||||
"going to change the frequency of the input.",
|
||||
"Remember, I want to look at the response of the circuit to a",
|
||||
"sinusoid. I am feeding a sinusoid here.",
|
||||
"I look at the response. I am going to change the",
|
||||
"frequency. That is a big shift that we are",
|
||||
"making in that the curve that we drew in the last lecture had to",
|
||||
"do with varying time. Now I am going to focus on",
|
||||
"sinusoids and vary their frequency.",
|
||||
"I am going to change the frequency.",
|
||||
"Stare at the blue curve as I increase the frequency and just",
|
||||
"think of what you might expect. Based on the knowledge you have",
|
||||
"so far you would expect that look, as I change the frequency,",
|
||||
"the frequency should change but I should see the same amplitude.",
|
||||
"OK but take a look. Let me increase the frequency",
|
||||
"of the input. What do you see at the output?",
|
||||
"I am increasing the frequency.",
|
||||
"",
|
||||
"What do you see happening there?",
|
||||
"If you don't see anything changing there you will need to",
|
||||
"see an optometrist. What do we see here?",
|
||||
"As I changed the frequency, as I increased the frequency",
|
||||
"what happened to the blue? The blue kept decreasing in",
|
||||
"amplitude. And you are saying whoa,",
|
||||
"what is happening here? We don't have the tools to deal",
|
||||
"with this. I expected that when I changed",
|
||||
"my frequency, my frequency here should change",
|
||||
"of course, but why is the amplitude changing?",
|
||||
"What is happening here? That is weird.",
|
||||
"I noticed that this amplitude became smaller because the",
|
||||
"amplitude of the green became smaller.",
|
||||
"And remember the green was the voltage across the capacitor.",
|
||||
"So this is your RC. And here is my input.",
|
||||
"My input has the amplitude, which I am holding more or less",
|
||||
"constant. And notice that vC decreased in",
|
||||
"value as I increased my frequency.",
|
||||
"Just hold that thought. As I increased the frequency of",
|
||||
"my input the amplitude of the output kept diminishing.",
|
||||
"In other words, the gain of the system seemed",
|
||||
"to have decreased as I increased by frequency.",
|
||||
"And today we will look at why that is so and how we can",
|
||||
"analyze that. The other thing that is not so",
|
||||
"obvious here is there is a phase shift.",
|
||||
"What I am going to do is try to see if we can observe the phase",
|
||||
"shift here.",
|
||||
"",
|
||||
"Notice here. What we have been used to is",
|
||||
"for the amplifier we get a complete inversion at the",
|
||||
"output. Inversion means a phase",
|
||||
"difference of 180 degrees for a sine wave, right?",
|
||||
"This peak should have been here, but notice that there is a",
|
||||
"shifting of the peak. In other words,",
|
||||
"if the yellow was my input my output should have had its",
|
||||
"minimum when the input had its maximum.",
|
||||
"But notice there is a shifting of the signal such that the",
|
||||
"output is a maximum, not quite at the point where",
|
||||
"the input is a minimum but a little bit after that.",
|
||||
"Also weird. Not only has this little",
|
||||
"circuit here lost its gain somehow, but also it seems to",
|
||||
"have shifted the signal in phase.",
|
||||
"That is weird. And today we will look at why",
|
||||
"that is so and try to understand the frequency behavior of this",
|
||||
"little subcomponent here. Notice that vC is exactly 180",
|
||||
"out of phase with vO. So vO is faithfully an inverted",
|
||||
"amplified form of the input vC. However, vC itself should have",
|
||||
"been the same as vI but it looks quite different.",
|
||||
"So let's understand why that is so.",
|
||||
"The subcircuit to model is the subcircuit comprising the",
|
||||
"source, resistor and the capacitor.",
|
||||
"And I am just showing that to you here.",
|
||||
"I have a vI, a resistor and capacitor.",
|
||||
"And I am going to understand how this behaves.",
|
||||
"And it is a first order circuit, single capacitor.",
|
||||
"My input is a vI cosine of omega t.",
|
||||
"vI is a real number for t greater than zero.",
|
||||
"And I am telling you that the capacitor voltage starts out",
|
||||
"being zero. And my vI is a sinusoid.",
|
||||
"It's not a step this time. It's a sinusoid.",
|
||||
"So vI is a sinusoid and I want to find out what vC looks like.",
|
||||
"The behavior here tells me, I will give you the answer,",
|
||||
"that when I feed a sinusoidal input as the frequency",
|
||||
"increases, vC should be decreasing somehow and also be",
|
||||
"shifting in phase. Let's do the derivation for",
|
||||
"that and see what happens. To give you some insight as to",
|
||||
"how to go about analyzing this let me draw a little graph as to",
|
||||
"the effort level of doing this. To determine vC of t on the",
|
||||
"y-axis here is our effort. How hard do we have to work to",
|
||||
"solve this circuit for a sinusoidal input?",
|
||||
"And on this graph, down here is easy and up here",
|
||||
"is pure agony. Sheer agony up here.",
|
||||
"So it's the scale of effort level ranging from easy to",
|
||||
"complete agony. And this is the time axis.",
|
||||
"And the time axis starts out at 11 o'clock, the early part of",
|
||||
"today's lecture, and ends at roughly 12,",
|
||||
"that is today's lecture and this is next lecture.",
|
||||
"What I am going to show you today is a method that uses a",
|
||||
"usual differential equation approach, and this is going to",
|
||||
"be pure agony. If you thought last Thursday",
|
||||
"was agony watch today. This is going to be sheer,",
|
||||
"sheer, sheer hell. So I am going to grunge through",
|
||||
"that, and I think I will sort of give up halfway because it's",
|
||||
"just too painful even for me here.",
|
||||
"Then what I am going to do is at the end of this lecture I am",
|
||||
"going to show you an approach that I give a cutesy name.",
|
||||
"I call it the \"sneaky approach\".",
|
||||
"We are going to sneak something in there it is going to be a lot",
|
||||
"easier. And then in the next lecture I",
|
||||
"am going to show you an even sneakier approach that is just",
|
||||
"going to be absolute bliss. So let's start here.",
|
||||
"Indulge me as I go through the agony part.",
|
||||
"I am going to blast through it because that is not of how we",
|
||||
"are going to do things, but you just need to know that",
|
||||
"that is agony. Let's do a usual differential",
|
||||
"equation approach. Steps one, two,",
|
||||
"three and four. Set up differential equation,",
|
||||
"find the particular solution, find the homogenous solution,",
|
||||
"add up the two and solve for the unknowns.",
|
||||
"It's a mantra. The four-step manta.",
|
||||
"Let's do it. Step one, write the DE.",
|
||||
"That's easy. We have done this before the RC",
|
||||
"circuit. It's RC dvc/dt+vc=vI.",
|
||||
"This is no different from what you got from what you got from",
|
||||
"your RC circuit with a step input, just that my input is VI",
|
||||
"cosine of omega t in this case. It is not just a DC voltage VI.",
|
||||
"Stare at that. Enjoy it while the going is",
|
||||
"easy. It's like traversing rapids,",
|
||||
"and before you come to a class five, you have calm and raging",
|
||||
"waters there, you kind of sit there saying",
|
||||
"oh, the scenery around here looks really good and so on.",
|
||||
"All you are doing is stalling before you have dive down to",
|
||||
"class five. We will get to class five",
|
||||
"rapids in a few seconds here, so just enjoy this.",
|
||||
"RC dvc/dt+vC=vI. You've seen this before.",
|
||||
"Nothing fancy. Good old stuff.",
|
||||
"VI cosine of omega t. You want to hold onto your",
|
||||
"seatbelts? OK.",
|
||||
"Let's find the particular solution to the cosine input.",
|
||||
"Let's use our standard method. What I will do is just so,",
|
||||
"there is going to be so much crapola up there,",
|
||||
"so that I draw your attention to vP, which is what we are",
|
||||
"trying to get, I am just going to put a box",
|
||||
"around vP in red. If you see like all sorts of",
|
||||
"garbage appear, just look for the red square.",
|
||||
"That is what we are trying to get at.",
|
||||
"That's the equation. Let's try.",
|
||||
"First try, A worked before. A constant value A worked",
|
||||
"before for DC inputs. Let's try that again.",
|
||||
"If it worked then it may work now.",
|
||||
"If I use A, a constant value, and I substitute it here,",
|
||||
"I get dA/dt goes to zero, vP is A, but on the right-hand",
|
||||
"side I have VI cosine omega t. So clearly A doesn't work.",
|
||||
"Sorry. I struck out.",
|
||||
"Well, cosine omega t here, let's try A cosine omega T as",
|
||||
"my particular solution. Things are getting a little",
|
||||
"harder now, a little more painful.",
|
||||
"So substitute A cosine omega t here.",
|
||||
"So I do get A cosine omega T for vP, but out here I get RCA",
|
||||
"sine omega t times omega times minus one.",
|
||||
"So I have a sine and a cosine, and I have a cosine on the",
|
||||
"right-hand side. Sorry, it doesn't work.",
|
||||
"Nope, doesn't work either. Well, let's try A cosine omega",
|
||||
"t plus phi. We are now embarking into the",
|
||||
"rapids here. You can begin feeling the",
|
||||
"pressure. Just to refresh your memories",
|
||||
"of sines and cosines. A is the amplitude of the",
|
||||
"cosine. Omega is the frequency.",
|
||||
"Phi is the phase. Remember the signal I showed",
|
||||
"you earlier? If something happens to the",
|
||||
"amplitude of the sine, something happens to the phase.",
|
||||
"A cosine omega t plus phi. Let me plug it in here and go",
|
||||
"by standard practice. Here is what I get.",
|
||||
"I plug in A cosine omega t to this equation,",
|
||||
"and this is what I get. I differentiate it.",
|
||||
"I get omega out minus sine, sine of negative d plus phi,",
|
||||
"A cosine omega t plus phi equals VI cosine omega t.",
|
||||
"That might work. Now we get into the class six",
|
||||
"part of the class five. All class fives have a little",
|
||||
"bit of class six rapids. Remember, the rapids go up on",
|
||||
"an exponential scale so it like earthquakes.",
|
||||
"What I do now is expand out sine omega t plus phi,",
|
||||
"blah, blah, blah, it goes on and on.",
|
||||
"I could go on and on, but this is even tiring me.",
|
||||
"This can be made to work, but I am not sure I want to put",
|
||||
"all of us through this trig nightmare here.",
|
||||
"If I am really, really nasty I could give this",
|
||||
"to you as a homework assignment or something,",
|
||||
"but I am not that nasty so you won't see that.",
|
||||
"But if I go down this path it will get me to the answer,",
|
||||
"but I would have to soon negotiate class six,",
|
||||
"class seven rapids to get to where I want.",
|
||||
"So let me punt on it, let me start from scratch.",
|
||||
"I am at step two, let me start from scratch.",
|
||||
"Instead what I would like to do is let's get sneaky here.",
|
||||
"Rather than negotiating the class five rapids,",
|
||||
"what we can say is ah-ha, we can take our canoes and jump",
|
||||
"onto shore and run down and then get back onto the river.",
|
||||
"Let's do that. That is called the sneaky",
|
||||
"approach. So that all our friends who are",
|
||||
"behind us think we are negotiating the rapids,",
|
||||
"but what we are going to do is get sneaky and take the shore",
|
||||
"path. Let's get sneaky,",
|
||||
"just walk down the shore and see what is there.",
|
||||
"I want to do something completely weird here.",
|
||||
"I want to look at solving this equation through the shore",
|
||||
"method. S stands for shore or S stands",
|
||||
"for sneaky, whatever you want. What I am going to do is rather",
|
||||
"than trying to solve for VI cosine omega t.",
|
||||
"I am going to say let's try a different input all together.",
|
||||
"And you will understand why in a second.",
|
||||
"It's like I am the captain of my canoe and I tell my",
|
||||
"teammates, hey, let's not negotiate the rapids,",
|
||||
"let's go and explore the shore. Maybe down the shore we can",
|
||||
"find a path that gets us across to the other side more easily.",
|
||||
"So here is me and my colleagues carrying our canoe and getting",
|
||||
"onto shore and taking a sneaky path.",
|
||||
"This is not what I set out to solve.",
|
||||
"I don't know where this will lead me.",
|
||||
"But let's see where the shore path leads us.",
|
||||
"I want to try solving this equation Vie^st.",
|
||||
"S stands for shore or sneaky or whatever you want.",
|
||||
"I don't know where I am going, but let's see where this leads",
|
||||
"us. Let's explore.",
|
||||
"Make believe you are Columbus or something.",
|
||||
"I don't know. Let's use the usual techniques",
|
||||
"and see how this works out. Let's try a particular",
|
||||
"solution, Vpe^st. My input is Vie^st.",
|
||||
"I am trying to solve the circuit for a different input.",
|
||||
"And let me try solution Vpe^st and see if that works out",
|
||||
"nicely. I substitute Vpe^st into my",
|
||||
"equation here, so RCVpe^st blah blah blah.",
|
||||
"What I get here is Vie^st, Vpe^st stays the same,",
|
||||
"but here vP comes out, s comes out and e^st stays the",
|
||||
"same. That is nice property of",
|
||||
"exponentials. This is what I get.",
|
||||
"A really cool property of exponentials is that when I",
|
||||
"differentiate it I get the exponential back.",
|
||||
"Unlike a cosine I got a sine, and for a sine I got a cosine.",
|
||||
"Exponentials are very plain and simple, are straightforward.",
|
||||
"What you see is what you get. You differentiate it.",
|
||||
"You get the same thing, you get scaling vP,",
|
||||
"S and so on, and some scaling here.",
|
||||
"You get S scaling here, but the basic form stays the",
|
||||
"same. This is quite nice.",
|
||||
"I have e^st in all three places, so I can cancel those",
|
||||
"out and I get this expression. And I get this.",
|
||||
"Wow. So if I go down the shore I get",
|
||||
"some place fast. I don't know where I am yet,",
|
||||
"but whatever I did, it was easy.",
|
||||
"I am just exploring this path, down the shore path.",
|
||||
"I am making progress. I don't know where I have",
|
||||
"gotten yet. We will see where we got to in",
|
||||
"a second, but I got some place quickly, fast.",
|
||||
"I was able to solve for this input Vie^st and get this",
|
||||
"solution very quickly. So what happened here?",
|
||||
"I assumed the solution of the form Vpe^st, substituted it",
|
||||
"back, and found that if vP were equal to Vi/(1+sRC) then Vpe^st",
|
||||
"is a solution. What I have done here is that",
|
||||
"Vi/(1+sRC) is a particular solution to this equation for",
|
||||
"the input Vie^st. I put a box around it because",
|
||||
"this is important. This was easy.",
|
||||
"We went down the shore, and said let's try this other",
|
||||
"input. We made rapid progress on shore",
|
||||
"and I got some place. I don't know where I am yet.",
|
||||
"I got this. Let me pause here and let me",
|
||||
"give you the final answer. I am going to show you over the",
|
||||
"next five minutes that this is our answer.",
|
||||
"You are staring at the answer already.",
|
||||
"I am a party, I have taken a shore path and",
|
||||
"we have gotten some place. We see the river there,",
|
||||
"so it turns out we are exactly where we want to be,",
|
||||
"just after the rapids. All I have to do now is get my",
|
||||
"colleagues into the river with myself in the canoe and we are",
|
||||
"done. You don't know that yet.",
|
||||
"My colleagues and I are sitting on the shore looking at the",
|
||||
"river. We've gotten some place.",
|
||||
"There are no rapids there. We have gotten some place.",
|
||||
"We don't quite know is this just after the rapids or not.",
|
||||
"We don't know yet, but I got there very quickly.",
|
||||
"And I will tell you right now, that is the place we wanted to",
|
||||
"go to. The next five view graphs I am",
|
||||
"going to blast through. There is going to be more pain",
|
||||
"and agony to show you why that is the case.",
|
||||
"It's me thinking I am Columbus and proving to my colleagues",
|
||||
"that this is where we want to be.",
|
||||
"And pulling out my sextant, and the compasses and so on",
|
||||
"that cartographers and people use to prove to my colleagues",
|
||||
"that this is where I want to be. This is the answer.",
|
||||
"The next five view graphs will be demonstrating that this is",
|
||||
"indeed the answer, or close enough to the answer",
|
||||
"that we will be satisfied. Isn't this spectacular?",
|
||||
"I am going to show you in about five minutes that this gives us",
|
||||
"all the information we need to know to compute the sinusoidal",
|
||||
"steady-state response to this differential equation.",
|
||||
"Let me write that down here just so you know.",
|
||||
"",
|
||||
"Just so you remember. I am going to put a marker on",
|
||||
"the shore that says this is where we are right now.",
|
||||
"Now let me prove to you. As I just said,",
|
||||
"vPS is Vi, it's this stuff here multiplied by e^st is the",
|
||||
"solution to Vie^st. This guy here is a solution for",
|
||||
"Vie^st and vP is simply the coefficient that multiplies",
|
||||
"e^st. Similarly, if I substitute S",
|
||||
"equals j omega. I told you five view graphs of",
|
||||
"more hell, but I am just going to prove to you that this is it.",
|
||||
"I am substituting S equals j omega.",
|
||||
"This is Columbus giving a big speech at the end convincing his",
|
||||
"colleagues that we are where we want to be.",
|
||||
"I substitute j omega for S and this is what I get.",
|
||||
"This is a solution for e to the st, and so this is a solution",
|
||||
"for e to the j omega t. And let me mark this for you as",
|
||||
"something to remember. Vi/(1+j omega RC).",
|
||||
"In terms of that, I am substituting j omega for",
|
||||
"S. And this is a complex number.",
|
||||
"It is a complex amplitude. It is a complex number because",
|
||||
"of j here, and it multiplies e to the j omega t.",
|
||||
"Just keep this in mind. So that was easy.",
|
||||
"The steps were easy. I am still proving to you that",
|
||||
"this is where we want to be. Now let me draw the connection",
|
||||
"back to vP. And the first fact was that",
|
||||
"finding the response to Vie^(j omega t) was easy.",
|
||||
"We know that. Second was the following",
|
||||
"observation that Vi cosine omega t is simply the real part of",
|
||||
"this number here. So Vi cosine omega t is simply",
|
||||
"the real part of Vie^(j omega t) from the Euler relation.",
|
||||
"So cosine omega t is simply the real part of this guy.",
|
||||
"Light bulbs beginning to go off?",
|
||||
"The first fast was that finding the response to Vie^(j omega t)",
|
||||
"was easy. And the response was this,",
|
||||
"right? Times e to the j omega t.",
|
||||
"That was easy. All right.",
|
||||
"And the second part is that the real part of this is Vi cosine",
|
||||
"omega t was our input. Draw the connection between two",
|
||||
"steps. Finding the response to Vie^(j",
|
||||
"omega t) was easy. The real part of that was the",
|
||||
"input we cared about. Are light bulbs going off?",
|
||||
"Let me draw you a little picture here to show you what is",
|
||||
"happening. Response to vI is vP.",
|
||||
"It's the particular response we are looking for.",
|
||||
"Remember the red square? But we threw in a sneaky input",
|
||||
"vIS and we formed the response vPS to that.",
|
||||
"This step was easy. This step was hard.",
|
||||
"vI to vP was hard, trig nightmare,",
|
||||
"remember? But vIS to vPS was easy.",
|
||||
"It was a simple Vpe^st thing. We also know that the real part",
|
||||
"of vIS is vI. The real part of this is simply",
|
||||
"vI. If you have a real circuit,",
|
||||
"if you have a real linear circuit, for a linear circuit,",
|
||||
"if the real part of this gives me vI then the real part of the",
|
||||
"solution should give me vP. So computing vPS was easy.",
|
||||
"If I take the real part of this, I take the corresponding",
|
||||
"real part of this. This is sort of an inverse",
|
||||
"superposition argument. Superposition,",
|
||||
"I said, take the response for A, take the response for B,",
|
||||
"add them up and you get the response for A plus B.",
|
||||
"Here what we are saying is that get the response to A plus B,",
|
||||
"or to A plus jB and the real part of the input will produce",
|
||||
"the response given by the real part of the output.",
|
||||
"So this is an inverse superposition argument.",
|
||||
"If it is a linear circuit, then if vI is the real part of",
|
||||
"this sneaky input then I find the response to the sneaky input",
|
||||
"and take its real part I should get vP.",
|
||||
"Here I am, Columbus, staring down at the entrance to",
|
||||
"this part of the river. I just proved to my colleagues",
|
||||
"that all we have to do is take the real part of what we have.",
|
||||
"We can just jump right back into the river and get back to",
|
||||
"vP. And what I am going to do next",
|
||||
"is just grind through the math and just show you that.",
|
||||
"I will just blast through it. It is not important,",
|
||||
"but you have it in your notes. I am telling you that vP is",
|
||||
"simply the real part of the sneaky output.",
|
||||
"And I take the real part of vP e to the j omega t.",
|
||||
"And I take the real part. And just a bunch of math here.",
|
||||
"I am just taking the real part and doing a bunch of complex",
|
||||
"math. Remember vP was given by this",
|
||||
"quantity here. And I take the real part and I",
|
||||
"end up with vP is simply this quantity multiplied by cosine",
|
||||
"omega t plus phi, where phi is given by is given",
|
||||
"by tan inverse of omega RC, and this is the coefficient",
|
||||
"multiplying the cosine. So by taking the sneaky path",
|
||||
"and then taking the real part of that output answer,",
|
||||
"I was able to very quickly get to where I wanted to be.",
|
||||
"So from here to here it is only math.",
|
||||
"Recall, that vP, the thing in the red was what",
|
||||
"we set out to find out, which was the particular",
|
||||
"response to VI cosine of omega t.",
|
||||
"And remember that two grunge is all of this stuff.",
|
||||
"I am going to blast through two or three more view graphs that",
|
||||
"just give you more insight and more math, nothing particular.",
|
||||
"And remember to solve the equation we have to find a",
|
||||
"homogenous solution, too.",
|
||||
"But recall that the homogenous solution for an RC circuit is of",
|
||||
"the form Ae^-t/RC. This means that as time becomes",
|
||||
"very large this part goes to zero.",
|
||||
"As time becomes large in the steady state,",
|
||||
"remember I care about the steady state?",
|
||||
"This goes to zero. I don't care about the",
|
||||
"homogenous solution. Isn't that fantastic?",
|
||||
"Most the circuits we will deal with, except for purely",
|
||||
"oscillatory ones, the homogenous part dies away.",
|
||||
"You have something like e to the -t whatever.",
|
||||
"It just dies away. It's gone.",
|
||||
"So the total solution has vH going away.",
|
||||
"And what I end up with is just vP.",
|
||||
"My total solution in the steady state is simply vP.",
|
||||
"And A is given by this that we just calculated.",
|
||||
"I just have a bunch more insight that I talk about that",
|
||||
"you can look through in your notes.",
|
||||
"And I just want to show you a very quick summary.",
|
||||
"In summary, what we have is we computed vP.",
|
||||
"It was a complex coefficient. And all these steps,",
|
||||
"2 grunge, 3 and 4 were a waste of time.",
|
||||
"And what I showed you was that for the input VI the coefficient",
|
||||
"vP was complex. And I can take the ratio and",
|
||||
"represent it in this manner as well.",
|
||||
"And from vP, I can then compute the",
|
||||
"multiplier for the cosine as follows.",
|
||||
"I divide by vP here. Remember the cosine was",
|
||||
"multiplied by, in the mathematical step that I",
|
||||
"did, VI divided one plus, this stuff here,",
|
||||
"so I could get the magnitude and phase of the transfer",
|
||||
"function of this circuit in the following manner.",
|
||||
"And to wrap up very quickly, I am going to cover this again",
|
||||
"the next time and show you a magnitude plot.",
|
||||
"Notice here that if I plot Vp/Vi.",
|
||||
"Remember this was Vp here. That's the answer.",
|
||||
"The magnitude looks like this. On a log scale Vp/Vi for small",
|
||||
"frequencies omega is at one, but as omega increases Vp/Vi",
|
||||
"keeps decreasing. That is the output.",
|
||||
"Remember Vp was the amplitude of the output?",
|
||||
"That keeps decreasing. And this is the reason why.",
|
||||
"As I increase the frequency, the amplitude of my output",
|
||||
"cosine kept decreasing. I could also plot the phase for",
|
||||
"you. And the phase,",
|
||||
"in the same manner as omega increased, my phase also kept",
|
||||
"shifting from zero initially to pi/2 finally.",
|
||||
"Let me stop here and start with this the next time and revisit",
|
||||
"this. Unfortunately,",
|
||||
"I won't have time for the demo. I will show it to you next",
|
||||
"time."
|
||||
]
|
||||
}
|
||||
@@ -1,1967 +0,0 @@
|
||||
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"text": [
|
||||
"So today we are going to talk about another process of lumping",
|
||||
"or another process of discretization what will lead to",
|
||||
"the digital abstraction. So today's lecture is titled",
|
||||
"\"Go Digital\". So let me begin with a usual",
|
||||
"review. And so in the first lecture we",
|
||||
"started out by looking at elements and lumping them.",
|
||||
"For example, we took an element and said for",
|
||||
"the purpose of analyzing electrical properties let's lump",
|
||||
"this element into a single lumped value called a resistor,",
|
||||
"R. And this led to the lumped",
|
||||
"circuit abstraction. The lumped circuit abstraction",
|
||||
"says let's take these elements, connect them with wires and",
|
||||
"analyze the properties of these using a sort of analysis",
|
||||
"technique.",
|
||||
"",
|
||||
"So a set of a methods. We've looked at the KVL,",
|
||||
"KCL method. Another example of a method we",
|
||||
"looked at was the node method. And of this category there is",
|
||||
"one method you should remember, which you can apply to every",
|
||||
"single circuit and it will simply work, is the node method.",
|
||||
"For linear circuits other methods also apply,",
|
||||
"and these include superposition,",
|
||||
"Thevenin method, and in recitation or in your",
|
||||
"course notes you would have looked at the Norton method.",
|
||||
"So that's what we did so far. So this is a toolkit.",
|
||||
"So now you have a utility belt with a bunch of tools in it,",
|
||||
"and you can draw from those tools.",
|
||||
"And, just like any good carpenter, you know,",
|
||||
"the carpenter has to cut a piece of wood.",
|
||||
"He could use a chisel. He could use a saw.",
|
||||
"He could use an electric saw. And the reason you pay",
|
||||
"carpenters $80 an hour in the Boston region is because they",
|
||||
"know which tool to use for what job.",
|
||||
"So what we'll learn today is, so this was one process of",
|
||||
"discretization. We discretized matter.",
|
||||
"This gave us the discipline here that we decided to follow,",
|
||||
"lumped matter discipline, that moved us from Maxwell's",
|
||||
"equations into this new playground called EECS.",
|
||||
"Where all elements looked like these rinky-dinky little values",
|
||||
"like resistors and voltage sources and so on.",
|
||||
"What we'll do today, if that wasn't simple enough,",
|
||||
"let's simplify our lives even further.",
|
||||
"What we're going to do is lump some more.",
|
||||
"So what else can we lump? We've lumped matter,",
|
||||
"so all matter is taken care of. So what can we lump to make",
|
||||
"life even easier? When in doubt,",
|
||||
"if things are complicated, discretize it or lump it,",
|
||||
"right? So what do you think?",
|
||||
"What we will do today is lump signal values.",
|
||||
"",
|
||||
"So we'll just deal with lumped values.",
|
||||
"And this will lead to the digital abstraction.",
|
||||
"",
|
||||
"And the related reading is Chapter 5 of the course notes.",
|
||||
"",
|
||||
"So before we do this kind of lumping, let me motivate why we",
|
||||
"do this. One reason is to simplify our",
|
||||
"lives, but there is no need to just go around simplifying",
|
||||
"things just because we can. Let's try to see if there are",
|
||||
"other reasons motivating the digital abstraction.",
|
||||
"So what I would like to start with is a simple example of a",
|
||||
"analog processing circuit that you should now be able to",
|
||||
"analyze. So I'm going to be motivating",
|
||||
"digital. So let's start with an analog",
|
||||
"circuit that looks like this, two resistors,",
|
||||
"R1 and R2. And what I'm going to do is",
|
||||
"apply a voltage source here, V1, apply another one here,",
|
||||
"V2, and make this connection. And let me call this voltage V",
|
||||
"nought and call this my output. This voltage with respect to",
|
||||
"ground node, rather than drawing this wire here,",
|
||||
"I often times draw a ground here and simply throw ground",
|
||||
"wherever I want. This symbol simply refers to",
|
||||
"the fact that the other terminal is taken at the ground node.",
|
||||
"So here is my V nought. Now, let's go and analyze this",
|
||||
"and see what it gives us. In this example,",
|
||||
"V1 and V2 may be outputs of two sensors, maybe heat sensors or",
|
||||
"something like that. This is a heat sensor on that",
|
||||
"side of the room and this is a heat sensor on this side of the",
|
||||
"room. And I pass their signals",
|
||||
"through two resistors and I look at the voltage there.",
|
||||
"So by now you should be able to write the answer V nought,",
|
||||
"or the value V nought almost by inspection.",
|
||||
"Just to show you, let me use superposition.",
|
||||
"When you see multiple sources, the first thing you should",
|
||||
"think about is can I use superposition to simplify my",
|
||||
"life? And let me do that.",
|
||||
"V nought here is the sum of two voltages, one due to V1 acting",
|
||||
"alone and one due to V2 acting alone.",
|
||||
"So what's the voltage here due to V1 acting alone?",
|
||||
"To find out that I short this voltage, I zero out this voltage",
|
||||
"and look at the effect of V1. So the effect of V1,",
|
||||
"if this were shorted out, is simply V1 x R2 / R1 + R2.",
|
||||
"This is now a voltage divider, right?",
|
||||
"A voltage V applied across two resistors and the output taken",
|
||||
"across one resistor. So that's this value.",
|
||||
"Then I could do the second part.",
|
||||
"To look at the effect of V2, what I will do is short this",
|
||||
"voltage and look at the effect of this.",
|
||||
"Now, this voltage is across this resistor divider.",
|
||||
"And so I get R1 / (R1 + R2) here.",
|
||||
"So you'll notice that for something like this,",
|
||||
"if I had applied KVL and KCL of the node method I would have",
|
||||
"gotten a bunch of equations, but here I wrote it just by",
|
||||
"inspection. You should be able to look at",
|
||||
"circuit patterns like this and write the answers down very",
|
||||
"quickly. Let's say if I chose R1 to be",
|
||||
"equal to R2 then V nought would simply be (V1 + V2) / 2.",
|
||||
"So if these two values were equal, I simply get the output,",
|
||||
"the average of the two voltages.",
|
||||
"So this guy is an adder circuit.",
|
||||
"It adds up these two voltages. But more precisely it's an",
|
||||
"averaging circuit. It takes two voltages and gives",
|
||||
"me the average value. Now, if you have two sensors in",
|
||||
"the room, you might think of why you want to take that average",
|
||||
"value to control the temperature of the room.",
|
||||
"But suffice it to say that V nought is the average of the two",
|
||||
"values. So let me show you a quick demo",
|
||||
"of this example and then look at what the problems are with this",
|
||||
"example. So let's say,",
|
||||
"as one example, I applied a square wave at V1,",
|
||||
"which is the top curve, the green curve,",
|
||||
"and I applied a triangular wave at V2, that's the second one.",
|
||||
"As you expect, the output is going to be the",
|
||||
"sum of the two voltages scaled appropriately.",
|
||||
"So notice that I have a square wave with a superimposed",
|
||||
"triangular wave on top. And I can play around.",
|
||||
"What I could do is change the amplitude of my wave form here.",
|
||||
"And, as you notice, the amplitude of the output",
|
||||
"component also changes accordingly.",
|
||||
"So this is one simple example of an adder circuit,",
|
||||
"and the two wave forms get summed up and I get the output.",
|
||||
"So I'll switch to Page 3. Let me just draw a little",
|
||||
"sketch for you here. Here, what I showed you was I",
|
||||
"had a triangular wave coming on one of these inputs and I had a",
|
||||
"square wave on the other one, and the output looks something",
|
||||
"like this.",
|
||||
"",
|
||||
"OK? No surprise here.",
|
||||
"This is a simple analog signal processing circuit which gives",
|
||||
"me the average of two wave forms.",
|
||||
"Now, let me do the following. Often times I may need to look",
|
||||
"at this value some distance away.",
|
||||
"So let's say this person here wants to look at the value.",
|
||||
"So I bring this wire here. And I also bring the ground",
|
||||
"connection and I look at it. I look at this value here.",
|
||||
"And when I have a long wire I can get noise added onto the",
|
||||
"circuit. So let's say a bunch of noise",
|
||||
"gets added into the signal there.",
|
||||
"And what I end up seeing here is not something that looks like",
|
||||
"this but something that looks like that.",
|
||||
"That's not unusual. And the problem with this is",
|
||||
"now when I look at this, if I'm looking to distinguish",
|
||||
"between, say, a 3.9 and a 3.8,",
|
||||
"it's really hard to do that because my noise is overwhelming",
|
||||
"my signal. I have a real problem,",
|
||||
"a real problem here. Noise is a fact of life.",
|
||||
"So what do we do? This is so fundamental.",
|
||||
"Large bodies of courses in electrical engineering are",
|
||||
"devoted to how do I carefully analyze signals in the presence",
|
||||
"of noise? You'll take courses in speech",
|
||||
"processing that look at clever techniques to recognize speech",
|
||||
"in the presence of noise and so on and so forth.",
|
||||
"One technique we adopt that we'll talk about here,",
|
||||
"which is fundamental to EECS, is using the digital",
|
||||
"abstraction. Let me show you how it can",
|
||||
"really help with the noise problem.",
|
||||
"So the idea is value lumping or value discretization.",
|
||||
"Much like we lumped matter, we've discretized matter into",
|
||||
"discrete chunks, let's discretize value into two",
|
||||
"chunks. Let's simply say that now I'm",
|
||||
"going to deal with two values and I can, say,",
|
||||
"call them high, low.",
|
||||
"I have a bunch of choices here. I may call it 5 volts and 0",
|
||||
"volts. I may call it true and false.",
|
||||
"What I'm doing is I'm just restricting my universe to deal",
|
||||
"with just two values, zero and one.",
|
||||
"This is like dealing with a number system with only two",
|
||||
"digits. And these are zero and one.",
|
||||
"So what I've now done is I'm saying that rather than dealing",
|
||||
"with all possible continuous values, 0.1, 3.9999 recurring",
|
||||
"and so on and so forth, what I'm going to do is simply",
|
||||
"deal with a high and a low. Dealing with this whole",
|
||||
"continuum of numbers is really complicated.",
|
||||
"Let me simplify my life and just postulate that I am going",
|
||||
"to be looking at high and low. Whenever I see something I'll",
|
||||
"look at it and say high or low, is it black or white,",
|
||||
"period. There's no choice here,",
|
||||
"just two individual values. So that sounds simple,",
|
||||
"and nice and so on, but what's the point?",
|
||||
"What do we get by doing that? Let's take our example.",
|
||||
"Let's take what might be a digital system.",
|
||||
"Let's take a digital system and let's say I have a sender.",
|
||||
"Much like I sent a signal value a long distance,",
|
||||
"let me have a sender, and I have a ground as well and",
|
||||
"here is a receiver. This symbol simply says that",
|
||||
"both of them share a ground wire.",
|
||||
"So the sender and a receiver. And what I'm interested in",
|
||||
"doing, the sender is interested in sending a signal to the",
|
||||
"receiver. And in the digital system,",
|
||||
"the way I would send a digital signal is all I can use is ones",
|
||||
"and zeros, OK? So let's say the sender sends",
|
||||
"something like this. The sender wants to send a",
|
||||
"value. This is my time axis and this",
|
||||
"is 2.5 volts, this is 0 volts and this is 5",
|
||||
"volts. My sender has some agreement",
|
||||
"with the receiver and says I'm just going to be sending to you",
|
||||
"low values and high values. And this signal here would",
|
||||
"correspond to \"0\" \"1\" \"0\". It's a symbol.",
|
||||
"That's why I have input zero in quotes there.",
|
||||
"We'll go into this in much more detail later,",
|
||||
"but for now suffice it to say that I'm sending a set of",
|
||||
"signals here \"0\" \"1\" \"0\". This simplistic scheme will not",
|
||||
"work in many situations but go along with this for a few",
|
||||
"seconds. So I send the signal sequence",
|
||||
"\"0\" \"1\" \"0\" out here. And notice that there is a high",
|
||||
"and a low. And the agreement the sender",
|
||||
"and the receiver have is that, look, if you see a value that's",
|
||||
"higher than 2.5 volts that's a high.",
|
||||
"If you see a value below 2.5 volts in the wire that's a low.",
|
||||
"And I'm going to send a 0 volt and a 5 volt from here.",
|
||||
"So now at the sending site let's say I don't have any noise",
|
||||
"in this system. Let's say this is my Vn,",
|
||||
"some noise being added. And let's say Vn is 0.",
|
||||
"Then in that case I will receive exactly what is sent \"0\"",
|
||||
"\"0\" 5, 2.5, 0 volts. And this is time.",
|
||||
"Nothing fancy here, right?",
|
||||
"My receiver receives a \"0\" \"1\" \"0\".",
|
||||
"Now, the beauty of this is that now suppose I were to impose",
|
||||
"noise much like I had noise out there and Vn was not 0.",
|
||||
"Rather Vn was some noise voltage, let's say 0.2 volts",
|
||||
"peak to peak. Let's say that simply got",
|
||||
"superposed on the signal. In which case what do I get?",
|
||||
"What I end up here with is a signal that looks like this.",
|
||||
"So the receiver gets that signal because a noise is added",
|
||||
"into my signal and that's what I get.",
|
||||
"But guess what? No problem.",
|
||||
"The receiver says oh, yeah, this is a 0 because the",
|
||||
"values are less than 2.5, this is a 1 and this is a 0.",
|
||||
"\"0\" \"1\" \"0\". So here my receiver was able to",
|
||||
"receive the signal and correctly interpret it without any",
|
||||
"problems. So because I used this value",
|
||||
"discretization and because I had this agreement with the",
|
||||
"receiver, I had better noise immunity.",
|
||||
"",
|
||||
"Consequently, I had what is called a noise",
|
||||
"margin. Noise margin says how much",
|
||||
"noise can I tolerate? And in this situation,",
|
||||
"because the sender sends 5 volts and 0 volts,",
|
||||
"the 5 volts can creep all the way down to 2.5,",
|
||||
"I'll still be OK. Similarly, 0 could go all the",
|
||||
"way up to 2.5, I'd still be OK.",
|
||||
"So in this case I have a noise margin of 2.5 volts for a 1 and",
|
||||
"similarly 2.5 volts for a 0, because there are 2.5 volts",
|
||||
"between a 0 volt and 2.5. So notice that I have a nice",
|
||||
"little noise margin here, which simply is the English",
|
||||
"meaning of the term there is a margin for noise.",
|
||||
"And even though I can change the signal value by up to 2.5",
|
||||
"volts, the receiver will still correctly interpret the signal.",
|
||||
"So I've decided to discretize values into highs and lows.",
|
||||
"And because of that, if all I wanted to do in life",
|
||||
"is send highs and lows I can send them very effectively.",
|
||||
"There are many complications, but if all I care about is",
|
||||
"sending highs and lows I can send it with a lot of tolerance",
|
||||
"to noise. So many of you are saying but",
|
||||
"what about this, but what about that?",
|
||||
"There are lots of buts here. And let's take a look at some",
|
||||
"of them. If you look up there.",
|
||||
"What I ended up doing was creating a design space that",
|
||||
"looked like this. This is on Page 6.",
|
||||
"What I did was I said with a range of values from 0 to 5,",
|
||||
"what I'm going to do is at 2.5 I drew a line and I said as a",
|
||||
"sender if you wanted to send a 0 then you would send a value",
|
||||
"here. And if you wanted to send a 1",
|
||||
"you would send a value here. Similarly, for a receiver.",
|
||||
"And if the sender sent a value all the way up in 5 volts that",
|
||||
"was the best thing, but technically the sender",
|
||||
"could send any value between 2.5 and 5.",
|
||||
"And if there was no noise then the receiver could correctly",
|
||||
"interpret a 1 if it was above this and 0 if it was below this.",
|
||||
"The problem with this approach really is that if I allow the",
|
||||
"sender to send any value above 2.5 all the way to 5 then there",
|
||||
"really is no noise margin in this situation.",
|
||||
"",
|
||||
"OK? Because if I allowed the sender",
|
||||
"to send any value between 2.5 and 5 then what if I have a",
|
||||
"value 2.5 for a 1? Then I may end up getting very",
|
||||
"little noise margin on the other side.",
|
||||
"Worse yet, what if I get a value 2.5?",
|
||||
"That's a much worse situation. What if the receiver receives a",
|
||||
"value of 2.5? Now what?",
|
||||
"What does the receiver do? The receiver cannot tell",
|
||||
"whether it's a 1 or a 0. The receiver gets hopelessly",
|
||||
"confused. So to deal with that,",
|
||||
"I'm going to fix this, what I'm going to do is the",
|
||||
"following. Switch to Page 7.",
|
||||
"What I'll do here is to prevent the receiver from getting",
|
||||
"confused, if the receiver saw 2.5, what I'm going to do is",
|
||||
"define what is called \"no man's land\".",
|
||||
"I'm going to define the region of my voltage space called the",
|
||||
"forbidden region. And what I'm going to do is,",
|
||||
"say, let's say I defined it as 2 volts, 3 volts and 5 volts,",
|
||||
"0, 2, 3 and 5. With my forbidden region,",
|
||||
"if I have a sender then I tell the sender you can send any",
|
||||
"value between 3 and 5 for a 1. And you can send any value",
|
||||
"between 2 and 0 for a 0. To send the symbol 0,",
|
||||
"I can send any voltage between 0 and 2, and similarly for 1.",
|
||||
"At the receiving side, if I see any value between 3",
|
||||
"and 5, I read that as a 0, and any value between 0 and 2 I",
|
||||
"read that as 2 volts. So I may label this value VH",
|
||||
"and label this threshold VL, so there's a high threshold and",
|
||||
"a low threshold. So this solves one problem.",
|
||||
"Now the receiver can never see a value in the forbidden region.",
|
||||
"Now, I can stand her and pontificate and say,",
|
||||
"oops, that's a forbidden region, thou shalt not go there.",
|
||||
"But what if I get some noise and a value goes in there?",
|
||||
"In real systems values may enter there.",
|
||||
"But what I'm saying, so this is the beauty of using",
|
||||
"a discipline. Let me use my playground",
|
||||
"analogy. This is my playground.",
|
||||
"We got into this playground using the discrete matter of",
|
||||
"discipline, the playground of EECS, but in that playground",
|
||||
"some region of that playground deals with just high and low",
|
||||
"values. I further restrict the",
|
||||
"playground and I say I'm only going to focus on that",
|
||||
"playground in which all signal values have a forbidden region.",
|
||||
"All senders and receivers adhere to a forbidden region.",
|
||||
"And if there is any signal in this space, in the forbidden",
|
||||
"space then my behavior is undefined.",
|
||||
"I don't care. You want to go there?",
|
||||
"Sure. I don't know what's going to",
|
||||
"happen to you. Now, we're engineers,",
|
||||
"right? So we've disciplined ourselves",
|
||||
"to play in this playground. It's like I tell my 9-year-old,",
|
||||
"don't go there, right?",
|
||||
"And of course he wants to go there.",
|
||||
"He says what will happen if I go there?",
|
||||
"And the answer here will be undefined, OK?",
|
||||
"Something really bad could happen to you.",
|
||||
"I don't know what it is but something really bad,",
|
||||
"you know, a lightening bolt or who knows what,",
|
||||
"but something really bad. And you as a designer of a",
|
||||
"circuit can, let's say you were Intel.",
|
||||
"Intel designs its chips. And let's say Intel decides to",
|
||||
"play in this playground and there is a forbidden region.",
|
||||
"So Intel says oh, it's really easy for me if in",
|
||||
"the forbidden region the chip simply burns up and catches",
|
||||
"fire, we'll sell more chips. That's fine.",
|
||||
"Whatever you want. The key here is that all I'm",
|
||||
"saying is that I am going to discipline myself into playing",
|
||||
"in this playground and that's where I will define my rules,",
|
||||
"and you stay within the boundaries and all the rules",
|
||||
"will apply. It's called a \"discipline.\"",
|
||||
"You're disciplining yourselves to stay within it.",
|
||||
"There's no logic to it. It's just a discipline.",
|
||||
"Just do it and you'll be OK. When we look at practical",
|
||||
"circuits and so on, we have to address the issue of",
|
||||
"what happens when things go in there.",
|
||||
"But let's postpone that discussion.",
|
||||
"For now I've solved one of my problems, which is,",
|
||||
"the previous problem was what does a receiver do if it saw a",
|
||||
"2.5? Now it can't see a 2.5.",
|
||||
"But then the receiver asks, Agarwal, but what if I see a",
|
||||
"2.5? I can tell the receiver you can",
|
||||
"do whatever you want to do. You can stomp it.",
|
||||
"You can squish it. You can burn it.",
|
||||
"You can chuck it. Whatever you want.",
|
||||
"It's up to you. Do whatever you want.",
|
||||
"You won't see a value. If you do, do whatever you",
|
||||
"want. It's undefined.",
|
||||
"That works. So you, as the receiver",
|
||||
"designer can do whatever you want when you see a 2.5.",
|
||||
"You can say yeah, I'll just put out a 1 if I see",
|
||||
"a 2.5 or a 2.6. I'll just do something.",
|
||||
"No one cares. So this is pretty good.",
|
||||
"This is pretty good. We still have a problem,",
|
||||
"though. Do people see the problem here?",
|
||||
"This still doesn't quite work. If Intel did this,",
|
||||
"instead of your laptops failing and blue-screening every hour",
|
||||
"they'd be doing it every millisecond.",
|
||||
"So the problem is this discipline have allowed the",
|
||||
"sender to send any value between 3 and 5 as a 1.",
|
||||
"And any value between 3 and 5 at the receiver is treated as a",
|
||||
"1. Do you see where the problem",
|
||||
"is? Yes?",
|
||||
"The sender sends a 1.99 and the noise pumps it into forbidden",
|
||||
"region. Exactly.",
|
||||
"So the sender says it's legitimate, I'm Intel.",
|
||||
"They've told me stick to 0 and 2.",
|
||||
"And Intel parts will be sending to values between 0 and 2.",
|
||||
"And Motorola parts, which are receivers,",
|
||||
"you know they have to receive 0 and 2.",
|
||||
"So Intel can send the value, 2.",
|
||||
"They can because it's 1.9 out of 2.",
|
||||
"It's legal. This way I can make really",
|
||||
"cheap parts. But now the problem is that",
|
||||
"even the smallest amount of noise will bump it into the",
|
||||
"forbidden region, and so therefore this one has a",
|
||||
"problem. And the problem is that this",
|
||||
"one offers zero noise margin. There is no noise margin.",
|
||||
"There is no margin for noise in the discipline.",
|
||||
"All right, back to the drawing board, folks.",
|
||||
"Switch to Page 8. Let's get rid of all this stuff",
|
||||
"and go back to the drawing board.",
|
||||
"",
|
||||
"OK, so what do we do now? How about the following?",
|
||||
"How, about as before I say, as a receiver,",
|
||||
"if you see a value between 3 and 5 you treat that as a 1 and",
|
||||
"a value between 0 and 2 you treat that as a 0.",
|
||||
"No difference. So as a receiver same as",
|
||||
"before. But now what I do is I hold the",
|
||||
"sender to tougher standards. I hold the feet of the sender",
|
||||
"to the fire and say you have to adhere to tougher standards.",
|
||||
"So what I'm going to do is hold the sender to tougher standards,",
|
||||
"maybe four walls. That is tell the sender that if",
|
||||
"you want to send to 0 or a 1, for a 1 you have to send a",
|
||||
"value between 4 and 5, and for a 0 a value between 0",
|
||||
"and 1. Sender is now held to tougher",
|
||||
"standards. This is what my chart looks",
|
||||
"like. So now I do have some noise",
|
||||
"margin. Can someone tell me what is the",
|
||||
"noise margin here for a 1? 1 volt.",
|
||||
"And the reason is that the lowest voltage a sender can send",
|
||||
"is 4 volts, OK? If the 4 leaks down to 2.99",
|
||||
"that's in the forbidden region, I'm in trouble.",
|
||||
"2.99. This is my forbidden region",
|
||||
"here. And 2.99 is in the forbidden",
|
||||
"region. I'm in trouble.",
|
||||
"So notice that the lowest value that the receiver can receive is",
|
||||
"3 volts. So if I sent the 4 and sent",
|
||||
"this over a long cable to you, the value can be beaten up by",
|
||||
"noise to such an extent that you may begin receiving 3s but",
|
||||
"nothing lower than a 3. So this is a noise margin,",
|
||||
"1 volt. Similarly, for a 0 the noise",
|
||||
"margin is also 1 volt. So let me label these.",
|
||||
"There are four important thresholds here.",
|
||||
"This threshold is called VOL. V output low.",
|
||||
"These have special meanings. This threshold here is called",
|
||||
"VOH, V output high. This threshold here is called V",
|
||||
"input high and this threshold here is called V input low.",
|
||||
"So VOH simply says that senders must send voltages higher than",
|
||||
"VOH. Receivers must receive values",
|
||||
"higher than VIH as a 1. So these four thresholds",
|
||||
"together give you your threshold.",
|
||||
"",
|
||||
"For the sender gets 2.5, what does sender do?",
|
||||
"It could do that. So, in that case,",
|
||||
"you can do that. If all you want to do is have",
|
||||
"one value here then what you have is an infinitesimal value",
|
||||
"here for the forbidden region. That's fine.",
|
||||
"It's up to you to design it that way.",
|
||||
"You can. But it turns out that when you",
|
||||
"design circuits, when we see some examples in",
|
||||
"the next lecture it turns out to be fairly practical and easy to",
|
||||
"do it this way. But, again, these are design",
|
||||
"choices. If I'm Intel,",
|
||||
"Intel wants all its parts to work together.",
|
||||
"So parts that follow a common discipline can work together,",
|
||||
"right? Because senders will send",
|
||||
"values, receivers will receive these values here,",
|
||||
"so it will simply work. So the noise margin for a 1",
|
||||
"here is simply VOH minus VIH and the noise margin for a 0 is VIL",
|
||||
"minus VOL. VIL minus VOL is the noise",
|
||||
"margin for a 0. So what do we have here?",
|
||||
"What we have here is a discipline that we've agreed to",
|
||||
"follow where senders are held to a tough standard and receivers",
|
||||
"are held to a different standard so that I allow myself some",
|
||||
"margin for error. And it's up to you as a",
|
||||
"designer to choose ranges for the forbidden region.",
|
||||
"Now, you may say that I want to make my forbidden region as",
|
||||
"small as possible. But you will see in practical",
|
||||
"circuits it's very hard to achieve that.",
|
||||
"Practical devices that you get, they have a natural region that",
|
||||
"gets very, very hard to break apart, and that tends to",
|
||||
"establish what that region looks like.",
|
||||
"So to continue with an example here, I may have the following",
|
||||
"voltage wave form for a sender. So I have some sender,",
|
||||
"I have a sender here.",
|
||||
"",
|
||||
"I have VOL, VIL, VIH, VOH and some other high",
|
||||
"voltage. And then, as a sender,",
|
||||
"if I want to send a \"0\" \"1\" \"0\" then I send a 0.",
|
||||
"I have to be within this band. And then for a 1 I have to be",
|
||||
"within this band. So this is an example of,",
|
||||
"say, \"0\" \"1\" \"0\" \"1\". And at the receiver --",
|
||||
"",
|
||||
"Let's have VOL, VIL, VIH, VOH.",
|
||||
"So at the receiver, I interpret any signal below",
|
||||
"VIL as a 0. So I may get some signal that",
|
||||
"looks like this.",
|
||||
"",
|
||||
"And I'll still interpret that as a \"0\" \"1\" \"0\" \"1\".",
|
||||
"So to summarize here, this discipline that forms the",
|
||||
"foundations of digital systems is called \"a static discipline\".",
|
||||
"",
|
||||
"The static discipline says if inputs meet input thresholds --",
|
||||
"So if an input to a digital system meets the input",
|
||||
"thresholds then outputs will meet, or the digital system",
|
||||
"should ensure that the outputs --",
|
||||
"",
|
||||
"Output thresholds. So this means that if I have a",
|
||||
"system like this then if I give it good inputs.",
|
||||
"And by giving it good inputs I mean for 1s I have signal values",
|
||||
"that are greater than VIH and for 0s signal values which are",
|
||||
"less than VIL. These are valid inputs.",
|
||||
"So if my inputs are valid, that is below VIL for a 0 and",
|
||||
"above VIH for a 1 then this digital system D will produce",
|
||||
"corresponding outputs that follow output thresholds.",
|
||||
"For a 1 it will produce outputs that are greater than VOH and if",
|
||||
"it needs to produce a 0 it will produce outputs that are less",
|
||||
"than VOL. So notice that there is this",
|
||||
"tough requirement in digital systems that for the inputs,",
|
||||
"I should recognize as a 1 anything higher than a VIH.",
|
||||
"But if I want to produce a 1, I have to produce a tough 1",
|
||||
"like a 4-volt 1. So there is a discipline that",
|
||||
"all my digital systems must follow, and that discipline is",
|
||||
"called a static discipline. So static discipline encodes",
|
||||
"the thresholds, encodes four thresholds that",
|
||||
"all digital systems must follow so that they can talk to each",
|
||||
"other. So if Intel and Motorola want",
|
||||
"to make parts that are compatible with,",
|
||||
"say, Pentium 4 devices then they will all talk over the",
|
||||
"phone or something and agree on a static discipline.",
|
||||
"We will say that, all right, all my peripherals",
|
||||
"will follow a static discipline with the following volted",
|
||||
"thresholds. And this way parts made by",
|
||||
"different manufacturers can interoperate and still provide",
|
||||
"immunity to noise. Yes.",
|
||||
"Question?",
|
||||
"",
|
||||
"Absolutely. There are many constraints on",
|
||||
"how you as a designer choose the noise margin.",
|
||||
"As a designer you want to make your noise margin as large as",
|
||||
"possible. The larger the noise margin the",
|
||||
"better you can tolerate noise which is why,",
|
||||
"how many people have heard of some devices called rad hard",
|
||||
"devices, radiation hard devices? Some of you have.",
|
||||
"There are a bunch of devices. Different manufacturers make",
|
||||
"different kinds of devices for different markets.",
|
||||
"For consumer markets they use parts which may have relatively",
|
||||
"poor noise margins because consumers can tolerate more",
|
||||
"faults. But if you're building devices",
|
||||
"for, say, the medical industry or for spaceships and so on,",
|
||||
"you need to be held to a much, much tougher standard.",
|
||||
"So for those devices you may end up having much,",
|
||||
"much tighter bands in which you have to operate so you have a",
|
||||
"tougher noise margin. So that leads us to,",
|
||||
"given these sort of voltage thresholds, we now move into the",
|
||||
"digital world. And in the digital world we can",
|
||||
"build a bunch of digital devices.",
|
||||
"The first device we will look at is called a combinational",
|
||||
"gate.",
|
||||
"",
|
||||
"A combinational gate is a device that adheres to the",
|
||||
"static discipline, Page 11, and this is a device",
|
||||
"whose outputs are a function of inputs alone.",
|
||||
"",
|
||||
"So I can build little boxes which take some inputs,",
|
||||
"produces an output where the outputs are a function of the",
|
||||
"existing inputs. And this kind of a device is",
|
||||
"called a combinational gate. And I can analyze such devices",
|
||||
"for the kinds of things that I would like to do.",
|
||||
"Before I go into the kinds of devices I'd like to build,",
|
||||
"let's spend a few minutes talking about how to process",
|
||||
"signals. How to process digital signals,",
|
||||
"Page 10. So notice that you have two",
|
||||
"values, 0 and a 1. So devices like my",
|
||||
"combinational gate, for example,",
|
||||
"can only deal with 0s and 1s. So I have to come up with some",
|
||||
"kind of a mathematics or some kind of a set of processing that",
|
||||
"can work with 0,1 values. So 0,1 map completely natural",
|
||||
"to the logic true and false. So I can borrow from logic and",
|
||||
"use true and false to do my processing of signals.",
|
||||
"So if all I care about is processing logic values,",
|
||||
"0s and 1s, trues and falses then that's all I need.",
|
||||
"I can also use numbers. How do I represent a number?",
|
||||
"3.9 which is 0s and 1s. It turns out that this is a",
|
||||
"whole field in itself. You'll hear more about this in",
|
||||
"recitation. Let me also point you to the",
|
||||
"last section of the course notes, Chapter 5.6 I believe,",
|
||||
"that talks about how to represent numbers.",
|
||||
"The basic insight is much like you can represent arbitrary long",
|
||||
"numbers with the digits 0 through 9 in the same way,",
|
||||
"but concatenating digits you can represent arbitrary long",
|
||||
"numbers with 0-1-1-1-0-0 and so on.",
|
||||
"So you can have a whole sequence of digits and you can",
|
||||
"build a binary number system. So you can read A&L Section",
|
||||
"5.6, I believe. It's the last section for",
|
||||
"numbers. And you will also discuss this",
|
||||
"in your recitation tomorrow. Let me spend some more time",
|
||||
"talking about Boolean logic, two-valued logic,",
|
||||
"and how to process these systems.",
|
||||
"So one way of processing it is using logic statements of the",
|
||||
"following form. If X is true and Y is true then",
|
||||
"Z is true, else is Z false. So this is a logic statement.",
|
||||
"It says if X is true and Y is true then Z is true,",
|
||||
"else Z is false. So I can process this with 0s",
|
||||
"and 1s, trues and falses. And I do this all the time so I",
|
||||
"have a succinct notation for this.",
|
||||
"I express this as Z is X anded with Y.",
|
||||
"X and Y is Z. So Z is true if X is true and Y",
|
||||
"is true. A shorthand notation for this",
|
||||
"is just a dot. And a circuit notation for this",
|
||||
"is called an \"AND gate\". That's a little circuit.",
|
||||
"I haven't told you what's inside it.",
|
||||
"It's an abstract little device called an AND gate which takes",
|
||||
"two inputs, produces one output Z where the output is related to",
|
||||
"the inputs in the following manner.",
|
||||
"That's a little device called an AND gate.",
|
||||
"I could also represent logic in truth tables.",
|
||||
"And truth tables simply enumerate all the values and the",
|
||||
"corresponding outputs. Inputs can be 0-0-0-1-1-0 or",
|
||||
"1-1. For an AND system output is 1,",
|
||||
"only if both are ones, it's a 0 otherwise.",
|
||||
"So that's a truth table for AND gate.",
|
||||
"So from 0s and 1s we deal with logic and we create devices like",
|
||||
"the AND gate to process digital signals.",
|
||||
"And what we will do is look at a whole bunch of little symbols",
|
||||
"like this, like the AND gate to process our input signals.",
|
||||
"And these devices might look like other functions like OR",
|
||||
"gates and so on. Let me show you a quick demo.",
|
||||
"What I'm going to show you is a signal feeding an AND gate.",
|
||||
"And one signal is going to look like this, and my signal Y is",
|
||||
"going to look like this. So you expect a processed",
|
||||
"output. So 1-0-1-0-1-0-1.",
|
||||
"And the output is simply going to be --",
|
||||
"This is my time axis going this way.",
|
||||
"It is going to be an AND-ing of these two signal values like so.",
|
||||
"What I'm also going to show you is I'm going to superimpose",
|
||||
"noise on this wire. I'm going to superimpose noise",
|
||||
"on the wire, and what I want you to observe is the output of this",
|
||||
"digital gate. The output will stay exactly",
|
||||
"like this, even though I impose noise.",
|
||||
"The ultimate test. So stay right there.",
|
||||
"Let's do this demo. Give me a couple of seconds.",
|
||||
"",
|
||||
"If you look at the signal up there, look at the middle wave",
|
||||
"form, and I'm imposing let's have a digital system in a noisy",
|
||||
"environment like a lumberyard, for example,",
|
||||
"or chopping a bunch of trees in my backyard and building digital",
|
||||
"systems on the side. And if I have my buddies",
|
||||
"revving up chainsaws superimposing noise on my second",
|
||||
"input, but look at the output. And just to show that I'm not",
|
||||
"bluffing here, what I'll do is I'll pass the",
|
||||
"noise through and make the noise larger.",
|
||||
"And you'll notice that when the noise begins to surpass the",
|
||||
"noise margins the output begins to go berserk.",
|
||||
"Watch. Can you increase it gradually?",
|
||||
"Notice that as I put in a lot more noise then the output",
|
||||
"begins to go berserk, but as long as my input is",
|
||||
"within the noise margin my output stays perfectly stable.",
|
||||
"So that's the \"Intro to Digital Systems\".",
|
||||
"You'll see numbers in recitation.",
|
||||
"And we'll see you at lecture on Tuesday."
|
||||
]
|
||||
}
|
||||
@@ -1,1607 +0,0 @@
|
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"text": [
|
||||
"Good morning, all. Good morning. I hope you guys did",
|
||||
"not spend all of last night celebrating the Red Sox victory,",
|
||||
"but there is one more tonight. OK. Let's see. I trust the quiz went",
|
||||
"OK. What I will do today is take off from where we left",
|
||||
"off on Tuesday. And continue our discussion of the",
|
||||
"large signal and small signal analysis of our amplifier.",
|
||||
"Today the focus will be on \"Small Signal Analysis\".",
|
||||
"So let me start by reviewing some of",
|
||||
"the material. And, as you know, our MOSFET amplifier",
|
||||
"looks like this.",
|
||||
"One of the things you will notice in circuits, as I have been mentioning",
|
||||
"all along in this course, is that certain kinds of patterns",
|
||||
"keep repeating time and time again. And this is one such pattern. A",
|
||||
"three terminal device like the MOSFET with an input and the drain",
|
||||
"to source port connected to RL and VS in series in the following manner,",
|
||||
"this is a very common pattern. There are several other common",
|
||||
"patterns. The voltage divider is a common pattern.",
|
||||
"We keep running into that again and again and again.",
|
||||
"The Thevenin form, a voltage source in series with the",
|
||||
"resistor is another very common form. The Norton equivalent form,",
|
||||
"which is a current source in parallel with a resistor is also",
|
||||
"very common. And it behooves all of us to be very familiar with the",
|
||||
"analyses of these things. Voltage dividers in particular are",
|
||||
"just so common that you need to be able to look at it and boom,",
|
||||
"be able to write down the expression for voltage dividers.",
|
||||
"I would also encourage you to go and look at current dividers.",
|
||||
"When you have two resistors in parallel and you have some current",
|
||||
"flowing into the resistors to find out the current in one branch versus",
|
||||
"the other very quickly. The expression is very analogous to",
|
||||
"the voltage divider expression. And some of these very common",
|
||||
"patterns are highlighted in the summary pages in the course notes,",
|
||||
"so it is good to keep track of those and be extremely familiar with those",
|
||||
"patterns to the point where if you see it you should be able to jump up",
|
||||
"and shout out the answer just by looking at it without having to do",
|
||||
"any math. So here was an amplifier. And then we noticed that when the",
|
||||
"MOSFET was in saturation it behaved like a current source.",
|
||||
"And this circuit would give us amplification while the MOSFET was",
|
||||
"in saturation. So we agreed to adhere to the",
|
||||
"saturation discipline which simply said that I was going to use my",
|
||||
"circuit in a way that the MOSFET would always remain in saturation in",
|
||||
"building things like amplifiers and so on. And by doing that throughout",
|
||||
"the analysis I could make the assumption that the MOSFET was in",
|
||||
"saturation. I didn't have to go through --",
|
||||
"Analysis became easier. I didn't have to figure out now,",
|
||||
"what region is the MOSFET in? Well, because of my discipline it is",
|
||||
"always going to be in saturation. But in turn what we had to do was",
|
||||
"conduct a large signal analysis.",
|
||||
"Again, in follow on courses you will be given circuits like this.",
|
||||
"In fact, this very circuit with a very high likelihood.",
|
||||
"And you will be looking at more complicated models of the MOSFET.",
|
||||
"Or you will be given the MOSFET like this and,",
|
||||
"let's say in that course the designers do not adhere to the",
|
||||
"saturation discipline, in which case you have to first",
|
||||
"figure out is my MOSFET in its triode region or in the saturation",
|
||||
"region? And depending on the region it is in you have to apply different",
|
||||
"equations. So it is one step more complicated than in 002.",
|
||||
"In 002 we simplified our lives by following a discipline.",
|
||||
"And let me tell you that following a discipline is quite OK.",
|
||||
"When it simplifies our lives and we can do good things with it,",
|
||||
"it is quite OK to do that. We are not wimps or anything like that.",
|
||||
"It is quite OK to have a discipline and agree that we are going to play",
|
||||
"in this region of the playground and build circuits in that manner.",
|
||||
"By doing so, we could assume the MOSFET was in saturation all the",
|
||||
"time. And analysis simply used a current source model.",
|
||||
"By the same token, what becomes important is to figure",
|
||||
"out what are the boundaries of valid operation of the MOSFET in",
|
||||
"saturation? To do that we conducted a large signal analysis.",
|
||||
"And it had two components to it. One of course was to figure out the",
|
||||
"output versus input response. And what this usually does is that",
|
||||
"it does a nonlinear analysis of this circuit.",
|
||||
"If it is a linear circuit it is a linear analysis.",
|
||||
"And figures out what the values of the various voltages and currents",
|
||||
"are in the circuit as a function of the applied inputs and chosen",
|
||||
"parameters. And the second step we said was to figure out valid",
|
||||
"operating ranges --",
|
||||
"-- for input and corresponding ranges for the other dependent",
|
||||
"parameters such as VO. You could also find out the",
|
||||
"corresponding operating range for the current IDS and so on.",
|
||||
"So by doing this you could first analyze the circuit,",
|
||||
"find out the \"bias\" parameters, find out the values of VI and VO and",
|
||||
"so on. And then you could say all right,",
|
||||
"provided, as long as VI stays within these bounds my assumption that this",
|
||||
"is in saturation will hold and everything will be fine.",
|
||||
"The reading for this is Chapter 8. And today we will take the next",
|
||||
"step and revisit small signal analysis. In the demo that I showed",
|
||||
"you at the end of last lecture, I showed you an input triangular",
|
||||
"wave. And the input triangular wave gave",
|
||||
"rise to an output. And we noticed that we did have",
|
||||
"amplification, I had a small input and a much",
|
||||
"bigger output. I did have amplification when the",
|
||||
"MOSFET was in saturation but it was highly nonlinear.",
|
||||
"The input was a triangular wave and the output was some funny,",
|
||||
"it kind of looked like a sinusoid whose extremities had been whacked",
|
||||
"down and kind of flattened. And its upward going peak had been",
|
||||
"shrunk. So it was a kind of weird nonlinear behavior.",
|
||||
"I will show that to you again later on. And so it amplified but it was",
|
||||
"nonlinear. And remember our goal of two weeks ago?",
|
||||
"We set out to build a linear amplifier. So today we will walk",
|
||||
"down that path and talk about building a linear amplifier.",
|
||||
"So to very quickly revisit the input versus output characteristic,",
|
||||
"VI versus VO, this is VT and this is VS, this is what things looked like.",
|
||||
"Also to quickly review the valid ranges, until some point here the",
|
||||
"amplifier was in saturation, the MOSFET was in saturation and",
|
||||
"somewhere here I had VO being equal to VI minus a threshold drop.",
|
||||
"At that point the MOSFET went into its triode region and I no longer",
|
||||
"was following the saturation discipline. So therefore this is my",
|
||||
"valid region of operation. We also know that the output was",
|
||||
"given by VS minus K (VI-VT) all squared RL over 2.",
|
||||
"Again assuming the MOSFET is in saturation. It is very important to",
|
||||
"keep stating this because this is true only when the MOSFET is in",
|
||||
"saturation, when I am following the discipline. Notice that this is a",
|
||||
"nonlinear relationship. So VO depends on some funny square",
|
||||
"law dependence on VI. The key here is how do we go about",
|
||||
"building our amplifier? Take a look at this point here.",
|
||||
"At this point here let's say I have a VI input. Corresponding output is",
|
||||
"VO. Focus is this point. And left to itself this was a",
|
||||
"nonlinear curve. Remember the trick that we used in",
|
||||
"our nonlinear Expo Dweeb example? We used the Zen Method.",
|
||||
"Remember the Zen Method? We said look, this is nonlinear,",
|
||||
"but if you can focus your mind on this little piece of the curve here",
|
||||
"this looks more or less linear. If I look at a small itty-bitty",
|
||||
"portion of the curve and I do the Zen thing, and kind of zoom in on",
|
||||
"here. This looked more or less linear. This means that if I could",
|
||||
"work with very small signals and apply the signal in a way that I",
|
||||
"also had a DC offset of some sort. Then I would be in a region of the",
|
||||
"curve, I would be delineating a small region of the curve which",
|
||||
"would be more or less linear. This was a small signal trick.",
|
||||
"And what we will do here is simply revisit the small signal model.",
|
||||
"Most of what I am going to do from here on will be more or less a",
|
||||
"repeat of what you saw for the light emitting expo dweeb.",
|
||||
"Just that here I have a three terminal device,",
|
||||
"with a little bit more complication. The equation is different. I don't",
|
||||
"have to resort to a Taylor series expansion. I will just do a",
|
||||
"complete expansion of this expression and develop the small",
|
||||
"signal values for you. Recall the small signal model.",
|
||||
"It had the following steps. The first step will operate at some",
|
||||
"bias point, VI, VO, and of course some corresponding",
|
||||
"point IDS. This is Page 3. And then superimpose a small signal",
|
||||
"VI on top of the big fat bias. Remember the \"boost\"?",
|
||||
"So VI is the boost. Boom. And above VI,",
|
||||
"I have small signal VI that I apply. And our claim is that response of",
|
||||
"the amplifier to VI is approximately linear.",
|
||||
"The key trick with this is that for",
|
||||
"my small signal model here, this is Page 3 here, and Page 2.",
|
||||
"The key trick here is that with the small signal model,",
|
||||
"I operate my amplifier at some operating point,",
|
||||
"VO, VI. I superimpose a small signal VI on top of small VI on top",
|
||||
"of big VI. And then I claim that the response to VI is",
|
||||
"approximately linear. And let me just embellish that curve",
|
||||
"a little bit more.",
|
||||
"Notice that in this situation this was my VI, which is my bias voltage,",
|
||||
"this is VO, which is the output bias, and of course not shown on this",
|
||||
"graph is the output operating current which is IDS.",
|
||||
"One nice way of thinking about this is to redraw this and think that",
|
||||
"your coordinate axes have kind of shifted in the following manner.",
|
||||
"This is VI. This is also on your Page 3. This is VT.",
|
||||
"Remember this was the operating point, VO and VI.",
|
||||
"And notice that we were operating in this small regime of our",
|
||||
"transfer curve here. And in effect what we are saying is",
|
||||
"that I am going to apply small variations about VI and call those",
|
||||
"variations delta VI or small VI. And the resulting variations are",
|
||||
"going to look like delta VO. Also referred to as small V,",
|
||||
"small O. So I will have small variations here.",
|
||||
"And they give rise to corresponding small variations there.",
|
||||
"One way to view this is as if we are working with a new coordinate",
|
||||
"system. Another way to view this is that so the capital VI and capital",
|
||||
"VO correspond to my VI and VO as the total voltages in my circuit,",
|
||||
"but at this bias point I can think of another coordinate system here",
|
||||
"with small VI and VO out there. And for small changes to VI,",
|
||||
"I can figure out the corresponding small changes to VO.",
|
||||
"Just that all the analysis I perform here is going to be linear.",
|
||||
"And I will prove it to you in a couple of different ways in the next",
|
||||
"few seconds. When I am doing small signal analysis I am operating here",
|
||||
"in this regime at some bias point. You have also seen this before.",
|
||||
"How do I get a bias? This is my amplifier RL and VS.",
|
||||
"This is Page 4. VO. The way I get a bias is I apply",
|
||||
"some DC voltage VI and superimpose on top of that my small signal small",
|
||||
"VI. This is my DC bias that has boosted up the signal to",
|
||||
"an interesting value. And because of that what I can get",
|
||||
"is by varying VI as a small signal with a very small amplitude,",
|
||||
"I am going to get a linear response here. And I can draw",
|
||||
"that for you as well.",
|
||||
"This is my bias point here. And if I vary my signal like so then",
|
||||
"my output should look like this. This is point VI, this is point VO,",
|
||||
"and this is my small signal VI and this is my small signal VO and this",
|
||||
"is capital VO. So this small thing here is VI.",
|
||||
"I would like to show you a little demo.",
|
||||
"I will start with the same demo I showed you the last time.",
|
||||
"I showed you the amplifier. In the demo I am going to apply a",
|
||||
"triangular wave. And initially I start with a large",
|
||||
"signal. And you will see that the output looks really corny,",
|
||||
"is going to look something like this. That's large signal response.",
|
||||
"And then I will begin playing with the input making it smaller,",
|
||||
"and you can see how it looks yourselves.",
|
||||
"There you go. So this is where I stopped the last time.",
|
||||
"The last lecture I applied this input, time is going to the right,",
|
||||
"and the purple curve in the background is the output.",
|
||||
"It looks much more like a sinusoid with some flattening of its tips.",
|
||||
"Nothing like an interesting triangular wave.",
|
||||
"What I will do next is that let me make sure I have enough of a boost",
|
||||
"here, enough of a DC voltage so that I am operating at some point here.",
|
||||
"I believe I already have that. Notice that I can shift up the",
|
||||
"triangular wave input, or I can shift it down.",
|
||||
"So let me bias it here. I have chosen a VI that's about,",
|
||||
"I forget how many volts per division it is, but I have chosen",
|
||||
"some VI here. And I biased it such that this is",
|
||||
"the input. You get a nonlinear response. It is amplified.",
|
||||
"It is much bigger. What I will do next is make VI that I apply smaller",
|
||||
"and smaller. I have already done the boosting. Boom,",
|
||||
"that's a boost. So I have boosted up your VI already.",
|
||||
"Next is I am going to shrink it, and hopefully you will see that if",
|
||||
"all that I am saying is truthful here you will see a triangular",
|
||||
"response. Let's go try it out.",
|
||||
"Watch the yellow. I am going to shrink the yellow and make it",
|
||||
"smaller and smaller. There you go. It is great when",
|
||||
"nature works like you expect it to. I have never seen a triangular wave",
|
||||
"looks so pretty in my life. It is awesome. Look at this.",
|
||||
"Here is a tiny triangular wave. And the output is also a triangular",
|
||||
"wave but it is much more linear. Yes. Question? What's that? The",
|
||||
"question is that the output here is only as big as the input used to be",
|
||||
"before. That's a good question. What I have done here is I am",
|
||||
"showing you a laboratory experiment. And let's assume that this input is",
|
||||
"the input I am getting from some sensor in the field.",
|
||||
"Assume that this is my input, not what I had before. Assume that",
|
||||
"this is my input to begin with and this is the amplified output.",
|
||||
"What I can also do is I can also change the bias.",
|
||||
"And we will see this at the end of the lecture, in the last ten minutes",
|
||||
"of lecture. How do you select a bias point? By changing your bias",
|
||||
"point you can change the properties of an amplifier to give you a",
|
||||
"preview of upcoming attractions. Let me ask you,",
|
||||
"what do you think should happen if I change the bias point?",
|
||||
"I have not shown you the math yet, so intuitively what do you think",
|
||||
"should happen? If I increase the bias what do you",
|
||||
"think is going to happen? Yes. Good insight. Higher bias",
|
||||
"will be more amplification. Let's see if our friend is correct.",
|
||||
"Let me set a higher bias.",
|
||||
"Not necessarily,",
|
||||
"I guess. You're actually right, by the way. I am playing a trick on",
|
||||
"everybody here.",
|
||||
"As I change my input bias. Notice that under certain",
|
||||
"conditions my output becomes smaller and gets more distorted.",
|
||||
"Under other conditions what is going to happen to my output is that",
|
||||
"it is becoming smaller and is going to get distorted again.",
|
||||
"So there are a bunch of funny effects happening that reflect on",
|
||||
"the bias point, but for an appropriate choice of",
|
||||
"bias point as I increase the bias the amplification should increase.",
|
||||
"And I will show you that in a few minutes. But it is a complicated",
|
||||
"relationship. Yes.",
|
||||
"This is finally getting fun. Here is the question. Professor",
|
||||
"Agarwal, we love your song and dance, but if you really want to get a high",
|
||||
"signal at the output and you want to amplify your big input signal",
|
||||
"how do you do it? So the question is let's say I have",
|
||||
"an input that is this big here, if it is this big, I have shown you",
|
||||
"how I can get things that are this big, but what if my input was this",
|
||||
"big? How do I get an output that is this big? Well,",
|
||||
"I will use one of those learned by questioning methods and have you",
|
||||
"tell me the answer. Someone tell me the answer.",
|
||||
"How do I do that? Yes. Use another amplifier.",
|
||||
"So the answer is I will use one amplifier to go from here to here.",
|
||||
"And the suggestion is use another amplifier to go from here to here.",
|
||||
"And, in fact, I believe that you may have a problem in your problem",
|
||||
"set where you will do that. And so you have only yourselves to",
|
||||
"blame. So how do you make this work?",
|
||||
"What you have to do is this VI has to be much smaller than the bias",
|
||||
"point VI on this one. I have to build a different",
|
||||
"amplifier, choose a different set of parameters such that VI prime,",
|
||||
"which is the VI for this guy, is much less than V capital I prime for",
|
||||
"this guy. It's a design question. You need to design it in a way that",
|
||||
"the signals of interest need to be much smaller than the bias voltage",
|
||||
"of this amplifier. So you may have to use much higher",
|
||||
"supply voltages. My amplifier, I believe,",
|
||||
"has a 4 volt supply or 5 volt supply. You might have to use an amplifier",
|
||||
"with a much bigger supply, different values of RL and so on.",
|
||||
"And I know that the course notes also have some exercises and problem",
|
||||
"sets that discuss that in more detail. Yes. This is even more fun.",
|
||||
"The question is, good question. The question is why do you need this",
|
||||
"guy here? Just use this guy, right? Why do you need this guy?",
|
||||
"Big guys rule, right? Who needs the little guys?",
|
||||
"Well, let me use the Socratic method again. Why don't you give me",
|
||||
"the answer? You guys are smart. Why do you need little guys? Why",
|
||||
"do you need the small guy here? Anybody with the answer?",
|
||||
"Yeah. The big guy may not be as sensitive. I like that.",
|
||||
"You know what? He is almost correct. I will show you why in a",
|
||||
"second. Anything else? Any other reason? Yes.",
|
||||
"Bingo. That is another good answer.",
|
||||
"So let me address both the answers. The answer given was that look,",
|
||||
"this amplifier is amplifying the signal by a certain amount,",
|
||||
"by a factor of 7. And I have designed this such that this",
|
||||
"amplifies a signal by a factor of maybe 10.",
|
||||
"So in all I am getting an amplification of 70.",
|
||||
"This would be a great design question for lab next year.",
|
||||
"I give you a bunch of components and ask you to design an amplifier",
|
||||
"given the constraints with the highest amount of amplification.",
|
||||
"It turns out that when you design your amplifier,",
|
||||
"in order to meet the saturation discipline and so on,",
|
||||
"you have to choose values of RL and VS and stuff like that and be within",
|
||||
"power constraints so the amplifier doesn't blow up and stuff.",
|
||||
"And by the end of it all you are going to get a measly 7X gain out of",
|
||||
"it. The same way here, to be able to deal with a very small",
|
||||
"signal here and get some amplification,",
|
||||
"another set of values and you get 10X. So they multiply.",
|
||||
"It is much harder to build one amplifier with a much larger gain.",
|
||||
"You know what? I just realized that we will be looking at this in",
|
||||
"the last five or seven minutes of lecture. I am going to show you",
|
||||
"what the amplification depends upon. It depends upon K. It depends upon",
|
||||
"RL. It depends upon VI. Now the question is I have had all",
|
||||
"this time to think about how to stitch in sensitive into this,",
|
||||
"and I believe I can. It turns out that when you have large voltages",
|
||||
"and so on and you have practical devices, it turns out that the more",
|
||||
"current you pump through devices they tend to produce noise of",
|
||||
"various kinds. So very powerful amplifiers are not",
|
||||
"very good at dealing with really tiny signals because they have some",
|
||||
"inherent noise capabilities. And so I guess that is sensitive.",
|
||||
"It is sensitive to noise. Another question? Yes.",
|
||||
"Ask me the question again.",
|
||||
"I didn't follow.",
|
||||
"Let me just explain it. It turns out that I will not be",
|
||||
"able to pass this through the big amplifier to begin with because it",
|
||||
"is just going to give me a gain of just a factor of 7.",
|
||||
"However, if I have a signal that is this big to begin with then I may",
|
||||
"just need this amplifier. I don't need the smaller guy.",
|
||||
"If my signal was this big to begin with, if I had a strong sensor that",
|
||||
"produced a strong signal to begin with, yeah, I can deal with",
|
||||
"just a single stage. I don't need to two stages.",
|
||||
"It is all a matter of design. And it is actually a fun design",
|
||||
"exercise. Given a budget, dollars, right? You go to your",
|
||||
"supply room and look at the parts that you have and you go to build",
|
||||
"what you have to build with the parts that you have.",
|
||||
"And so sometimes you need to build two amplifiers to get the gain or",
|
||||
"build a signal amplifier. It's all a design thing.",
|
||||
"All right. Moving on to Page 7. That brings us to the small signal",
|
||||
"model.",
|
||||
"Page 5. What I showed you up on the little",
|
||||
"demo was that provided the signal input in this example VI was much",
|
||||
"smaller than capital VI out there as I shrank my input,",
|
||||
"I was able to get a more or less linear response at the output.",
|
||||
"And so to repeat my notation at the input, the total input is a sum of",
|
||||
"the operating point input plus a small signal input.",
|
||||
"This is called the total variable. This is called the DC bias. It is",
|
||||
"also called the operating point voltage. And this is called my",
|
||||
"small signal input. It is also variously called",
|
||||
"incremental input. This is more a mathematical term",
|
||||
"relating to incremental analysis or perturbation analysis.",
|
||||
"So VI, call it small signal, call it small perturbation, call it",
|
||||
"increment, whatever you want. Similarly, at the output I have my",
|
||||
"total variable at the output a sum of the output operating voltage and",
|
||||
"the small signal voltage. I do not like using Os in symbols",
|
||||
"because big O and small O is simply a function of how big you write them.",
|
||||
"It is not super clear. And in terms of a graph,",
|
||||
"let me plot the input and output for you. Let's say this is the total",
|
||||
"input and that is the total output. I may have some bias VI.",
|
||||
"And corresponding to that I may have some bias VO. Hold that thought for",
|
||||
"a second while I give you a preview of something that we will be",
|
||||
"covering in about three or four weeks. Notice that as I couple",
|
||||
"amplifiers together, the output operating point voltage",
|
||||
"of this amplifier in this connection becomes the input operating point",
|
||||
"voltage of this amplifier, right? So when they connect this output to",
|
||||
"this input, the output operating point voltage becomes coupled to the",
|
||||
"input here so it becomes the input operating point voltage here.",
|
||||
"Now I have a nightmare on my hands. As I adjust the bias of this guy,",
|
||||
"the bias of this guy changes, too. The two are dependent. It is",
|
||||
"a pain in the neck. And we being engineers find ways to",
|
||||
"simplify our lives. And you will learn another trick in",
|
||||
"about three or four weeks. And that trick will let you decouple",
|
||||
"these two stages in a way that you can design this stage in isolation,",
|
||||
"go have a cup of coffee and then come back to this stage and design",
|
||||
"this stage in isolation. For those of you who want to run",
|
||||
"ahead and think about how to do it, think about it. What trick can you",
|
||||
"use to get them in isolation? Moving on.",
|
||||
"What I would like to do next is address this from a mathematical",
|
||||
"point of view. And much as I did for the light",
|
||||
"emitting expo dweeb analyze this mathematically and show you that if",
|
||||
"VI is much smaller than capital VI, I indeed get a linear response.",
|
||||
"This time around I won't use Taylor series because it turns out that",
|
||||
"this expression can be expanded fully.",
|
||||
"So you don't have to buy into Taylor series and so on.",
|
||||
"I am going to list everything down for you. We know,",
|
||||
"to begin with, that VO for the amplifier is VS-RLK/2 (VI-VT)^2.",
|
||||
"What I am going to do for this, much as I did for the LED,",
|
||||
"what I'm going to do is derive for you the output as a function of the",
|
||||
"input when the input VI is very small.",
|
||||
"In other words, when I substitute for VI,",
|
||||
"V capital I squared plus small VI. Much as I did for the expo dweeb, I",
|
||||
"want to substitute for VI a big DC VI. So VI is much smaller than VI.",
|
||||
"And show you for yourselves that the output response,",
|
||||
"V small O is going to be linearly connected to VI.",
|
||||
"Notice that, let me write another equation here.",
|
||||
"This is a total variable. This simply says that if the input",
|
||||
"is VI then the output is going to be VO, which means that the operating",
|
||||
"point input voltage should satisfy this equation,",
|
||||
"correct? In other words, the operating point output voltage V",
|
||||
"capital O should equal VS-RLK/2 (VI-VT)^2.",
|
||||
"This is at VI equals capital VI. This is very simple but may seem",
|
||||
"confusing. All this is saying is that look, this equation gives me",
|
||||
"the relationship between VI and VO. Therefore, if I apply capital VI as",
|
||||
"the input, I'm given that my corresponding output is capital VO,",
|
||||
"so they must satisfy this equation, right?",
|
||||
"Those are bias point values and that must satisfy this equation.",
|
||||
"Simple. I know that. So hold that thought. Stash it away in the back",
|
||||
"of your minds. Now let me go through a bunch of",
|
||||
"grubby math and substitute for VI in this expression here.",
|
||||
"Let me go ahead and do that. VS-RLK/2((VI+vi)-VT)^2. When I do",
|
||||
"something that is other than math I will wake you up.",
|
||||
"I will just keep doing a bunch of steps that are pure math.",
|
||||
"No cheating. No nothing. Watch my fingers. When I do",
|
||||
"anything that is not obvious math I will wake you up.",
|
||||
"Next I am going to simply move VT over and rewrite this as follows,",
|
||||
"RLK/2((VI-VT)+vi)^2. Again, I haven't done anything interesting so",
|
||||
"far. I have just substituted this. I am just juggling things around",
|
||||
"just to pass away some time, I guess. All right.",
|
||||
"Next what I am going to do is simply expand this out and write it this",
|
||||
"way RLK/2, expand that out and treat this as one unit VS -",
|
||||
"RLK/2((VI-VT)^2+2(VI-VT)vi+vi^2). Nothing fancy here.",
|
||||
"This is like the honest board. Nothing fancy here. Standard stuff.",
|
||||
"Only math. I will move to this blackboard here where I do some fun",
|
||||
"EE stuff. Yes.",
|
||||
"Good. At least one person isn't asleep here.",
|
||||
"Thank you. So just math here. Nothing fancy. Plain old simple",
|
||||
"math. I have not done any trickery. I still have all my ten fingers.",
|
||||
"Now what I am going to do, now watch me. I am not using Taylor",
|
||||
"series here because this expression lends itself to this analysis.",
|
||||
"Notice VI squared here. I made the assumption that VI is",
|
||||
"much smaller than capital VI, so what I can do is assuming that VT",
|
||||
"is small enough that VI minus VT is still a big number compared to small",
|
||||
"VI, what I can do is ignore this in comparison to the capital VI terms.",
|
||||
"So I have a capital VI term here. I am going to ignore VI squared.",
|
||||
"So, for example, if capital VI was 5 volts and small",
|
||||
"VI was 100 millivolts 0. , so 0.1 squared is 0.01.",
|
||||
"So it is comparing 0.01 to 5. So I am off by a factor of 500.",
|
||||
"So now watch me. Now I begin playing some fun and games here.",
|
||||
"I eliminate this, and because I eliminate that it now becomes",
|
||||
"approximately equal. What I do in addition is let me",
|
||||
"write down the output. The total variable is the sum of",
|
||||
"the DC bias and some variation of the output. And let me simply",
|
||||
"expand that term and write it down again. VS-RLK/2(VI-VT)^2-RLK/2.",
|
||||
"I get a two here. And I get VI-VT. I won't forget",
|
||||
"the VI this time. Again, from here to there nothing",
|
||||
"fancy. This is the one step where I have used a trick.",
|
||||
"I have said small VI is much smaller than capital VI,",
|
||||
"and so I have simply expanded this out and written it here.",
|
||||
"So do you see the obvious next trick here?",
|
||||
"From star look at this guy.",
|
||||
"I can cancel this out from star because I know that at the operating",
|
||||
"point these two expressions are equal, and so therefore I can cancel",
|
||||
"out the operating point voltage and this.",
|
||||
"What I am left with is small VO is simply minus RLK(VI-VT) times vi.",
|
||||
"Only one place where I did something funny.",
|
||||
"Other than that it is purely math. So this is what I get.",
|
||||
"Notice that this whole thing is a constant, minus RLK(VI-VT).",
|
||||
"This whole thing is a constant. And so VO is equal to some constant",
|
||||
"times VI. Let me just define some terms for you that you will use",
|
||||
"again and again. For reasons that will be obvious",
|
||||
"next lecture, I am going to call this term here GM.",
|
||||
"I am going to call this term a",
|
||||
"constant, K(VI - VT). It is a constant for a given bias",
|
||||
"point voltage. So I am going to call that GM.",
|
||||
"And then I am going to call this whole thing A.",
|
||||
"And of course this is VI. There you go.",
|
||||
"I have my linear amplifier. A is the gain times small VI.",
|
||||
"And the gain has these terms in it. I just call this GM. You will see",
|
||||
"why later. But notice that the gain relates to RL.",
|
||||
"The size of the load resistor RL, how big it is, 1K, 10K, whatever. K,",
|
||||
"this is a MOSFET parameter, and VI minus VT.",
|
||||
"That is a constant for a given bias point voltage and small VI.",
|
||||
"So VO equals small VI.",
|
||||
"I won't give you a graphical interpretation,",
|
||||
"but I encourage you to go and look at Figure 8.9 in the course notes.",
|
||||
"And it gives you a graphical interpretation of that expression.",
|
||||
"Move to Page 7. Another way of looking at this,",
|
||||
"another way of mathematically analyzing it, here I went through a",
|
||||
"full blown expansion and pretty much deriving the small signal response.",
|
||||
"What I can also do is take a shortcut here.",
|
||||
"So let me just give you the shortcut. You might find this handy.",
|
||||
"VO=VS-KRL/2(VI-VT)^2. And my shortcut is as follows.",
|
||||
"My small signal response is simply this relationship.",
|
||||
"I find the slope at the point capital VI and multiply by the",
|
||||
"increment. Slope times the increment gives me the incremental",
|
||||
"change in VO as follows. d/dI (VS-KRL/2(VI-VT)^2) evaluated",
|
||||
"at vI=VI times vi. This is math again.",
|
||||
"I want to find out the change in VO for a small change in VI,",
|
||||
"and I do that by taking the first derivative of this with respect to",
|
||||
"VI substituting V capital I and multiplying by the small change",
|
||||
"delta VI or small VI. So this is simply the slope of the",
|
||||
"VO versus VI curve at VI. And so therefore taking the",
|
||||
"derivative here of this. This is a constant so it vanishes.",
|
||||
"But twice 2 to cancel out, so I get KRL(VI-VT) times small vi",
|
||||
"evaluated at capital VI. So I get twice KRL,",
|
||||
"VI evaluated at capital VI, so it is VI minus VT times small VI.",
|
||||
"Same thing. Oh, and I have a minus sign here.",
|
||||
"I get the same expression that I derived for you up there,",
|
||||
"and this is just taking the slope and going with it.",
|
||||
"And this, as I mentioned before, this is A. The last few minutes let",
|
||||
"me kind of pull everything together and also hit upon something that",
|
||||
"many of your questions are touched upon.",
|
||||
"And that all relates to how to choose the bias point.",
|
||||
"So here I have taken an analysis approach. When teaching we often",
|
||||
"teach you are given something, you analyze it, but as you begin to",
|
||||
"master it you can begin to design things where you can ask a lot of",
|
||||
"questions and so on. And here what we have is an",
|
||||
"analysis given a value of RLK, VI and so on.",
|
||||
"How to choose the bias point becomes more of a design issue.",
|
||||
"If you are designing an amplifier, you asked me the question, how do I",
|
||||
"choose two small amplifiers versus one big amplifier,",
|
||||
"that sort of stuff? It boils down to how do you choose",
|
||||
"the bias point? How do you choose VI?",
|
||||
"How do you choose RL and so on? What I would like to do is touch",
|
||||
"upon some of these things. First of all, gain or the",
|
||||
"amplification. One of the most important design",
|
||||
"perimeters for an amplifier is what is the gain? Let's say you get a",
|
||||
"job at Maxim Integrated Technologies, and they say we would like you to",
|
||||
"build a linear power amplifier for cell phones. You can say I know how",
|
||||
"to do that. And then they say the next stage needs a 100",
|
||||
"millivolt input. While this thing coming from the",
|
||||
"antenna is only a few tens or a few hundreds of a microvolt.",
|
||||
"So you sit down and say oh, my gosh, I need an amplification of",
|
||||
"so much, and you go design an amplifier. So gain tends to be a",
|
||||
"key parameter. And notice that gain is",
|
||||
"proportional to RL. It relates to VI minus VT,",
|
||||
"so proportional to VI. It is also related to RL.",
|
||||
"The second point is the gain point determines where I bias something.",
|
||||
"If I choose my bias too high I get distortion, or if I choose my bias",
|
||||
"too low I get distortion.",
|
||||
"So depending on how I choose my bias point, as a signal goes up it may",
|
||||
"begin clipping or begin distorting. And I will show you a demo the next",
|
||||
"time on that particular example. So bias point will determine how",
|
||||
"big of a signal you can send without getting too much distortion.",
|
||||
"And the other thing is that, relates to how big of an input,",
|
||||
"what is a valid input range? So let's say you have a signal.",
|
||||
"And you want that signal to have both positive and negative",
|
||||
"excursions of the same value. Then, depending on where you choose",
|
||||
"a bias point, your input range may become smaller or larger.",
|
||||
"And we will go through these in the context of and amplifier and look at",
|
||||
"some design issues in the next lecture."
|
||||
]
|
||||
}
|
||||
@@ -1,2003 +0,0 @@
|
||||
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|
||||
"text": [
|
||||
"So, one question to ask ourselves is,",
|
||||
"what is engineering? How do we define,",
|
||||
"what is engineering? Well, the definition I like to",
|
||||
"use is one put forth by Steve Senturia, one of our professors",
|
||||
"who is now retired. He defined engineering to be",
|
||||
"the purposeful use of science. All right, so what is 6.002",
|
||||
"about? So, 6.002 is a first course in",
|
||||
"engineering. And I like to view 6.002 as the",
|
||||
"gainful employment of Maxwell's equations.",
|
||||
"Many of you have seen Maxwell's equations before.",
|
||||
"Most of you should have. And they are hard stuff.",
|
||||
"6.002 is all about teaching you how to simplify our lives,",
|
||||
"make things simple. So, if you can gainfully employ",
|
||||
"Maxwell's equations, gainfully employ the facts of",
|
||||
"nature to build very interesting systems.",
|
||||
"So let me show you how the transition is made.",
|
||||
"So, there's a world around us, nature, so we made some",
|
||||
"observations in nature. We make measurements,",
|
||||
"and we can write down large tables of measurements.",
|
||||
"So, for example, we can take objects and measure",
|
||||
"the voltage across them, and look at the resulting",
|
||||
"current through the elements. So, we may end up getting a",
|
||||
"bunch of values such as [CHALKBOARD].",
|
||||
"So, we start out life with making measurements on what",
|
||||
"exists. And we build a bunch of tables.",
|
||||
"Now, we could directly take these tables,",
|
||||
"and based on observations of these tables,",
|
||||
"we could go ahead and build very interesting engineering",
|
||||
"systems that help us out in day-to-day lives.",
|
||||
"But that's incredibly hard. Imagine having to resort to a",
|
||||
"set of tables to do any kind of useful work.",
|
||||
"So what we do as engineers, we first layer a level of",
|
||||
"abstraction. We look at all the data,",
|
||||
"and somehow layer abstraction such that we can simplify or",
|
||||
"much more succinctly put in a simple equation or a simple",
|
||||
"statement what these numbers are telling us.",
|
||||
"OK, so for example, our physics laws,",
|
||||
"so laws of physics for example are simply abstractions,",
|
||||
"the laws of abstractions. So, these sets of numbers can",
|
||||
"be codified by Ohm's law, for example,",
|
||||
"V is equal to RI, the voltage current,",
|
||||
"relates to the resistance of the object.",
|
||||
"So, V is equal to RI is a law that succinctly describes a set",
|
||||
"of experiments, and replaces a large number of",
|
||||
"tables with a very simple statement.",
|
||||
"You could call this the law, or you could call it an",
|
||||
"abstraction. OK so you see laws of physics,",
|
||||
"call them abstractions of physics if you like.",
|
||||
"Similarly, there are Maxwell's equations and so on and so",
|
||||
"forth. So, this is what is.",
|
||||
"This is what's out there. OK, and a law as an abstraction",
|
||||
"describe the properties of nature, as we see it,",
|
||||
"in some succinct form. Now, if you want to go and",
|
||||
"build useful things, we could take these",
|
||||
"abstractions, take Maxwell's equations,",
|
||||
"and go and build things. But it's hard.",
|
||||
"It's really, really hard.",
|
||||
"And what you learn in, at MIT is this place is all",
|
||||
"about simplifying things. Take complicated things,",
|
||||
"build layers of abstraction, and simplify things so that we",
|
||||
"can build useful systems. Even in 6.002 we start life by",
|
||||
"making a huge leap from Maxwell's equations to a couple",
|
||||
"of very, very simple laws. OK, I'm going to show you that",
|
||||
"leap that we will make today. So, the first abstraction that",
|
||||
"we layer is called the lump circuit abstraction.",
|
||||
"OK, in the lump circuit abstraction, what we do is we",
|
||||
"make a set of simplifications that allows us to view a set of",
|
||||
"objects as discrete or lumped elements.",
|
||||
"So, we may, I will define voltage sources.",
|
||||
"We'll define resistors. We'll define capacitors,",
|
||||
"and so on. OK, and I'm going to make the",
|
||||
"jump, and show you how we make the jump in a few minutes.",
|
||||
"So, on that sort of abstraction, we then layer yet",
|
||||
"another abstract layer. And let me call that the",
|
||||
"amplifier abstraction. OK, remember,",
|
||||
"here we are absolutely down and dirty.",
|
||||
"We are setting the probes, measuring objects,",
|
||||
"and building huge tables. We abstracted things into",
|
||||
"simple laws, and life got a little better.",
|
||||
"OK, I'm going to show you can abstract things further out and",
|
||||
"build discrete objects, and, you could build even more",
|
||||
"interesting components called amplifiers and begin playing",
|
||||
"around with amplifiers. OK, so when you are using",
|
||||
"amplifiers, you don't really have to worry about the details",
|
||||
"of Maxwell's equations. OK, I'll give you some very",
|
||||
"simple abstract rules of behavior for an amplifier,",
|
||||
"and you can go build very interesting systems without",
|
||||
"really, really knowing how Maxwell's equations applies to",
|
||||
"that because you will be working at this abstract layer.",
|
||||
"However, since you're engineers, and you are good at",
|
||||
"building such systems, it's very important for you to",
|
||||
"understand how we make this leap from the laws of physics into",
|
||||
"some of our very primitive engineering abstractions.",
|
||||
"So, once we make the amplified abstraction in 6.002,",
|
||||
"by the way, 6.002 starts here. We start from the laws of",
|
||||
"physics and then proceed all the way out.",
|
||||
"So, once we talk about amplifiers we will take two",
|
||||
"pads. On the amplifier,",
|
||||
"you will build the next abstraction called the digital",
|
||||
"abstraction. OK, and with the digital",
|
||||
"abstraction, we will build new elements such as inverters and",
|
||||
"combinational gates, OK?",
|
||||
"So, notice we are building bigger, and bigger things,",
|
||||
"which have more and more complicated behavior inside",
|
||||
"them, but which are very simple to describe, right?",
|
||||
"So, following the digital abstraction, we will superimpose",
|
||||
"the combinational logic abstraction on top of that,",
|
||||
"and define functional blocks that look like this:",
|
||||
"some inputs, some function,",
|
||||
"some outputs. The next abstraction on top of",
|
||||
"that will be the clock digital abstraction, where we will have",
|
||||
"some notion of time introduced into the system.",
|
||||
"There will be a clock, and this will be some function.",
|
||||
"And there will be a clock that introduces time into the sort of",
|
||||
"logic values that functions operate upon.",
|
||||
"Following that, the next level of abstraction",
|
||||
"that we build is called instruction set abstraction.",
|
||||
"OK, now you begin to see things that consumers get to look at.",
|
||||
"Can someone give me an example of, or name an instruction set,",
|
||||
"or instruction set abstraction? Bingo.",
|
||||
"So, x86 is one set of abstractions.",
|
||||
"And in fact, in many universities,",
|
||||
"education could well start just by saying, OK,",
|
||||
"here's an abstraction. These are the x86 instructions,",
|
||||
"OK? Some MIT gurus have designed",
|
||||
"this awesome little microprocessor,",
|
||||
"OK? So you just worry about,",
|
||||
"you take this abstraction layer here, the assembly instructions,",
|
||||
"and you go and build systems on top of that.",
|
||||
"OK, so this is an abstraction layer called the x86 layer.",
|
||||
"There are other abstraction layers.",
|
||||
"In 6.004, you will learn about, I believe, the alpha or the",
|
||||
"beta, OK, and various other abstractions at this point.",
|
||||
"So, 6.002 kind of goes until here.",
|
||||
"6.002 takes me from the world of physics all the way to the",
|
||||
"world of interesting analog and digital systems.",
|
||||
"OK, 004, the course on computation structures,",
|
||||
"will show you how to build computers all the way from",
|
||||
"simple digital objects all the way to big systems.",
|
||||
"Following that, you learn about language",
|
||||
"abstractions, Java, C, and other languages,",
|
||||
"and that's in 6.002. And there are several other",
|
||||
"courses that will cover that. Following this,",
|
||||
"you learn about software system abstractions,",
|
||||
"and software systems, you will learn about operating",
|
||||
"systems. Any example of an operating",
|
||||
"system abstraction that people know out there?",
|
||||
"What's that? Linux.",
|
||||
"What else? I'm just wondering how long",
|
||||
"I'll have to go before I hear what I want to hear.",
|
||||
"[LAUGHTER] OK, so we have a bunch of software",
|
||||
"systems. So, if we have a bunch of",
|
||||
"software systems, these are nothing but",
|
||||
"abstractions. Linux simply implies a set of",
|
||||
"system calls that the programs must adhere to.",
|
||||
"Windows is another set of system calls.",
|
||||
"That's it. And see how much money they",
|
||||
"made out of it? OK, it's all about abstraction",
|
||||
"layers, that all start from nature.",
|
||||
"All right? Build abstraction upon",
|
||||
"abstraction upon abstraction upon abstraction,",
|
||||
"and someone out here are lots of dollars.",
|
||||
"OK, so based on these abstractions,",
|
||||
"we can then build useful things for human beings.",
|
||||
"We can build very useful things, video games,",
|
||||
"so we can send space shuttles up, and a whole bunch of other",
|
||||
"systems. But it's based on these",
|
||||
"abstraction layers. What's unique about education",
|
||||
"at MIT? What's unique about 6.002 and",
|
||||
"EECS? Is to my knowledge,",
|
||||
"there are not many other places in the world where you will get",
|
||||
"an education in everything going all the way from nature to how",
|
||||
"to build very complicated analog and digital systems.",
|
||||
"OK, we will show you layer upon layer upon layer upon layer,",
|
||||
"peel away the onion until you are down to raw nature,",
|
||||
"OK, through Maxwell's equations.",
|
||||
"So, 6.002, 004, this is 033,",
|
||||
"OK, 6.170, and so on. OK, the whole EECS is about",
|
||||
"building abstraction layers, one on top of the other.",
|
||||
"So that's one path. There's the analog path.",
|
||||
"The analog path would take an amplifier, and build an",
|
||||
"abstraction layer called the op-amp.",
|
||||
"See how similar they all look? You know the amplifier,",
|
||||
"the inverter of the digital world, and the operational",
|
||||
"amplifier in the analog world, just different ways of looking",
|
||||
"at the same devices. So, to build an analog system,",
|
||||
"to build an operational amplifier, and then,",
|
||||
"here we go end up building a whole bunch of different",
|
||||
"interesting analog system components.",
|
||||
"OK, and these components might look like oscillators.",
|
||||
"They might look like filters. OK, they look like power",
|
||||
"supplies, a whole bunch of very interesting abstract components,",
|
||||
"which pulled together can then give you the next set of",
|
||||
"systems. And these systems might be",
|
||||
"toasters, or say for example other analog systems like the",
|
||||
"various control systems for various power plants and so on",
|
||||
"and so forth, and ultimately,",
|
||||
"fun and dollars. OK, so 6.002 is about going",
|
||||
"from physics all the way to this point.",
|
||||
"We will build interesting analog systems,",
|
||||
"and take you up to interesting digital system components,",
|
||||
"from which 004 will take you all the way to building computer",
|
||||
"architectures. So that, in a nutshell,",
|
||||
"kind of gives you a feel for the space of EECS.",
|
||||
"OK, this chart here is almost a vignette of what EECS at MIT is",
|
||||
"all about. And this is the world according",
|
||||
"to Agarwal, because he's teaching 002.",
|
||||
"OK, so this is 6.002, and the rest of EECS is",
|
||||
"somewhere out there. OK, so I'm going to do now is",
|
||||
"throughout this course; I want you to think about which",
|
||||
"part in this vignette we are in. So, right now,",
|
||||
"I'm going to start here and take you here.",
|
||||
"OK, and as you get closer and closer, things get simpler,",
|
||||
"and simpler, and simpler.",
|
||||
"Still, the final abstractions are pedal, brake,",
|
||||
"steering wheel. I mean, that's the abstraction",
|
||||
"to play a game, right, four or five very simple",
|
||||
"interfaces, and that's all you need to know.",
|
||||
"And everybody in the world can play stuff.",
|
||||
"So remember, this stuff is complicated.",
|
||||
"This stuff is very, very simple.",
|
||||
"OK, and the more we build abstractions and come to this",
|
||||
"side, things get simpler and simpler.",
|
||||
"So, a large part of what I'll cover today is make the biggest",
|
||||
"simplification. The biggest simplification we",
|
||||
"will make his go from Maxwell's equation to some very,",
|
||||
"very simple algebraic rules. OK, I did Maxwell's equations",
|
||||
"myself. And I tell you,",
|
||||
"they were very interesting stuff but complicated.",
|
||||
"I can't imagine building efficient systems using",
|
||||
"Maxwell's equations. So, let's take an example,",
|
||||
"OK? So, let's say I have a battery.",
|
||||
"Just switch to page three of your course notes.",
|
||||
"And let's say I connect that to a bulb.",
|
||||
"OK, and this is a wire. And, the battery supplies some",
|
||||
"voltage, V, and I ask you a simple question.",
|
||||
"What is the current through the bulb?",
|
||||
"OK, so here is something that I can build using objects.",
|
||||
"I can pick a round from stores and so on.",
|
||||
"And I can collect them up in this way, and ask the question,",
|
||||
"what is the current, I?",
|
||||
"Now, if all you've done is learn about Maxwell's equations,",
|
||||
"you can roll up your sleeves and say, ah-ha!",
|
||||
"The first step is to write down all of Maxwell's equations,",
|
||||
"and you can say, del cross E is minus del and go",
|
||||
"on, and on, and on, OK, and write out all of",
|
||||
"Maxwell's equations and say, now how do I get from there to",
|
||||
"here? OK, it's very good.",
|
||||
"You can do it. OK, you can do it,",
|
||||
"but it's very complicated. OK, so instead,",
|
||||
"what you're going to do is take the easy way.",
|
||||
"So, what I want to remind you is that this course is actually",
|
||||
"very easy. OK remember,",
|
||||
"we're going to be building abstraction upon abstraction to",
|
||||
"make your lives easier. If you think your lives are",
|
||||
"getting more complicated, then you are not using",
|
||||
"intuition enough. OK, just remember the big I",
|
||||
"word. It's all about making things",
|
||||
"simple. OK, so let me give you an",
|
||||
"analogy. So, suppose you have an object.",
|
||||
"OK, and I apply a force to the object.",
|
||||
"It's an analogy, OK to get some insight into how",
|
||||
"to do this. So, I say here's an object.",
|
||||
"I apply a force, and I ask you the question.",
|
||||
"What is the acceleration of the object when I apply a force,",
|
||||
"F? So, how would you do it?",
|
||||
"OK, and eighth, or ninth, or tenth grader can",
|
||||
"do this. OK, they would ask me,",
|
||||
"what's the mass of the object? OK, I ask you what is the",
|
||||
"acceleration? You would turn around and ask",
|
||||
"me, what is the mass of the object?",
|
||||
"I tell you, the mass of the object is M.",
|
||||
"And then you say, oh sure, A is F divided by M,",
|
||||
"done. It's as simple as that.",
|
||||
"OK, I could have gone into all kinds of differential equations",
|
||||
"and so on to figure that out, but you asked me for the mass.",
|
||||
"And you gave me the answer, A is F divided by M.",
|
||||
"So, you ignored a bunch of things.",
|
||||
"You ignored the shape of the object.",
|
||||
"You ignored its color. You ignored its temperature.",
|
||||
"OK, and you ignored the soft or hard or whatever.",
|
||||
"OK, you ignored a whole bunch of things.",
|
||||
"You were focused on one thing. OK, you're focused on its mass.",
|
||||
"And, it turns out that the process really was developed",
|
||||
"from a set of simplifications. That is called,",
|
||||
"does anybody remember this? Point mass simplification.",
|
||||
"OK, so, in physics, you've done this before.",
|
||||
"OK, you've simplified your lives by viewing objects as",
|
||||
"having a mass at a point, and force is acting at that",
|
||||
"point. OK, M is that property of the",
|
||||
"object that is of interest to you.",
|
||||
"This process is called, in physics, point mass",
|
||||
"discretization. OK, now using an analogy,",
|
||||
"and I'm going to show you a similar simple process to do the",
|
||||
"problem with the light bulb. OK, so take my light bulb",
|
||||
"again,",
|
||||
"",
|
||||
"And I focus on the filament of the light bulb.",
|
||||
"OK, all I care about is the current flowing through the",
|
||||
"light bulb. OK, I don't care about whether",
|
||||
"the filament is twisted, whether it's hot.",
|
||||
"I don't care about its shape. I don't care about its color.",
|
||||
"All I care about is the current.",
|
||||
"OK, so to do that, what we can do here at a very",
|
||||
"high level is since we just need the current and don't care about",
|
||||
"a bunch of other properties, we will simply replace the bulb",
|
||||
"with a discrete object called a resistor.",
|
||||
"So the discrete object is a resistor, much like the point",
|
||||
"mass simplification that we did earlier that replaced the bulb",
|
||||
"filament with a object called a resistor, a discrete object",
|
||||
"called a resistor. Or a lump object called",
|
||||
"resister, and put a value next to it just like the mass for the",
|
||||
"object, a resistance value, R.",
|
||||
"OK, now what I can do is in the same manner, replace the battery",
|
||||
"with an object called a battery object, and connect that here,",
|
||||
"the voltage, V, applied to it.",
|
||||
"V falls across the resistor, and I get my I simply from",
|
||||
"Ohm's law as we divide by R. So, notice here,",
|
||||
"to replace this complicated bulb, this really twisty,",
|
||||
"weird old thing with this discreet thing called a",
|
||||
"resistor, and its only property of interest was its resistance",
|
||||
"value, R, direct analogy to what we did there.",
|
||||
"So, since R represents the only property of interest,",
|
||||
"we can simply ignore all the other things.",
|
||||
"So, notice here, we've done things the simple",
|
||||
"way. And remember,",
|
||||
"in EE, in the electrical engineering, we do things the",
|
||||
"simple way. OK, we could go the hard route",
|
||||
"and do Maxwell's equations, and get PhD's in physics,",
|
||||
"and so on. But out here,",
|
||||
"we are looking to do useful, interesting systems in the",
|
||||
"simplest way that we can. OK, we do things a simple way.",
|
||||
"All right, so we just did this, and boom, I found out what the",
|
||||
"current was. Now, I cheated a little bit.",
|
||||
"I've cheated a little bit. R is a lumped abstraction for",
|
||||
"the bulb. So, you look at this resistor",
|
||||
"here. That is simply a placeholder.",
|
||||
"It's a stand-in for this complicated thing called a bulb.",
|
||||
"It's a discreet object. It's a lumped object,",
|
||||
"and represents the bulb. Now, so most of 6.002 will take",
|
||||
"off from here, OK, and that's it.",
|
||||
"To very simple stuff, like V is equal to IR,",
|
||||
"it's a simple high school algebra to take off in that",
|
||||
"direction. But before we go there,",
|
||||
"it's important to understand, why was it that we were able to",
|
||||
"make the simplification? OK, we did something else.",
|
||||
"Something's going on under the covers here.",
|
||||
"On the one hand, I say let's use Maxwell's,",
|
||||
"and then I jump out and say, hey, we can just use this",
|
||||
"simple thing. I did something that allowed me",
|
||||
"to go from here to here. And you need to understand why",
|
||||
"I did that and how I did that. Understand it once,",
|
||||
"and then you won't have to need that information again.",
|
||||
"You just need to understand it. So, let's take a closer look at",
|
||||
"the bulb filament, and look at what we really did.",
|
||||
"So, here's my filament, A, and let's say that the",
|
||||
"surface area here, I label that SA,",
|
||||
"and the one down here SB, my voltage, V,",
|
||||
"applied there, and this is what I call my",
|
||||
"black box that I've replaced with a resistor.",
|
||||
"Notice that, in order for this to work,",
|
||||
"V and I need to be defined. So I needs to be defined,",
|
||||
"and V needs to be defined. OK, if I give you a random",
|
||||
"object, and I don't tell you anything else about the object,",
|
||||
"it's not clear I can do that. OK, if it's a much more general",
|
||||
"situation, I have to write down Maxwell's equations,",
|
||||
"and this is what I would write down.",
|
||||
"Write down J dot dS as a function of the coordinate here",
|
||||
"integrated over the area minus, OK, I would have to start from",
|
||||
"there from one of Maxwell's equations.",
|
||||
"All right, notice that this becomes IA, and this becomes IB",
|
||||
"in our simplification. But, if I don't tell you",
|
||||
"anything else, you have to start from here.",
|
||||
"You will have some varying current here by point.",
|
||||
"You might have some other current coming out here because",
|
||||
"I may have some charge buildup happening inside.",
|
||||
"If charge is building up inside the filament;",
|
||||
"then I would have to put del q by del t out here,",
|
||||
"right, the current in minus the current out must equal charge",
|
||||
"buildup. Whoa, where is this and where",
|
||||
"is that? So this is reality.",
|
||||
"This is really, really what I have to do.",
|
||||
"But how did I get there? How did I get there?",
|
||||
"The key answer is, as engineers,",
|
||||
"when in doubt we simplify. Remember, we are engineers.",
|
||||
"Our goal in life is to build interesting systems.",
|
||||
"OK and some are motivated by money.",
|
||||
"OK, so our goal is to build interesting systems and do good",
|
||||
"to humanity. So, as long as we can build a",
|
||||
"good light bulb, we are happy.",
|
||||
"So what we can do is we can say, look, all I care about is",
|
||||
"building interesting systems. So I can say,",
|
||||
"hey, this stuff is too hard. Let's make the assumption that",
|
||||
"all the systems that we will consider will have this thing be",
|
||||
"zero. OK, in other words,",
|
||||
"if I take a complete object, if I take an element like a",
|
||||
"resistor or a capacitor, the box around the entire",
|
||||
"element, OK, and I want to just deal with those systems in which",
|
||||
"this thing is zero. You can come and beat me up and",
|
||||
"say, but why? Why not?",
|
||||
"Why am I doing this? And I am saying the world is",
|
||||
"arbitrary. I'm an engineer;",
|
||||
"I want to build good systems. By making this simplification,",
|
||||
"I eliminate this squiggle thing, and so on.",
|
||||
"I don't want to deal with it. I want to make my life simple.",
|
||||
"So this is gone to zero because, why?",
|
||||
"Because I have said that in the future I will only deal with",
|
||||
"those elements for which this is true.",
|
||||
"I'm going to discipline myself. I'm going to discipline myself",
|
||||
"to only deal with those systems. OK, Maxwell is turning around",
|
||||
"and, you know, mad at me and all that stuff,",
|
||||
"but tough. So this, what I've said about",
|
||||
"making a simplification here, and this is one of the",
|
||||
"simplifications I'm making. And I give a name to the",
|
||||
"simplification. And that's called the lumped",
|
||||
"matter discipline. OK, so I'm saying I will only",
|
||||
"deal with elements for which if I put a black box around it,",
|
||||
"this is going to be true. And if this is going to be",
|
||||
"true, then notice, there is no charge buildup.",
|
||||
"Current in must equal current out.",
|
||||
"Ah-ha! So this becomes IA.",
|
||||
"This becomes IB. Yes.",
|
||||
"OK, I can now deal with IA's and IB's.",
|
||||
"And IB and IA are equal because this is zero.",
|
||||
"Notice that there is a whole bunch of depth here in the jump",
|
||||
"from here to here. As MIT graduates,",
|
||||
"you really, really need to understand why it is that we",
|
||||
"made that jump, and then go and use that,",
|
||||
"and do cool things. All right, this allows us to",
|
||||
"define I. We have a unique I associated",
|
||||
"with an element for the current through the element.",
|
||||
"We still have to worry about B, and I won't go through that in",
|
||||
"detail. The course notes have some",
|
||||
"discussion of that and so does the textbook.",
|
||||
"So V, AB is defined when del phi B, the rate of change of",
|
||||
"magnetic flux is zero. So, if I take the element and I",
|
||||
"take any region outside the element, this must be true.",
|
||||
"And you say, why should that be true?",
|
||||
"That's not true in general. Absolutely.",
|
||||
"It's not true in general. But I, because I choose to,",
|
||||
"I going to deal with only those elements.",
|
||||
"I will discipline myself. But these are only those",
|
||||
"elements for which this is true, and this is true.",
|
||||
"I'm going to limit my world. I'm going to create a play",
|
||||
"field for myself. You want to play;",
|
||||
"follow my rules. OK, and that's called the",
|
||||
"lumped matter discipline. So once you say that I'm going",
|
||||
"to adhere to the lump matter discipline, and this is true",
|
||||
"inside your elements. This is true outside the",
|
||||
"elements. You can define VA and VB,",
|
||||
"and good things happen to you. OK, let me show you a few",
|
||||
"examples of lumped elements. But remember,",
|
||||
"a large part of what we're doing is based on these two",
|
||||
"assumptions. And to just go through the",
|
||||
"background on that, I would encourage you to go to",
|
||||
"chapter 1 of your course notes and read through just as how",
|
||||
"this came about, that comes about.",
|
||||
"So, by doing that by adhering to a lumped matter discipline,",
|
||||
"we can now lump objects. We could lump a bulb into a",
|
||||
"resistor. OK, so to be clear,",
|
||||
"a certain number of lumped objects, and now,",
|
||||
"the universe is going to be comprised into lumped objects.",
|
||||
"OK, so before this, when he went home,",
|
||||
"we talked about eggs, and omelets,",
|
||||
"and light bulbs, and switches,",
|
||||
"but once you come to MIT, and after you've taken 6.002,",
|
||||
"you begin talking about lumped elements, you know,",
|
||||
"resistors, voltage sources, capacitors, little inky-dinky",
|
||||
"objects that follow the lumped matter discipline.",
|
||||
"OK, they stick to very simple rules, and the math that you",
|
||||
"have to do to analyze them is incredibly simple.",
|
||||
"What could be simpler than V is equal to IR?",
|
||||
"So, let me give you an example of interesting lumped elements,",
|
||||
"and then show you a couple of really nasty lumped elements.",
|
||||
"OK.",
|
||||
"",
|
||||
"OK, so what you see out here, so we characterize lumped",
|
||||
"elements by the VI characteristics.",
|
||||
"OK, you apply voltage, measure the current.",
|
||||
"OK, so what I can do is I can plot I here, and V here,",
|
||||
"and see what it looks like. OK, I can characterize elements",
|
||||
"by their VI relationship. And there are a bunch of",
|
||||
"elements that I can create based on the VI relationship.",
|
||||
"So let me show you a few examples.",
|
||||
"So for the resistor, since V is directly",
|
||||
"proportional to I, and R is a constant,",
|
||||
"I get a straight line. That's the I axis,",
|
||||
"the V axis, and this is the resistor.",
|
||||
"What I actually have is a variable resistor,",
|
||||
"so I'm going to change the resistance value,",
|
||||
"R, and the curve will also change slope.",
|
||||
"OK, I changed the value of R because it's a variable",
|
||||
"resistor, and the changes slope because my R is different.",
|
||||
"OK, next, let me go to a fixed resistor, and this guy here on",
|
||||
"the screen to your left is a fixed resistor.",
|
||||
"And you see that its IV characteristic is a line of a",
|
||||
"given slope, 1 by R, and that's it.",
|
||||
"I can't change it. Number three,",
|
||||
"I have another lumped element called a Zener diode that you",
|
||||
"will see in the fourth week of this class, and the",
|
||||
"characteristics for the Zener diode look like this:",
|
||||
"IV. If my voltage goes across the",
|
||||
"Zener diode goes up slightly, the current shoots up.",
|
||||
"But if the voltage becomes negative I don't have any",
|
||||
"current flowing into it until the voltage passes on the",
|
||||
"threshold, at which point my current begins to build up.",
|
||||
"OK, so I can increase the voltage a little bit,",
|
||||
"and it can show that the current starts building up",
|
||||
"again. So that's another interesting",
|
||||
"lumped element called a Zener diode.",
|
||||
"Let's switch to the next one called a diode.",
|
||||
"So a diode looks like this: IV.",
|
||||
"As the voltage across the diode becomes positive,",
|
||||
"around .6 volts, or thereabout,",
|
||||
"the current begins to shoot up. But when the voltage is below",
|
||||
"that threshold of .6, then my current is almost zero.",
|
||||
"It's another lumped element called a diode.",
|
||||
"And you will begin using these elements in your 002 lives to",
|
||||
"build interesting systems. The next example is a",
|
||||
"thermistor. A thermistor is a resistor",
|
||||
"whose resistance varies with temperature.",
|
||||
"OK, so this is a very expensive little hairdryer,",
|
||||
"and what I'm going to do is blow some hot air at my",
|
||||
"resistor, and you're going to see that its value is going to",
|
||||
"change depending on how much I heat it.",
|
||||
"So as it cools down, let me cool it down,",
|
||||
"so you can see it's coming down.",
|
||||
"I can zap it again. I could do this all day.",
|
||||
"This is so much fun. OK, so that's another",
|
||||
"interesting lumped element. As the temperature rises,",
|
||||
"its resistance changes. The next thing is called a",
|
||||
"photo resistor. It's a resistor.",
|
||||
"It used to be a resistor; Lorenzo?",
|
||||
"Oh OK, that's fine. So this is a photo resistor.",
|
||||
"And notice that it almost behaves like an open circuit.",
|
||||
"But what I'm going to do is shine some light on it.",
|
||||
"When I shine light on it, it begins to conduct and",
|
||||
"becomes a resistor of some value.",
|
||||
"There you go. OK, so that's a photo resistor.",
|
||||
"So now I'm going to show you a battery.",
|
||||
"Notice we did talk about batteries before.",
|
||||
"I'll show you a battery. So before you show a battery,",
|
||||
"just thinking your own minds, what should the IV",
|
||||
"characteristic of a battery look like?",
|
||||
"IV. A battery supplies a constant",
|
||||
"voltage. You know your little cell,",
|
||||
"the AA battery, 1.5 volts?",
|
||||
"So, think of what the IV characteristic of a battery",
|
||||
"should look like for three seconds before it shows you.",
|
||||
"This is the one I showed, Lorenzo?.",
|
||||
"It's a straight line. This is a good battery.",
|
||||
"It's a straight, vertical line,",
|
||||
"but says that the voltage is 1.5 volts, or thereabouts.",
|
||||
"No matter what current it supplies as an ideal voltage",
|
||||
"source, it has a fixed voltage, V, and no matter what the",
|
||||
"current going through is. Now, I'll show you a dud,",
|
||||
"a bad battery, and this is what the bad",
|
||||
"battery looks like. So, many of you have had your",
|
||||
"car batteries die on you. When you go to the store,",
|
||||
"they check your batteries. They use exactly this",
|
||||
"principle, that dead batteries have resistance.",
|
||||
"By the way, you see slopes here.",
|
||||
"You're thinking of resistance. OK, they can use this property",
|
||||
"to figure out that your battery is dead.",
|
||||
"So that's a dead battery. And finally,",
|
||||
"let me show you a bulb. We started with a bulb,",
|
||||
"and so I need to end, OK, we started with a bulb,",
|
||||
"so I need to end with a bulb. And what you will see is that a",
|
||||
"bulb simply behaves like a resistor.",
|
||||
"Its IV curve is going to look like this.",
|
||||
"OK, notice this is my bulb. And guess what,",
|
||||
"it behaves like a resistor. It's a very interesting kind of",
|
||||
"resistor, so I won't go into details for now.",
|
||||
"But notice its IV characteristic behaves like a",
|
||||
"resistor. OK, so those are some pretty",
|
||||
"standard lumped elements. You deal with a lot more sets",
|
||||
"of lumped elements, switches, MOSFETs,",
|
||||
"capacitors, inductors, a bunch of other fun stuff.",
|
||||
"But before we do that, what I wanted to tell you,",
|
||||
"don't go berserk on this abstraction binge.",
|
||||
"Too much of anything is bad for you.",
|
||||
"So what I'm going to show you is, abstractions or models are",
|
||||
"only valid provided you work within a set of constraints.",
|
||||
"Notice, we have already had this tacit handshake which said",
|
||||
"that we follow the discipline. Even after we follow the",
|
||||
"discipline, there are ranges to how well physical elements can",
|
||||
"behave like ideal lumped elements.",
|
||||
"OK, for example, what we will do is show you the",
|
||||
"resistor. And it's going to look like a",
|
||||
"resistor. And I'm going to keep",
|
||||
"increasing the voltage around it.",
|
||||
"OK, what's going to happen at some point?",
|
||||
"I just keep doing that. If it's an ideal element,",
|
||||
"if you're a theorist, you say, oh yeah,",
|
||||
"the curve will keep extending until I reach infinity.",
|
||||
"But this is a practical resistor, so people out here can",
|
||||
"cover your eyes or something. OK, so you're abstraction can't",
|
||||
"predict that. All it says is the current is",
|
||||
"an amp. It can't predict the heat,",
|
||||
"light, or the smell. In the laboratory,",
|
||||
"even, you get the smell. You know what somebody has just",
|
||||
"done. So that's one example of the",
|
||||
"lumped abstraction breaking down.",
|
||||
"So, if I really believe that my own BS, anything is a lumped",
|
||||
"element. So here's a pickle.",
|
||||
"A pickle is a lumped element. I can choose it as a lumped",
|
||||
"resistor. But this is a very interesting",
|
||||
"lumped resistor. Don't try this at home.",
|
||||
"This is a standard pickle into which you are pumping 110 V AC.",
|
||||
"I promise you, this is a standard pickle.",
|
||||
"So, it has a fixed resistance, but your lumped abstraction",
|
||||
"cannot predict the nice light and sound effect.",
|
||||
"OK, so the last two or three minutes what I want to do,",
|
||||
"so remember, don't get carried away by",
|
||||
"abstractions. There are limits.",
|
||||
"OK, you can't predict everything.",
|
||||
"OK, that's the smell of a pickle.",
|
||||
"OK, so let me give you a preview of some upcoming",
|
||||
"attractions, and show you one more quick simplification in the",
|
||||
"last few minutes. So what we can do,",
|
||||
"once we build these lumped elements, we can connect them in",
|
||||
"circuits. OK, so I can build a circuit,",
|
||||
"of the sort. So here's a voltage source with",
|
||||
"a bunch of resistors. I can connect them with wires",
|
||||
"and build a circuit of the sort. One interesting question we can",
|
||||
"ask ourselves is, under the lumped matter",
|
||||
"discipline, what can we say about the voltages?",
|
||||
"OK, if I go around the loop, provided my world adheres to",
|
||||
"the lumped matter discipline, what can I say about the",
|
||||
"voltages around this loop? Ah-ha, Maxwell again,",
|
||||
"right? So, I can write Maxwell's",
|
||||
"appropriate equation to solve that.",
|
||||
"OK, voltages have something to do with E and your integral of E",
|
||||
"dot dl and all of that stuff, right?",
|
||||
"So this is the appropriate Maxwell's equations to use.",
|
||||
"And I want to find out what happens here.",
|
||||
"Now remember, under LMD, I made the",
|
||||
"assumption. OK, my world,",
|
||||
"my playground, has del phi B by del t being",
|
||||
"zero. The rate of change of flux is",
|
||||
"zero. So, under these circumstances,",
|
||||
"I can write this. I can break up this line",
|
||||
"integral into three parts across the voltage source and across",
|
||||
"the two resistors and write that down.",
|
||||
"OK, and then when I can do, is now that the right-hand side",
|
||||
"is zero, I can simply take this. And I know that E dot dl across",
|
||||
"this element is simply VCA. This is VAB,",
|
||||
"and this is VBC equals zero. OK, so when I make the",
|
||||
"assumption that del phi B by del t is zero, and I go around this",
|
||||
"loop, apply Maxwell's equations, what do I find?",
|
||||
"I find that the sum of the voltages, VCA plus VAB plus VBC,",
|
||||
"is zero. That's fantastic.",
|
||||
"So now, I could say hasta la vista to this baby here.",
|
||||
"And I can focus on this guy and say, Maxwell's equations,",
|
||||
"this thing with squiggles and dels and all that stuff,",
|
||||
"can be simplified to the sum of the voltages across a set of",
|
||||
"elements in a loop in a circuit is zero.",
|
||||
"OK, and this is called Kirchhoff's first first law,",
|
||||
"KVL. OK, similarly,",
|
||||
"in recitation section, you'll see the application of",
|
||||
"Kirchhoff's current law, which comes from this be equal",
|
||||
"to zero, and all the currents coming into a node being zero.",
|
||||
"So, KVL and KCl directly come out of the lumped matter",
|
||||
"discipline. And you can use those to solve",
|
||||
"circuits like this."
|
||||
]
|
||||
}
|
||||
@@ -1,1961 +0,0 @@
|
||||
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"text": [
|
||||
"Good morning. Today we move in the direction",
|
||||
"that takes a big turn from the direction we have been going in",
|
||||
"so far. All the devices we have had up",
|
||||
"until now, resistors and voltage sources, and even your digital",
|
||||
"devices like the AND gate or the inverter and so on had a very",
|
||||
"specific property. We didn't dwell on that",
|
||||
"property, but that property was that these were not what are",
|
||||
"called memory devices. In other words,",
|
||||
"the outputs at any given time are a function of the inputs",
|
||||
"alone. In other words,",
|
||||
"if you took your inverter or your NAND gate for that matter",
|
||||
"and you build a circuit comprising 50 NAND gates",
|
||||
"connected in structures that we have talked about,",
|
||||
"you apply an input and boom you get an output.",
|
||||
"And your output is a function of the inputs alone,",
|
||||
"right? The same thing with your",
|
||||
"resistors and voltage sources. At any given point in time your",
|
||||
"output VO of T was some function of the input VI of T.",
|
||||
"What we are going to do today is discuss a new element which",
|
||||
"will introduce a whole new class of fun stuff for all of us to",
|
||||
"deal with. And that is called storage.",
|
||||
"In other words, the output of a circuit is now",
|
||||
"going to depend not just on the inputs but it is going to depend",
|
||||
"on the background or it is going to depend on where the circuit",
|
||||
"has been in the past. So past is going to matter.",
|
||||
"It is a very fundamental difference.",
|
||||
"And what I would like to do is start by giving you folks a",
|
||||
"little bit of a surprise. I am going to do a little demo",
|
||||
"taking two of your inverter circuits.",
|
||||
"",
|
||||
"I am going to start by taking a couple of inverters.",
|
||||
"Remember, I am using this structure here as an inverter.",
|
||||
"And I am going to couple this to another inverter and take an",
|
||||
"output C, some VS, some load resistance RL,",
|
||||
"my B terminal and my A terminal.",
|
||||
"So I'm going to apply some input between ground and my A",
|
||||
"terminal. And for fun I want to apply a",
|
||||
"square wave at the input. A square wave between zero and",
|
||||
"5 volts. And this is how my time goes.",
|
||||
"Let's assume that VS is 5 volts.",
|
||||
"So what I am going to do is plot for you the behavior of",
|
||||
"this inverter. I am going to plot for you A,",
|
||||
"which would look like this. I am going to plot for you B,",
|
||||
"which would be the inverted wave form.",
|
||||
"And then plot C, which would be a wave form that",
|
||||
"looks like this again. Let me do a plot here.",
|
||||
"So this is A.",
|
||||
"",
|
||||
"-- and so on. Time goes this way.",
|
||||
"And let's say this is between zero and 5 volts.",
|
||||
"And B should be an inverted wave form that should look like",
|
||||
"this.",
|
||||
"",
|
||||
"If all that we believe of the world so far is true then this",
|
||||
"is how things should behave, so C should look like this.",
|
||||
"",
|
||||
"This is what the world should look like and if everything that",
|
||||
"you learned about is true and correct and all of the good",
|
||||
"stuff. Let me show you a little demo",
|
||||
"and see if I can try to pull the rug out from under all that you",
|
||||
"have learned so far and show you some surprising stuff.",
|
||||
"",
|
||||
"Here are the three wave forms that I showed you up here.",
|
||||
"This is my A. This is my A wave form.",
|
||||
"This is the B wave form. Notice that B,",
|
||||
"as you expect, is an inverted form of A.",
|
||||
"And this is C. We all expect this,",
|
||||
"correct? But what I am going to do is",
|
||||
"let me expand the time scale on this so that I can look at these",
|
||||
"transitions a little bit more carefully.",
|
||||
"I am just going to expand the time scale.",
|
||||
"There you go. All I have done is expanded the",
|
||||
"time scale and spread that out a little bit.",
|
||||
"And what you see there is quite different from what you expect.",
|
||||
"A is a square wave as expected, but B is stunningly different.",
|
||||
"It is a zero as expected because this is a one.",
|
||||
"But here I get some really strange behavior,",
|
||||
"behavior that is like nothing on earth.",
|
||||
"Like nothing you have seen before.",
|
||||
"And then, of course, it becomes a one eventually,",
|
||||
"but there's some really, really shady stuff going on",
|
||||
"here. And so far you are not prepared",
|
||||
"to deal with this. We have not given you the",
|
||||
"facility to deal with his issue. What is the problem with this?",
|
||||
"We could say who cares? What is the problem with this?",
|
||||
"Let's look at the result. I am looking at this,",
|
||||
"I am focusing on this piece here.",
|
||||
"And notice that instead of being a sharp rise it looks like",
|
||||
"this. It is going up a little bit",
|
||||
"more slowly. What kind of problem would that",
|
||||
"create? The problem that it creates is",
|
||||
"the following. Let me play around with this",
|
||||
"graph a little bit more. What I am going to do is just",
|
||||
"take this output here, the C output and line it up",
|
||||
"against the A output. And so I am going to line up",
|
||||
"the C wave form on top of the A wave form.",
|
||||
"So you can see for yourself if something really,",
|
||||
"really strange and nasty is happening, I am just going to",
|
||||
"move up the C wave form and line it up.",
|
||||
"",
|
||||
"What is happening out there? If you look carefully,",
|
||||
"what you observe is that the C wave form transitions just ever",
|
||||
"so slightly later than the A wave form.",
|
||||
"Look here. And I claim that it is because",
|
||||
"of this. Because of this,",
|
||||
"the C wave form falls just a little bit later,",
|
||||
"and that little thing we see out there is a delay.",
|
||||
"So nothing you have learned so far prepares you for this.",
|
||||
"Suddenly, instead of the output exactly following the input,",
|
||||
"my output is following the input but a little bit later.",
|
||||
"And it is this fact of life that things happen a little bit",
|
||||
"later, is really the reason why each of you and all of us needs",
|
||||
"to buy new computers every couple of years.",
|
||||
"This simple basic fact. If this fact of life didn't",
|
||||
"exist, you would buy one computer and be done with it for",
|
||||
"life. Intel would make gobs of money",
|
||||
"one year, and so would Dell and Gateway and so on,",
|
||||
"and then no more. That's it.",
|
||||
"This is it. But because of this a little",
|
||||
"itty-bitty difference here the entire semiconductor technology",
|
||||
"is charging along trying to do something about that.",
|
||||
"You buy newer and newer computers each year.",
|
||||
"It turns out this little itty-bitty thing here,",
|
||||
"that is called the delay, the inverter delay.",
|
||||
"And it happens because of a specific element that has been",
|
||||
"introduced here that we have not shown you so far.",
|
||||
"And a large part of the semiconductor industry and",
|
||||
"follow-on courses and design and so on focuses on how could I",
|
||||
"make my delay smaller, how can I get to be faster and",
|
||||
"faster and faster? This relates to how fast we can",
|
||||
"clock your Pentium IV. Remember it came all the way to",
|
||||
"1.3 gigahertz? What's the fasted Pentium money",
|
||||
"can buy today? What is the fastest P4?",
|
||||
"Oh, 3.2 have come out? I don't know.",
|
||||
"Ken claims 3.2. But, yeah, there you go,",
|
||||
"3.2 gigahertz. It all has to do with this",
|
||||
"little itty-bitty thing. You saw it for the first time",
|
||||
"here. When some of you become CTOs at",
|
||||
"Intel and so on, just remember that it all began",
|
||||
"on October 16th with this little rinky-dink thing here.",
|
||||
"What you are going to learn now is some really cool stuff that",
|
||||
"has huge implications for life. So why does that happen?",
|
||||
"Why did this transition happen just a little bit later?",
|
||||
"The reason is that remember when this wave form reaches VT,",
|
||||
"the threshold voltage of this MOSFET, this guy is going to",
|
||||
"switch, right? So because of the slower rise",
|
||||
"of the voltage, the VT is going to be reached a",
|
||||
"small amount of time later. So I am going to hit VT",
|
||||
"slightly later. And because of that this guy is",
|
||||
"going to transition just a bit later because this intermediate",
|
||||
"wave form B is slower. It hits VT just a little bit",
|
||||
"later than if it would have made an instantaneous transition.",
|
||||
"And therefore my output falls just a little bit later and this",
|
||||
"gives rise to my delay in the inverter.",
|
||||
"We can call that d if you would like, some delay.",
|
||||
"In your course notes, this material is covered in",
|
||||
"Chapters 9 and 10. That was to kind of motivate",
|
||||
"why we are going to be doing all that you we will be doing.",
|
||||
"Don't anybody come within a foot of this even by mistake.",
|
||||
"I mean it. It is pretty deadly stuff.",
|
||||
"Today we will talk about the capacitor.",
|
||||
"And in the next couple of lectures I am going to tie it",
|
||||
"all together and show you how this relates to that.",
|
||||
"I will show you exactly how the delay happens.",
|
||||
"You can compute it based on some simple principles that you",
|
||||
"will learn about in the next couple of lectures.",
|
||||
"What I am going to do is first of all show you,",
|
||||
"I claim that that delay happens because of the presence of a",
|
||||
"capacitor somewhere in there. What I will do now is take you",
|
||||
"into a closer look, take a closer look at the",
|
||||
"MOSFET and show you were the capacitor is.",
|
||||
"This is the MOSFET that you have seen so far,",
|
||||
"drain, gate and source. This is called an n-channel",
|
||||
"MOSFET. And what I am going to do is",
|
||||
"dissect this and show you what is actually happening,",
|
||||
"what this looks like on silicon.",
|
||||
"So here is my slab of silicon. It is very thin.",
|
||||
"And let's say this is, I won't go into details here.",
|
||||
"You will learn a lot more about this in future device classes",
|
||||
"like 301 and so on, but suffice it to say I will",
|
||||
"just introduce it here to give you a sense of where the",
|
||||
"capacitor is. This is p-type silicon.",
|
||||
"And the way you build a MOSFET is you create a couple of tubs",
|
||||
"in which you dope to be n-type. The basic silicon is dope",
|
||||
"p-type. And this guy here is n-type.",
|
||||
"And what you do is a thin oxide layer is placed on top of that",
|
||||
"and then on top of that a thin metal layer.",
|
||||
"This is a metal layer. This is a thin piece of oxide,",
|
||||
"silicon dioxide. And this is my P substrate.",
|
||||
"Now this is a little metal layer that is really a wire on",
|
||||
"top of the silicone. This metal layer could be some",
|
||||
"sort of a wire that meanders around on the surface of",
|
||||
"silicone. And this is a wire that",
|
||||
"connects to the gate. This is the gate of my MOSFET.",
|
||||
"And this guy here is the drain. And this guy here is the",
|
||||
"source. And this is my gate.",
|
||||
"So there is a little piece of metal here.",
|
||||
"This is this piece of metal here.",
|
||||
"And there is a piece of oxide and then my silicone substrate.",
|
||||
"Notice that this is my oxide. When I apply a positive voltage",
|
||||
"to the gate here with respect to the substrate,",
|
||||
"what happens is that I draw up negative charges.",
|
||||
"I draw up electrons here into this channel region and I have",
|
||||
"corresponding plus type out here so that I get a view here that",
|
||||
"looks like a couple of plates. And I end up with an oxide in",
|
||||
"the middle. There is no connection.",
|
||||
"Two plates separated by a small distance with plus q and minus q",
|
||||
"on the plates. And, because of that,",
|
||||
"what ends up happening here is that this piece behaves like a",
|
||||
"capacitor. So a capacitor has two plates",
|
||||
"with a thin insulating material in the middle with some",
|
||||
"permittivity epsilon. And so I get a little piece of",
|
||||
"a capacitor here. That is the capacitor that is",
|
||||
"forming. I did not set out to build that",
|
||||
"capacitor, but there is a capacitor nonetheless.",
|
||||
"So when I apply a positive voltage at the gate,",
|
||||
"negative electrons are pulled up here which forms a channel,",
|
||||
"and then a current can then flow.",
|
||||
"And that is how the MOSFET turns on.",
|
||||
"So n-type electrons back to n-type, and I get electron flow",
|
||||
"here and that gives me my channel.",
|
||||
"This is just kind of devices in four minutes or less.",
|
||||
"You will do an entire course on this, if you like,",
|
||||
"if you take 301. What we do is to be able to",
|
||||
"capture the behavior that we just saw, the funny delayed",
|
||||
"behavior, we have to augment our model.",
|
||||
"We have to introduce a new element.",
|
||||
"So what we do is here is a MOSFET, gate,",
|
||||
"drain and source. And notice here we model this",
|
||||
"by putting a little capacitor, CGS between our gate and the",
|
||||
"source. So this becomes a simple model",
|
||||
"for our MOSFET device which is the good old gate drain source",
|
||||
"device from the past with a little capacitor CGS having some",
|
||||
"value for CGS in maybe ten to the minus 14 or thereabouts",
|
||||
"farads. So that is a little capacitor",
|
||||
"that has come about in this device that we fabricated here.",
|
||||
"It is that capacitor that is at between node B and ground",
|
||||
"because it is between the gate and the source of the second",
|
||||
"inverter. And it is that capacitor that",
|
||||
"is playing the games that we saw out there.",
|
||||
"",
|
||||
"So let's look at some of the behavior of an ideal linear",
|
||||
"capacitor. A capacitor,",
|
||||
"as I said, has a couple of plates.",
|
||||
"There are a couple of plates. Between the plates is some",
|
||||
"dieletric, permittivity epsilon. Let's say the area of the",
|
||||
"plates is A, and let's say the plates are separated by a",
|
||||
"distance D. I get some charge here,",
|
||||
"let's say q. So q and minus q on the",
|
||||
"capacitor. And the capacitance C is given",
|
||||
"by epsilon A divided by D. Epsilon, as I said,",
|
||||
"is the productivity of the dielectric.",
|
||||
"So if it is free space then it would be epsilon zero which is",
|
||||
"the permittivity of free space. That is the capacitance in",
|
||||
"farads. And the symbol looks like this.",
|
||||
"Capacitor C. Voltage v.",
|
||||
"Current i. So this, much like the",
|
||||
"resistor, voltage source and so on, this now becomes a primitive",
|
||||
"element in your tool chest of elements like the voltage source",
|
||||
"and so onn. Capacitance with the voltage v",
|
||||
"across it and a current i. And I have assigned the",
|
||||
"associated variables here according to the associated",
|
||||
"variable discipline. A question to ask ourselves is",
|
||||
"remember we said we are all now in a playground from all of",
|
||||
"nature, in this playground where the lumped matter discipline",
|
||||
"holds? And also remember that we said",
|
||||
"that for the lumped matter discipline to hold we have to",
|
||||
"make a couple of assumptions. One of those assumptions was",
|
||||
"that dq/dt, for all their elements should be zero for all",
|
||||
"time. So right now what about the",
|
||||
"capacitor? It has got some charge q.",
|
||||
"So charge must have built up somehow.",
|
||||
"Does that mean that I lied all along, that we are no longer in",
|
||||
"this playground, that we have been ejected from",
|
||||
"the playground because of the capacitor, or are we still in",
|
||||
"the circuits playground in which the lumped matter discipline",
|
||||
"holds and all good things happen and so on?",
|
||||
"It seems like a contradiction, doesn't it?",
|
||||
"I took you from Maxwell's playgrounds to the EECS",
|
||||
"playground where I said the lumped matter discipline holds.",
|
||||
"And one of the foundations of the LMD was that dq/dt should be",
|
||||
"zero for all time inside the elements that we are going to",
|
||||
"deal with. And right now boom,",
|
||||
"it's not four weeks into the course and Agarwal introduces an",
|
||||
"element and it has q in it. It turns out that the capacitor",
|
||||
"also adheres to the lumped matter discipline.",
|
||||
"Remember the discipline says that dq/dt is zero for all time",
|
||||
"within elements. So I am going to be clever.",
|
||||
"What I am going to do is I want to choose element boundaries in",
|
||||
"a very cleaver way. Notice that if I have q here on",
|
||||
"this plate then I get minus q on the other plate.",
|
||||
"So if I take the whole element, the element as a whole,",
|
||||
"if I am careful in terms of how I package my boundaries,",
|
||||
"if I put both my plates inside my element boundary then I still",
|
||||
"do get the net charge being zero.",
|
||||
"So dq/dt is indeed zero for all time provided I make sure that",
|
||||
"my element has both the plates. Therefore, if you come across",
|
||||
"somebody else that gives you an element that says I have an",
|
||||
"idea. Let's create a new branch of",
|
||||
"electrical engineering in which we model the capacitor not as",
|
||||
"one element for two plates, but let's build a capacitor by",
|
||||
"combining two new elements, two garbage elements called G1",
|
||||
"and G2. G1 is like the top plate.",
|
||||
"G2 is the bottom plate. I put them together and I get a",
|
||||
"capacitor. But notice if I just pick one",
|
||||
"plate then the element G1 will not adhere to the LMD.",
|
||||
"It adheres to the LMD because I choose my element boundaries in",
|
||||
"a way that both plates come within it.",
|
||||
"So it is very fundamental and key.",
|
||||
"And you can read a lot more about it in the course notes.",
|
||||
"I purposely dwelt on that simple point because I think it",
|
||||
"is foundational and important. And you really need to",
|
||||
"understand that the capacitor does satisfy LMD.",
|
||||
"We are still in the good old playground.",
|
||||
"A few simple facts here. These are in the notes.",
|
||||
"And you have also seen this before, I am sure.",
|
||||
"I can relate the charge to the capacitance and the voltage as q",
|
||||
"is equal to Cv. And q is in coulombs,",
|
||||
"this is in farads and this is in volts.",
|
||||
"So there is some charge q stored on the capacitor and it",
|
||||
"is in coulombs and q is equal to Cv.",
|
||||
"So I can differentiate this with respect to time to get the",
|
||||
"current, and that becomes i=dq/dt.",
|
||||
"So the current at any given time is dq/dt.",
|
||||
"And so I substitute for q in terms of Cv here.",
|
||||
"That is what I get. So the current i=d(Cv)/dt.",
|
||||
"A 6.002 assumption, capacitance in general can be",
|
||||
"time-varying. I can get time-varying",
|
||||
"capacitors. In fact, there are some sensors",
|
||||
"which are capacitive. And, as I talk,",
|
||||
"my sound waves can change the pressure on the top plate of the",
|
||||
"capacitor. And move the top plate of the",
|
||||
"capacitor, thereby changing the capacitance by moving the plate.",
|
||||
"Remember d here, as the plate moves closer I get",
|
||||
"a higher capacitance. So we won't be dealing,",
|
||||
"unless explicitly said so, with time-varying capacitances.",
|
||||
"So what we can do is 6.002 allows us to write Cdv/dt.",
|
||||
"So my current source capacitor is Cdv/dt.",
|
||||
"I can also write down the energy, capacitors store energy.",
|
||||
"E=1/2Cv^2. I am sure you have seen all",
|
||||
"this before in physics and so on.",
|
||||
"That is the amount of energy stored in the capacitor if it is",
|
||||
"holding a charge q. Let me do a little",
|
||||
"demonstration for you. They don't make glasses like",
|
||||
"they used to. Our friend Lorenzo has charged",
|
||||
"up this capacitor. It is a huge capacitor.",
|
||||
"It is a 250 volt capacitor so it is nasty.",
|
||||
"He has charged it up and has kept it there.",
|
||||
"And to show you that it does contain stored charges it has",
|
||||
"been sitting there holding charge.",
|
||||
"Maybe the first row should go backwards, just step back for a",
|
||||
"second. I think you guys would be safe",
|
||||
"but I just don't want to take any chances.",
|
||||
"This is holding a bunch of charge.",
|
||||
"It is kind of sitting there. If I short the terminals it",
|
||||
"should try to say oh, I've got a path,",
|
||||
"let me get my charge out. All right.",
|
||||
"Let's do it. This is always a scary moment",
|
||||
"for me. And I say a little prayer",
|
||||
"before I do this.",
|
||||
"",
|
||||
"Good? OK.",
|
||||
"Gee, you guys would love to see me getting fried,",
|
||||
"huh? All right.",
|
||||
"Let's see.",
|
||||
"",
|
||||
"So it did contain charge.",
|
||||
"",
|
||||
"So there is a reason why Lorenzo puts one hand inside his",
|
||||
"pocket when he shorts it, because there is a natural",
|
||||
"tendency to hold the wire with both hands, and la,",
|
||||
"la, la, la, la and put it across the capacitor.",
|
||||
"By doing this you are guaranteed that you will just be",
|
||||
"touching it with one hand. Hopefully you folks will",
|
||||
"remember for life that a capacitor can sit around and",
|
||||
"hold its charge for a while. All right.",
|
||||
"That is enough of fun and games.",
|
||||
"Let's get on with our business of building circuits.",
|
||||
"What I am going to do is, as I promised you,",
|
||||
"I am going to close the loop on that example by halfway through",
|
||||
"the next lecture. I'm going take you on a bit of",
|
||||
"a journey involving capacitors and resistors and involving some",
|
||||
"analysis, and then we will close it all up for you at about the",
|
||||
"middle of next lecture. What I would like to do next is",
|
||||
"here is a new element. And let's do some fun stuff",
|
||||
"with elements. Well, you know about voltage",
|
||||
"sources, you know about resistors, let's put them",
|
||||
"together and see how they behave.",
|
||||
"Let's have a capacitor here, C, vc(t) and some current i.",
|
||||
"What I am going to do, in general, whenever I have",
|
||||
"something new or something strange, let's say like a",
|
||||
"capacitor or some other device. It is interesting to model the",
|
||||
"rest of the circuit behind it if it contains only resistors and",
|
||||
"voltages and linear elements as a Thevenin equivalent.",
|
||||
"So let me do that. This is R and this is vi.",
|
||||
"This stuff in the back is my standard pattern,",
|
||||
"voltage source in series with a resistor, and I connect that",
|
||||
"across my capacitor. But remember,",
|
||||
"although you saw those funny wave forms and so on,",
|
||||
"the capacitor is a linear device.",
|
||||
"Because you can see from here that the current relates to",
|
||||
"dv/dt. That is a linear operation.",
|
||||
"You don't see V squareds and Vis and things like that in",
|
||||
"there. It's is a linear device.",
|
||||
"Let's go back to our trusty old method, the node method.",
|
||||
"If you just blindly apply the node method and simply grunge",
|
||||
"through a bunch of math, you should be able to get to",
|
||||
"the answer, that is for some voltage v or some form of",
|
||||
"voltage vi, I should be able to figure out what vc looks like.",
|
||||
"So let's do that. This is the node that is of",
|
||||
"interest here with the unknown node voltage vc.",
|
||||
"So let me apply the node method.",
|
||||
"(vc-vi)/R is the current going this way.",
|
||||
"That plus the current through the capacitor should equal zero.",
|
||||
"And what is the current through the capacitor?",
|
||||
"The node method tells me that, get the current in terms of the",
|
||||
"element values. We know that the current is",
|
||||
"given by CdvC/dt.=O. Just shuffling things around a",
|
||||
"little bit, I can write RC dvc/dt+vc=vi.",
|
||||
"We are writing the node equation and then getting the",
|
||||
"equation that characterizes this little circuit.",
|
||||
"Notice here that this has units of volts.",
|
||||
"And since I have time here, this also must have units of",
|
||||
"time.",
|
||||
"",
|
||||
"Let's go about solving this little circuit and understanding",
|
||||
"how it behaves. The specific example that we",
|
||||
"will look at looks like this. Let's say the capacitor voltage",
|
||||
"at time T=0 is V0. This is given.",
|
||||
"So at time T=0, I am telling you that the",
|
||||
"capacitor contains a charge. And because of that there is a",
|
||||
"voltage V0 across it. That capacitor had a voltage of",
|
||||
"250 volts across it and most of the devices we deal with in",
|
||||
"laptops and so on today, like the Pentium IV,",
|
||||
"voltages are on the order of 1.5 volts, very small voltages.",
|
||||
"So that is the value in the capacitor, the voltage.",
|
||||
"That is called a state. This is called the state,",
|
||||
"capacitor state. It is the state of the",
|
||||
"capacitor. And I also give you that",
|
||||
"vi(t)=VI. So my voltage is VI.",
|
||||
"And somehow, I am not telling you how,",
|
||||
"but some how it arranged to have the capacitor voltage be V0",
|
||||
"at time T=0. Now I want to look to the",
|
||||
"solution to this for t greater than or equal to zero.",
|
||||
"And in that time my voltage vi is at some capital VI,",
|
||||
"some DC voltage VI. So I am going to solve the",
|
||||
"differential equation RC dvc/dt+vc=vi given these two",
|
||||
"values. Input is DC voltage VI and VC0",
|
||||
"is V0, the initial charge in the capacitor.",
|
||||
"So from now until almost to the end of the lecture,",
|
||||
"it is just going to be math by solving this very simple first",
|
||||
"order differential equation. And the key here will be that",
|
||||
"throughout 6.002 we will be following one method to solve",
|
||||
"these. There are many methods to",
|
||||
"solving differential equations, and we will follow one method.",
|
||||
"That method is called the method of homogenous and",
|
||||
"particular solutions. In 1802, I believe,",
|
||||
"you would have learned maybe this, and certainly other",
|
||||
"methods. You can use any method to solve",
|
||||
"it. We will just stick to one",
|
||||
"method. And this is also used in the",
|
||||
"course notes. In this method what we do is",
|
||||
"take the solution VC by finding two other components.",
|
||||
"One is called the homogenous solution.",
|
||||
"And summing that up with the particular solution.",
|
||||
"And that is the total solution. So total solution is the sum of",
|
||||
"the homogenous and the particular solutions.",
|
||||
"And the method has three steps. As I said before,",
|
||||
"we will be using this method again and again with every",
|
||||
"differential equation that we encounter in this course.",
|
||||
"And you won't encounter a while lot.",
|
||||
"The first step we find the particular solution.",
|
||||
"The second step, find the homogenous solution.",
|
||||
"The total solution is the sum of the two.",
|
||||
"And then find ---",
|
||||
"",
|
||||
"There will be some unknown constants depending on the",
|
||||
"equation that you have. And in the end we simply find",
|
||||
"the unknown constants by applying the initial conditions",
|
||||
"that we have. Boom, boom, boom.",
|
||||
"Particular. Homogenous.",
|
||||
"Find constants. Three things.",
|
||||
"So let's go about solving this equation and apply those three",
|
||||
"conditions. Again, remember,",
|
||||
"what I am doing now for the next 10 minutes or 15 minutes is",
|
||||
"using math that you know about to simply solve this first order",
|
||||
"of differential equations. There is nothing really new",
|
||||
"that I am going to talk about here.",
|
||||
"One is to find the particular solution vCP,",
|
||||
"which will then be added into the vCH to get me the solution.",
|
||||
"So the way you find the vCP is you find any solution that",
|
||||
"satisfies this equation. This is the equation.",
|
||||
"You find any solution that satisfies it.",
|
||||
"And find the simplest possible solution that money can buy.",
|
||||
"Find it. That's the particular solution.",
|
||||
"Any solution is fine. In this case,",
|
||||
"a really simple one would be vCP equals VI.",
|
||||
"Let's see if a constant works. One thing you will realize in",
|
||||
"differential equations is that they are actually much simpler",
|
||||
"than they seem. And the reason is that almost",
|
||||
"every time you have to assume you know the answer,",
|
||||
"and then you are checking to see what you assumed was",
|
||||
"correct. Assume the answer is this like",
|
||||
"you are really smart, and then check it out and say",
|
||||
"oh, yeah, that must have been the answer.",
|
||||
"So here we assume that I think VI is going to work so let's try",
|
||||
"it out. Substituting in here.",
|
||||
"RC dvc/dt is 0. vi is a constant.",
|
||||
"So I get vi equals vi, so therefore this is a",
|
||||
"particular solution. Done.",
|
||||
"I substitute vi here. So dvi/dt=0.",
|
||||
"This vanishes and vi=VI. Bingo.",
|
||||
"Therefore, VI is a solution to this equation.",
|
||||
"So I am done with my vCP.",
|
||||
"",
|
||||
"And in general what you have to do is use trial and error.",
|
||||
"By trial and error try out a bunch of solutions until you get",
|
||||
"lucky. In general, again,",
|
||||
"in all of 6.002 for many of the excitations a simple constant",
|
||||
"usually suffices. Our second step is to find the",
|
||||
"homogenous solution. And we can also do that very",
|
||||
"quickly. And to do that we have to find",
|
||||
"a general solution to the homogenous equation.",
|
||||
"The homogenous equation is the same differential equation but",
|
||||
"with the drive set to zero.",
|
||||
"",
|
||||
"We want to follow a set pattern to solve the differential",
|
||||
"equations here, and the set pattern is find",
|
||||
"vCP, vCH, find constants. And to find vCH we are also",
|
||||
"going to follow a set pattern to find the homogenous solution.",
|
||||
"So we set the drive to zero, so vi is set to be zero.",
|
||||
"And I need to find a general solution to this.",
|
||||
"As I promised earlier, diff equations are really,",
|
||||
"really simple because the way we are going to solve them is we",
|
||||
"are going to assume we know the answer and then go check it.",
|
||||
"So let's try Ae^st. Let's try and see if this can",
|
||||
"solve this particular equation for some values of A and S.",
|
||||
"I am telling you that the solution is going to be of this",
|
||||
"form. Assume it.",
|
||||
"And then simply go ahead and find me A and S,",
|
||||
"and do that by substituting it back into the equation and find",
|
||||
"out the corresponding As and Ss. So let's go ahead and do that.",
|
||||
"I get RC. I substitute this back up so I",
|
||||
"get dAe^(st)/dt+Ae^st=0. And let me plug that in and see",
|
||||
"what comes. I get RCAse^st+Ae^st=0.",
|
||||
"I want to discard the trivial solution of A being 0.",
|
||||
"That is a trivial solution so I will discard that.",
|
||||
"And what I will do is cancel out the As from here,",
|
||||
"assuming A is not zero, and cancel e^st here.",
|
||||
"And what is left is RCs+1=0. What this is saying is that if",
|
||||
"I can find an S such that this is true then Aest is a general",
|
||||
"solution to my homogenous equation.",
|
||||
"This is easy enough. And so S=-1/RC.",
|
||||
"If I choose my S to be -1/RC then the simple math that I have",
|
||||
"gone through shows me that this must be the solution to the",
|
||||
"homogenous equation. Or in other words",
|
||||
"vCH=Ae^(-t/RC). All this is saying is that",
|
||||
"Ae^(-t/RC) is a solution to my homogenous equation.",
|
||||
"A is an unknown constant. A is some constant.",
|
||||
"I don't know what that is yet. Notice RC has popped up again.",
|
||||
"And the cool thing about RC is that, this is time,",
|
||||
"this also has units of time. We commonly represent RC as",
|
||||
"some time constant tau, as units of time.",
|
||||
"Associated with that circuit is the time constant tau,",
|
||||
"which is simply RC. I commonly write this as",
|
||||
"Ae^(-t/tau).",
|
||||
"",
|
||||
"I am very the end here. I have the particular solution",
|
||||
"here. I have got the homogenous",
|
||||
"solution there. I need to tell you about",
|
||||
"something else. The way I found the homogenous",
|
||||
"solution was in four steps. I assumed a solution of the",
|
||||
"form Ae^st. I created this equation here in",
|
||||
"S. This is called the",
|
||||
"characteristic equation for that circuit.",
|
||||
"We will see this time and time again for RC and other forms of",
|
||||
"circuits. Assume a solution of this form.",
|
||||
"Construct the characteristic equation.",
|
||||
"Find the roots of the characteristic equation.",
|
||||
"In this case it is an equation in S.",
|
||||
"So this is the root. And then form the solution",
|
||||
"based on that root. Four steps.",
|
||||
"Ae^st, characteristic equation, root and then write down the",
|
||||
"general homogenous solution. Four steps there.",
|
||||
"And finally I want to write down the total solution.",
|
||||
"And the total solution is simply vCP+vCH.",
|
||||
"And vCP was VI and vCH was Ae^(-t/tau).",
|
||||
"tau was simply RC. That is my solution.",
|
||||
"Now, remember the last step. The last step was form the",
|
||||
"total solution and find out the remaining constants.",
|
||||
"Find out the remaining constants by using my initial",
|
||||
"conditions. At t=0, I know that vC=V0.",
|
||||
"I know that. And so therefore I can",
|
||||
"substitute t=0 to find the constant.",
|
||||
"So I know that VO=VI+A. t=0, this thing becomes 1,",
|
||||
"and so I get this equation from which I get A=V0-Vi.",
|
||||
"In other words, my solution vC is simply",
|
||||
"VI+(VO-VI) e^(-t/tau). So the last 15 minutes have",
|
||||
"just been math. No electrical engineering here,",
|
||||
"but electrical engineering stopped at the point where you",
|
||||
"wrote this differential equation down, went through a bunch of",
|
||||
"math and came up with a solution.",
|
||||
"Purely mathematically. So here I simply used math to",
|
||||
"get you the solution. And, as I have been promising",
|
||||
"you throughout this course, in the next lecture I will give",
|
||||
"you an intuitive EE method of doing it.",
|
||||
"Real electrical engineers, real EECS folks don't do it",
|
||||
"this way. Real EECS folks do it",
|
||||
"intuitively. And I will show you how to do",
|
||||
"it in four easy seconds in the next lecture.",
|
||||
"But you need to understand the foundations of how this comes",
|
||||
"about, and so this is the answer.",
|
||||
"You can also get the current iC is simply Cdvc/dt.",
|
||||
"I won't do that for you, but you can simply",
|
||||
"differentiate it and get the current.",
|
||||
"So I can plot for you vC, time t, vC.",
|
||||
"The intuitive way of looking at this is I have VI which is the",
|
||||
"final value of the voltage. When t is infinity this part",
|
||||
"goes to zero so the vC is simply VI.",
|
||||
"And then there is a component V0-VI which decays according to",
|
||||
"this starting out at an initial value of V0.",
|
||||
"Notice when t is zero vC is V0, you can see that in the",
|
||||
"equation, and so it starts out at V0 and ends up at VI.",
|
||||
"I start here, I end up here.",
|
||||
"And this portion V0-VI decays out over time like this.",
|
||||
"And this decay is governed by the RC time constant or tau.",
|
||||
"I am going to show you very quickly a couple of examples of",
|
||||
"wave forms, one that goes like this and one that looks like",
|
||||
"this. This is when I start with some",
|
||||
"value V0 and I don't apply any input, it should decay down to",
|
||||
"zero, t, t, vC, vC.",
|
||||
"If I apply zero for VI then this should simply decay down to",
|
||||
"nothing over time. And if I apply some VI but",
|
||||
"there is no state in the capacitor then that same",
|
||||
"equation is going to look like this.",
|
||||
"You can go and confirm for yourselves that when I apply",
|
||||
"some input but the capacitor has zero state, I start at zero,",
|
||||
"I finish up at VI and my wave form looks like this.",
|
||||
"There you go. That's the first one.",
|
||||
"The second one where I have 5 volts on the capacitor and no",
|
||||
"input. Assume that at time equals zero",
|
||||
"I take away an input, short the input voltage to",
|
||||
"ground for example, apply zero volts.",
|
||||
"You will see the decay from 5 volts to 0 volts.",
|
||||
"And in the first case I start with zero volts in my capacitor,",
|
||||
"I apply input of 5 volts, and notice that at t=0 the",
|
||||
"capacitor rises up to that level.",
|
||||
"So notice that these circuits with capacitor and resistors are",
|
||||
"typified by wave forms that are exponential rises and",
|
||||
"exponential decays. We will see more of that next",
|
||||
"time."
|
||||
]
|
||||
}
|
||||
@@ -1,1583 +0,0 @@
|
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|
||||
"text": [
|
||||
"All right, let's get moving. Good morning.",
|
||||
"Let me take a quick poll. So, how many of you have",
|
||||
"completed Lab 4. Completed Lab 4?",
|
||||
"Wow, that's great. So, how many people have begun",
|
||||
"Lab 4? OK, well that's good.",
|
||||
"I won't ask the last question. OK so, well I hope you're",
|
||||
"having fun with this lab. Lab 4 was designed to be almost",
|
||||
"like a mini-project. And, it sort of ties together a",
|
||||
"lot of the content of the entire course.",
|
||||
"And, it's not unlike the kind of systems that people design in",
|
||||
"industry, in systems that go into a variety of devices like,",
|
||||
"say, for example, digital CD players and stuff",
|
||||
"like that. A lot of mixed signal stuff",
|
||||
"goes in. OK, so today,",
|
||||
"I'm going to continue with our discussion of energy and CMOS.",
|
||||
"CMOS will be a new topic that I will introduce.",
|
||||
"So, the last lecture, we spent a fair bit of time",
|
||||
"talking about energy, and how to compute the energy",
|
||||
"of our inverter. So, let me start from where I",
|
||||
"left off, and I've given you a couple of extra pages of notes",
|
||||
"today just to sort of tie it to the previous lecture.",
|
||||
"Right now, I'm going to start off on page three.",
|
||||
"So, what we saw last time was an inverter of this sort,",
|
||||
"Vs, VIN, and we said, let's study the situation where",
|
||||
"this inverter was driving a load capacitor, C.",
|
||||
"Where did this load capacitor come from?",
|
||||
"Well, this inverter could be driving one, or two,",
|
||||
"or three, or four other larger gates, OK?",
|
||||
"So, this C is lumped value of the gate capacitances of all of",
|
||||
"those inverters. This may also include some",
|
||||
"component due to wiring capacitance and stuff like that.",
|
||||
"So, for an inverter like this, we showed in the last lecture",
|
||||
"that the formula for the average power was,",
|
||||
"so this was a static power independent of frequency,",
|
||||
"and this was called dynamic power, and it had some bearing,",
|
||||
"it's related to the frequency at which you clocked your",
|
||||
"circuit. So, this was related to standby",
|
||||
"power, and this to dynamic. So, what I also said is that I",
|
||||
"gave you a bunch of numbers so you could compute the power",
|
||||
"consumption of a chip that included 10^8 gates,",
|
||||
"100 million gates, and at a frequency of 1 GHz,",
|
||||
"and a bunch of other numbers. C was given to be 0.1",
|
||||
"femtofarads. Femto is 10^-15.",
|
||||
"So, F was 10^9. VS was 5V, and for these",
|
||||
"numbers, if you plonk them down in something like this,",
|
||||
"for 10^8 gates on a chip, the average power would be 10^8",
|
||||
"times these two. So, this would be five squared,",
|
||||
"which is 25, divided by twice.",
|
||||
"RL was given to be 10 kilo-ohms, so,",
|
||||
"twice, 10^4. And here we had CVS^2.",
|
||||
"So, C was 10^-16, 0.1 femtofarads.",
|
||||
"Vs^2 was 25, and F was 10^9.",
|
||||
"So, if you commence through the numbers here,",
|
||||
"what you end up getting is something that looks like this,",
|
||||
"10^8 times this guy here. This is 1.25mW plus this guy",
|
||||
"ends up being 2.5 microwatts. So, this should come as a bit",
|
||||
"of a shocker. If I take 1.25mW,",
|
||||
"and multiply that out by 10^8, this says that each gate",
|
||||
"suffers a standby power loss of 1.25mW.",
|
||||
"So times 10^8, I get 125kW,",
|
||||
"and this guy yields 250W. OK, the 250W is manageable.",
|
||||
"It's still high, and just so you don't think",
|
||||
"that this is unreasonable, when the Pentium 4 first came",
|
||||
"out, it was consuming 170W of power.",
|
||||
"OK, you should see the heat sinks on there.",
|
||||
"There's actually a huge heat sink with a fan built into the",
|
||||
"top of the heat sink. OK, today it's down to more",
|
||||
"reasonable numbers like 100W and so on, but when it came out it",
|
||||
"was in this range. So it's high but not",
|
||||
"unreasonable. But this, of course,",
|
||||
"is totally wacko. OK, imagine carrying a laptop",
|
||||
"around, and the sucker is blowing 125kW.",
|
||||
"That'll be fun. So, clearly there's something",
|
||||
"wrong here. What this is saying is that",
|
||||
"this gate here consumes 125kW, there are 10^8 of these on a",
|
||||
"single chip. OK, so we clearly have to do",
|
||||
"something about this, otherwise the semiconductor",
|
||||
"industry would fail. So, anybody have any ideas?",
|
||||
"What do you think you might do here?",
|
||||
"What do you think you might do to this inverter to make this",
|
||||
"look better, to bring it down? What can I do?",
|
||||
"Anybody? Any ideas?",
|
||||
"What do you think? Well, the problem is that if I",
|
||||
"look at this 125kW, well, there's a VS term here",
|
||||
"and an RL term here. So, I can increase RL.",
|
||||
"OK, I can make RL four times or eight times as large.",
|
||||
"That'll bring the power down somewhat.",
|
||||
"Can anybody think of any problem with increasing RL?",
|
||||
"If I make RL really, really large,",
|
||||
"will I run into other problems? Yes?",
|
||||
"Exactly, the slowdown of the inverter.",
|
||||
"Remember, the rise time of the inverter depends on how quickly",
|
||||
"I can charge this capacitor through RL.",
|
||||
"So, if I make my RL really large, I will consume less",
|
||||
"standby power from hundreds of kilowatts to merely tens of",
|
||||
"kilowatts. But my gates will run as slow",
|
||||
"as molasses. So, clearly that's not a",
|
||||
"tradeoff I would like to make. So, I can reduce my voltage to",
|
||||
"maybe a volt. But that just reduces it by a",
|
||||
"factor of 25, VS squared.",
|
||||
"So clearly, this is not going to work.",
|
||||
"I have to somehow do something else, and that will be the topic",
|
||||
"of today's lecture. Also, I will dwell for a moment",
|
||||
"on this term. So, if you look at the spec",
|
||||
"sheet for the IBM's ASIC processor that we handed out,",
|
||||
"if you recall, we talked about power",
|
||||
"dissipation of 0.006 microwatts per MHz per gate.",
|
||||
"OK, now you see where this is coming from.",
|
||||
"Per MHz, that's because it's a multiple of f,",
|
||||
"the power. Second is that it's per gate,",
|
||||
"so this is the power per gate. So, as I have more gates,",
|
||||
"I just have that much more power dissipation.",
|
||||
"It also says power supply voltage in the range of 0.7 to",
|
||||
"1.3 right next to the power expression.",
|
||||
"So, you can see why they tell you all of that,",
|
||||
"because both voltage, and the frequency,",
|
||||
"and the number of gates come into the power of equation.",
|
||||
"OK, this really simple expression here,",
|
||||
"it's amazing how close this is to what people use for the",
|
||||
"dynamic power in chips. OK, so as the next step,",
|
||||
"what I'd like to do is, this guy, what do we do about",
|
||||
"that? OK, so we've taught you to",
|
||||
"build gates in a particular matter, but it's a non-starter.",
|
||||
"So, how do we get rid of static power?",
|
||||
"How do we get rid of static power?",
|
||||
"OK, to do so, let's build up a little bit of",
|
||||
"intuition. OK, so the intuition goes as",
|
||||
"follows. So let's say I take my",
|
||||
"inverter. Let me draw the circuit both on",
|
||||
"the on state and in the off state.",
|
||||
"",
|
||||
"So, when VIN is high, when VIN is high,",
|
||||
"I get the MOSFET turning on and has a resistance,",
|
||||
"RON, and Vo is the output voltage.",
|
||||
"Similarly, when VIN is low, so when VIN was high,",
|
||||
"Vo was low because RON is much less than RL.",
|
||||
"So, this voltage was low, while here, when VIN is low,",
|
||||
"the MOSFET is off, and so I have an open circuit",
|
||||
"out here. And because of that open",
|
||||
"circuit, the voltage here was going to be high because VS",
|
||||
"would simply appear there. So let's tailor this and see if",
|
||||
"we can build up some intuition as to what to do.",
|
||||
"So, when VIN is low, I don't have any static power",
|
||||
"being dissipated because I don't have a connection from VS to",
|
||||
"ground. OK, the current,",
|
||||
"i, is zero. And, VS simply appears at the",
|
||||
"output. The reason this is so is have a",
|
||||
"switch here. So when this is low,",
|
||||
"the switch opens up and cuts the path from power to ground.",
|
||||
"This is a nice situation. Here, when VIN was high,",
|
||||
"there was no switch that turns off.",
|
||||
"Rather, I get a connection from VS to ground.",
|
||||
"OK, so think about this situation here.",
|
||||
"The insight here is, just imagine if I could do the",
|
||||
"following. Imagine if I could somehow",
|
||||
"magically elevate RL to be a very, very, very large number,",
|
||||
"if I could make this so high as to make the power really low",
|
||||
"only in the situation when the input was high,",
|
||||
"OK? So, imagine if I could do",
|
||||
"something like this. Imagine I could open circuit",
|
||||
"this guy, RON, so when VIN was high,",
|
||||
"if I could, instead of having an RL here, what if somehow I",
|
||||
"could make this RL become infinity?",
|
||||
"OK, so in this case, output VO would be low.",
|
||||
"OK, I get many benefits by doing this.",
|
||||
"One benefit is that, look, I have opened this switch",
|
||||
"here so I don't have any standby current.",
|
||||
"OK, the standby current is zero.",
|
||||
"The second benefit is that my output gets dragged down to",
|
||||
"ground, OK? Out here, my output was VS",
|
||||
"multiplied by RON divided by the sum of these two.",
|
||||
"Out here, I have a direct connection to ground,",
|
||||
"and nothing to the power supply, VS, and so therefore I",
|
||||
"have a nice, solid low. So the question is that,",
|
||||
"can I get this situation? OK, that is a key insight.",
|
||||
"So, imagine that somehow, when this was high,",
|
||||
"I could get this to open up, much like when this was low,",
|
||||
"I got this to open up. OK, so think about it.",
|
||||
"So, the intuition is that what I need instead of a resistor",
|
||||
"here, what if I have something like the MOSFET that I have",
|
||||
"here? So, I have a MOSFET here that",
|
||||
"turned off when VIN was low. OK, what if I did the",
|
||||
"complementary thing? What if I put in some kind of",
|
||||
"MOSFET here that would turn off when VIN was high?",
|
||||
"OK, so, much like the MOSFET turned off when VIN was low down",
|
||||
"here, imagine if I could find a device that could turn off when",
|
||||
"VIN was high? OK, this would be on,",
|
||||
"but this would be off. So the behavior of this device",
|
||||
"would have to be complementary to this device.",
|
||||
"So, we need some sort of a switch to introduce this new,",
|
||||
"little MOSFET device with slightly different properties,",
|
||||
"let me quickly review for you the properties of the MOSFET",
|
||||
"that we know about, so our N channel MOSFET,",
|
||||
"also called the NFET, this is what we've been seeing",
|
||||
"all this while, is drawn like this.",
|
||||
"I have a gate; I have a drain;",
|
||||
"I have a source. And this guy is on when VGS is",
|
||||
"greater than or equal to VT, OK, and off when VGS is less",
|
||||
"than VT. You saw this before,",
|
||||
"OK, nothing new here. So, what I need is a device",
|
||||
"that behaves in a complementary manner.",
|
||||
"OK, so the device is a P channel MOSFET.",
|
||||
"By the way, I must point out, till about 1983-84 until the",
|
||||
"early '80s, that's exactly pretty much how chips were",
|
||||
"designed, OK, using an NFET for the switch",
|
||||
"looking down here, and a variety of different",
|
||||
"kinds of devices to be used as resistors.",
|
||||
"OK, that's when technology began moving towards this new",
|
||||
"kind of technology I'm going to talk about, and that",
|
||||
"dramatically reducing the power consumed.",
|
||||
"And, the P channel MOSFET was created, and this guy's called",
|
||||
"the PFET. It's a complementary device",
|
||||
"that looks as follows. OK, the difference here is",
|
||||
"that, to show this is complementary,",
|
||||
"I'll put a little circle here. It has a gate.",
|
||||
"Just to make things a little clearer, flip the drain and",
|
||||
"source terminals, and this guy is on at a",
|
||||
"distinguished threshold voltage of this with the NFET device,",
|
||||
"let me put an N here to say that this is the VT for the N",
|
||||
"channel device. And for this guy,",
|
||||
"this guy came on when VGS was greater than some voltage.",
|
||||
"So, VTN could be, for example,",
|
||||
"one volt. So, VGS was more than one.",
|
||||
"This turned on. In this case,",
|
||||
"I wanted this to turn on when VGS is some value which is lower",
|
||||
"than, or much lower than, the source voltage.",
|
||||
"OK, so this guy turns on when the gate voltage is higher.",
|
||||
"This guy should turn on when the gate voltage is",
|
||||
"significantly lower than the source voltage,",
|
||||
"just the complementary behavior.",
|
||||
"OK, so when VGS is less than or equal to VTP.",
|
||||
"And in this case, the threshold voltage for the",
|
||||
"PMOS device, say, just as an example,",
|
||||
"maybe -1V. So this means that if the",
|
||||
"source is at, say, 5V, OK,",
|
||||
"then this device would turn on if the gate, for example,",
|
||||
"using that example was less than 4V.",
|
||||
"So, this is five. If the gate fell below 4V,",
|
||||
"this guy would turn on. In this situation,",
|
||||
"remember, if this was at zero, the gate would have to be",
|
||||
"greater than 1V to turn on. In this situation,",
|
||||
"the gate has to be less than 4V if the source was at five to",
|
||||
"turn on. And, it's off.",
|
||||
"OK, so this is a complementary device that I postulate that",
|
||||
"behaves in a complementary manner.",
|
||||
"So, the gate voltage rises, this guy turns on,",
|
||||
"and in this situation, when the gate voltage drops",
|
||||
"below the source voltage, this guy turns on.",
|
||||
"OK, so when there's a rising guy that turns on in this",
|
||||
"particular situation when it falls, the gate turns on and",
|
||||
"shows some resistance. In this case,",
|
||||
"the resistance would be RON. And to show that it's N",
|
||||
"channel, let me say N. And in this case,",
|
||||
"the resistance, when it turns on,",
|
||||
"would be RONp to represent P channel.",
|
||||
"OK, so now consider the following circuit for the",
|
||||
"inverter. So, instead of my resistor,",
|
||||
"I put a complementary device, OK, and that's it.",
|
||||
"So all I've done here is replace my resistor with a",
|
||||
"MOSFET that behaves complementary to the N channel",
|
||||
"MOSFET. So this is my gate,",
|
||||
"my drain. This is my source,",
|
||||
"my gate, my source, and my drain.",
|
||||
"OK, and this guy is called a pull up, and this guy is called",
|
||||
"a pull down. OK, and the reason is that this",
|
||||
"guy pulls the output to ground when it's turned on,",
|
||||
"while this guy, when switched on,",
|
||||
"will pull this node up to VS. So, I pull it down or pull it",
|
||||
"up based on when the VIN is high or low.",
|
||||
"So, let's look at the two situations.",
|
||||
"So, let's say, as an example,",
|
||||
"my VS is 5V, and let's say VIN in one",
|
||||
"situation being 5V, and another situation being",
|
||||
"equal to 0V. Let's draw the equivalent",
|
||||
"circuit in both these cases. So, when VIN is high,",
|
||||
"I have my usual circuit. When VIN is high,",
|
||||
"this MOSFET, as before, when VIN is 5V,",
|
||||
"the N channel MOSFET below is turned on, and so I have an RON",
|
||||
"resistance here. But remember,",
|
||||
"VIN is 5, and VS is 5V, then the voltage across the",
|
||||
"source and the gate of this P channel FET is now equal,",
|
||||
"five and five. OK, so this one would turn off.",
|
||||
"And that's the circuit that I get.",
|
||||
"The output is suitably low. In this situation,",
|
||||
"if VIN is zero, what happens in this situation?",
|
||||
"Here's my output. If VIN is 0V,",
|
||||
"the lower device turns off. This is zero.",
|
||||
"This is zero. This guy turns off,",
|
||||
"and that's the situation for the N channel MOSFET.",
|
||||
"How about this guy here? What happens here?",
|
||||
"This is at 5. So let me just,",
|
||||
"this is at 5V. OK, and VIN is at 0V.",
|
||||
"OK, so therefore, the GS of this is -5V.",
|
||||
"If this is zero and this is five, G, source,",
|
||||
"and drain, GS is -5V, and -5V is significantly less",
|
||||
"than the threshold -1V in our example.",
|
||||
"So, this one will switch on. And if this one switches on,",
|
||||
"what I end up getting is RONp out there.",
|
||||
"So, when this one kicks in, it pulls the output high and VO",
|
||||
"goes high. So, all I've done is replaced",
|
||||
"my resistor with a complementary device, which switches off when",
|
||||
"the input is high, and switches on when the input",
|
||||
"is low. And the beauty of this is that",
|
||||
"at no point, assuming all the devices are ideal here,",
|
||||
"at no point do I have a short circuit between the output,",
|
||||
"do I have a current path from the output to the ground from",
|
||||
"the supply to ground, OK, I have this turned off or",
|
||||
"this turned off. So, this type of logic",
|
||||
"involving a PMOS transistor here, and the N channel",
|
||||
"transistor here is called CMOS logic for, OK,",
|
||||
"it's called complementary MOS logic.",
|
||||
"That's what CMOS comes from. OK, so I'm sure you've read in",
|
||||
"a number of places that most digital chips today use CMOS",
|
||||
"technology. It comes from complementary",
|
||||
"MOS, and complementary comes from the use of complementary",
|
||||
"transistors: N channel, P channel, turns on when high,",
|
||||
"turns off when high, turns off when low,",
|
||||
"turns on when low. OK, that's exactly",
|
||||
"complementary to each other. OK, so what you've seen here",
|
||||
"has been the workhorse of the digital industry for the past",
|
||||
"two decades, 20 years, CMOS logic.",
|
||||
"OK, and even the most advanced chip from Intel has an inverter",
|
||||
"that looks exactly like that. OK, if you count all the",
|
||||
"inverters in the universe today, I would say a significant",
|
||||
"fraction of those look exactly like that, no difference,",
|
||||
"just so simple. So, the key with something like",
|
||||
"that is there is no path from the power supply to the ground,",
|
||||
"and so by that model, I did not consume any standby",
|
||||
"power. OK, my standby power in that",
|
||||
"idealized model is zero. So, let's compute P.",
|
||||
"So, what is P dynamic? Let's use the method that we",
|
||||
"adopted in the last lecture, and draw the equivalent",
|
||||
"circuit, and compute the power. OK, so I'm going to model the",
|
||||
"following situation, and assume that I drive a",
|
||||
"capacitive load, C.",
|
||||
"OK, and as an input, as I did the last time,",
|
||||
"I'm going to assume I have some input voltage,",
|
||||
"VIN, that looks like this. The cycle time,",
|
||||
"T, and the frequency is 1/t, and let me assume that this is",
|
||||
"T1, and this is T2. OK, and I'm assuming that T1",
|
||||
"and T2 are both much larger than the respective time constants.",
|
||||
"OK, the time constants when, for discharging here,",
|
||||
"is C RONn, and here the relevant resistance is RONp.",
|
||||
"The charging time constant is RONp times C.",
|
||||
"OK, so T1 and T2 are assumed to be much greater than these two.",
|
||||
"So when you look at this, there's one other benefit",
|
||||
"besides the power benefit, OK, of using CMOS logic",
|
||||
"compared to using NMOS. OK, it not only cuts out my",
|
||||
"standby power, but there is another",
|
||||
"significant advantage which is almost equal to the power",
|
||||
"advantage of this kind of CMOS technology.",
|
||||
"Anybody have any ideas? What's the advantage?",
|
||||
"What does intuition tell you? Is CMOS going to be faster or",
|
||||
"slower than NMOS? Why?",
|
||||
"That's right. The key here is that the NMOS",
|
||||
"design I showed you earlier was relatively slow because it took",
|
||||
"me a while to charge up the load capacitor from RL.",
|
||||
"In this situation, RL will become really,",
|
||||
"really small; it's RONp.",
|
||||
"It's roughly the same magnitude as RONm.",
|
||||
"OK, if so both of these on resistances are more or less",
|
||||
"equal and small, then the rise time will be of",
|
||||
"the same order of magnitude as the fall time,",
|
||||
"which makes this much faster than the NMOS.",
|
||||
"In NMOS, my time constant was RLC, and RL was pretty large.",
|
||||
"In this case it's RONp C, and RONp can be made to be very",
|
||||
"small because when it's switched off, the resistance here is",
|
||||
"infinity. So, in this situation,",
|
||||
"if I assume T1 and T2 are much larger than the respective time",
|
||||
"constants, I can go ahead and draw my equivalent circuit.",
|
||||
"So, here's VS. So, for charging up,",
|
||||
"let's say this one is going to a one, or to a high.",
|
||||
"So, I have VS going through a resistor, RONp,",
|
||||
"to a capacitor, and this thing is a switch.",
|
||||
"So I have RONp, an ideal switch,",
|
||||
"going to a capacitor, C, this is my V out node,",
|
||||
"OK, so it's VS going through a resistance, RONp,",
|
||||
"an ideal switch, to a capacitor,",
|
||||
"C. That's a charging circuit.",
|
||||
"For discharging, I have C, discharging through",
|
||||
"an ideal switch with RONn. So, this situation,",
|
||||
"I have an ideal switch, RONn.",
|
||||
"OK, so that's the equivalent circuit for something like this.",
|
||||
"So, in this circuit, during T1, this guy's off,",
|
||||
"and this guy's on, on during T1,",
|
||||
"and off otherwise. This guy is on during T2,",
|
||||
"and off otherwise. OK, so just imagine,",
|
||||
"this guy switches on, this guy switches off,",
|
||||
"this guy switches on, this guy switches off,",
|
||||
"OK? And remember,",
|
||||
"this is exactly the circuit I had analyzed last time in the",
|
||||
"last lecture, and the result given by v",
|
||||
"double asterisk. And that result was simply",
|
||||
"average power being CVS^2f. That's the exact circuit we",
|
||||
"used to compute the dynamic power, CVS^2f.",
|
||||
"OK, so we're done. And how did this come about?",
|
||||
"This came about because the intuition here is that I'm",
|
||||
"charging up the capacitor fully, and then I'm discharging the",
|
||||
"capacitor through this other side, OK, and I'm consuming",
|
||||
"power, dissipating power, in these two resistances during",
|
||||
"charge up and during the discharge.",
|
||||
"Half the power gets consumed during charge up,",
|
||||
"and half during the discharge. So, I'd like to go back to",
|
||||
"doing a few numbers here, and taking a look at how,",
|
||||
"even with this expression, life can get pretty thorny as",
|
||||
"we go ahead into the next decade.",
|
||||
"OK, so for our previous example, we assumed that 10^8",
|
||||
"gates, F=1 GHz, C=0.1 femtofarads,",
|
||||
"VS was 5V, and I don't need RL anymore.",
|
||||
"OK, why is it that I don't have any resistance component here?",
|
||||
"I don't have it here because the power consumed by this",
|
||||
"circuit is independent of those resistances, provided T1 and T2",
|
||||
"are long enough, are much longer than the two",
|
||||
"time constants, RONp C, and RONn C.",
|
||||
"OK, so I don't have RL in my equation anymore.",
|
||||
"I don't have any standby power. So, based on this calculation,",
|
||||
"the calculation I did up there showed that I had 2.5 microwatts",
|
||||
"per gate, and for 10^8 gates I had 250W for a chip with 10^8",
|
||||
"gates. So, I'd like to dwell on this,",
|
||||
"if you can move over to page eight in your notes,",
|
||||
"here. Let me dwell on this for some",
|
||||
"time, and pontificate on a few things.",
|
||||
"First of all, this number,",
|
||||
"as I said before, is high, but not a disaster.",
|
||||
"OK, so you can't use this in laptops, but it's quite OK for a",
|
||||
"desktop or a server, and so on.",
|
||||
"If you just go and put your ear to a pedestal computer,",
|
||||
"you'll always hear it making a sound, and that sound is because",
|
||||
"of a big fan that's inside it. And, if you have a big enough",
|
||||
"fan, 250W is not such a big deal.",
|
||||
"But, this is certainly a real problem for mobile devices.",
|
||||
"For a laptop, this is unthinkable.",
|
||||
"OK, so we have to deal with this.",
|
||||
"The second issue is the following, that it's 250W for",
|
||||
"1GHz. Now, the fastest Pentium 4s",
|
||||
"that money can by today are, what, how many GHz?",
|
||||
"What's the fastest Pentium 4 you can buy today?",
|
||||
"What's that? Does anybody have a 4GHz",
|
||||
"Pentium 4 here? Oh, darn, you beat me.",
|
||||
"Anybody have a 3? 3GHz?",
|
||||
"A couple. So, I have a couple of 3GHz",
|
||||
"machines, and our lab has a whole ton of them.",
|
||||
"So, if Intel comes out with 4GHz machines today,",
|
||||
"they've been going up by about 1GHz roughly every year for the",
|
||||
"past couple of years. And, within three or four",
|
||||
"years, you're going to see chips, microprocessors that are",
|
||||
"in the 5-10GHz range, OK, assuming that all other",
|
||||
"things stay equal, which of course they're not,",
|
||||
"but just to give you some insight here,",
|
||||
"if I clock these guys and build circuits that are ten times",
|
||||
"faster, I very soon go up to 2.5kW, again as I said,",
|
||||
"all things being equal which they're not.",
|
||||
"But just to give you a sense, as I increase my frequency,",
|
||||
"so does the power consumed by the chip, OK?",
|
||||
"So, I really have to do something here.",
|
||||
"So, if I stare at this equation, CVS^2f,",
|
||||
"I want to increase f because people will buy computers if I",
|
||||
"have higher frequencies. And, Intel has managed to use",
|
||||
"its marketing campaigns to pretty much convince consumers",
|
||||
"that high frequencies are a good thing.",
|
||||
"OK, and whether they really mean anything or not,",
|
||||
"that's a different issue. So, we've got this huge power",
|
||||
"for assuming 5V, OK, so it turns out that",
|
||||
"microprocessors, as they come out,",
|
||||
"newer and newer versions run at lower and lower voltages.",
|
||||
"OK, they invent technologies that use lower and lower",
|
||||
"voltages, and go from VS 5V to, today, VS on the order of 1.5",
|
||||
"to 1V, somewhere in that range. So the moment you do that,",
|
||||
"you get a 25x reduction in power.",
|
||||
"OK, so in going from 2.5kW, you would now come down to",
|
||||
"something on the order of 100W, which is, again,",
|
||||
"much more reasonable, again, all other things being",
|
||||
"equal. It turns out that the",
|
||||
"capacitance of devices also changes as you go to smaller and",
|
||||
"smaller devices. And, 100W is also pretty high,",
|
||||
"and still not good enough for mobile computers.",
|
||||
"So, there are many, many other tricks that people",
|
||||
"use to get even lower powers. One trick is to play games with",
|
||||
"the clock. OK, what you do is,",
|
||||
"let's say for example in some computation you are not going to",
|
||||
"be using your floating point unit.",
|
||||
"Or let's say I'm going to be using your integer adder unit.",
|
||||
"OK, so what you can do is you can turn off the clock to those",
|
||||
"devices so that those devices do not even switch when they're not",
|
||||
"working. OK, if I turn off the clock to",
|
||||
"a device, the device isn't even going to switch,",
|
||||
"it's just going to sit there in limbo without consuming any",
|
||||
"power. It's equivalent to turning off",
|
||||
"both transistors. If you turn off both the PMOS",
|
||||
"and NMOS somehow, OK, it's not consuming any",
|
||||
"power. And by doing that,",
|
||||
"you can further cut down the power.",
|
||||
"So, if you can idle some of your function units,",
|
||||
"it's called idling a function unit, idle a function unit for,",
|
||||
"let's say, half the time. OK, you would cut down power by",
|
||||
"another factor of two. We can idle,",
|
||||
"then, 75% of the time, come down to 25W.",
|
||||
"So, those are the classes of tricks that people play.",
|
||||
"I'm going to stop here and allow the underground guide",
|
||||
"folks to do the survey. But, suffice it to say that the",
|
||||
"power discussion that I've gone through with you is a very high",
|
||||
"level discussion as to the real thing.",
|
||||
"In real life, what actually happens is that",
|
||||
"there is a fair amount of standby power even for CMOS",
|
||||
"logic. It turns out that although I",
|
||||
"don't have a path from VS to ground for my two transistors,",
|
||||
"it turns out that there are many leakage currents.",
|
||||
"OK, currents leak through all kinds of places through the",
|
||||
"drain of the inverter, and so on and so forth.",
|
||||
"And so, there is some standby power.",
|
||||
"So, let me show you a quick demo while, I guess,",
|
||||
"the review handouts are going around.",
|
||||
"And this shows the temperature of my CMOS inverter,",
|
||||
"and as I increase the frequency, you can just watch",
|
||||
"the temperature go up, and hopefully we'll blow this",
|
||||
"transistor. So, I'm increasing the",
|
||||
"frequency as you can see on the side here, and higher frequency",
|
||||
"implies more power consumption, more temperature,",
|
||||
"OK, and hopefully you will see some smoke coming out of,",
|
||||
"OK, I think I blew the inverter.",
|
||||
"So, the output is gone. So, it's at 110 degrees there,",
|
||||
"and that blew it. Sometimes we see smoke come",
|
||||
"out, but I guess today is not one of our lucky days.",
|
||||
"OK, so let me stop here and have the underground guide folks",
|
||||
"go through the reviews."
|
||||
]
|
||||
}
|
||||
@@ -1,1982 +0,0 @@
|
||||
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"text": [
|
||||
"OK, good morning all. So before we begin,",
|
||||
"I just thought I'd show you a little news item that I happened",
|
||||
"to read that was very relevant to what we covered recently in",
|
||||
"6.002. So you recall when we did the",
|
||||
"digital section a few days ago last Thursday,",
|
||||
"we talked about a switch. We talked about the MOSFET",
|
||||
"switch, which when turned on and off, by input signals could help",
|
||||
"build gates which would then be combined in tens of millions of",
|
||||
"quantities and go into chips like the Pentium 4 and AMD",
|
||||
"Athlon 64, and so on it so forth.",
|
||||
"So I just saw this news item that I came across,",
|
||||
"and this says they are rethinking the basic",
|
||||
"construction of the products. It talks about the",
|
||||
"semiconductor manufacturers like AMD, Intel, and others that",
|
||||
"build digital chips. They are rethinking the basic",
|
||||
"construction of the products down to the architecture of the",
|
||||
"transistor. That's a MOS transistor,",
|
||||
"and the on/off switch inside the chip.",
|
||||
"OK, now this might imply that there is a single switch inside",
|
||||
"the chip, but no, there's tens of millions of",
|
||||
"transistors, or tens of millions of switches inside a chip.",
|
||||
"And pretty much any advancement that can be made to the basic",
|
||||
"transistor can have a 10 million to 20 million times effect",
|
||||
"because there are that many of them on a single chip.",
|
||||
"So I thought that was very appropriate.",
|
||||
"OK. Let's dive into a quick review.",
|
||||
"So this week, we had begun nonlinear",
|
||||
"analysis, and I just thought I'd blast through a few animations",
|
||||
"that I've created, trying to give you more insight",
|
||||
"into the behavior of some of the things that we have done.",
|
||||
"Now first of all, as I did the last time,",
|
||||
"let me try to put it in perspective most of what you've",
|
||||
"learned thus far, and what we will be learning",
|
||||
"today. So the past week,",
|
||||
"we have been focusing on nonlinear analysis.",
|
||||
"And as I pointed out, here is how this fits into the",
|
||||
"big picture. So, we had our 6.002 world,",
|
||||
"at what we said is that we are engineers.",
|
||||
"We are going to devise our own playground in which to play with",
|
||||
"our own rules. And that's our playground.",
|
||||
"That's what we're going to learn about in 002,",
|
||||
"and for that matter, the rest of EECS at MIT.",
|
||||
"It's all within this playground here.",
|
||||
"And this is the playground with lumped circuit abstraction,",
|
||||
"and good old KVL, KCl, node method,",
|
||||
"your basic composition rules apply within this playground",
|
||||
"that directly come from Maxwell's equations because you",
|
||||
"have made the lumped matter discipline assumptions.",
|
||||
"OK, so then we said a large part of the playground is",
|
||||
"linear, and some other much more intuitive techniques apply",
|
||||
"within the linear portion of that playground,",
|
||||
"techniques like the superposition,",
|
||||
"Thevenin and Norton. In most exercises,",
|
||||
"and quizzes, and experiments,",
|
||||
"and so on that you do in real life, you can pretty much apply",
|
||||
"these simple techniques. Very rarely do you have to go",
|
||||
"into the node method for circuits that are more",
|
||||
"complicated than single source and a couple of elements.",
|
||||
"And then, there's the nonlinear part.",
|
||||
"Remember, the reason I showed this is that this is the same",
|
||||
"playground. OK, linear and nonlinear are",
|
||||
"part of the same playground. OK, even nonlinear elements are",
|
||||
"lumped circuit elements, and they follow KVL,",
|
||||
"KCl, the node equation, and so on.",
|
||||
"And then, last week we spent some time talking about the",
|
||||
"digital abstraction. So we focused on a smaller",
|
||||
"region of the playground. And the assumptions we made in",
|
||||
"there were even tighter. We said that it is part of the",
|
||||
"playground we shall only deal with binary values.",
|
||||
"We'll digitize or lump values into highs and lows,",
|
||||
"and that's where our circuits are going to be.",
|
||||
"And these circuits, when looked at as a whole,",
|
||||
"were nonlinear. So, this is a simple NAND gate",
|
||||
"circuit. And this is the input/output",
|
||||
"characteristic. So, for example,",
|
||||
"if I hold B at zero, and I apply a zero to one",
|
||||
"transition at A, then this is the output that I",
|
||||
"will see at C. So notice, this is decidedly",
|
||||
"nonlinear. Then I said that,",
|
||||
"look, suppose we had to fix the input values at a given set.",
|
||||
"OK, so let's say, for example,",
|
||||
"I fix A at one, and B at one.",
|
||||
"OK, and then look at the circuit in this situation.",
|
||||
"What do I find? What I find is that the entire",
|
||||
"digital set of circuits that we were looking at move over into",
|
||||
"the linear space for a given set of switch settings,",
|
||||
"OK? So, when I set A 1 and B 1,",
|
||||
"A equal to one and B equal to one, my NAND gate becomes like",
|
||||
"this. OK, it's a simple resistive",
|
||||
"network with a voltage source, VS.",
|
||||
"So, for a fixed set of inputs, for a given set of inputs,",
|
||||
"if I don't change my inputs, then my circuit looks like a",
|
||||
"linear circuit, and my good old linear analysis",
|
||||
"techniques apply. So that was last week.",
|
||||
"And this week, we are looking at the nonlinear",
|
||||
"space. And we looked at a couple of",
|
||||
"techniques in the nonlinear space, analytical techniques and",
|
||||
"graphical techniques. And then, I showed you an",
|
||||
"example. OK, I showed you an example",
|
||||
"circuit that was something that I would like to build involving",
|
||||
"the light emitting expo dweeb, my little garage door opener",
|
||||
"thingamajig, and I wanted to transmit music over that light",
|
||||
"beam. I also showed you that it was",
|
||||
"highly distorted because it was in the nonlinear space.",
|
||||
"So, today what I'm going to do is introduce a new part of the",
|
||||
"playground. There's a new part of the",
|
||||
"playground, and I'll show you a technique whereby by focusing on",
|
||||
"this part of the playground and disciplining ourselves in the",
|
||||
"kind of inputs we apply to circuits, I'm going to show you",
|
||||
"that certain kinds of nonlinear circuits also move over,",
|
||||
"when used in a particular way, also move into the linear",
|
||||
"analysis domain. OK, so let me leave that for",
|
||||
"now and go back into quickly reviewing the motivating example",
|
||||
"of music that I had taken last time.",
|
||||
"OK, so here was a little example.",
|
||||
"So I have a music source, VI, and I apply that.",
|
||||
"This device that I call the, lightheartedly,",
|
||||
"the Light Emitting Expo Dweeb has a current,",
|
||||
"VD, across it, or a voltage,",
|
||||
"VD, across it, and a current ID through it.",
|
||||
"And the light intensity, I said, was proportional to the",
|
||||
"current. And because of that,",
|
||||
"I was able to get the light to impinge on a receiving device,",
|
||||
"which produced a current that was proportional to the",
|
||||
"intensity of light falling on it.",
|
||||
"And that signal would then be amplified somehow.",
|
||||
"We haven't talked about all of this stuff yet.",
|
||||
"This will happen next week. But let's say we somehow",
|
||||
"amplify the signal and then played out through a set of",
|
||||
"speakers. All right, so if I had some",
|
||||
"sort of a music signal here, then I could then transmit the",
|
||||
"music signal over to the side on top of this light beam.",
|
||||
"But the problem, as I said the last time,",
|
||||
"was that our device, the Light Emitting Expo Dweeb",
|
||||
"had an exponential characteristic,",
|
||||
"so that I had some trouble in getting undistorted music.",
|
||||
"So, the characteristic of the VI characteristics of my device",
|
||||
"looked like so. The ID versus VD curve looked",
|
||||
"as follows. OK, it was decidedly nonlinear.",
|
||||
"And because of that, I was getting a lot of",
|
||||
"distortions in my signal, and I showed you a little trick",
|
||||
"to plot, given an input waveform at a transfer function such as",
|
||||
"here to plot the output function.",
|
||||
"OK, let me show you another little animation that I have",
|
||||
"created here for you that should give you even more intuition in",
|
||||
"terms of how it happens. So, this is a characteristic I",
|
||||
"showed you up here. It's on both sides,",
|
||||
"but I guess it points to only one unless I shuttle back and",
|
||||
"forth really fast. So on average,",
|
||||
"I'll be in both places. But anyway, so here's my ID",
|
||||
"versus VD characteristic. And as I said,",
|
||||
"there's an exponential ID versus VD curve.",
|
||||
"And I want to see what the output looks like,",
|
||||
"for example, a sinusoidal input.",
|
||||
"So I said, let's place the input along a little graph,",
|
||||
"rotate it so, and take a sinusoid,",
|
||||
"and apply a sinusoid to the input, VI, which would also",
|
||||
"appear across the Light Emitting Expo Dweeb.",
|
||||
"And then, what I wanted to see was how the output looked.",
|
||||
"OK, so let me tell you that the output is going to look like",
|
||||
"this. OK, the output is going to look",
|
||||
"like so. And, a little artifice to",
|
||||
"discover curves like this is to think about a point here",
|
||||
"corresponding to the point on the transfer curve here,",
|
||||
"because this is VD, looking at the Y intercept.",
|
||||
"That's a value of ID, and that's a value of ID here.",
|
||||
"And, time moves along here, and time moves along here.",
|
||||
"So, I did this little animation.",
|
||||
"You'd better be impressed. It took me six hours to do it.",
|
||||
"So, here it goes. So, let's say I start by",
|
||||
"focusing on this little point that corresponds to this point",
|
||||
"on the transfer function, which then, in turn,",
|
||||
"points to a time, zero, this point on my ID",
|
||||
"curve. OK, I hope this works.",
|
||||
"So, as my point moves down [LAUGHTER], this was fun to do,",
|
||||
"I promise you. So notice that as this point",
|
||||
"has the following excursion, this had the following",
|
||||
"excursions here. OK, all right.",
|
||||
"So let me pause that little animation there.",
|
||||
"At the end of the lecture, I'll put that up again if you",
|
||||
"like, and you all can come and play with it.",
|
||||
"So, you can actually do this in PowerPoint.",
|
||||
"It took me quite a bit of time to figure out how to do it,",
|
||||
"though, but it's fun. OK, so let me show you a little",
|
||||
"demo, and show you a sinusoid, and show you what the output",
|
||||
"looks like if I apply a sinusoid for VI.",
|
||||
"So, I'll show you ID as a function of VI when VI is a",
|
||||
"sinusoid. There you go.",
|
||||
"So, I applied my sinusoid VI, and this is the current that I",
|
||||
"get. And notice, this is the",
|
||||
"transfer function that I talked about, the ID versus VD curve of",
|
||||
"my Light Emitting Expo Dweeb. And I get this highly nonlinear",
|
||||
"transformation of the input as I get to the output.",
|
||||
"OK, so that is a problem. And then, I also played some",
|
||||
"music for you. Let's do that,",
|
||||
"too. I played some music for you.",
|
||||
"I applied the music as an input to the circuit,",
|
||||
"and that's the output. OK, that's the output that I'm",
|
||||
"observing at the amplifier. It's highly distorted.",
|
||||
"OK, we can stop that. There you go.",
|
||||
"OK, so that was my problem. OK, so we had covered,",
|
||||
"we had gone this far last Tuesday.",
|
||||
"I set the problem up for you, motivated what we had to do,",
|
||||
"and showed you that I was able to transmit music over my garage",
|
||||
"door opener, but I did not think I could listen to that music for",
|
||||
"very long. So, I challenged all of us to",
|
||||
"think about how a trick that I could use to be able to transmit",
|
||||
"music and have a linear response.",
|
||||
"So, did you people get time to think about it?",
|
||||
"So how many people here think they know the answer?",
|
||||
"It's OK, don't be modest. Go ahead.",
|
||||
"Could you speak louder? Yeah, you find another",
|
||||
"something, kind of element, that's got the opposite graph",
|
||||
"so that when you add them together.",
|
||||
"Oh, this guy wants to cheat. No.",
|
||||
"He wants a new element. So, no, no new elements.",
|
||||
"Pardon? Build an MP3 encoder.",
|
||||
"Ah-ha, so that will happen much later.",
|
||||
"Yes? Digitize the signal before you",
|
||||
"send it to the LED? Digitize the signal before you",
|
||||
"send it to the LED. But in some sense,",
|
||||
"each of these solutions is a huge sledgehammer approach to",
|
||||
"look at solving it. There's a much simpler",
|
||||
"technique I can apply here. Yeah?",
|
||||
"Add a voltage offset. Ah, ah-ha, that might work.",
|
||||
"What else? So let's say,",
|
||||
"here's my signal, right?",
|
||||
"If I add a voltage offset, that will just bump the signal",
|
||||
"up here. Then the curve is still",
|
||||
"nonlinear. But you're getting there.",
|
||||
"Well, I'll tell you what. Let's pause here.",
|
||||
"Let me quit while I'm ahead. OK, so the answer here,",
|
||||
"folks, is Zen. OK, what I want you to do is,",
|
||||
"so, in Zen, what you have to do is you have to sit down in a",
|
||||
"courtyard, and look at a rock, like a small rock on the",
|
||||
"ground. And you got a focus on it till",
|
||||
"the rest of Earth kind of vanishes.",
|
||||
"Just focus on the rock. OK, now make like you're in a",
|
||||
"courtyard, and you're looking at this little area here.",
|
||||
"Just look at this. OK, and I'll give you ten",
|
||||
"seconds. Sit down quietly,",
|
||||
"and no sounds. Just stare at the spot here.",
|
||||
"OK, make believe this is your little rock, and just stand",
|
||||
"there and think about it. OK, I'll give you five seconds",
|
||||
"to do that. Just stare at it.",
|
||||
"And very soon, the answer should pop into your",
|
||||
"heads. OK, what do you see?",
|
||||
"This guy, if I focus on this really small region of the",
|
||||
"graph, this small little piece looks more or less linear.",
|
||||
"OK, hmm, so that should give me some insight.",
|
||||
"This whole thing, the macrograph is nonlinear.",
|
||||
"But I focus on a little rinky dinky piece of that graph like",
|
||||
"so, that appears more or less linear.",
|
||||
"If it's small enough, that appears linear.",
|
||||
"So, I'm staring at this, and that appears linear.",
|
||||
"The question is, how do I exploit this little",
|
||||
"small, little, linear region to get a linear",
|
||||
"response from my device. OK, so here's the trick that",
|
||||
"I'm going to use. The little trick that I'm going",
|
||||
"to use is the following. Notice that,",
|
||||
"let me call this voltage at the center of this region capital",
|
||||
"VD. What I can do,",
|
||||
"if I take my input signal, and I just pointed out earlier,",
|
||||
"I bump it up. I boost it.",
|
||||
"OK, so I apply a DC offset to my input signal,",
|
||||
"like so. So I apply some input signal,",
|
||||
"VI, which is also equal to the VD if I look at a variable",
|
||||
"across the nonlinear element. If I apply a DC offset,",
|
||||
"VI, and I superimpose the music on top of that,",
|
||||
"let me call my music, just to distinguish between the",
|
||||
"two, capital VI, and the small vi.",
|
||||
"OK, that's my music. So here's my capital VD,",
|
||||
"my DC offset. And I want to superimpose my",
|
||||
"music on top of that. OK, so I've gotten halfway",
|
||||
"there. By superimposing my music here",
|
||||
"instead of having excursions out here, I now have excursions out",
|
||||
"here. OK, and so I'm using some",
|
||||
"portion of the graph here. But that's still way beyond the",
|
||||
"small little element there. So a second think that I do in",
|
||||
"addition to boosting up the signal is shrink it.",
|
||||
"Think of boost and shrink, BS.",
|
||||
"So what I want to do is boost up the signal using a DC offset,",
|
||||
"and shrink the sucker. OK, so I'm going to go with a",
|
||||
"small signal and bump it up. OK, so now what happens is that",
|
||||
"small signal in its excursions, only uses that little portion",
|
||||
"of the graph. OK, again, remember:",
|
||||
"bump and shrink, bump and shrink,",
|
||||
"two things, boost and shrink. So what do you think of that",
|
||||
"trick? So, by doing that,",
|
||||
"what happens is that signal that has excursions here will",
|
||||
"produce a corresponding response in this region,",
|
||||
"OK? And I argue that since this is",
|
||||
"more or less like a straight line, I invoke Zen here,",
|
||||
"and argue that this little signal now gets transformed,",
|
||||
"and I get a linear response. OK: boost and shrink.",
|
||||
"So in terms of my circuit, let me draw it out for you.",
|
||||
"My Light Emitting Expo Dweeb, and this whole signal was what",
|
||||
"I used to call V capital I, and that's made up of two",
|
||||
"components now, a bump offset,",
|
||||
"and a shrunk voltage VI. It shrunk, so therefore I've",
|
||||
"used the small v and small i, like, really,",
|
||||
"really small. In the same manner,",
|
||||
"I get a VD ID across the LED, and the corresponding values",
|
||||
"here will also have a DC offset and a small response.",
|
||||
"Let me call that ID plus I small d.",
|
||||
"I'll do all this mathematically in a second as well,",
|
||||
"but first let me do it completely intuitively so you",
|
||||
"get some insight into what's going on.",
|
||||
"And, VD is simply capital VD plus small vd.",
|
||||
"OK, and this is the same as VI, I, and VI.",
|
||||
"OK, so what have I done? I've done two things.",
|
||||
"I have said, as an engineer,",
|
||||
"OK, I care about getting music across my garage door opener.",
|
||||
"And I'll do what it takes to do that.",
|
||||
"OK, so as an engineer, I'll do two things.",
|
||||
"I'm going to bump my signal up and shrink it.",
|
||||
"And the bumping and shrinking, and I do it like this.",
|
||||
"I shrink my signal, the music signal here,",
|
||||
"and add a DC offset. OK, and I claim that the music",
|
||||
"I listened on the other side now, provided I have enough",
|
||||
"amplification there, is going to be undistorted.",
|
||||
"OK, so far I've showing this to you completely intuitively using",
|
||||
"little sketches, no math.",
|
||||
"I promise you, I'll give you a bunch of math",
|
||||
"in a few seconds, but just get the basic idea,",
|
||||
"and get the intuition behind it.",
|
||||
"So let's go back to our demo and take a look.",
|
||||
"So remember, BS, right, bump and shrink.",
|
||||
"So what I'm going to do is first of all,",
|
||||
"let me bump up the signal. So, what I'll do is I want to",
|
||||
"add an offset to my input, and let me bump it up.",
|
||||
"Let me shrink it first. It'll make the point a little",
|
||||
"clearer. So, the big input,",
|
||||
"green, is a big input. Let me shrink it.",
|
||||
"",
|
||||
"OK, so I've made my input small, and in the middle of that",
|
||||
"picture out there, you see the region of the",
|
||||
"transfer curve that's being articulated.",
|
||||
"OK, this region of the curve is being articulated by the small",
|
||||
"signal. It's a much smaller signal.",
|
||||
"And the output is still distorted because I have to do",
|
||||
"two things: bump and shrink. I've only shrunk.",
|
||||
"OK, let me bump it up now. What's the yellow curve?",
|
||||
"It's going to get linear. It's going to get proportional",
|
||||
"to the input. Then I'm bumping it up now.",
|
||||
"I can make it smaller, make it even smaller,",
|
||||
"there you go. Isn't that fantastic?",
|
||||
"So, I'm making nature do my bidding here,",
|
||||
"OK? So, this is one of those,",
|
||||
"when I learned electronics and so on many, many years ago,",
|
||||
"this was one of those really big ah-ha moments for me,",
|
||||
"saying, wow, that stuff is cool.",
|
||||
"It's something that I couldn't think about myself,",
|
||||
"and it's not obvious, and by being disciplined and",
|
||||
"creative in how I use circuits, I can do really,",
|
||||
"really cool things. OK, remember this as a big",
|
||||
"ah-ha moment for you. So, here's my little signal",
|
||||
"that I've shrunk and bumped up, and my output is a sinusoid,",
|
||||
"and not this funny, distorted waveform.",
|
||||
"And notice that this is the region of the curve that is",
|
||||
"being articulated. So, I can make the signal even",
|
||||
"smaller if I like. OK, and what I'd like to do",
|
||||
"next is play music for you, and if you don't believe your",
|
||||
"eyes, you can at least believe your ears.",
|
||||
"Let me go to the distorted signal again,",
|
||||
"switch to music, and raise it up.",
|
||||
"OK, now what we'll do is shrink the music signal and then bump",
|
||||
"it up. Can I turn the volume down a",
|
||||
"little bit? That's good.",
|
||||
"OK, so if I shrunk the volume a little bit, and let me bump it",
|
||||
"up, now. [MUSIC PLAYS] Just remember",
|
||||
"this as a big ah-ha moment. OK, the signal is really,",
|
||||
"really small. I like that.",
|
||||
"I like the enthusiasm. OK, so the signal's very small,",
|
||||
"and I get a more or less linear response.",
|
||||
"OK. All right, so that's intuition,",
|
||||
"and the approach that I've taken is called,",
|
||||
"it's variously called small signal analysis,",
|
||||
"incremental analysis, small signal method,",
|
||||
"small signal discipline, whatever you want.",
|
||||
"",
|
||||
"OK, this simply says that by boosting and shrinking my",
|
||||
"signal, I get a response that's more or less linear even when I",
|
||||
"have a nonlinear device. And this technique is called",
|
||||
"the small signal approach. So, just to focus on that a",
|
||||
"little bit longer, switch to page five of your",
|
||||
"notes and let me draw something out for you.",
|
||||
"",
|
||||
"OK, so what I have here, this is my offset VD,",
|
||||
"and from the VD offset I have my little signal V small d,",
|
||||
"and the total signal is called V capital D.",
|
||||
"Offset, small signal, and that's my total signal.",
|
||||
"OK, notice the offset is all capital.",
|
||||
"The total signal is small v capital D, and the music or the",
|
||||
"small signal is small v small d. Similarly, the output is going",
|
||||
"to look like this, and here I get an offset in the",
|
||||
"output ID. I get a corresponding signal,",
|
||||
"I small d, and I get a total signal, I capital D,",
|
||||
"OK? The cool thing to notice is",
|
||||
"that the signal here, the output signal here",
|
||||
"corresponding to the input signal, the music signal,",
|
||||
"VD, is small I small D, and that is more or less",
|
||||
"linear. OK, and I can even plot the",
|
||||
"signal like so. This is my input,",
|
||||
"v capital D. That's T.",
|
||||
"This is VD, V small d. That is my total input.",
|
||||
"And similarly, I have an output.",
|
||||
"And this is my output ID. And, that looks like this,",
|
||||
"I capital D, small i small d,",
|
||||
"total signal I capital D. OK, so that's the small signal",
|
||||
"method. So, let me summarize that for",
|
||||
"you.",
|
||||
"",
|
||||
"There are three steps to the method.",
|
||||
"So, first of all, operate at some DC offset.",
|
||||
"This is also called DC bias, and in that example it's VDID.",
|
||||
"OK, so I choose an operating point that bumps up the",
|
||||
"operation in some region of interest.",
|
||||
"The second step is to superimpose small signal on top",
|
||||
"of VD, capital V capital D, to superimpose a small signal,",
|
||||
"and the third step is observe the response --",
|
||||
"-- and the response, small i small d,",
|
||||
"that's the music part of the response, ID,",
|
||||
"is approximately linear. OK, three steps to the method",
|
||||
"here, and just remember this notation.",
|
||||
"And, my notation in the small signal model is as follows.",
|
||||
"My total signal ID is the sum of two signals,",
|
||||
"I capital D plus small i small d.",
|
||||
"This is called the total signal.",
|
||||
"That's called the DC offset. And this is the superimposed",
|
||||
"small signal. OK, total signal,",
|
||||
"DC offset, plus the small signal.",
|
||||
"And sometimes, especially when doing math,",
|
||||
"and so on, we may oftentimes represent ID as a delta,",
|
||||
"I capital D, OK, to show that ID is",
|
||||
"incremental change in the value of I capital D.",
|
||||
"And because of that, this method is also often",
|
||||
"called the incremental method, incremental analysis.",
|
||||
"OK, so far what I've done is given you some intuition.",
|
||||
"I've developed a small, simple method,",
|
||||
"given you some insight into why we use this method,",
|
||||
"and also shown you some demonstrations that show that",
|
||||
"when I bump and shrink, and observe the response,",
|
||||
"I do get a more or less linear response.",
|
||||
"So let me now do this mathematically and show you that",
|
||||
"mathematically, you can also derive your",
|
||||
"response to be a linear response.",
|
||||
"This is page seven. So, I know that ID is some",
|
||||
"function of the diode voltage. F was my nonlinear function.",
|
||||
"OK, so my function F was a nonlinear function.",
|
||||
"So therefore, ID was nonlinearly related to",
|
||||
"VD. So, let's do the math.",
|
||||
"So as a first step, what we did was replace VD by a",
|
||||
"DC offset, the small signal method, a DC offset,",
|
||||
"plus a small incremental change.",
|
||||
"OK, by doing the math, let me simply use the delta VD",
|
||||
"notation to show you that I'm dealing with small increments,",
|
||||
"and also because in the mathematics community,",
|
||||
"when you learn about some of these techniques,",
|
||||
"they will use the incremental change notation,",
|
||||
"which is the delta VD notation. In electrical engineering,",
|
||||
"we use a small v, small d notation.",
|
||||
"So, this is a large DC offset, and this is a small change",
|
||||
"about that offset. So, you folks have taken math",
|
||||
"courses before, and been looking at finding out",
|
||||
"the value of a function, which is a small change for an",
|
||||
"input value, which is a small change about a big input value",
|
||||
"or a big DC point is Taylor's expansion.",
|
||||
"OK, so let's use Taylor's series expansion,",
|
||||
"OK, and substitute VD plus delta VD into this,",
|
||||
"and see what ID looks like. Again, let me tell you where",
|
||||
"I'm going with this. ID equals F of VD.",
|
||||
"This is a nonlinear function, OK?",
|
||||
"I claim that by replacing VD, the input, with the DC offset",
|
||||
"plus a small value, the resulting response to the",
|
||||
"small value will be linear, OK?",
|
||||
"So what I'm going to do next is replace VD with this sum here,",
|
||||
"and then do the math, and show you that the response",
|
||||
"corresponding, or the change in ID",
|
||||
"corresponding to the change in VD is going to be linear.",
|
||||
"All right, so let's expand this function using Taylor's series",
|
||||
"near the DC offset point, capital V capital D.",
|
||||
"OK, so ID is simply, by Taylor's series,",
|
||||
"I want to find out a value of the function close to V capital",
|
||||
"D. OK, so I take the value of the",
|
||||
"function at that point, and then I add a few terms in",
|
||||
"my Taylor's series expansion. The first term is simply the",
|
||||
"good old Taylor's series stuff. OK, the first term is the first",
|
||||
"derivative of the function times the change.",
|
||||
"And then, the second one is second derivative.",
|
||||
"",
|
||||
"OK, and then I get higher order terms.",
|
||||
"So this is nothing new here. This is good old Taylor series",
|
||||
"expansion, and again, let me tell you where I'm",
|
||||
"going. I want to look at the response",
|
||||
"for an input that looks like this, and I want to show you at",
|
||||
"the end of the day that the response in ID,",
|
||||
"the effect on ID of using an input like this is as if that",
|
||||
"effect, the incremental change is linearly related to the small",
|
||||
"input, delta VD. So here's my Taylor's series",
|
||||
"expansion for delta V. Now remember,",
|
||||
"I told you that delta VD is much, much smaller than V",
|
||||
"capital D. OK, it's a very,",
|
||||
"very small quantity. But that quantity is really",
|
||||
"very small. Then what I'm going to get is",
|
||||
"that my output is, I can begin to ignore my second",
|
||||
"order terms. OK, delta VD is very,",
|
||||
"very, very small. Then, what I'm going to do is",
|
||||
"that ignore higher order terms. So I'll go and ignore higher",
|
||||
"order terms. They'll all go to zero.",
|
||||
"Remember, I can do this because by design I've chosen delta VD",
|
||||
"to be very, very, very small.",
|
||||
"OK, remember, we are engineers.",
|
||||
"I've chosen it in a way that this is very small.",
|
||||
"OK, so I'm telling you that's the case, and under those",
|
||||
"conditions, I can ignore second higher order terms,",
|
||||
"in which case I am left with this expression here.",
|
||||
"So let me rewrite this. Let me rewrite this down here.",
|
||||
"",
|
||||
"OK, I've just copied this turnout, I've ignored all these",
|
||||
"terms here, and so I have a more or less equal to sign that",
|
||||
"remains. So what I'm going to do is when",
|
||||
"I apply a small input of this form to a large DC offset,",
|
||||
"my output is also going to look like some output offset with a",
|
||||
"change in the output offset. And let me call the output",
|
||||
"offset I capital D, and some small change in the",
|
||||
"output delta ID. OK, we'll make sure we can",
|
||||
"convince ourselves that this is indeed the case.",
|
||||
"Notice that this guy here, F of capital V capital D is a",
|
||||
"constant. That's a constant with respect",
|
||||
"to the incremental change, delta VD.",
|
||||
"Similarly, this part here is a constant.",
|
||||
"Notice that this term here is the first derivative of the",
|
||||
"function evaluated at the DC bias point, capital V capital D.",
|
||||
"OK, so this term is also a constant with respect to delta",
|
||||
"VD. So notice, then,",
|
||||
"I have a constant term plus a constant term multiplying a",
|
||||
"small change, delta VD.",
|
||||
"So what I can do next is, in this case,",
|
||||
"given that I have a constant term on both sides,",
|
||||
"and on this side it's a time varying term,",
|
||||
"what I can do is equate the two constant terms.",
|
||||
"I can go ahead and equate these two terms.",
|
||||
"Remember, I have a constant plus a time varying term,",
|
||||
"OK, if I'm assuming here that delta VD, my little music signal",
|
||||
"is a time varying term. So, this constant will equal",
|
||||
"this, so ID must equal F of VD. And I know that's the case",
|
||||
"because the function evaluated at the DC offset gives me the DC",
|
||||
"current ID. And similarly,",
|
||||
"ID is equal to that component. Delta ID is equal to D,",
|
||||
"F of --",
|
||||
"",
|
||||
"OK, so my incremental change in the output is the first",
|
||||
"derivative multiplied by the small change in the current.",
|
||||
"OK, so I'm pretty much done. So, therefore,",
|
||||
"notice that delta ID is proportional to delta VD.",
|
||||
"OK, and that's what I had set out to show.",
|
||||
"Remember, I had set out to show that provided my input is a",
|
||||
"small excursion around a large DC offset,",
|
||||
"then my output could also be a large DC offset with a small",
|
||||
"excursion on top of it where the two excursions,",
|
||||
"the input excursion and the output excursion would be",
|
||||
"linearly related like so. OK, and the method is very",
|
||||
"simple. I simply expanded the function",
|
||||
"about that point, that DC point,",
|
||||
"neglected higher order terms, and notice that my incremental",
|
||||
"term was simply the derivative plus the incremental change,",
|
||||
"a derivative times the incremental change in the input.",
|
||||
"Move onto page nine, and I'd like to give you a",
|
||||
"quick graphical interpretation of this.",
|
||||
"So I gave an intuitive explanation earlier.",
|
||||
"This is a mathematical explanation that shows you that",
|
||||
"the input could be linearly related to the output,",
|
||||
"provided, the outputs would be linearly related to the input,",
|
||||
"provided the input has a DC offset, and small excursions",
|
||||
"about that DC offset. So, let me give you some",
|
||||
"intuition in what you've really done here, using a little graph",
|
||||
"here. So, I'm going to plot ID versus",
|
||||
"VD, and notice that I have some point here, V capital D,",
|
||||
"I capital D. That's my DC bias.",
|
||||
"So, I have some DC bias point here.",
|
||||
"OK, what is this? That is simply the slope of the",
|
||||
"curve at that point. OK, it's the slope of this",
|
||||
"curve evaluated at this point. So this guy here is simply the",
|
||||
"slope of this curve evaluated at ID VD.",
|
||||
"OK, now, what I care about is this point here,",
|
||||
"and this point here. So let's say that this is delta",
|
||||
"VD, all right, and that corresponds to this",
|
||||
"point here. So what I've done is taken the",
|
||||
"slope and multiplied that by delta VD.",
|
||||
"So I've taken the slope, and multiplied it by delta VD,",
|
||||
"OK, and that gives me this component here.",
|
||||
"OK, and so, this is the point that I'm going to get.",
|
||||
"So in other words, what I've done is approximated",
|
||||
"point A using the Taylor trick by the point B.",
|
||||
"OK, so this is a point, A, which is what I really want,",
|
||||
"and I've approximated that by taking the slope of the function",
|
||||
"at V capital D, and multiplying that by the",
|
||||
"change in the input to get the corresponding Y offset,",
|
||||
"and that's the point that I get.",
|
||||
"And notice that if I make this delta VD small enough,",
|
||||
"then the error between these two points becomes smaller and",
|
||||
"smaller. So back to our example,",
|
||||
"so ID was a e to the BVD. This was the relation for our",
|
||||
"Expo Dweeb, and let me just plug in the values.",
|
||||
"So, ID plus small id. Notice, I'm just shuttling back",
|
||||
"and forth between the notation delta VD, and small v small d.",
|
||||
"",
|
||||
"OK, and so that is given by a e to the BVD, oops,",
|
||||
"plus, I'm just writing that equation up there.",
|
||||
"Let me call this equation X. And so, I get the second term",
|
||||
"is the derivative, ab times e to the BVD times",
|
||||
"delta VD, small VD, and equating this term that the",
|
||||
"DC offset. Notice that this is the DC",
|
||||
"offset in the output, and the small signal,",
|
||||
"ID is, further notice that in this particular example,",
|
||||
"what's that? a e to the BVD.",
|
||||
"That's simply ID again. It just happens to be that way",
|
||||
"in this example. So, I get ID times BVD.",
|
||||
"So, for my input, small id, my incremental change",
|
||||
"in the output is some ID times B times VD.",
|
||||
"And notice that this is a constant.",
|
||||
"And because that is a constant, my small signal behavior ID is",
|
||||
"going to be linearly related to the signal, VD,",
|
||||
"the input signal VD. OK, in the last three minutes,",
|
||||
"I'd like to give you one additional insight.",
|
||||
"So what we've shown so far is if I have an offset and a small",
|
||||
"change above it, then my output ID will be",
|
||||
"linearly related to my input. Now let's stare at this thing",
|
||||
"again. Let me rewrite it.",
|
||||
"It's some constant IDB times VD.",
|
||||
"So, where have we seen such an expression before?",
|
||||
"OK, where ID was some constant times VD.",
|
||||
"OK, remember, I equals V divided by R:",
|
||||
"Ohm's law. What I want to show you now is",
|
||||
"how we constantly keep simplifying our lives.",
|
||||
"The moment we hit some complication and things get too",
|
||||
"painful to analyze, as engineers,",
|
||||
"we come up with some clever tricks to make an analysis and",
|
||||
"use of circuits simple again. And so, notice that this is",
|
||||
"similar to some, one by RD VD,",
|
||||
"where RD is simply one over IDB.",
|
||||
"I'm just defining this to be RD.",
|
||||
"And what that means is that I can take a nonlinear circuit",
|
||||
"that looks like this. OK, and what I can do is",
|
||||
"replace this by its incremental equivalent, and build what is",
|
||||
"called a small signal circuit. And I'll just introduce it",
|
||||
"here. And we will revisit the circuit",
|
||||
"in much more gory detail a couple of weeks from now.",
|
||||
"So, what I can do is build a small signal circuit where I",
|
||||
"have all the small signal variables, and replace a",
|
||||
"nonlinear device by a simple little resistor whose value is",
|
||||
"given by IDB. OK, so therefore,",
|
||||
"what I can do is take my nonlinear circuit,",
|
||||
"and for small, incremental changes,",
|
||||
"replace that circuit with this equivalent small signal circuit,",
|
||||
"and go back to doing simple stuff again.",
|
||||
"Thank you."
|
||||
]
|
||||
}
|
||||
@@ -1,1838 +0,0 @@
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"text": [
|
||||
"",
|
||||
"Good morning.",
|
||||
"",
|
||||
"All right. Today we are going to take a",
|
||||
"fresh look at some of the stuff we covered in the last two",
|
||||
"lectures. And the graph I want you to",
|
||||
"keep in mind as we go through this lecture in terms of what to",
|
||||
"expect. This was time.",
|
||||
"And last Tuesday's lecture we covered some stuff.",
|
||||
"I talked about a method for the sinusoidal response which was",
|
||||
"agony, I warned you it will be agony, and then towards the end",
|
||||
"I showed you another method that was quite a bit easier but still",
|
||||
"pretty hard. And I promised you that today",
|
||||
"there will be a new method which is going to be so easy ,",
|
||||
"actually almost trite. Just imagine.",
|
||||
"I am going to make a statement right now that I think you will",
|
||||
"all find hard to believe. What I am going to say is just",
|
||||
"imagine your RLC circuit, your resistor,",
|
||||
"inductor and capacitor, a parallel form or series form.",
|
||||
"Imagine that you could write down the characteristic equation",
|
||||
"for that by observation in 30 seconds or less.",
|
||||
"Just imagine that. By observation,",
|
||||
"boom, write down the characteristic equation for",
|
||||
"virtually any RLC circuit or RC circuit or whatever.",
|
||||
"And we all know that once you have the characteristic equation",
|
||||
"you could very easily go from there to the time domain",
|
||||
"response intuitively or to the sinusoidal steady-state",
|
||||
"response, too. So just keep that thought in",
|
||||
"mind. Imagine 30 seconds.",
|
||||
"And that is what you should expect in today's lecture.",
|
||||
"Students often ask me, if this stuff is actually so",
|
||||
"easy why do you take us through this tortuous path?",
|
||||
"Are we just mean? Do we just want you show you",
|
||||
"how hard things are and then show the easy way?",
|
||||
"I have argued with myself every year as to whether to just go",
|
||||
"ahead and give the easy path and that's it.",
|
||||
"But I think the reason we cover the basic foundations is that it",
|
||||
"gives you a level of insight that you would not have",
|
||||
"otherwise gotten if I directly jumped into the easy method.",
|
||||
"So you need to understand the foundations and you need to have",
|
||||
"seen that at least once. And second, once you do",
|
||||
"something the hard way, you appreciate all the more the",
|
||||
"easy method. All right.",
|
||||
"Today we cover what is called \"The Impedance Model\".",
|
||||
"",
|
||||
"First let me do a review just because of the large amount of",
|
||||
"content in the last two lectures.",
|
||||
"I did them using view graphs. I usually don't like to do",
|
||||
"that, but even then it was quite rushed.",
|
||||
"So let me quickly summarize for you kind of the main points.",
|
||||
"We have been looking at, on Tuesday, the sinusoidal --",
|
||||
"",
|
||||
"--looking at the sinusoidal steady state response.",
|
||||
"Also fondly denoted as SSS. And the readings for this were",
|
||||
"Chapters 14.1 and 14.2. what we said was if you took",
|
||||
"this example circuit and we fed as input cosine of omega t,",
|
||||
"we have an R and a C, and let's say we cared about",
|
||||
"the output response and we cared about the capacitor voltage.",
|
||||
"What we talked about was focused on the sinusoidal",
|
||||
"steady-state response. And what that meant was first",
|
||||
"of all focus on steady-state. In other words,",
|
||||
"just to capture the steady-state behavior when t",
|
||||
"goes to infinity after a long period of time.",
|
||||
"And for most of the circuits that we consider,",
|
||||
"because of the R or presence of any resistance,",
|
||||
"the homogenous response usually would die out because the",
|
||||
"homogenous response is usually of the form minus t by tau.",
|
||||
"And as t goes to infinity this term tends to go to zero.",
|
||||
"We are just looking at the steady-state.",
|
||||
"And therefore, because of the circuits we",
|
||||
"looked at, we can ignore the homogenous response.",
|
||||
"All we are left to do is to find the particular response to",
|
||||
"sinusoids of this form. And second was focus on",
|
||||
"sinusoids. We said the reason for this was",
|
||||
"that, let's say we did not care particularly",
|
||||
"What happened when I just turned on my amplifier.",
|
||||
"I just turned on my amplifier, often times you see some",
|
||||
"distorted sound coming out for a few seconds and then hear a much",
|
||||
"clearer sound. And that initial part is due to",
|
||||
"the transient response. And let's say we don't care",
|
||||
"about that. We care about the steady state.",
|
||||
"Second we focus on sinusoids because based on the Fourier",
|
||||
"series experience that you had previously, we can represent",
|
||||
"repeated signals as a sum of sines.",
|
||||
"And therefore it is important to understand the behavior of",
|
||||
"these circuits when the input is a sinusoid.",
|
||||
"And what was important was this introduced a new way of looking",
|
||||
"at circuits, and that was the frequency viewpoint.",
|
||||
"When we looked at transient responses, we plotted response",
|
||||
"as a function of time. And when we look at sinusoidal",
|
||||
"steady-state, it becomes interesting to plot",
|
||||
"the response as a function of the frequency,",
|
||||
"a function of omega.",
|
||||
"",
|
||||
"What I will do is draw a little chart for you to sort of",
|
||||
"visualize the various processes we have been going through.",
|
||||
"We can liken obtaining the sinusoidal steady-state response",
|
||||
"to following these steps. Here is my input.",
|
||||
"What I did as a first step was fed my input to a usual circuit",
|
||||
"model. My elements were lumped",
|
||||
"elements, built the circuit and wrote down the VI relationship",
|
||||
"for the element. As a second step I set up the",
|
||||
"differential equation.",
|
||||
"",
|
||||
"This was the first of four steps, set up a differential",
|
||||
"equation. And then the path that I took",
|
||||
"first was fraught with real nightmarish trig.",
|
||||
"",
|
||||
"By the end of the day it would still yield an answer.",
|
||||
"It could be a nightmare. But I would get something",
|
||||
"cosine omega t plus something, some phase.",
|
||||
"I could grunge through the trig.",
|
||||
"And I gave up halfway in class here, but you could grunge",
|
||||
"through it if you would like. And you would get the answer to",
|
||||
"be some sinusoid with some amplitude and some phase.",
|
||||
"So Vi cosine omega t would produce the response that was",
|
||||
"something cosine omega t plus some phase.",
|
||||
"We said this was too painful so let's punt this.",
|
||||
"Instead, what we said we would do is take a detour,",
|
||||
"take an easier path. And the easier path looked like",
|
||||
"this. I said let's sneak in --",
|
||||
"",
|
||||
"-- Vie^(j omega t) drive. That is just imagine,",
|
||||
"do the math as if you had fed in not a Vi cosine omega t but a",
|
||||
"Vie^(j omega t). And from Euler's relation you",
|
||||
"know that the real part is Vi cosine omega t.",
|
||||
"So we said that I am going to sneak in this thing,",
|
||||
"find the response and just take the real part of that because",
|
||||
"the real part of the input gives me this.",
|
||||
"So this is my \"sneaky path\". And what I did there,",
|
||||
"as soon as we fed in the e^(j omega t), because of the",
|
||||
"property of exponentials, the e^(j omega t) cancelled out",
|
||||
"in my equation. And what was left was some",
|
||||
"fairly simple complex algebra. And at the end of the day,",
|
||||
"after I grunged through some fairly simple complex algebra,",
|
||||
"I ended up with some response that looked like this.",
|
||||
"Vpe^(j omega t). What I would find is that for",
|
||||
"the input Vie^(j omega t), I would get a response Vpe^(j",
|
||||
"omega t). And then what I said we would",
|
||||
"do is take the real part. Why take the real part?",
|
||||
"Because this is a fake, a sneaky input.",
|
||||
"The input I really care about is the real part of the sneaky",
|
||||
"input. So this is my sneaky output.",
|
||||
"And what I care about is the real part of the sneaky output.",
|
||||
"That is sort of the inverse superposition argument that I",
|
||||
"made on Tuesday that if what I care about is the real part of",
|
||||
"this input, then I just take the real part and get the output",
|
||||
"that I care about. So I take the real part.",
|
||||
"Notice that Vp here, in the examples we did,",
|
||||
"we did an RC example. The Vp here was a complex",
|
||||
"number. So I could represent that",
|
||||
"complex number as, in many ways.",
|
||||
"This is e^(j omega t). I could represent Vp in an",
|
||||
"amplitude, as a phasor, actually polar coordinates.",
|
||||
"I can say that the equivalent to Vpe to the j angle Vp.",
|
||||
"Vp is a complex number. If you look at the complex",
|
||||
"appendix in your course notes, I can represent a complex",
|
||||
"number as an amplitude multiplied by e raised to j",
|
||||
"times some phase. It's simple complex algebra.",
|
||||
"And then what I could do here is take the real part of that.",
|
||||
"And when I took the real part of that what came about was that",
|
||||
"this was simply Vp. Notice that the angle Vp goes",
|
||||
"in here so it becomes j times omega t plus angle Vp.",
|
||||
"It is Vp amplitude times e raised to j omega t plus j angle",
|
||||
"Vp. And the real part of that is",
|
||||
"simply Vp cosine of that stuff. What I end up getting here is",
|
||||
"Vp cosine omega t plus Vp. The cool thing to notice was",
|
||||
"that once I found out this response here,",
|
||||
"I could immediately write down the output based on Vp.",
|
||||
"In other words, once I had Vp,",
|
||||
"I could stop right there in my math.",
|
||||
"I got Vp very quickly here. This step produced Vp very",
|
||||
"quickly, after two algebraic steps.",
|
||||
"And then from here I could directly write down the answer",
|
||||
"as homogenous of Vp cosine omega t plus angle Vp.",
|
||||
"Boom, right there. So this was a much shorter",
|
||||
"path. And here I just described to",
|
||||
"you how this yields an expression for Vp and angle Vp.",
|
||||
"And for our example Vp was 1/(1+j omega RC).",
|
||||
"And we often times write a shorthand notation 1+sRC,",
|
||||
"where S is simply j omega. We commonly jump back and forth",
|
||||
"between the shorthand notation S and j omega.",
|
||||
"S has some other fundamental, has another fundamental",
|
||||
"significance you will learn about in future courses,",
|
||||
"but for now S is simply a short form for j omega.",
|
||||
"This was the path that we took. There is a hard path and an",
|
||||
"easier path. Today I am going to claim that",
|
||||
"even this was too hard. There is an even easier path.",
|
||||
"And today what I am going to show you is that from here we",
|
||||
"are going to take one step and get here.",
|
||||
"I am going to show you today that we won't do this,",
|
||||
"we won't do this, not this, not this,",
|
||||
"none of this. One step and then we are going",
|
||||
"to get the answer. So let's do that.",
|
||||
"",
|
||||
"Before we jump into the impedance method and get into",
|
||||
"doing that, I just would like to plot for you this function here",
|
||||
"just so we can understand a little bit better exactly what",
|
||||
"is going on. As I mentioned to you,",
|
||||
"the output vO for our circuit there was simply Vp cosine of",
|
||||
"omega T plus angle Vp. Oh, that's Vp so this one",
|
||||
"should be Vi here. I am showing you Vp so there is",
|
||||
"a Vi in there. Vp/Vi=1/(1+j omega RC).",
|
||||
"This is a complex number, and it is simply a number that",
|
||||
"when multiplied with Vi gives me the output.",
|
||||
"This is also called a transfer function and represented as H(j",
|
||||
"omega). This guy is a transfer",
|
||||
"function, much like the gain of my amplifier.",
|
||||
"Which when multiplied by the input to get me the output.",
|
||||
"This guy is a complex multiplier which when multiplied",
|
||||
"by Vi gives me Vp. And as such we call it a",
|
||||
"transfer function H(j omega). And we can plot this function.",
|
||||
"Notice that this a function of omega.",
|
||||
"Remember we are taking the frequency domain view,",
|
||||
"so where has time vanished? Remember that we are taking the",
|
||||
"steady state view. So we are saying in the steady",
|
||||
"state, if I wait long enough this is how my circuit is going",
|
||||
"to behave, this is how a circuit is going to behave.",
|
||||
"And the transient responses have died away and I have time",
|
||||
"in my output here so my output is a cosine.",
|
||||
"But that in itself is not very interesting.",
|
||||
"It is a cosine of some amplitude and has some phase.",
|
||||
"What we will plot is we are going to plot this property",
|
||||
"here, Vp as a function of the frequency.",
|
||||
"Vp is frequency dependent. As an example,",
|
||||
"I could plot the absolute value of Vp/Vi, the modulus of that",
|
||||
"versus omega. And notice that when omega is",
|
||||
"zero again intuitive ways of plotting this is to look at the",
|
||||
"value at zero and look at the value at large omega.",
|
||||
"For small omega, omega goes to zero this is one,",
|
||||
"so it starts off here. And when omega is very large",
|
||||
"then it is much bigger than one here, so this goes down.",
|
||||
"Far away this one looks like 1/omega RC.",
|
||||
"And this function, assuming I have linear scales",
|
||||
"on my X and Y axes looks like this.",
|
||||
"We also commonly plot this using log-log scales.",
|
||||
"And when you do log-log scales you get a straight line here,",
|
||||
"and then you actually get a straight line of slope minus one",
|
||||
"because the log of this gives you a line with a constant",
|
||||
"slope, it's a slope of negative one so it becomes a straight",
|
||||
"line going down. The other interesting thing to",
|
||||
"realize is that this magnitude is simply one by one plus omega",
|
||||
"squared R squared C squared, the square root of this.",
|
||||
"That's the magnitude here. And notice when omega equals",
|
||||
"1/RC, this thing, the denominator becomes one by",
|
||||
"square root of 2. Somewhere here when omega",
|
||||
"equals 1/RC The output is one by square",
|
||||
"root 2 times the input. It's an interesting point.",
|
||||
"And this is called the \"break frequency\".",
|
||||
"You can view it as a frequency where I am getting this",
|
||||
"transition from one to a lower value, and it is where the",
|
||||
"output is one by square root two times the value of the input.",
|
||||
"Now you can think back on the demo we showed you earlier.",
|
||||
"And in the demo remember that as I increased the frequency of",
|
||||
"my input sinusoid my output kept becoming smaller and smaller and",
|
||||
"smaller. And you notice that you can see",
|
||||
"this dying out or decaying of the amplitude as I increase my",
|
||||
"omega. Let me go back.",
|
||||
"What you have done is that, we're going to apply a bunch of",
|
||||
"sinusoids to the same circuit and plot the frequency response,",
|
||||
"the ratio of the output versus input as a function of",
|
||||
"frequency. And kept applying a variety of",
|
||||
"frequencies. So you can listen to the",
|
||||
"frequencies as they go by, and we will plot the amplitude",
|
||||
"up on the screen for you. Just for fun we are going to",
|
||||
"play frequencies between, say, 10 hertz and 20 kilohertz.",
|
||||
"It will be fun for you to figure out at what point you",
|
||||
"stop hearing the frequencies. We are going to play from 10",
|
||||
"hertz to 20 kilohertz. And figure out where your ears",
|
||||
"cut out. That will tell you what the",
|
||||
"break frequency of your ear is.",
|
||||
"",
|
||||
"You can see the amplitude being articulated.",
|
||||
"The bottom figure is the phase. This is the frequency axis.",
|
||||
"This is the amplitude, log-log scales.",
|
||||
"",
|
||||
"I am not sure about you but I cannot hear anymore.",
|
||||
"If you bring your canine friends to class it is quite",
|
||||
"possible that they would go berserk somewhere here.",
|
||||
"As I promised you, when I plot this on a log-log",
|
||||
"scale I get a straight line here and a straight line out there as",
|
||||
"well and the bottom line gives you the phase.",
|
||||
"Now, what you can also do is you can also go to Websim.",
|
||||
"Websim is now linked on your course homepage.",
|
||||
"You can go to Websim and you can play with various L and C",
|
||||
"and R values. And if you plot frequency",
|
||||
"response, if you click on the frequency response button,",
|
||||
"boom, it will give you frequency responses for your",
|
||||
"circuit that look exactly like that.",
|
||||
"You can go and play around with that.",
|
||||
"Thank you. All right.",
|
||||
"As the next step I promised to show you an easier path.",
|
||||
"And let's build some insight.",
|
||||
"",
|
||||
"Is there a simpler way to get where we would like to get?",
|
||||
"In particular, is there a simpler way to get",
|
||||
"Vp? Let's focus on Vp.",
|
||||
"Why Vp? Because remember Vp was the",
|
||||
"complex amplitude of e to the j omega t.",
|
||||
"And once I know Vp then I know this expression here.",
|
||||
"Also notice that this here, the denominator is simply the",
|
||||
"characteristic equation for, I wonder how many of you",
|
||||
"noticed it, is simply the characteristic equation for the",
|
||||
"RC circuit. If I can write down Vp,",
|
||||
"I can write down the characteristic equation,",
|
||||
"it will be in the denominator. I can also write down the",
|
||||
"frequency response very easily by taking the magnitude and",
|
||||
"phase of Vp. So Vp has all the information",
|
||||
"humankind needs for those circuits.",
|
||||
"Is there a simpler way to get Vp?",
|
||||
"To bring some insight, let's go ahead and write down",
|
||||
"--",
|
||||
"",
|
||||
"Let's stare at this for a while longer and see if light bulbs go",
|
||||
"off in our minds. Of course, I could write this",
|
||||
"as Vi/(1+sRC). I just replaced the shorthand",
|
||||
"notation for a j omega. And I simply divide by SC",
|
||||
"throughout. So I get Vi times,",
|
||||
"I simply divide by SC throughout.",
|
||||
"Here is Vi. I have one by SC,",
|
||||
"one by SC plus R. Light bulbs beginning to go",
|
||||
"off?",
|
||||
"",
|
||||
"The form we have here is 1/SC, some function of my capacitance",
|
||||
"divided by something connected to my capacitance plus R.",
|
||||
"This is Vi multiplied by something connected to",
|
||||
"capacitance divided by something connected to capacitance plus R.",
|
||||
"And remember your circuit.",
|
||||
"",
|
||||
"What is that reminiscent of? What does that remind you of?",
|
||||
"Voltage divider? Hmm.",
|
||||
"There is some voltage divider thing going on here.",
|
||||
"I just cannot quite pin it. It is something about the",
|
||||
"capacitor, capacitor plus booster, some voltage divider",
|
||||
"thingamajig happening here. We will try to figure that out.",
|
||||
"What I will do is replace those terms with something called Zc.",
|
||||
"Zc plus Zr. If I can find out the Zr and Zc",
|
||||
"somehow, I can write down the Vp by inspection by the voltage",
|
||||
"divider action, by some generalization of the",
|
||||
"good old Ohm's law that I know about.",
|
||||
"Let's proceed further and see if we can make some kind of a",
|
||||
"connection between this and this.",
|
||||
"If I can make the connection then boom, I'm done.",
|
||||
"I will just use voltage dividers and I am home.",
|
||||
"",
|
||||
"OK, so let's play around and see.",
|
||||
"There is something in there. By now you should know that we",
|
||||
"are very close. There is something going on in",
|
||||
"there. I just need to get that spark.",
|
||||
"I just need to make that spark so I can bridge the gap between",
|
||||
"something that is really easy versus where I am.",
|
||||
"Let's take a look at the resistor.",
|
||||
"",
|
||||
"I have my resistor with the voltage vR across it and a",
|
||||
"current iR. Remember to get to any sort of",
|
||||
"steady state you are going to be dealing with the drives of the",
|
||||
"form vI e to the j omega t, exponential drives.",
|
||||
"And by taking the real part, I know I get the input,",
|
||||
"and the real part of the output gives me the actual output.",
|
||||
"Let's say my iR is simply Ire^st and my vR is Vre^st.",
|
||||
"The S is, again, a shorthand notation for j",
|
||||
"omega. If my current Ire^st of the",
|
||||
"exponential form shown there and here is Vr, I need to find out",
|
||||
"what relates Vr and Ir for the element relationship for the",
|
||||
"resistor to hold. In general, Ir and Vr are",
|
||||
"complex numbers. For the resistor,",
|
||||
"I know that Vr=RIr. And I substitute using my",
|
||||
"complex drives here. So it is Vre^st=RIre^st.",
|
||||
"I am just substituting for these drives,",
|
||||
"Ohm's law should apply, and I cancel off e^st.",
|
||||
"And so I get Vr=RIr. Interesting.",
|
||||
"For the resistor I find that, based on the fundamental",
|
||||
"principles of resistor action, the complex amplitude of the",
|
||||
"voltage simply relates to the complex amplitude of the input",
|
||||
"by the proportionality factor R. In other words,",
|
||||
"for the resistor -- Just as the time domain V and I",
|
||||
"were related by the proportionality constant R,",
|
||||
"the complex amplitudes Vr and Ir are also related in the same",
|
||||
"way. That's interesting.",
|
||||
"Now let's look at the capacitor.",
|
||||
"",
|
||||
"Some current ic flowing through it and a voltage vc.",
|
||||
"Let's say the current is Ice^st and the voltage is Vce^st.",
|
||||
"Let's plug these into the element law for the capacitor",
|
||||
"and see if we can find out a way of relating vc and ic.",
|
||||
"I know that ic is simply Cdvc/dt.",
|
||||
"So I replace this with Ice^st=Cd/dt(vce^st),",
|
||||
"which is simply Ice^st=CsVce^st.",
|
||||
"So I can cancel this out again. Interesting.",
|
||||
"Ic=CsVc. Very interesting.",
|
||||
"What is interesting here? Notice that in the time domain",
|
||||
"Ic=Cdvc/dt, the element law for the capacitor.",
|
||||
"So I said let's use exponential drives, Ice^st,",
|
||||
"Vce^st, that's an exponential drive, and try to find out what",
|
||||
"the relationship between the complex amplitudes are.",
|
||||
"I plug them and what do I find? I find that if my input is",
|
||||
"Vce^st, and Vc is the amplitude of the input,",
|
||||
"then the current is simply given by something multiplied",
|
||||
"Vc. It's very similar in form to",
|
||||
"what I saw here. The resistor,",
|
||||
"Vr=RIr. For the capacitor,",
|
||||
"Vc=Ic/sc. 1/sc kind of plays the role of",
|
||||
"R. In other words,",
|
||||
"the complex amplitudes around the capacitor are related by Vc",
|
||||
"equals some constant times Ic. Almost like a funny Ohm's law",
|
||||
"kind of relationship where Vc and IC are complex amplitudes.",
|
||||
"For the inductor it is the same way, iL, vL and L.",
|
||||
"Let's say iL=Ile^st and vL=Vle^st.",
|
||||
"Substitute the values for the inductor into its element",
|
||||
"relationship as well. I know that vL=LdiL/dt.",
|
||||
"Therefore, substituting the complex amplitudes is L.",
|
||||
"And diL/dt will simply be Ilse^st.",
|
||||
"So I cancel out the exponentials.",
|
||||
"The reason we're able to do all of this is simply the remarkable",
|
||||
"beauty of exponentials. Exponentials are absolutely",
|
||||
"stunningly beautiful. The reason is that when I",
|
||||
"differentiate them what I get back is the exponential times",
|
||||
"some constant, and the constant was in its",
|
||||
"numerator multiplying t. And that's the beauty of",
|
||||
"exponentials. If this was a sine then I would",
|
||||
"get cosine and a sine. With exponentials these cancel",
|
||||
"out and what I am left with is something that is LsIl.",
|
||||
"Again, for the inductor, the voltage across the inductor",
|
||||
"relates to some constant Ls here times Il.",
|
||||
"This is absolutely stunning and almost looks like a form of",
|
||||
"Ohm's law here. What I am going to do is let's",
|
||||
"give this the name Zr. Let's give this 1/sC the name",
|
||||
"Zc. And let's give this the name",
|
||||
"ZL. It kind of behaves like a",
|
||||
"resistor, so the resistor simply becomes Zr.",
|
||||
"And 1/sC behaved like a resistor so I called it Zc.",
|
||||
"And this is a ZL. These are called \"impedances\".",
|
||||
"",
|
||||
"In other words, for a capacitor,",
|
||||
"as far as complex inputs and outputs are concerned,",
|
||||
"if Vc and Ic is fed to it, the capacitor can be replaced",
|
||||
"by an impedance Zc where I can write the relationship between",
|
||||
"Vc and Ic as Vc=ZcIc. Where Zc is simply one by sc.",
|
||||
"Similarly, for an inductor --",
|
||||
"",
|
||||
"-- I can write its impedance ZL as sL and I get Vl=ZLIl.",
|
||||
"And finally for a resistor it is pretty simple.",
|
||||
"",
|
||||
"What I am saying is that if I am in the region of the",
|
||||
"playground, if I constrain myself in the region of the",
|
||||
"playground where my inputs are something Vi e to the j omega t",
|
||||
"or exponentials, in that little region of the",
|
||||
"playground now, I am focusing more and more on",
|
||||
"small parts of the playground so I am kind of boxed in right now.",
|
||||
"In that region of the playground this applies.",
|
||||
"In that region of the playground, I can replace",
|
||||
"resistors by impedances, capacitors with impedances of",
|
||||
"value 1/sC. And within that playground the",
|
||||
"beauty of analysis there is that in that region of the playground",
|
||||
"where the inputs are of the form Vie^st, it turns out that the",
|
||||
"element laws are simply generalizations of Ohm's law.",
|
||||
"That is absolutely stunning. It is one of the biggest",
|
||||
"hallelujah moments in learning circuits.",
|
||||
"This is really big. And I think this is almost as",
|
||||
"big as the realization that you can take a nonlinear circuit,",
|
||||
"operate it at a given operating point, and you can sit around",
|
||||
"doing Zen things, looking at small perturbations",
|
||||
"in there, those are going to be linearly related.",
|
||||
"This is one of the big hallelujah moments in 6.002.",
|
||||
"And this is of the same magnitude as the small signal",
|
||||
"response being linear. It is something that is",
|
||||
"completely non-intuitive. It is something that you just",
|
||||
"would not have known until you had seen it happen.",
|
||||
"The same way here. This is very important so I",
|
||||
"will repeat it again. I have boxed myself into this",
|
||||
"small region of the playground where all I care about are",
|
||||
"sinusoidal inputs and steady-state responses.",
|
||||
"So there I focus on complex inputs, Vi e to the j omega t.",
|
||||
"And I have just shown you that I can replace inductors,",
|
||||
"capacitors, resistors with their impedances.",
|
||||
"And the amplitudes of the corresponding signals around",
|
||||
"them are related by just a simple Ohm's law like",
|
||||
"relationship using impedances. I am sort of boxed into this",
|
||||
"playground, right? In my playground it is all",
|
||||
"about e to the ij omega t. e to the ij omega t is implicit",
|
||||
"everywhere. I just don't show it.",
|
||||
"If I want to talk to somebody else outside but within MIT in",
|
||||
"this small region, it's all e to the ij omega t in",
|
||||
"there. If I want to talk to somebody",
|
||||
"outside, get out of MIT, get out of this playground,",
|
||||
"what else do I have to do? I have to take the real part.",
|
||||
"Don't forget that. Remember that,",
|
||||
"take for example Vc here, so Vc is this,",
|
||||
"so implicit in all of this is that if I measure Vc at some",
|
||||
"place it is really going to be Vce to the j omega t.",
|
||||
"And if we the cosine, the real part,",
|
||||
"then I have to take a real part of this.",
|
||||
"And the real part of that would Vc cosine of omega t angle Vc.",
|
||||
"This piece here kind of goes unsaid.",
|
||||
"We will agree that we have to do it, but we just skip that",
|
||||
"step because it is obvious. We just deal with Vcs and Vls",
|
||||
"now. So a new notation certainly",
|
||||
"sneaked by you, and that notation looks like a",
|
||||
"big letter and a small letter. Remember you have seen vL,",
|
||||
"this is the total behavior, you have seen vl,",
|
||||
"that's a small signal behavior, and now you see this,",
|
||||
"Vl, capital V small l. And we also have DC,",
|
||||
"we have labeled operating point values as VL,",
|
||||
"capital V, capital L. We have one thing left so",
|
||||
"nobody go out there inventing something new because we would",
|
||||
"be in trouble. This is capital V,",
|
||||
"small l, and this is simply \"complex amplitude\" in the small",
|
||||
"boxed region of my playground where good things happen and",
|
||||
"exponentials fly. Whenever someone gives you a",
|
||||
"variable, capital V, small l, remember it's a",
|
||||
"complex amplitude, a complex number,",
|
||||
"and you know how to get to the time domain from there.",
|
||||
"You take that number, take the real part,",
|
||||
"multiple the number by e to the j omega t and take the real",
|
||||
"part, which is tantamount to magnitude cosine omega t plus",
|
||||
"angle of that number. Actually, you know what?",
|
||||
"Let's send this up.",
|
||||
"",
|
||||
"Back to an example.",
|
||||
"",
|
||||
"Oh, I'm sorry. I'm sorry.",
|
||||
"This is not good. This is my time domain circuit.",
|
||||
"Remember this was my time domain circuit.",
|
||||
"A vI input. A vC output.",
|
||||
"I wanted to analyze this. What I am telling you now is",
|
||||
"let's box ourselves in this impedance playground.",
|
||||
"And in the impedance playground the input becomes the complex",
|
||||
"amplitude of the input, my resistance gets replaced by",
|
||||
"a box Zr, my capacitor gets replaced by a box Zc.",
|
||||
"And the voltage I care about here is Vc.",
|
||||
"Zr = R and Zc=1/sC. Now, there we go.",
|
||||
"I can write down Vc using a voltage divider action as Vc is",
|
||||
"simply Zc/(Zc+Zr), done, times Vi of course.",
|
||||
"And that gives me 1/sC divided by 1/sC+R and multiplying",
|
||||
"throughout by sC I get 1/1+sCR where S is j omega.",
|
||||
"Just cannot get any simpler. How long did I take to do this?",
|
||||
"30 seconds. Where I spent a whole lecture",
|
||||
"on Tuesday grinding through first trig, giving up halfway",
|
||||
"and collapsing, and then showing you the sneaky",
|
||||
"path which was still pretty painful, but 30 seconds,",
|
||||
"boom. This stuff is spectacularly",
|
||||
"beautiful. The really cool thing here is",
|
||||
"that in this impedance domain for linear circuits all your",
|
||||
"good old tricks apply. Your Thevenin,",
|
||||
"your Norton, your superposition,",
|
||||
"name it and it applies for this linear circuit.",
|
||||
"If you close your eyes and make believe that Zr is like an R and",
|
||||
"simply apply all the techniques you have learned so far in this",
|
||||
"linear playground. Just a little hack at the end",
|
||||
"where this is the complex amplitude.",
|
||||
"And if you want to go to the time domain part then you do the",
|
||||
"usual thing. Modulus Vc cosine omega t plus",
|
||||
"angle Vc. Just remember that.",
|
||||
"That's the jump to get back to the time domain.",
|
||||
"Just to show you that this not just works for one little",
|
||||
"rinky-dink circuit here, let me take a more complicated",
|
||||
"circuit. If I believe in my own BS,",
|
||||
"I should be able to apply this theory to my series RLC,",
|
||||
"the big painful circuit that we did differential equations for",
|
||||
"about a week ago. Let's do it.",
|
||||
"",
|
||||
"I have an inductor, a capacitor and a resistor.",
|
||||
"What I am going to do is replace this with the impedance",
|
||||
"model. Input Vi.",
|
||||
"Let's say this was vI. Let's say I cared about vR.",
|
||||
"L, C and R. The impedance model would",
|
||||
"simply be Vi. What's the impedance of an",
|
||||
"inductor? SL.",
|
||||
"And for the capacitor it is 1/sC.",
|
||||
"And for a resistor it is simply R.",
|
||||
"And just remember, if I can find out VR then for",
|
||||
"an input cosine of the form Vi cosine omega t the output will",
|
||||
"given by |Vr| cosine of omega t plus angle Vr.",
|
||||
"Just remember this last step. But Vr itself is trivially",
|
||||
"determined. It is the voltage divider",
|
||||
"action again times Vi. And the voltage divider action",
|
||||
"is in the denominator I sum these thingamajigs,",
|
||||
"so ZL+ZC+ZR, ZR in the numerator.",
|
||||
"And Zr is simply R. ZL is sL.",
|
||||
"Zc is 1/sC. And R is R.",
|
||||
"Vi. And I multiply through by,",
|
||||
"in this particular situation, by s/L.",
|
||||
"I want to get it into the same form as you've seen before.",
|
||||
"Multiply throughout, the numerator and denominator",
|
||||
"by s/L, what do I get? I get RS/L and out here I end",
|
||||
"up getting S squared plus 1/LC, and I get plus R/L S.",
|
||||
"I am done. Look at that.",
|
||||
"Well, a little more than 30 seconds.",
|
||||
"Maybe a minute. What is this?",
|
||||
"Where have you seen this before?",
|
||||
"The denominator of this expression here?",
|
||||
"Ah, characteristic equation for the RLC.",
|
||||
"Remember I promised you in the beginning that when we come to",
|
||||
"the end of the day using a simple one-minute expression I",
|
||||
"am going to write down the characteristic equation?",
|
||||
"Boom, here is what I get. Did somebody hear an echo in",
|
||||
"there? Notice that just by doing a",
|
||||
"simple voltage divider thingamajig, I got this",
|
||||
"expression. And now I can write down the",
|
||||
"frequency response by replacing s is equal to j omega.",
|
||||
"Even more beautiful and what is even more stunningly pretty here",
|
||||
"is that remember the intuitive method I taught you about?",
|
||||
"The characteristic equation gives you alpha,",
|
||||
"omega nought, omega d and Q.",
|
||||
"And based on those we can sketch even the time domain",
|
||||
"response. Guess what?",
|
||||
"RLC circuits are pass\u00e9 now. You can just write this thing",
|
||||
"down and you're done, 30 seconds or less.",
|
||||
"No DEs, no trig, no nothing.",
|
||||
"OK."
|
||||
]
|
||||
}
|
||||
@@ -1,1934 +0,0 @@
|
||||
{
|
||||
"start": [
|
||||
0,
|
||||
11000,
|
||||
14680,
|
||||
20333,
|
||||
27431,
|
||||
34267,
|
||||
41425,
|
||||
45859,
|
||||
49288,
|
||||
53722,
|
||||
59076,
|
||||
64063,
|
||||
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"text": [
|
||||
"",
|
||||
"All right. Let's get started.",
|
||||
"I guess this watch is a couple minutes fast.",
|
||||
"First a quick announcement. In case you have forgotten,",
|
||||
"your lab notebooks are due tomorrow with the post-lab",
|
||||
"exercises for the first lab. OK, so I am going to continue",
|
||||
"with amplifiers today. And to just give you a sense of",
|
||||
"where we headed, we have this five lecture",
|
||||
"sequence covering different aspects of amplifiers with",
|
||||
"dependent sources and showed how we could build an amplifier with",
|
||||
"it on Tuesday. Today I am going to show you a",
|
||||
"real device that implements a dependent source.",
|
||||
"And then next Tuesday we will talk about analysis of an",
|
||||
"amplifier. Wednesday is our quiz.",
|
||||
"Thursday and the Tuesday after that we then talk about small",
|
||||
"signal analysis and small signal use of the amplifier.",
|
||||
"Today we will talk about the MOSFET amplifier.",
|
||||
"",
|
||||
"So let's start with a quick review.",
|
||||
"And in the last lecture, I showed you that I could build",
|
||||
"a amplifier using a dependent source.",
|
||||
"",
|
||||
"And a dependent source worked as follows.",
|
||||
"Let's say I had a circuit and I connected a dependent source",
|
||||
"into the circuit. Let's say in this example I",
|
||||
"have a current source. So this is some circuit.",
|
||||
"And the current i is a function of some parameter in the",
|
||||
"circuit. That's why this is a dependent",
|
||||
"source. This is a dependent current",
|
||||
"source. So it could be that I have some",
|
||||
"element inside. And I measure,",
|
||||
"I sample the voltage across the element or between any two",
|
||||
"points in the circuit. And, in this little example",
|
||||
"here, this current could be dependent on that voltage.",
|
||||
"So notice that although I showed you the two terminals of",
|
||||
"the dependent source that carried a current,",
|
||||
"there is another implicit port, another implicit terminal",
|
||||
"there. And that terminal there is",
|
||||
"called the \"control port\" of the dependent source at which I",
|
||||
"apply a voltage or current that will control the value of the",
|
||||
"current source. As a quick aside.",
|
||||
"",
|
||||
"There is a small glitch with the tools in your tool chest.",
|
||||
"We talked about the superposition technique where",
|
||||
"you were taught to turn on one source at a time,",
|
||||
"for a linear circuit one source at a time, and then sum up the",
|
||||
"responses to all the sources acting one at a time.",
|
||||
"Well, what do you do about dependent sources?",
|
||||
"A dependent source is a source. And we have to modify the",
|
||||
"superposition statement just a little bit.",
|
||||
"And for details you can look at Section 3.5.1 of your course",
|
||||
"notes on the details and some examples on how to do this.",
|
||||
"So the approach is very simple, actually.",
|
||||
"The approach is, for the purpose of",
|
||||
"superposition, to not treat your dependent",
|
||||
"source as sources that you turn on and turn off.",
|
||||
"So what you do is when you do superposition with dependent",
|
||||
"sources simply leave all your dependent sources in the",
|
||||
"circuit. Just leave them in there and",
|
||||
"turn on and off only your independent sources.",
|
||||
"So look at the response of the circuit by turning on your",
|
||||
"independent sources one at a time and summing up the",
|
||||
"responses. And your dependent sources stay",
|
||||
"within the circuit and simply analyze them as you do anything",
|
||||
"else. So essentially what it says is",
|
||||
"that just be a little cautious when you have dependent sources,",
|
||||
"but the basic method applies almost without any change.",
|
||||
"The readings for today's lecture are Section 7.3 to 7.6.",
|
||||
"",
|
||||
"So since we are going to build up on the dependent source",
|
||||
"amplifier, let me start with a quick review of that amplifier.",
|
||||
"We built our amplifier as follows.",
|
||||
"",
|
||||
"We connected our dependent source in the following manner.",
|
||||
"And the current through the dependent source in the example",
|
||||
"we took was related to an input voltage vI.",
|
||||
"",
|
||||
"So some voltage vI. And so these two were the",
|
||||
"control port of the dependent source and a vI was applied",
|
||||
"there. And I showed you a simple",
|
||||
"amplifier built with a dependent source that behaved in this",
|
||||
"manner. And again I will keep reminding",
|
||||
"you, just remember that the dependent source is actually",
|
||||
"this box here, the control port and the output",
|
||||
"port. And commonly we don't",
|
||||
"explicitly show the control port for those dependent sources for",
|
||||
"which the control port does not have any other affect on the",
|
||||
"circuit, like it doesn't draw any current or things like that.",
|
||||
"So in this particular example we said that this behaved in the",
|
||||
"following manner for vI greater than or equal to 1 volt and iD",
|
||||
"was zero otherwise.",
|
||||
"",
|
||||
"So we can analyze the circuit to figure out what vO is going",
|
||||
"to look like. And a simple application of KVL",
|
||||
"at this loop here, again, you know,",
|
||||
"when I say this loop here, I am pointing at something",
|
||||
"here. That is the VS source that is",
|
||||
"implicitly across these two nodes.",
|
||||
"Again, this is a shorthand notation where this little up",
|
||||
"arrow here implies that I have a voltage source connected between",
|
||||
"these two terminals here. And so there is a loop here",
|
||||
"that involves VS. So Vo is simply VS minus the",
|
||||
"drop across this resistor. So it's VS minus the drop",
|
||||
"across this resistor gives me vO.",
|
||||
"And the drop across the resistor is simply iD RL.",
|
||||
"iD is the current here and that's the drop across the",
|
||||
"resistor. And I could get the explicit",
|
||||
"relationship of vO versus vI by substituting for iD as vI minus",
|
||||
"one all squared. So vO relates to vI in the",
|
||||
"following manner. Nothing new so far.",
|
||||
"I have pretty much reviewed what we did the last time.",
|
||||
"Here is where we take our next step forward with some new",
|
||||
"material. Up to now I have talked as a",
|
||||
"theoretician would where I said just imagine that you had",
|
||||
"spherical cow or something like that.",
|
||||
"Here I just asked you to imagine this ideal dependent",
|
||||
"source, control port and an output port, and it behaved in",
|
||||
"this manner. So as a next step what I would",
|
||||
"like to do is show you a practical dependent source which",
|
||||
"turns out to be a little bit more complicated than this",
|
||||
"idealized dependent source that I showed you in many dimensions.",
|
||||
"Real life tends to impose a bunch of practical constraints",
|
||||
"on you, and we will look at those in a second.",
|
||||
"If I could find a dependent source that looked like this --",
|
||||
"",
|
||||
"We had a control port A prime and output port B prime.",
|
||||
"And I looked at some examples where the current through the",
|
||||
"dependent current source was some function of the input",
|
||||
"voltage. This is a \"voltage controlled",
|
||||
"current source\". What I am going to do is talk",
|
||||
"about a device that can give me this behavior or some close",
|
||||
"approximation to it. It turns out that under certain",
|
||||
"conditions the MOSFET that you have already looked at behaves",
|
||||
"in this manner. The MOSFET that you've seen",
|
||||
"sort of behaves like this. And let me show you under what",
|
||||
"conditions the MOSFET behaves in that manner.",
|
||||
"Let me create some room for myself.",
|
||||
"Notice that I need a control port, needed an output port.",
|
||||
"And I am going to view my MOSFET in a slightly different",
|
||||
"manner than you have seen before.",
|
||||
"I draw these two terminals here.",
|
||||
"And this was a three terminal MOSFET.",
|
||||
"This was my drain, my gate and my source terminal.",
|
||||
"It was a three terminal device, but what I do is I view the",
|
||||
"MOSFET slightly differently. I will just use this terminal",
|
||||
"to be common across both the gate and the drain.",
|
||||
"And so this voltage here is vGS.",
|
||||
"I am just using the source port, the source terminal along",
|
||||
"with the gate as a terminal pair.",
|
||||
"I am using the same source along with the drain as another",
|
||||
"terminal pair. So I have a vDS out there and I",
|
||||
"have some current iDS that flows out here.",
|
||||
"Notice that when I view the MOSFET in this manner I have",
|
||||
"accomplished my first step, which is I seem to have a box",
|
||||
"which has a port here and a port here.",
|
||||
"And I also explained to you that a MOSFET behaves in a",
|
||||
"particular manner. For one, the output port",
|
||||
"behaved as an open circuit under certain conditions when --",
|
||||
"This was vGS, G, drain and source.",
|
||||
"When vGS was less than a threshold voltage VT this MOSFET",
|
||||
"had an equivalent circuit that looked like this.",
|
||||
"So when vGS was less than some threshold voltage VT then there",
|
||||
"was an open circuit between the drain and the source.",
|
||||
"And you saw this before. So far nothing new here.",
|
||||
"However, when vGS is greater than or equal to VT --",
|
||||
"",
|
||||
"vGS was greater than VT. The MOSFET behavior we looked",
|
||||
"at earlier showed that this behaved either like a short",
|
||||
"circuit in the simplest form or in a slightly more detailed form",
|
||||
"it behaved like a resistor. We call that the SR model of",
|
||||
"the MOSFET. So when vGS was greater than VT",
|
||||
"we said that a simple way to approximate MOSFET behavior was",
|
||||
"to view this as a resistor connected between the drain and",
|
||||
"the source. That was our SR model use of",
|
||||
"the MOSFET. It turns out that we kind of",
|
||||
"lied. We were sort of looking at the",
|
||||
"MOSFET in a really funny way. And I shone the light on the",
|
||||
"MOSFET in a really, really clever way.",
|
||||
"Well, I shouldn't say clever. A really, really tricky way.",
|
||||
"And tricked you into believing that it was just a resistor.",
|
||||
"And we constrained how you use the MOSFET.",
|
||||
"So that behavior was indeed a resistive behavior.",
|
||||
"But it turns out that in real life the behavior of the MOSFET",
|
||||
"between the drain and the source terminals is much more",
|
||||
"complicated than the limited form in which you saw it.",
|
||||
"So today what I am going to do is take the wraps off the",
|
||||
"complete MOSFET and show you its full behavior in all its gory",
|
||||
"glory. And I will spend a bit of time",
|
||||
"on that to clearly emphasize under what conditions the MOSFET",
|
||||
"behaves like a resistor, as you saw when you did digital",
|
||||
"circuits, or behaves differently in other domains of use.",
|
||||
"Let me pause for a second and leave this space blank here.",
|
||||
"And let's do some investigations.",
|
||||
"",
|
||||
"Let me leave this here. I won't draw in anything yet.",
|
||||
"You will figure out what it looks like yourselves under",
|
||||
"certain conditions. What I will do next is apply",
|
||||
"some voltages on a MOSFET and observe the current versus vDS",
|
||||
"behavior and plot that on a scope and take a look at it.",
|
||||
"What I am going to do --",
|
||||
"",
|
||||
"-- is figure out what iDS looks like for --",
|
||||
"",
|
||||
"Remember iG into the gate for 6.002 is always going to be",
|
||||
"zero. In much more detailed analyses",
|
||||
"of the MOSFET, in future courses you may see",
|
||||
"slightly more complex behavior. But as far as we are concerned",
|
||||
"it is an open circuit looking into the gate.",
|
||||
"So I am going to apply a vGS across the MOSFET,",
|
||||
"apply a vDS across the MOSFET and plot iDS versus vDS.",
|
||||
"First let me show you what you already know.",
|
||||
"What you already know --",
|
||||
"",
|
||||
"This is vDS. I will just keep doing as much",
|
||||
"as I can of what you already know.",
|
||||
"And then when I do some new stuff I will tell you",
|
||||
"explicitly. You've seen this before.",
|
||||
"The MOSFET behaves like an open circuit when vGS less than VT.",
|
||||
"That is when vG is less than a threshold voltage VT,",
|
||||
"I have zero current flowing through the MOSFET.",
|
||||
"And when vGS was greater than VT then the S model of the",
|
||||
"MOSFET the switch model simply said that look,",
|
||||
"we can model the D2S as a short circuit.",
|
||||
"You saw this in your labs and you saw that it was a very,",
|
||||
"very small resistance between the drain and the source and it",
|
||||
"kind of looked like a short circuit.",
|
||||
"But then we said well, that's not quite it.",
|
||||
"There is some resistance. And so we said a slightly more",
|
||||
"accurate model would have this line droop a little bit to imply",
|
||||
"that there was some resistance R_on between the drain and the",
|
||||
"source, so vDS iDS. So this was when vGS less than",
|
||||
"VT and vGS greater than or equal to VT.",
|
||||
"I have some resistance. And that showed me a straight",
|
||||
"line kind of like behavior. And I showed you that behavior.",
|
||||
"So far absolutely nothing new. Now what I have plotted there",
|
||||
"for you is that behavior. Up here notice that this is the",
|
||||
"vDS axis, this is the iDS axis. I am plotting iDS versus vDS.",
|
||||
"And when vGS -- The gate voltage is more than a",
|
||||
"threshold, notice that I see what looks like something more",
|
||||
"or less like a straight line. And this is a straight line",
|
||||
"with some slope, more or less a straight line",
|
||||
"implying resistive behavior. And we also had some fun and",
|
||||
"games here. We said hey,",
|
||||
"what if I turn vGS off? Boom.",
|
||||
"That would be my iDS of zero implying that the MOSFET behaved",
|
||||
"like an open circuit between the drain and the source.",
|
||||
"I applied a positive vGS more than VT and it began to look",
|
||||
"like a resistor. Open circuit,",
|
||||
"resistor, open circuit, resistor, OK?",
|
||||
"Up until now nothing new. So you shouldn't have learned",
|
||||
"anything at all that is new until now in today's lecture.",
|
||||
"Now watch. What I am going to do is,",
|
||||
"as I said, I kind of lied all this time and I just showed you",
|
||||
"this behavior. And what I have been doing all",
|
||||
"along is very carefully using a very small value of vDS.",
|
||||
"Notice it's a small values of vDS.",
|
||||
"I haven't told you what it looks like as vDS increases.",
|
||||
"Well, let's go try it out. We have a scope here.",
|
||||
"We have the MOSFET here. Now, I am not sure what is",
|
||||
"going to happen now. You may see smoke or have an",
|
||||
"explosion, who knows what? But look up there for a second.",
|
||||
"I am just going to increase vDS and you can figure out what",
|
||||
"happens for yourselves. I increase vDS.",
|
||||
"Whoa, what a liar. Agarwal is a liar.",
|
||||
"I have been kind of tricking you.",
|
||||
"I have been putting -- Covering up all this part here",
|
||||
"and showing you just this region of the curve for small values of",
|
||||
"vDS. But as I increase vDS this is",
|
||||
"nothing that looks even close to that of resistive behavior.",
|
||||
"So what's happening here? What's happening is that as I",
|
||||
"increase my vDS the iDS curve tails off and saturates at some",
|
||||
"value of current. Notice it saturates at some",
|
||||
"value of current. And so I am going to look at",
|
||||
"this region of behavior. Notice that what we have looked",
|
||||
"at so far was the behavior for small vDS.",
|
||||
"It kind of looks resistive. But when I pump up the vDS,",
|
||||
"really whack this node really hard with a much larger vDS the",
|
||||
"guy says, oh, I give up.",
|
||||
"And the current saturates out and flattens out and holds the",
|
||||
"value steady at some value. So what's that behavior look",
|
||||
"like? What is my horizontal line",
|
||||
"above the X axis in terms of V I elements?",
|
||||
"What is that behavior like? Current source,",
|
||||
"exactly. So this is current source like",
|
||||
"behavior. And so let me start by drawing",
|
||||
"you a little model and explaining it in more detail.",
|
||||
"What happens is that under certain conditions,",
|
||||
"and the conditions are the following, when vDS,",
|
||||
"that is my drain to source voltage is greater than or equal",
|
||||
"to vGS minus VT. When my drain voltage goes",
|
||||
"above vGS minus VT, so if vGS is 3 volts and if VT",
|
||||
"is 1 volt, then if vDS goes above 2 volts,",
|
||||
"if I am hammering the drain of the MOSFET with a higher voltage",
|
||||
"then this guy says I give up, can't show you nice restive",
|
||||
"behavior, and the current saturates out and it doesn't",
|
||||
"allow you draw any more current than a maximum value.",
|
||||
"And that's the current source behavior.",
|
||||
"This one behaves like a current source.",
|
||||
"And the current iDS is given by the following expression.",
|
||||
"",
|
||||
"The current is given by iDS is equal to a constant K divide by",
|
||||
"two times (vGS-VT) all squared. Kind of reminiscent of the",
|
||||
"carefully chosen dependent source example,",
|
||||
"just that this one here is VT. This model, which applies when",
|
||||
"vGS is greater than VT, the MOSFET has to be on and the",
|
||||
"drain to source voltage in the MOSFET must be larger than some",
|
||||
"value, and that value is vGS minus VT then this guy begins to",
|
||||
"behave like a current source. This model of the MOSFET is",
|
||||
"called the \"switch current source model\".",
|
||||
"",
|
||||
"So in the region of the MOSFET characteristics where vGS is",
|
||||
"greater than VT and the drain to source voltage is larger than",
|
||||
"vGS minus VT, the MOSFET behaved like a",
|
||||
"current source between its drain and source terminals.",
|
||||
"And in that part we model the MOSFET as a current source.",
|
||||
"And so not surprisingly that part of the model is called the",
|
||||
"SCS model in contrast with the SR model where we had a",
|
||||
"resistor. Again, remember,",
|
||||
"this is not meant to be conflicting.",
|
||||
"It is not like gee, how can the MOSFET look like a",
|
||||
"resistor, and then suddenly what happens it becomes a current",
|
||||
"source. Well, the two regions are",
|
||||
"different. It is not that it is behaving",
|
||||
"as a current source for the same parameters, no.",
|
||||
"When vDS is less than this right-hand side it does behave",
|
||||
"resistive. The SR model applies.",
|
||||
"But increase vDS beyond a point, the current saturates and",
|
||||
"the SCS applies like so. So let's draw.",
|
||||
"The SCS behavior can be drawn here vDS and iDS.",
|
||||
"As I mentioned to you, for small values of vDS,",
|
||||
"let's say I pick some value of vGS, let's say vGS3,",
|
||||
"some value vGS, it is going to look like a",
|
||||
"resistor until vDS becomes equal to vGS3 minus VT.",
|
||||
"And after that it saturates out and begins to look like a",
|
||||
"current source. And this point is where vDS",
|
||||
"becomes equal to vGS minus VT. And this way is when this equal",
|
||||
"sign becomes a greater than sign, vDS becomes larger then I",
|
||||
"move into this part of the curve.",
|
||||
"Similarly, for various other values of vGS it will look like",
|
||||
"this --",
|
||||
"",
|
||||
"-- and so on. And it behaved like an open",
|
||||
"circuit as before when vGS less than VT.",
|
||||
"When vGS less than VT it is still behaving like an open",
|
||||
"circuit. And so as I increase my vGS,",
|
||||
"provided I keep my vDS greater than vGS minus VT,",
|
||||
"I get current source like behavior.",
|
||||
"And notice that this is increasing vGS.",
|
||||
"I have purposely drawn these curves at greater distances from",
|
||||
"each other to imply that it is a nonlinear relationship in that",
|
||||
"if I increase vGS by some amount, the increase in vDS is",
|
||||
"related to the square of vGS. It is vGS minus VT all squared.",
|
||||
"So I get a family of curves of that look like this.",
|
||||
"And this is in the region of operation where vDS equals vGS",
|
||||
"minus VT. And this applies in this regime",
|
||||
"where vDS less than vGS minus VT.",
|
||||
"This region of operation is called, as you might expect,",
|
||||
"the \"saturation region\".",
|
||||
"",
|
||||
"We say the MOSFET has been hammered, the MOSFET has been",
|
||||
"walloped, the MOSFET is in saturation.",
|
||||
"So the MOSFET is in saturation. This region,",
|
||||
"corresponding to this, is called the triode region.",
|
||||
"",
|
||||
"This is really very simple. All we are doing is saying that",
|
||||
"when vDS is increased beyond a certain limit,",
|
||||
"given my vGS minus VT, the MOSFET begins to behave",
|
||||
"like a current source. It cannot draw any more",
|
||||
"current. It limits the current to a",
|
||||
"given value like a current source.",
|
||||
"But on the left-hand side of this it behaves in a resistive",
|
||||
"manner. So what I would like to do is",
|
||||
"--",
|
||||
"",
|
||||
"What I will do is, we've plotted for you,",
|
||||
"for the MOSFET, all its characteristics in its",
|
||||
"full glory for a whole bunch of values of vGS and a whole bunch",
|
||||
"of values of vDS. And let me stare at those",
|
||||
"curves with you for a few seconds and walk you through",
|
||||
"them. So what do I have here?",
|
||||
"One of these curves corresponds to a given value of vGS.",
|
||||
"This may be vGS equals 2 volts. This is vDS,",
|
||||
"the drain to source voltage, and this is the current.",
|
||||
"So focus on this curve for now. In the beginning I hid the",
|
||||
"right-hand side behavior from you and showed you just the",
|
||||
"resistive behavior out here. When I increase vDS to be much",
|
||||
"larger the curve saturated and I got the saturation region",
|
||||
"operation of the MOSFET. And notice as I increase my",
|
||||
"value of vGS the saturation current also increases according",
|
||||
"to a square law behavior. So these are the entire curves",
|
||||
"of the MOSFET. Finally the truth comes out.",
|
||||
"And notice that when vDS is less than vGS minus VT,",
|
||||
"I have more or less resistive behavior.",
|
||||
"But when vDS is greater than vGS minus VT I get current",
|
||||
"source like behavior. So one question you may ask is",
|
||||
"when do I use one model or the other?",
|
||||
"When do I use the SR model and when do I use the SCS model?",
|
||||
"If you want to do a real detailed analysis then you can",
|
||||
"use the SR model when vDS is less than vGS minus VT.",
|
||||
"And you would use this model when vDS is greater than or",
|
||||
"equal to vGS minus VT. That is simple enough.",
|
||||
"In 6.002, to eliminate confusion we constrain how we",
|
||||
"look at things a little bit more stringently.",
|
||||
"And what we do is that for our entire digital analysis,",
|
||||
"for the entire digital world we focus on the SR model.",
|
||||
"And I will tell you why in a second.",
|
||||
"So for all digital circuits, invertors, look at power of",
|
||||
"invertors, look at delay, a bunch of other things,",
|
||||
"we will be using the SR model in 6.002.",
|
||||
"And I will tell you why in a second.",
|
||||
"And for analog -- That is for amplifier designs",
|
||||
"and situations like that, we will be operating the MOSFET",
|
||||
"in a saturation region. And I will talk about that in a",
|
||||
"second. What I am saying here is that",
|
||||
"in 6.002, when we do analog designs, we are going to",
|
||||
"discipline ourselves to using the MOSFET only in this region.",
|
||||
"We are going to constrain ourselves to play in only this",
|
||||
"region of the playground where vDS is quite large.",
|
||||
"Why? Because I am asking you to.",
|
||||
"I am saying let's play in that part of the playground and keep",
|
||||
"your vDS high. And so the MOSFET is going to",
|
||||
"be operating somewhere in here. So we can apply just the SCS",
|
||||
"model, just the current source behavior in that region.",
|
||||
"There is another important reason, which I will get to in a",
|
||||
"second. And for digital designs we will",
|
||||
"simply use the SR model. And it turns out that this is",
|
||||
"realistic because in the digital designs that you have you seen",
|
||||
"and will be seeing in this course, the pull down MOSFET is",
|
||||
"on, or when these pull down MOSFETs are on,",
|
||||
"the output voltage is pulled down close to ground.",
|
||||
"So vDS is very, very small.",
|
||||
"So it does make sense that this model apply.",
|
||||
"And when we talk about amplifiers, I am asking you to",
|
||||
"follow this discipline. I will tell you why in a",
|
||||
"second. I am saying analog designs",
|
||||
"follow this discipline that I call the saturation discipline.",
|
||||
"It says simply operate the MOSFET operating in saturation",
|
||||
"as a current source. We will look at an amplifier in",
|
||||
"a second, and I will tell you why.",
|
||||
"",
|
||||
"Now let's do a MOSFET amplifier.",
|
||||
"Remember my amplifier had an input port and an output port.",
|
||||
"And in general in our use we are going to have a common",
|
||||
"ground. And we have a VS and a ground",
|
||||
"here as well. That is the power port of the",
|
||||
"amplifier. The input port and the output",
|
||||
"port.",
|
||||
"",
|
||||
"And let me redraw the circuit putting a MOSFET in place of the",
|
||||
"current source, RL, VS, vO, drain,",
|
||||
"gate, source, vI.",
|
||||
"So my input is vI. Again, the MOSFET output is vO.",
|
||||
"And I have a resistor RL. Hey, we've seen that before.",
|
||||
"It turns out this is not surprising.",
|
||||
"You've seen this before. This was our primitive inverter",
|
||||
"circuit. So what's different here?",
|
||||
"We showed you the circuit as an inverter.",
|
||||
"What's different here is that when we look at MOSFET behavior",
|
||||
"as a current source, this behaves like an amplifier.",
|
||||
"In other words, when vDS is greater than some",
|
||||
"value then this behaves like a current source.",
|
||||
"When vDS is small, in other words,",
|
||||
"in the digital design when vDS was small here,",
|
||||
"because when the MOSFET was on it pulled the voltage down to",
|
||||
"ground, we could view this behavior as a resistor.",
|
||||
"And exactly the same thing, it is an amplifier.",
|
||||
"And with digital designs, I was driving it with 5 volts",
|
||||
"and 0 volts and that was it, rail to rail.",
|
||||
"As an amplifier, what I am doing now is looking",
|
||||
"at a small region of its behavior when vDS is greater",
|
||||
"than vGS minus VT. What I am saying is that for",
|
||||
"amplification let's follow the saturation discipline.",
|
||||
"And the reason is that when this behaves like a current",
|
||||
"source, what I have shown you is that if this behaves like a",
|
||||
"current source I have shown you that this expression up here",
|
||||
"gives you amplification. In last lecture we plotted a",
|
||||
"bunch of values for vO versus vI, and we saw that we were",
|
||||
"getting amplification. For a small change in vI,",
|
||||
"I was getting a larger change in vO, and that was when I had",
|
||||
"the equation for a current source in there.",
|
||||
"And so we know for a fact that if I can operate this as a",
|
||||
"current source, with a reasonable choice of",
|
||||
"values here, I am going to be able to get amplification.",
|
||||
"What I haven't told you is if this is operated in the linear",
|
||||
"region, in fact, you do not get amplification.",
|
||||
"I won't cover that, but you can check that out in",
|
||||
"your course notes as a discussion or you can try it out",
|
||||
"for yourself. Replace this with the SR model",
|
||||
"for small vDS and you can show yourselves that you don't get",
|
||||
"any amplification. In order to get the",
|
||||
"amplification we are telling ourselves let's focus on this",
|
||||
"part of the playground where vDS is greater than or equal to vGS",
|
||||
"minus VT. And for vGS greater than or",
|
||||
"equal to VT. So when vGS is greater than VT",
|
||||
"the MOSFET is on. Further, when vDS is large,",
|
||||
"larger than vGS minus VT this behaves like a current source.",
|
||||
"So we have now created a small playground for ourselves where",
|
||||
"we can build lots of fun little amplifiers and other circuits.",
|
||||
"And provided our circuits follow the saturation discipline",
|
||||
"where for the MOSFET or MOSFETs in the circuit these expressions",
|
||||
"are true then the MOSFETs are going to be in saturation,",
|
||||
"the current source model applies, and I will be indeed",
|
||||
"getting saturation. In future courses you may",
|
||||
"actually see the MOSFET used in other regimes of operation for a",
|
||||
"variety of reasons. But in 6.002 when we talk about",
|
||||
"amplifiers and so on we will be adopting the saturation",
|
||||
"discipline. And your homework problems and",
|
||||
"so on will state that. Assume that the MOSFETs are in",
|
||||
"saturation. What that means is that you can",
|
||||
"begin to model them as a current source and simply analyze their",
|
||||
"behavior accordingly. One minor nit.",
|
||||
"Note that vDS for the MOSFET is the same as vO.",
|
||||
"And vGS for the MOSFET is the same as vI.",
|
||||
"So if you see me jumping back and forth using vOs and vIs or",
|
||||
"vDSs and vGSs they are the same thing in this circuit.",
|
||||
"If you are dealing with circuits with many MOSFETs then",
|
||||
"you will have vDS1s and vGS1s and so on and so forth.",
|
||||
"But for this simple circuit, vO and vDS are the same,",
|
||||
"vI and vGS are the same. So we could go ahead and",
|
||||
"analyze that circuit. What I do to analyze the",
|
||||
"circuit, I am telling you this. I am telling you that the",
|
||||
"MOSFET is behaving in saturation.",
|
||||
"I am telling you this. We have disciplined ourselves",
|
||||
"to say that in that circuit the MOSFET is in saturation.",
|
||||
"As soon as we tell you that we can then go ahead and analyze",
|
||||
"that circuit. And to analyze that circuit",
|
||||
"what you will do is simply replace the MOSFET with its",
|
||||
"equivalent model, and that looks like this.",
|
||||
"Since you have been told that it is in saturation,",
|
||||
"we can replace the MOSFET with its current source model.",
|
||||
"",
|
||||
"And the current iDS for the MOSFET is given by K/2(vI-VT)^2.",
|
||||
"And it is always good to write the constraints under which you",
|
||||
"are implicitly working close by. So the constraints are one,",
|
||||
"vGS is greater than or equal to VT, vDS is greater than or equal",
|
||||
"to vGS minus VT. These constraints immediately",
|
||||
"follow from a statement of the type we are operating under the",
|
||||
"saturation discipline or the MOSFET is in saturation.",
|
||||
"Let me just mark this equation as A, and we will refer to it",
|
||||
"again.",
|
||||
"",
|
||||
"So with this new little circuit with the MOSFET working as a",
|
||||
"current source, let's go ahead and analyze our",
|
||||
"amplifier. Notice that to analyze the",
|
||||
"circuit I have a current source. It's a dependent current source",
|
||||
"where the current depends on the square of the input.",
|
||||
"So I want to go and analyze it. This is a nonlinear circuit.",
|
||||
"So I can apply any one of the methods that we talked about",
|
||||
"last week for nonlinear circuits.",
|
||||
"To analyze it I will go ahead and use the analytical method.",
|
||||
"And my goal will be to obtain vO versus vI.",
|
||||
"Again, remember where are we here?",
|
||||
"The MOSFET circuit operating in saturation so I can replace this",
|
||||
"with a current source. It is nonlinear.",
|
||||
"And so I can apply one of the two methods, the analytical",
|
||||
"method or the graphical method. Let's do both and start with",
|
||||
"the analytical method. The analytical method simply",
|
||||
"says go forth, apply the node method and",
|
||||
"solve. Simple stuff.",
|
||||
"Let's go ahead and do that. Node method.",
|
||||
"I have a single node here that is of interest.",
|
||||
"I know the voltage vI at this node.",
|
||||
"I know the voltage VS at this node.",
|
||||
"So the only unknown is here at vO.",
|
||||
"So I will go ahead and do that. Let me go ahead and equate the",
|
||||
"currents into the node to be zero.",
|
||||
"So the currents out of the node here are iDS.",
|
||||
"And that was equal the current into that same node.",
|
||||
"So iDS must equal VS minus vO divided by RL.",
|
||||
"iDS=VS-vO/RL. For later reference,",
|
||||
"let me call that B. Simplifying,",
|
||||
"what I can do is, we know that iDS is given by",
|
||||
"K/2(vI-VT)^2. So I replace iDS with this",
|
||||
"expression and I multiply that by RL.",
|
||||
"So I get K/2(vI-VT)RL. So iDS gets multiplied by RL",
|
||||
"and I get vO on this side and VS remains out here.",
|
||||
"All I have done is multiplied both sides by RL.",
|
||||
"So it is RL iDS, taken RL iDS to this side,",
|
||||
"that is here, I get the minus sign,",
|
||||
"and VS stays here, vO comes here.",
|
||||
"So that is my final expression. Remember this is true under",
|
||||
"certain conditions. I will keep hammering that home",
|
||||
"because some of the most common errors made by people is in",
|
||||
"forgetting the constraints under which this was obtained.",
|
||||
"And the constraint under which this was obtained is the",
|
||||
"saturation discipline. And that was true when vGS for",
|
||||
"a MOSFET was greater than or equal to VT and vDS for a MOSFET",
|
||||
"was greater than or equal to vGS minus VT.",
|
||||
"I also know that for vGS less than VT, vO=VS.",
|
||||
"So when vGS is less than VT then this one turns off.",
|
||||
"That's why it is the SCS model, switch current source model.",
|
||||
"When vGS is less than zero it turns off and VS directly",
|
||||
"appears at vO. I would like to stare at this",
|
||||
"constraint with you for a second, vDS greater than or",
|
||||
"equal to vGS minus VT here. And vDS is simply vO.",
|
||||
"I want to rewrite this constraint in terms of iDS.",
|
||||
"It will come in handy. So iDS is K/2(vI-VT)^2.",
|
||||
"This is vI-VT. So vI-VT is simply square root",
|
||||
"of 2iDS/K. In other words,",
|
||||
"I can write iDS less than or equal to K/2vO^2.",
|
||||
"So this constraint expressed in terms of iDS is simply iDS less",
|
||||
"than or equal to K/2vO^2.",
|
||||
"",
|
||||
"So all I've done here is analyzed this nonlinear circuit.",
|
||||
"I can also analyze it using the graphical method.",
|
||||
"And in order to do that, for my nonlinear circuit,",
|
||||
"in order to do that, all I have to do is plot.",
|
||||
"Let's have iDS here and vDS here.",
|
||||
"And as we did with a nonlinear expo dweeb, what I do is I plot",
|
||||
"the device characteristics iDS versus vDS.",
|
||||
"The device characteristics under saturation look like this,",
|
||||
"so vGS increasing. iDS versus vDS has a bunch of",
|
||||
"curves that look like current sources of increasing values.",
|
||||
"That simply reflects equation A.",
|
||||
"And then I superimpose on top of that the expression that",
|
||||
"comes up due to equation B which is iDS equals,",
|
||||
"let me write that down here, iDS equals VS/RL - vO/RL.",
|
||||
"That's B. And let me plot that.",
|
||||
"That is a straight line relationship between iDS and vO.",
|
||||
"And so when vO is zero iDS is VS/RL.",
|
||||
"And when iDS is zero vO equals VS.",
|
||||
"Remember, vO and vDS are the same.",
|
||||
"So this is what I get. This is the straight line",
|
||||
"corresponding to equation B here.",
|
||||
"",
|
||||
"And, as before, we just find the point where",
|
||||
"the two intersect. Let's say I am given some value",
|
||||
"of vGS. And let's say I am given some",
|
||||
"known value of vDS. So for that I can go ahead and",
|
||||
"find out the corresponding value of iDS from this graph.",
|
||||
"Just as I told you when we did the expo dweeb stuff,",
|
||||
"this line here is called a load line.",
|
||||
"You will be seeing that again and again and again where we",
|
||||
"have the equation corresponding to the one shown here,",
|
||||
"the equation written for the output loop superimposed on the",
|
||||
"device characteristics. That's called a load line.",
|
||||
"So I can get this point corresponding to the operating",
|
||||
"point of the MOSFET for this iDS, vDS and vGS by using the",
|
||||
"graphical method. In the next lecture we are",
|
||||
"going to look at, given a device of this sort,",
|
||||
"how do we figure out the boundaries of valid operation so",
|
||||
"that the MOSFET stays in saturation?"
|
||||
]
|
||||
}
|
||||
@@ -1,1841 +0,0 @@
|
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"text": [
|
||||
"-- will try it again at the end of this lecture and you show you",
|
||||
"that stuff hopefully next time. For today we are going to start",
|
||||
"with nonlinear analysis. Before we do that I wanted to",
|
||||
"do a little bit of review.",
|
||||
"",
|
||||
"I wanted to give you the past three weeks in perspective and",
|
||||
"show you how all of these things fit into the grand scheme of",
|
||||
"things. We began by building a great",
|
||||
"little playground, and within that playground we",
|
||||
"said that by enforcing upon ourselves the lumped matter",
|
||||
"discipline we created the lumped circuit abstraction.",
|
||||
"So within that playfield we assumed that we had dq by dt and",
|
||||
"d phi by dt to be 0 so that gave us as the lumped circuit",
|
||||
"abstraction. And within that lumped circuit",
|
||||
"abstraction, within this playground we looked at several",
|
||||
"methods of analyzing circuits, including the KVL,",
|
||||
"KCL method. We also learned the method",
|
||||
"involving composing resistors, the voltage dividers and so on",
|
||||
"and solving circuits intuitively.",
|
||||
"And we also looked at the node method, which is kind of the",
|
||||
"workhorse of the circuits industry.",
|
||||
"So when in doubt apply the node method and it will get you where",
|
||||
"you want to go. Now, we also said that this is",
|
||||
"good, here is our playground. We said hey,",
|
||||
"if we focus on those circuits that are linear we come to the",
|
||||
"left part of our playground. And we said that for linear",
|
||||
"circuits in this part of the playground we can further use a",
|
||||
"couple of techniques, a few techniques,",
|
||||
"superposition, Thevenin, Norton and so on.",
|
||||
"So these techniques allow you to very quickly analyze",
|
||||
"complicated circuits, especially when you're looking",
|
||||
"to find a single current, or voltage or some parameter of",
|
||||
"interest. Whenever you see,",
|
||||
"if you see a circuit containing multiple voltage sources or two",
|
||||
"or more voltage sources or current sources,",
|
||||
"as a first step think superposition.",
|
||||
"And so these are very powerful techniques that let you analyze",
|
||||
"very complicated circuits very effectively.",
|
||||
"After we did this we said, oh, let me draw another",
|
||||
"playground here. This is another piece of our",
|
||||
"playground. And if these are linear circuit",
|
||||
"then this half of the playground is nonlinear circuits.",
|
||||
"And we said that if you further focus on discretized values,",
|
||||
"if you discretized values and focused only on circuits that",
|
||||
"dealt with binary signals, highs and lows,",
|
||||
"then we came into this small regime of the playground.",
|
||||
"And notice that digital circuits are,",
|
||||
"by their very nature, nonlinear.",
|
||||
"Remember the circuit, A, B, this was one of our NOR",
|
||||
"gate circuits? And if you look at transfer",
|
||||
"functions, that is if I plot, let's say for example,",
|
||||
"for some combination of input values.",
|
||||
"Let's say I plot v in verses v out.",
|
||||
"Let's say, for example, I turned this guy off by",
|
||||
"setting B to 0 and then I simply apply a low to high transition",
|
||||
"at v in, then what I would see at the output is a transfer",
|
||||
"function of the following sort where as v in changes the output",
|
||||
"switches at some point and then stays at a low value.",
|
||||
"So when v in is low v out is high and v in and high v out is",
|
||||
"low. So that's kind of the v out",
|
||||
"versus v in when B is set at 0. So notice that this is a",
|
||||
"nonlinear curve. This is not a straight line.",
|
||||
"It's a nonlinear curve. And so therefore in the digital",
|
||||
"domain we see highly nonlinear functions that look like this",
|
||||
"and so on. However, take a look at this",
|
||||
"circuit. Suppose I focus on the circuit",
|
||||
"for a given set of switch settings.",
|
||||
"Let's say, for example, I focus on the circuit when A",
|
||||
"and B are both 1s. For a given set of switch",
|
||||
"settings, notice that I'm going to be either in this region or",
|
||||
"in this region. Notice that this region is a",
|
||||
"straight line. So if I focus on let's say both",
|
||||
"A and B at once then I get something like this.",
|
||||
"",
|
||||
"And in this situation, for a given set of switch",
|
||||
"settings, notice that my digital circuit now can be analyzed",
|
||||
"using linear techniques. So therefore my digital gets",
|
||||
"moved into the linear domain for a given set of switch settings.",
|
||||
"",
|
||||
"So if I fix my switch settings and look at the circuit then",
|
||||
"each circuit, for a given set of switch",
|
||||
"settings, is comprised of voltage sources and some",
|
||||
"resistors and it's a linear circuit.",
|
||||
"Again, I can go back and apply all my linear techniques to",
|
||||
"virtually all the digital circuits that you will be",
|
||||
"dealing with in 6.002. Again, remember if I fix my",
|
||||
"switch settings, if I fix the inputs then the",
|
||||
"output can be determined using linear techniques.",
|
||||
"Because the digital circuits we're showing you in 6.002",
|
||||
"simply comprise linear elements like voltage sources and",
|
||||
"resistors and so on. You'll see some more later.",
|
||||
"But you can apply your linear techniques and analyze them.",
|
||||
"The cool thing here is that with just two weeks of stuff",
|
||||
"that you've learned in 6.002, you are well on our way to",
|
||||
"being able to analyze certain classes of digital circuits for",
|
||||
"a given set of switch settings and many, many,",
|
||||
"many linear circuits. What we will do today is focus",
|
||||
"on nonlinear circuits. So we look at this space.",
|
||||
"Notice again that up until now we've dealt with these three",
|
||||
"methods, which apply to all circuits within this playground,",
|
||||
"the lumped circuit playground. And the subset of that is the",
|
||||
"linear domain. And we can analyze linear",
|
||||
"circuits in this way. And digital circuits,",
|
||||
"for a given set of switch settings, also fall within this",
|
||||
"category. So notice that you can go ahead",
|
||||
"and analyze the digital circuits using superposition or other",
|
||||
"techniques like that. The next big step for us is to",
|
||||
"begin our analysis of nonlinear circuits today.",
|
||||
"The important thing to remember is that nonlinear circuits are",
|
||||
"also within this big playground in which we are going under the",
|
||||
"lumped matter discipline. So nonlinear circuits are also",
|
||||
"lumped circuits. And therefore because we are in",
|
||||
"that playground we can use any one of our techniques,",
|
||||
"KVL, KCL or the node method to analyze nonlinear circuits.",
|
||||
"So if you see a nonlinear circuit, don't get daunted.",
|
||||
"Just remember this is meant to be simple stuff.",
|
||||
"So let me simply write down the node equation and analyze it.",
|
||||
"There is really nothing new in today's lecture.",
|
||||
"I'm just going to show you a nonlinear circuit and analyzing",
|
||||
"using techniques that you already know.",
|
||||
"Today nonlinear circuits. And we look at several methods",
|
||||
"of analyzing nonlinear circuits. We look at the \"Analytic",
|
||||
"Method\". We look at a \"Graphical",
|
||||
"Method\". You will look at a \"Piecewise",
|
||||
"Linear Method\" in the book.",
|
||||
"",
|
||||
"I won't be covering this in lecture.",
|
||||
"You can read Section 4.4 for the piecewise linear method.",
|
||||
"In this method you take your curves and you approximate them",
|
||||
"with a bunch of straight line segments, kind of like the v",
|
||||
"out, v in curve I've shown you there, and analyze the circuit",
|
||||
"using linear techniques within any given straight line segment.",
|
||||
"We will also do incremental analysis.",
|
||||
"This is also called small signal analysis.",
|
||||
"So I will cover these two today, I will introduce this one",
|
||||
"today, and wrap that up during the next lecture.",
|
||||
"",
|
||||
"Let's start with a simple example.",
|
||||
"",
|
||||
"So I have some voltage, V, some voltage source V.",
|
||||
"And I have some resistor, R.",
|
||||
"And I have a fictitious device here that I labeled D.",
|
||||
"Let's call this fictitious device the \"Expo Dweeb\".",
|
||||
"I purposely chose a funky name because this is a fictitious",
|
||||
"device. Let's call it the Expo Dweeb.",
|
||||
"And let me write down the associated variables for this",
|
||||
"device as follows. iD is the current flowing into",
|
||||
"this terminal and vD is the voltage across this device.",
|
||||
"So this is a nonlinear device.",
|
||||
"",
|
||||
"And this device is characterized by the following",
|
||||
"equation. Much like resistors were",
|
||||
"characterized by an iV relation, V is equal to iR,",
|
||||
"or i is equal to V/R. This device is also",
|
||||
"characterized by the following element relationship.",
|
||||
"It's a e raised to bvD. So there is an exponentiation",
|
||||
"here. Again, this is a fictitious",
|
||||
"device. And I'll show some funky things",
|
||||
"that it does in a second. It's a very simple relation.",
|
||||
"It's an exponential relation where the current relates to the",
|
||||
"exponentiated value of the voltage vD across the element.",
|
||||
"So I can plot iD versus vD for this element as follows.",
|
||||
"Notice that when vD is 0 iD is a, so I have a here,",
|
||||
"and it looks like this. It's a funny device,",
|
||||
"a fictitious device. So when vD is 0,",
|
||||
"I have some current flowing the device, and as vD increases I",
|
||||
"get an exponential increase in the current through that device.",
|
||||
"This device is funny in the sense that it is not a passive",
|
||||
"device in that notice that when vD and iD are positive the",
|
||||
"product is positive, which is fine,",
|
||||
"which says that it is consuming power.",
|
||||
"On the other hand, on the left-hand side notice",
|
||||
"that the vI relation is negative, which means that when",
|
||||
"I put a negative voltage on it, it can still sustain a positive",
|
||||
"current. This must imply that the device",
|
||||
"is producing power. But for the purpose of a",
|
||||
"nonlinear analysis we don't have to worry about that.",
|
||||
"Let's just do it mathematically and find out what it looks like.",
|
||||
"So back to this again. I have a voltage source,",
|
||||
"a resistor and my Expo Dweeb connected in that manner.",
|
||||
"Now, again, reflect on this pattern.",
|
||||
"A voltage source or a current source, a resistor and some",
|
||||
"device. This is a very standard pattern",
|
||||
"you will see again and again and again.",
|
||||
"In particular, if you look at this device,",
|
||||
"it's a nonlinear device here. And facing the nonlinear device",
|
||||
"is a voltage source in series with a resistor.",
|
||||
"And the reason I say that this is an incredibly important",
|
||||
"pairing is the following. Notice that if on the left-hand",
|
||||
"side I had any linear circuit and I had a single nonlinear",
|
||||
"element in that circuit. Notice that by a Thevenin",
|
||||
"reduction that you've learned you can take this entire mess.",
|
||||
"If all you care about is the behavior of the nonlinear",
|
||||
"device, for the purpose of analyzing this nonlinear device,",
|
||||
"you can take this entire linear circuit, no matter how",
|
||||
"complicated it is, voltage sources,",
|
||||
"current sources, resistors and a bunch of other",
|
||||
"funky stuff, you can boil all of that down to a Thevenin",
|
||||
"equivalent, a voltage and a resistor in series.",
|
||||
"So we can trick you. We can give you a complicated",
|
||||
"circuit and say ah-ha, tell me what the current is",
|
||||
"through this device if I apply some voltage,",
|
||||
"3 volts there. What you can do is you can say",
|
||||
"ah-ha, I don't care what happens here so I'm just going to",
|
||||
"replace the whole thing with a Thevenin equivalent.",
|
||||
"And you've done your homework now and you can calculate",
|
||||
"Thevenin equivalents for circuits.",
|
||||
"And simply replace this and then go ahead and solve the",
|
||||
"circuit. Again, remember we are",
|
||||
"engineers. We are looking for answers.",
|
||||
"We are looking to build interesting systems.",
|
||||
"And, in general, we like to take the simplest",
|
||||
"path possible to the solution. So simplify your lives and",
|
||||
"create a simple Thevenin coupled to a nonlinear device and then",
|
||||
"you will be rolling. When we talk about a variety of",
|
||||
"other circuits, nonlinear circuits,",
|
||||
"time-varying circuits and so on in the rest of this course,",
|
||||
"we will look at this pattern again and again and again and",
|
||||
"again until we are blue in the face.",
|
||||
"And, just remember, the reason we keep looking at",
|
||||
"this pattern is that whenever you have some big linear mess",
|
||||
"connected to some interesting device what you can do is if all",
|
||||
"you care about is analyzing the behavior of that device,",
|
||||
"you can take this linear mess and simply figure out the",
|
||||
"Thevenin equivalent, or the Norton equivalent if you",
|
||||
"like and replace this whole thing with its equivalent and",
|
||||
"then go ahead and analyze it. So boil an arbitrarily circuit",
|
||||
"down to a very simple pattern of this sort.",
|
||||
"What this means is because of this brilliant Thevenin",
|
||||
"simplification, going forward through the rest",
|
||||
"of this course we will mostly deal with very simple circuits",
|
||||
"like this, voltage source, resistor and the device.",
|
||||
"That's it. Very, very, very rarely will",
|
||||
"you see multiple sources and lots of resistors in a circuit.",
|
||||
"It's usually going to be simple stuff.",
|
||||
"And remember how we got here, by making a Thevenin",
|
||||
"simplification of a linear mess. All right.",
|
||||
"If in homeworks or quizzes or in real life,",
|
||||
"or in many examples of real life, if you find that you have",
|
||||
"to deal with a lot of grunge and a lot of mess,",
|
||||
"step back and think a little bit.",
|
||||
"Try to use intuition and see if you can simplify things using",
|
||||
"some clever trick or method. Method 1 of analysis.",
|
||||
"Let's go ahead and analyze this pattern here,",
|
||||
"this template circuit, if you will,",
|
||||
"a voltage source a resistor and a nonlinear device.",
|
||||
"This is the analytical method. And remember the node method",
|
||||
"applies, so let me go ahead and apply the node method.",
|
||||
"To apply the node method, what do I do?",
|
||||
"I first have to select a ground node.",
|
||||
"Let me insulate this as my ground node.",
|
||||
"Let me label all the nodes with their voltages.",
|
||||
"So this node has voltage V and this node has label the capital",
|
||||
"D. So let me go ahead and analyze",
|
||||
"this using the node method. So the node method says for",
|
||||
"each of the nodes in the circuit whose voltage is not known go",
|
||||
"ahead and write down KCL implicitly applying the element",
|
||||
"relationships to replace the current values with the voltage",
|
||||
"values. Let's start with the current",
|
||||
"going in that direction. Current going from the vD node",
|
||||
"through resistor R, which looks as follows,",
|
||||
"vD - V divided by R. That's a current going that",
|
||||
"way. And the current going down is",
|
||||
"iD. In general, when I apply the",
|
||||
"node method, I don't write iD here but I go ahead and write",
|
||||
"the element relation ae to the bvD here.",
|
||||
"Then I get an equation in vD and I just solve the mode",
|
||||
"voltage. However, just to make a couple",
|
||||
"of extra points later, let me go ahead and do that in",
|
||||
"two steps, write down this and then go ahead and write down iD",
|
||||
"separately as ae to the bvD. Again, remember,",
|
||||
"don't get confused here. In a node method,",
|
||||
"I don't write down a second step.",
|
||||
"I directly write down ae to bvD in place of iD.",
|
||||
"I get one equation in vD, I go solve it.",
|
||||
"Just for fun today, I'm taking two steps here,",
|
||||
"writing iD and explicitly putting down iD as ae to the",
|
||||
"bvD. Now, that's it.",
|
||||
"I mean this is all there is to it.",
|
||||
"You guys can now go ahead and analyze nonlinear circuits.",
|
||||
"You get a bunch of equations, a bunch of unknowns,",
|
||||
"go solve. I have two equations here.",
|
||||
"vD and iD are my unknowns and I can just go ahead and solve for",
|
||||
"them. Now, in general with nonlinear",
|
||||
"circuits, often times it's hard to get a closed form solution so",
|
||||
"you may have to use a bunch of methods.",
|
||||
"You can try a closed form solution or you can try",
|
||||
"numerical solutions or you can do trial and error.",
|
||||
"In this case, I'll just go ahead and tell",
|
||||
"you. Suppose I choose V as 1 volt,",
|
||||
"R is 1 ohm and b is 1 over volt and a is \u017a amps for those",
|
||||
"values, approximately vD is roughly 0.5 volts and iD is",
|
||||
"roughly 0.4 volts. You can do this by using trial",
|
||||
"and error or other methods. In 6.002 we don't dwell on",
|
||||
"working too hard to solve equations of this sort.",
|
||||
"If you cannot substitute this in here and solve it directly,",
|
||||
"we don't ask you to go and learn numerical method and the",
|
||||
"techniques and so on to solve it.",
|
||||
"But just remember that you can use trial and error or you can",
|
||||
"use back substitution and other techniques that you will learn",
|
||||
"in future numerical methods classes and apply it here.",
|
||||
"But suffice it to say that, for here we can stick with",
|
||||
"trial and error if you like. And for these values,",
|
||||
"vD and iD are 0.5 and approximately 0.4.",
|
||||
"You're done. It's really that simple.",
|
||||
"Yes. Oh, I'm sorry.",
|
||||
"Good catch. I know there is one person",
|
||||
"that's not sleeping here. Good.",
|
||||
"So, as I said, there's not a whole lot to it.",
|
||||
"Whether it's a nonlinear circuit or a linear circuit and",
|
||||
"as long as I am inside this playground here where the lumped",
|
||||
"circuit abstraction holds, I can apply my node equations",
|
||||
"and then go ahead and solve it.",
|
||||
"",
|
||||
"Let me show you a few more methods so we can articulate",
|
||||
"your repertoire of tools for nonlinear circuits.",
|
||||
"And I'd like to show you a graphical technique.",
|
||||
"I personally rarely use a graphical technique to solve",
|
||||
"circuits. And why am I sharing this with",
|
||||
"you? It turns out that often times",
|
||||
"by looking at things graphically you can get some better insights",
|
||||
"into circuit behavior. You can also show cool demos",
|
||||
"when you show graphs of responses kind of playing with",
|
||||
"each other and so on. So this is fun for getting",
|
||||
"intuition and things like that. Graphically all I'm really",
|
||||
"going to do is solve those two equations graphically.",
|
||||
"So I'm going to plot equation one.",
|
||||
"Let me rewrite equation one as follows.",
|
||||
"iD is --",
|
||||
"",
|
||||
"I'm just rewriting equation one as follows.",
|
||||
"V/R - vD/R. And I can also draw the second",
|
||||
"guy --",
|
||||
"",
|
||||
"OK, I can do this as well. I can do an iD versus vD plot.",
|
||||
"And in this particular situation, you've seen this",
|
||||
"already, that's my iD versus vD curve right there.",
|
||||
"And I can do the same for this one here.",
|
||||
"So this equation establishes the following straight line",
|
||||
"relationship. It says that when vD is 0,",
|
||||
"iD is V/R. So that's here.",
|
||||
"And similarly when iD is 0 then vD is equal to V so I get",
|
||||
"something here. So that's my straight line",
|
||||
"relationship corresponding to this equation here.",
|
||||
"So what I can do is I can simply solve these by",
|
||||
"superimposing the two curves on the same vD, iD template here",
|
||||
"and finding the intersection of the curves.",
|
||||
"So I can take this curve corresponding to two and I can",
|
||||
"take this curve corresponding to one, and this is V/R and this is",
|
||||
"V, 0, and I can find the intersection point.",
|
||||
"This curve here, for reasons that will be",
|
||||
"obvious about three weeks from now, is called the load line.",
|
||||
"It's called the load line. You will understand why that is",
|
||||
"so in a later lecture. So I've given you a template on",
|
||||
"Page 6 to boil these two down into one equation.",
|
||||
"So there, again, you can substitute the values",
|
||||
"for V is 1 volt and R is 1 and so on and so forth and get the",
|
||||
"same kind of result as you did previously.",
|
||||
"",
|
||||
"So there is really nothing new here.",
|
||||
"All I've done in the second method is combined the two",
|
||||
"equations graphically and found the solution by looking at where",
|
||||
"the two curves intersect.",
|
||||
"",
|
||||
"At the start of the lecture I also told you that you may want",
|
||||
"to go and check out the piecewise linear technique --",
|
||||
"",
|
||||
"-- in Section 4.4 of the course notes.",
|
||||
"",
|
||||
"All right. For today let me do a third",
|
||||
"method called \"Incremental Analysis\".",
|
||||
"",
|
||||
"This technique is also called the small signal method.",
|
||||
"",
|
||||
"I'm going to show you, before I go into the method,",
|
||||
"in today's lecture what I'll do is I'll give you a motivating",
|
||||
"example for why we need the small signal approach.",
|
||||
"I'll give you a motivating example and show you a little",
|
||||
"demo. And then I will close with",
|
||||
"showing you a problem with applying a standard approach,",
|
||||
"and I'll ask you to see if you can figure out a way to handle",
|
||||
"it in time for next lecture. So let me give you the",
|
||||
"motivation here.",
|
||||
"",
|
||||
"So here is what I want to do. Many of you have seen one of",
|
||||
"those electric eye garage door openers, right?",
|
||||
"You have a receiver at one end and you have some kind of a",
|
||||
"light beam at the other, and when you walk through it",
|
||||
"stops, or rather it cuts the circuit and stops the door from",
|
||||
"closing. And when no one is going",
|
||||
"through it maintains a connection and lets the door",
|
||||
"close. So what we did is we went to",
|
||||
"Home Depot, or one of those stores, and bought a very",
|
||||
"standard device that essentially produces some response when",
|
||||
"light impinges on it. And my goal will be to see if I",
|
||||
"can send music over the light beam using a simple garage door",
|
||||
"opener device. So here is the little circuit",
|
||||
"that I will do. We actually went there and",
|
||||
"built this. I will also show you a demo.",
|
||||
"",
|
||||
"Here is my time-varying voltage, vI(t),",
|
||||
"and this is some music signal.",
|
||||
"",
|
||||
"And get some music signal. And I want to connect this to",
|
||||
"this device, which is a device found in garage door openers.",
|
||||
"I am going to call it a LED. If you like,",
|
||||
"you can view it as, this is very similar to our",
|
||||
"Expo Dweeb. This is called a \"Light",
|
||||
"Emitting Expo Dweeb\". That's why it is LED.",
|
||||
"So what the LED does is, as I apply this voltage across",
|
||||
"it, that same voltage appears across the Light Emitting Expo",
|
||||
"Dweeb. And there is some current that",
|
||||
"flows through the device. And for our analysis we will",
|
||||
"assume that this device virtually has an identical iD",
|
||||
"characteristic to the Expo Dweeb just that it emits light.",
|
||||
"So when I pass a current through it, it emits light.",
|
||||
"And the light intensity is proportional to the current that",
|
||||
"flows through. So it emits light and light",
|
||||
"intensity, LD, is proportional to iD.",
|
||||
"",
|
||||
"Here is my little light emitting device,",
|
||||
"which when current flows through it, itproduces light",
|
||||
"because its intensity is proportional to the current.",
|
||||
"And what I will do is I will stick in the receiver here.",
|
||||
"Think of it as a photo resistor or some other device where I am",
|
||||
"going to connect that in a circuit.",
|
||||
"I am not going to spend too much time on this side.",
|
||||
"I'm going to focus on the left-hand side here.",
|
||||
"And let's say I have some kind of amplifier and speakers and so",
|
||||
"on and so forth. Suffice it to say that when the",
|
||||
"light falls on this device PR that iR that goes through here",
|
||||
"is proportional to the received light intensity.",
|
||||
"So if the current is proportional to the received",
|
||||
"light intensity then I amplify that signal in my amplifier and",
|
||||
"I get the music playing out here.",
|
||||
"And notice that the following chain of dependences apply.",
|
||||
"So I have an input music signal VI.",
|
||||
"That gets converted to some iD. These are all time-varying",
|
||||
"signals, so VI is a time-varying signal and so is iD.",
|
||||
"And iD gets converted to light of some intensity LD.",
|
||||
"This in turn gets attenuated somewhat and is received at the",
|
||||
"photo resistor. And I get some intensity LR",
|
||||
"impinging on that device there. And that in turn produces a",
|
||||
"current iR and then iR is amplified and goes through a",
|
||||
"speaker and so on and produces sound.",
|
||||
"Notice that using this chain I've taken a music signal here",
|
||||
"and I am playing it here. And just imagine that this is",
|
||||
"your garage door opener device here where the light emitted is",
|
||||
"being articulated by the voltage signal VI.",
|
||||
"And received here. So notice that if I cut this,",
|
||||
"if I stick something in here and block it then I get no",
|
||||
"response here, but if I take my hand away then",
|
||||
"I do get some response. But this is fine.",
|
||||
"This should work. You could try this at home if",
|
||||
"you'd like. If you have a garage door",
|
||||
"opener, just stick a little circuit like this and it should",
|
||||
"simply work. We have a problem,",
|
||||
"though. The problem is that,",
|
||||
"as I said, I'm using the Expo Dweeb here, the light emitting",
|
||||
"Expo Dweeb, and its characteristics are as follows.",
|
||||
"iD is exponentially related to the voltage vD,",
|
||||
"so this is nonlinear.",
|
||||
"",
|
||||
"And that's a real problem. Because this is nonlinear,",
|
||||
"I am going to get a distorted output.",
|
||||
"Let me show you a little wave form, a little graph to show you",
|
||||
"how the distortion happens and then show you a little demo",
|
||||
"showing you the distortion. Let me graphically show you the",
|
||||
"kind of distortion that is happening here,",
|
||||
"and I will do it by drawing the following graph.",
|
||||
"",
|
||||
"So this is the vD, iD curve for our device.",
|
||||
"And what I'm going to plot for you is if I have a time-varying",
|
||||
"vD voltage, I just want to see what the time-varying iD current",
|
||||
"looks like. And a trick to plot that is to",
|
||||
"take your input voltage like so. And let's say I apply a",
|
||||
"sinusoid. So I am just taking a",
|
||||
"time-varying sinusoidal voltage and rotating the plot 90 degrees",
|
||||
"like so, so I can see where these points correspond to on",
|
||||
"that curve. So what this says is that at",
|
||||
"some point here, for example,",
|
||||
"where vI, at this point and time, vI is here.",
|
||||
"Notice vI and vD are the same thing because vI is applied",
|
||||
"across vD. vI directly applies across the",
|
||||
"device, and so vI equals vD at all time.",
|
||||
"So this voltage here corresponds to this voltage,",
|
||||
"it corresponds to this current and then I can find out what the",
|
||||
"current is for that voltage. By using the same artifice I",
|
||||
"can plot the output current iD like so.",
|
||||
"So for this value I get some current here.",
|
||||
"And so at time T0 I start here. And notice that as this signal",
|
||||
"moves up here, I can find out the",
|
||||
"corresponding values of iD by looking at where a straight line",
|
||||
"intersects here and plotting the values here.",
|
||||
"I have a nice little graphical animation to show you this.",
|
||||
"Hopefully, the laptop will work tomorrow and we can check that.",
|
||||
"I am doing nothing new here. Just showing you a trick to be",
|
||||
"able to plot vI versus v out relationships,",
|
||||
"or vI or versus other relationships based on some kind",
|
||||
"of a transfer function. So what you end up getting is",
|
||||
"something that looks like this. Why is that?",
|
||||
"Notice that this curve here corresponds to the signal.",
|
||||
"As this signal moves from here to here, this point moves from",
|
||||
"here to here and that corresponds to this iD.",
|
||||
"When this moves from here to here that corresponds to a point",
|
||||
"moving from this part of the curve to here,",
|
||||
"and that looks like so. And then for the whole negative",
|
||||
"incursion, notice that the whole negative incursion moves here,",
|
||||
"so for that entire negative incursion I get an output that",
|
||||
"looks like this. Notice that this device has",
|
||||
"completely cut off and hammered negative going signals.",
|
||||
"What it's done is that rather than giving me a nice little",
|
||||
"negative spike incursion here, or excursion here,",
|
||||
"what this is doing is that it is taking this excursion and",
|
||||
"simply slamming it down to this value here.",
|
||||
"And then again, when I go back up,",
|
||||
"I get this peak here. So notice that what was a nice",
|
||||
"little sinusoid out there gets hammered and squished into this",
|
||||
"funny curve here. What this device is doing is",
|
||||
"for positive values it tends to produce exponentially greater",
|
||||
"current so I get boom, high-rising peaks corresponding",
|
||||
"to these two, and for negative going voltages",
|
||||
"it simply compresses them to a low positive value here.",
|
||||
"And that's what I see here corresponding to negative",
|
||||
"excursion. So notice that what this will",
|
||||
"do, if I view sound, if I input sound here,",
|
||||
"and sound has negative going excursions it will simply",
|
||||
"scrunch them. But more or less let the",
|
||||
"positive things through. And that is going to give rise",
|
||||
"to a bunch of distortion in my signal.",
|
||||
"So I would like to show you a little demo.",
|
||||
"Actually, we've gone ahead and built a little device like this.",
|
||||
"We have an honest to goodness little device costing,",
|
||||
"I don't know, 50 cents or $1 or something,",
|
||||
"which is a little voltage, it's a device that emits light",
|
||||
"proportional to the current flowing through it.",
|
||||
"I have a receiver. And I am going to play some",
|
||||
"music, and you will listen to the output here.",
|
||||
"And hopefully you should see a bunch of distortion because of",
|
||||
"that effect that I showed you.",
|
||||
"",
|
||||
"And what I will do is, before we do that,",
|
||||
"you will see two curves up there.",
|
||||
"The yellow, I believe is the vI, is the input,",
|
||||
"and the green, I believe, is a signal",
|
||||
"proportionate to -- The other way around.",
|
||||
"Oh, I see. So green is the input.",
|
||||
"So green, the lower one is the input and the upper one is the",
|
||||
"distorted output. So we are going to play some",
|
||||
"sound through it, music through it and you can",
|
||||
"listen, through a little CD player.",
|
||||
"",
|
||||
"So a couple of things. The good news is that it works.",
|
||||
"However, I doubt that music artists will come to my studio",
|
||||
"to record if this is the quality of what I produce.",
|
||||
"Do notice that there are hardly any negative going excursions in",
|
||||
"that curve up there, right?",
|
||||
"All the negative ones have been like scrunched up down into a",
|
||||
"flat line there, and that's the reason I get",
|
||||
"this distortion. And just to prove to you that I",
|
||||
"am indeed using a garage door opener device and not faking it",
|
||||
"here, I am going to just shut the signal off by stopping the",
|
||||
"light using a piece of paper here.",
|
||||
"So notice that this device here is the little device that has a",
|
||||
"light beam going through the center, and I am going to take",
|
||||
"this piece of paper, can you turn it up?",
|
||||
"",
|
||||
"So let's have some fun with this.",
|
||||
"If I were to put this piece of paper halfway down,",
|
||||
"I should get half the intensity, right.",
|
||||
"So my sound should diminish in volume a little bit.",
|
||||
"Maybe that will work. Let's see if it works.",
|
||||
"Nothing to do with 002 but it's just fun.",
|
||||
"Louder. You can make it loud.",
|
||||
"",
|
||||
"Too much coffee. My hand is shaking.",
|
||||
"I guess you did see the lowering of volume,",
|
||||
"right?",
|
||||
"",
|
||||
"OK. Just way too much coffee,",
|
||||
"and so my hand was shaking too fast imposing its own sine wave",
|
||||
"on top of the signal. What did I show you?",
|
||||
"This was garbage, right?",
|
||||
"We had a nice little signal input, and the output was",
|
||||
"completely distorted because I was playing sound over this and",
|
||||
"this is what happened. Switch to Page 9.",
|
||||
"Now, this is what I would have liked to have happened.",
|
||||
"On Page 9 what I would have liked to see happen is this.",
|
||||
"",
|
||||
"Suppose I had a light emitting device that looked linear,",
|
||||
"a straight line where the current was linearly related to",
|
||||
"vD. Then what I would see,",
|
||||
"if I had a sinusoid here then I would get a sinusoid here.",
|
||||
"No distortion there, right?",
|
||||
"If only things were like I wanted them, if I had a linear",
|
||||
"device, but I don't have a linear device.",
|
||||
"I have an Expo Dweeb. Now you know why I call it a",
|
||||
"dweeb. Well, I'd like a linear device",
|
||||
"and it's exponential. But this is what I would like.",
|
||||
"",
|
||||
"And if I had this I wouldn't show it to you today.",
|
||||
"If I had this my music would go through without any distortion",
|
||||
"and I wouldn't have to run cables through my attic.",
|
||||
"I could just use my garage door opener to play signals from my",
|
||||
"bedroom and living room and so on, right?",
|
||||
"So the key thing here is how do I get this?",
|
||||
"And what I would like you to do is think about it yourselves.",
|
||||
"What I am given is something like this.",
|
||||
"This about it yourselves, you know, what would you do?",
|
||||
"See if you can come to me before lecture tomorrow or",
|
||||
"Thursday and tell me the answer, OK?"
|
||||
]
|
||||
}
|
||||
@@ -1,1901 +0,0 @@
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"text": [
|
||||
"",
|
||||
"We have put some of the quiz stats here.",
|
||||
"The mean was about 75%. And I must tell you that that",
|
||||
"is very impressive. I guess MIT undergrads never",
|
||||
"cease to amaze me. And this was not an easy quiz.",
|
||||
"This was a relatively hard quiz.",
|
||||
"And that average implies that you guys did well on a",
|
||||
"relatively hard quiz. Good.",
|
||||
"Let's get back to our final lecture on amplifiers and small",
|
||||
"signal circuits. And as always let me start with",
|
||||
"a review. Very quickly --",
|
||||
"",
|
||||
"-- we came up with a notation to represent small signals.",
|
||||
"And our notation looked like this.",
|
||||
"Our total variable was small and capital, and this was a DC",
|
||||
"bias and this was a small signal.",
|
||||
"",
|
||||
"This is also called the operating point.",
|
||||
"And the small signal is also called the incremental signal.",
|
||||
"In general, if you have some function, some variable of",
|
||||
"interest in the circuit, say a total variable V out,",
|
||||
"let's say it relates to some input variable as F of VI.",
|
||||
"So mathematically we can find out V out by simply finding the",
|
||||
"slope of this function at the operating point and then",
|
||||
"multiplying it by the incremental change in the input.",
|
||||
"Gold standard math. So we do the slope of this",
|
||||
"function and evaluate it at the operating point.",
|
||||
"So this would give us the slope of the function.",
|
||||
"And multiply that by small VI, which is incremental change.",
|
||||
"This is standard math. What this will tell you is",
|
||||
"given a small change in VI this function gives you,",
|
||||
"this expression gives you the small change in V out.",
|
||||
"And in lecture we have pretty much used this method so far,",
|
||||
"used the math to get to where we wanted it to be.",
|
||||
"And then the way we provided biasing and so on was for our",
|
||||
"amplifier in particular we had a bias voltage,",
|
||||
"some small signal value, VS.",
|
||||
"And this was output which was also given to be some output",
|
||||
"operating point plus a small change, which was a change in",
|
||||
"the output voltage. So what we have done here is",
|
||||
"mathematically computed small V out.",
|
||||
"And what I am showing you here is to get the same effect in a",
|
||||
"circuit is you build your circuit and replace what used to",
|
||||
"be a total variable with a DC bias plus a small change.",
|
||||
"And then you will get your output here.",
|
||||
"And this output will relate to this input using this",
|
||||
"expression.",
|
||||
"",
|
||||
"So this is more review. To continue on with the math",
|
||||
"review, for our amplifier VO was given to be VS-K/2(vI-VT)^2 RL.",
|
||||
"So this was the output versus input relationship for the",
|
||||
"amplifier. And mathematically I could get",
|
||||
"the small change in the output VO by simply differentiating",
|
||||
"this function with respect to VI, evaluating that function,",
|
||||
"at capital VI and multiplying by the small change in the",
|
||||
"input. And the resulting expression",
|
||||
"that we got for small VO --",
|
||||
"",
|
||||
"-- was simply minus K, this was our DC value,",
|
||||
"and RL times small VI. So we derived all of this the",
|
||||
"last time. So nothing new so far.",
|
||||
"So my small signal output was some function given by",
|
||||
"K(VI-VT)RL times small vi. And notice that this is how VI",
|
||||
"relates to VO. And this is a constant with",
|
||||
"respect to VI. V capital I is a DC bias,",
|
||||
"so this is a constant. So therefore this is the linear",
|
||||
"relationship that we had set out to get.",
|
||||
"This term here, for reasons we will see today,",
|
||||
"this term here K(VI-VT) is called gm.",
|
||||
"Transconductance. We will look at it in more",
|
||||
"detail a little later.",
|
||||
"",
|
||||
"Even more review.",
|
||||
"",
|
||||
"So I can draw the transfer function and plot VO versus VI.",
|
||||
"Another way to graphically view what is going on is by plotting",
|
||||
"the load line curve for this circuit, so this is VI.",
|
||||
"And I said we draw that by first plotting the --",
|
||||
"",
|
||||
"These were our MOSFET curves. And we know that at some point",
|
||||
"the MOSFET gets into saturation, so this curve was iDS=K/2 VO^2.",
|
||||
"And to the right side of the curve the MOSFET is in",
|
||||
"saturation. And we said we will adhere to",
|
||||
"the saturation discipline and operate in this regime.",
|
||||
"When the MOSFET gets into this region it is in its triode",
|
||||
"region. And then we could draw the load",
|
||||
"line here. The load line codified the",
|
||||
"following relationship, iDS=VS/RL-VO/RL.",
|
||||
"This was a load line. So I have superimposed a load",
|
||||
"line on the device characteristics,",
|
||||
"and I am going to show you a little demonstration based on",
|
||||
"that at this point. So these curves were drawn for",
|
||||
"increasing values of VI. And if I choose some operating",
|
||||
"point here then this point would correspond to some bias,",
|
||||
"this bias point would correspond to some input voltage",
|
||||
"VI, a corresponding output bias VO and a corresponding current",
|
||||
"iDS. So iDS capitals,",
|
||||
"VO capitals, VI capitals represent the",
|
||||
"operating point values for our little circuit.",
|
||||
"So far there is nothing new. One thing we stopped the last",
|
||||
"time by pointing out that the gain of our amplifier,",
|
||||
"this is the gain, -K(VI-VT)RL.",
|
||||
"That is the gain A of the amplifier.",
|
||||
"That gain related to VI. A gain was proportional to",
|
||||
"VI-VT. So therefore if I increased VI,",
|
||||
"I would get more gain. So the question is how do we",
|
||||
"choose a bias point? And in our particular example,",
|
||||
"let's say we are free to play around with VI.",
|
||||
"So we play around with VI and I can choose various bias points.",
|
||||
"So where do you set the bias point?",
|
||||
"What are the various characteristics of the circuit",
|
||||
"that relate to my bias point? Well, first,",
|
||||
"of course, is gain. The gain depends on how I",
|
||||
"choose VI. I will show you that in a",
|
||||
"moment. The second important thing,",
|
||||
"in other words, if I choose a bias point that",
|
||||
"is a small VI then my gain is going to be smaller.",
|
||||
"If I choose a bias point that's at a much higher value of VI,",
|
||||
"I get a bigger gain. The second important",
|
||||
"consideration is operating range.",
|
||||
"",
|
||||
"Notice that if I choose a bias point here then as the input",
|
||||
"changes -- Notice VI in this graph goes up",
|
||||
"or down, and I would be traversing and following",
|
||||
"different lines here in my MOSFET characteristic.",
|
||||
"And as VI increases the operating point would come up",
|
||||
"here and so on. So if about this operating",
|
||||
"point I varied my input voltage VI then, so let's say about this",
|
||||
"operating point, if my input VI,",
|
||||
"my small signal VI varied about a small range then",
|
||||
"correspondingly the output value would vary about this part of my",
|
||||
"load line. So notice now that the",
|
||||
"operating range, how far can VI vary before the",
|
||||
"MOSFET goes out of its saturation discipline?",
|
||||
"Well, on the low side my VI can come down to here.",
|
||||
"And we looked at the operating ranges for an amplifier.",
|
||||
"And I can come all the way down to VT.",
|
||||
"At that point the output will come here.",
|
||||
"Similarly at the high end VI could get up to a high value.",
|
||||
"And we computed that value in the last lecture.",
|
||||
"And the corresponding value of the input would be here.",
|
||||
"So in some sense I can traverse all the way from here to here",
|
||||
"and have the MOSFET remain in saturation.",
|
||||
"Remember we are not talking about linearity right now,",
|
||||
"just about the valid operating range based on my definition",
|
||||
"which is that the MOSFET should stay in saturation.",
|
||||
"So if I chose my operating point here then I get this range",
|
||||
"here. And, on the other hand,",
|
||||
"if I chose my operating point to be here, for negative",
|
||||
"excursions of the input signal I have a very small amount before",
|
||||
"I hit cutoff. So if I chose my operating",
|
||||
"point here then for negative traversals of VI about the",
|
||||
"operating point I very quickly hit cutoff.",
|
||||
"So if I want symmetric swings then this is the best that I can",
|
||||
"do in terms of the valid input operating range if I want",
|
||||
"symmetric swings given that this is my bias point.",
|
||||
"On the other hand, if I chose my bias point",
|
||||
"somewhere here, or very carefully chose my bias",
|
||||
"point then my input can vary on a much wider region and still",
|
||||
"get symmetric swings. And so therefore the choice of",
|
||||
"bias point also influences the maximum swing range of my input",
|
||||
"signal. I shouldn't call this operating",
|
||||
"range. I should call it input swing",
|
||||
"range. We defined the valid input",
|
||||
"operating range as the range for which the amplifier satisfied",
|
||||
"the saturation discipline. So the two key issues,",
|
||||
"gain and the input swing. Let me show you a quick demo",
|
||||
"and try to point out on a graph some of the characteristics that",
|
||||
"relate to the matter we have been talking about so far.",
|
||||
"So what I show here are these curves for the MOSFET.",
|
||||
"This is VO and this iDS. This is the zero point.",
|
||||
"Ignore this line down here. This line up here corresponds",
|
||||
"to the output voltage VO. What I am going to do now is,",
|
||||
"through some careful circuit hacking, I'm going to show show",
|
||||
"you a load line and show you the bias point, and show you how the",
|
||||
"bias point can be moved up and down by changing the input",
|
||||
"voltage which changes the corresponding output voltage.",
|
||||
"",
|
||||
"It is hardly visible out there.",
|
||||
"",
|
||||
"Is it there? OK.",
|
||||
"It is not really clear, but notice that as I increase",
|
||||
"my input, I am increasing my input.",
|
||||
"My output keeps coming down. And I hope your eyesight is",
|
||||
"better than mine because I don't see a dot up there.",
|
||||
"I am amazed. This is the first time this has",
|
||||
"happened to me. That's OK.",
|
||||
"All right. As you can see,",
|
||||
"as I change the input value the output operating point changes,",
|
||||
"and the dot out there traverses, articulates a load",
|
||||
"line. I guess I have to believe that",
|
||||
"there is a dot out there. Next what I will do is show you",
|
||||
"some more fun stuff. What I will do is instead of",
|
||||
"having just a dot by having a DC voltage, let me apply an input",
|
||||
"sinusoid. So if I apply an input sinusoid",
|
||||
"at some bias then I should see an articulation of the",
|
||||
"corresponding region of the load line corresponding to the input.",
|
||||
"So, as you can see here, now the bottom line,",
|
||||
"here is my input and this is my output.",
|
||||
"And notice that this the region of the load line articulated",
|
||||
"when the input is of this magnitude.",
|
||||
"Now let's have some fun. As I increase my input,",
|
||||
"you can see that a larger portion of the load line is",
|
||||
"articulated, right? There you go.",
|
||||
"And as I decrease my input a smaller region of the load line",
|
||||
"is articulated. Let's leave it here for a",
|
||||
"moment. And what I will do next,",
|
||||
"this is the region here that we are looking at,",
|
||||
"let me increase the bias. If I increase the bias,",
|
||||
"if I increase VI, what do you think should happen",
|
||||
"to this line here? Well, if I increase the bias,",
|
||||
"the line should go up, right?",
|
||||
"Because remember the dot? The dot is in the middle of",
|
||||
"this thing here. If I increase the bias this",
|
||||
"should move up here. So that line moves up.",
|
||||
"Do you expect anything else to happen to that line?",
|
||||
"Pardon? It increases,",
|
||||
"exactly. If I increase the bias point to",
|
||||
"here then this must also increase because my gain has",
|
||||
"increased. Let me do that.",
|
||||
"So let me increase the input bias.",
|
||||
"Indeed notice that the region of the load line articulated is",
|
||||
"larger now. Let me decrease the bias.",
|
||||
"And notice that because the gain is smaller the little",
|
||||
"segment shown is also smaller. I have shown you two things so",
|
||||
"far. One is that I as I increase my",
|
||||
"bias the line indeed rises up corresponding to a higher value",
|
||||
"for the input operating point. And the second is that I get a",
|
||||
"larger swing in the output as I increase the bias.",
|
||||
"Just to show that for those like me who were visually",
|
||||
"challenged in terms of viewing that little dot up there,",
|
||||
"let me get some audio so you can actually hear the sinusoidal",
|
||||
"tone. It is a big annoying.",
|
||||
"",
|
||||
"As I reduce the bias the gain is decreased.",
|
||||
"As I increase the bias you can see that the gain is increased",
|
||||
"and the tone is louder. Let's have some more fun and",
|
||||
"let's play some music now. And what I am going to show you",
|
||||
"with the music -- The reason I play the music is",
|
||||
"not just for fun. Well, it's 85% fun and 15%",
|
||||
"learning. Can we turn it on for a second?",
|
||||
"What I would like to do is, as we play the music,",
|
||||
"the reason I am playing the music for that 15% is so you can",
|
||||
"listen to distortion. I want you to listen to the",
|
||||
"distortion. That is when the articulation",
|
||||
"is here you are not going to get much distortion.",
|
||||
"But as I get into cutoff you should be getting a bunch of",
|
||||
"distortion. Similarly, as you get into the",
|
||||
"triode region you should also be getting distortion because the",
|
||||
"amplification from being somewhat nonlinear here becomes",
|
||||
"highly nonlinear at those two points.",
|
||||
"So let's just play the signal. So volume increases,",
|
||||
"or rather the amplitude increases by increasing the",
|
||||
"bias. Now you should hear the volume",
|
||||
"go down and distortion.",
|
||||
"",
|
||||
"So notice now that the bias point is way down here.",
|
||||
"So the gain is very low, and plus there is a distortion",
|
||||
"because of cutoff. Now what I will do is blast it",
|
||||
"up here, and you will see that the volume has gone up but then",
|
||||
"you see distortion again. Let's see if you can stand the",
|
||||
"volume here.",
|
||||
"",
|
||||
"Even the CD doesn't like that.",
|
||||
"",
|
||||
"Notice that as I went up here the volume kept increasing",
|
||||
"because the gain kept increasing, but as I got into",
|
||||
"the triode region I began to lose my gain because,",
|
||||
"remember, the amplifier doesn't have gain in the triode region,",
|
||||
"MOSFET in its triode region, and we also get a bunch of",
|
||||
"distortion out there. Finally, it turns out that as",
|
||||
"people are building amplifiers --",
|
||||
"I think this was in the mid to late `50s and `60s and so on.",
|
||||
"They said man, electrical engineers are not",
|
||||
"going to get their thing right. So they invented a new kind of",
|
||||
"music which was much more tolerant to distortion.",
|
||||
"And I will play that music for you.",
|
||||
"It is called hard rock. I challenge you to tell me it",
|
||||
"is distorting.",
|
||||
"",
|
||||
"Sounds good to me.",
|
||||
"",
|
||||
"OK. All right.",
|
||||
"That'll do it. Thank you.",
|
||||
"I hope there are no hard rock musicians in here who will come",
|
||||
"and beat me up after lecture or something.",
|
||||
"All right. Believe it or not most of that",
|
||||
"was review. There is nothing new today",
|
||||
"besides some fun and games and so on.",
|
||||
"I will give you a breather for five seconds before jumping into",
|
||||
"something even more fun.",
|
||||
"",
|
||||
"I want you to look at the middle board here.",
|
||||
"And, as I told you in the beginning of 6.002,",
|
||||
"engineering is about building useful systems.",
|
||||
"Engineering is not about showing off at math or saying",
|
||||
"man, I am really cool in math and stuff.",
|
||||
"Engineering is about building useful systems,",
|
||||
"and you want to find the simplest, easiest,",
|
||||
"cheapest way to get there. Unlike deep areas of math and",
|
||||
"theory and so on, the beauty is in the",
|
||||
"simplicity. So the aesthetics are in how",
|
||||
"simply can we make things and still get to where we want to",
|
||||
"be? All through the course what you",
|
||||
"will be seeing happening again and again and again is when",
|
||||
"things begin to get too grovelly in terms of math,",
|
||||
"we will step back and say oops, we are engineers,",
|
||||
"remember? Let's find a much simpler way",
|
||||
"to do it and use intuition. So time and time and time",
|
||||
"again, I am going to take you on a simpler path where you can",
|
||||
"solve things by inspection by pure intuition.",
|
||||
"Most circuit designers do that. So take a look at this.",
|
||||
"I don't like this nasty differentiation here.",
|
||||
"That's getting into late high school calculus and so on.",
|
||||
"Let's avoid the math and let's see if you find some way of",
|
||||
"doing it that is even much more simpler.",
|
||||
"And that is what I will do next and show you what is called the",
|
||||
"small signal circuit view. A purely circuit way of",
|
||||
"developing the small signal model.",
|
||||
"So let me just start by drawing the large signal equivalent",
|
||||
"circuit for you. I will draw it here for reasons",
|
||||
"that will be obvious at the end of the class.",
|
||||
"",
|
||||
"All right. This is the large signal",
|
||||
"equivalent circuit model for our MOSFET amplifier.",
|
||||
"VS and here is my current source.",
|
||||
"iDS relates to the square of VI minus VT.",
|
||||
"So stare at that for a second. And that is a nonlinear",
|
||||
"circuit. iDS relates to the square of VI",
|
||||
"minus VT. Let me start by making the",
|
||||
"following claim. Let me shoot from the hip here",
|
||||
"and make the following grand claim, and then I will show you",
|
||||
"how I can prove that claim. The grand claim I am about to",
|
||||
"make says the following. A bunch of little devices here.",
|
||||
"It is a nonlinear circuit. Just suppose for a moment we do",
|
||||
"a Gedanken experiment. Suppose I replace each of my",
|
||||
"circuit elements here with its linearized element equivalent.",
|
||||
"In other words, here is a VS source,",
|
||||
"here is a dependent current source, let me replace them with",
|
||||
"their linear equivalent circuit models.",
|
||||
"In other words, with their corresponding small",
|
||||
"signal element models. And I will show you what those",
|
||||
"are in a second. The resistor has a",
|
||||
"corresponding small signal element.",
|
||||
"The dependent current source has a corresponding small signal",
|
||||
"behavioral element model. And what I am going to do is",
|
||||
"keep the same circuit connections and simply pull out",
|
||||
"the large signal model for the element and replace it with a",
|
||||
"small signal element model. And by the nature of the small",
|
||||
"signal model they are all going to be linear.",
|
||||
"So what I am going to be left with is a linear circuit with",
|
||||
"simple linear circuit elements in there.",
|
||||
"And then once I have a linear circuit, I should be able to",
|
||||
"analyze that linear circuit using methods 1,",
|
||||
"2 and 3, superposition, Thevenin, node method and so",
|
||||
"on. And certainly the intuitive",
|
||||
"methods like superposition and Thevenin, which make life a lot",
|
||||
"easier for me with linear models, and thereby get the",
|
||||
"function that I am looking for very quickly.",
|
||||
"Again, my claim is that I can replace each of these large",
|
||||
"signal models by just small signal equivalents and then just",
|
||||
"analyze the resultant circuit. And I claim that I should be",
|
||||
"able to get the same answer. That's a claim.",
|
||||
"All right? So what I will do is give you",
|
||||
"an informal proof for why I can do that.",
|
||||
"And I also ask you to refer to Section 8.2.1 of the course",
|
||||
"notes to go through the foundations of the small circuit",
|
||||
"model in more detail. The intuition is that,",
|
||||
"remember KVL and KCL? I can write down KVL and KCL",
|
||||
"for every loop in that circuit and every node in that circuit.",
|
||||
"If I do KVL and KCL, I will end up with something",
|
||||
"like this. For the input loop I get VI",
|
||||
"something or the other applying KVL.",
|
||||
"For the output loop I get V out something or the other.",
|
||||
"And then applying KCL I get some other equation in iDS.",
|
||||
"So here are my KVL and KCL equations for that circuit.",
|
||||
"Now, KVL and KCL are simply a different representation of the",
|
||||
"circuit because within those KVL and KCL is encoded the topology",
|
||||
"of the circuit. Remember each KVL equation",
|
||||
"represents a loop and each KCL equation represents how nodes",
|
||||
"are connected together. So KVL and KCL equations encode",
|
||||
"within them the topology of my circuit.",
|
||||
"What I do next is, say, I replace each of these",
|
||||
"with the bias plus the small signal, so I get the bias plus",
|
||||
"the small signal and keep the equations the same.",
|
||||
"",
|
||||
"All I have done in my big set of KVL, KCL equations,",
|
||||
"I have simply replaced the total variable with the large",
|
||||
"signal variable and the small signal quantity.",
|
||||
"Then comes a key trick. The key trick is that because",
|
||||
"the bias point variables, they are a valid solution to",
|
||||
"the circuit. The circuit is in this",
|
||||
"quiescent state, and those are valid solutions",
|
||||
"to circuit. So therefore I can cancel them",
|
||||
"out. So the VI, the large signal",
|
||||
"values can be cancelled out leaving just small signal",
|
||||
"variables in there. So from the KVL,",
|
||||
"KCL equations I can cancel out the large signal values,",
|
||||
"the DC bias points because they satisfy the KVL and KCL",
|
||||
"themselves. In other words,",
|
||||
"I could have written VI plus V out and so on.",
|
||||
"Since they are satisfied I just strike out the large signal",
|
||||
"variable from both sides of each of these equations,",
|
||||
"so what is left is the same KVL, KCL equations but with",
|
||||
"small variables in place of the big variables.",
|
||||
"What that should tell you, this informal proof should tell",
|
||||
"you is that the small signal variables should then satisfy",
|
||||
"the same form of the KVL, KCL equations that the total",
|
||||
"variables satisfy. And because the KVL,",
|
||||
"KCL equations are a reflection of the topology of the circuit,",
|
||||
"what that says is that the small signal variables must also",
|
||||
"satisfy KVL and KCL. And since these arrive from the",
|
||||
"small signal elements that says that I can replace the big",
|
||||
"elements with the small elements and KVL and KCL will hold for",
|
||||
"the resulting circuit. This is a very quick breeze",
|
||||
"through, an informal proof to show that I can replace the big",
|
||||
"elements with the corresponding little element models and then",
|
||||
"simply apply linear techniques. Refer to Section 8.2.1 for more",
|
||||
"foundations and more discussion about the foundations for why we",
|
||||
"can do this. That brings up the small signal",
|
||||
"circuit method. The circuit method for small",
|
||||
"signal analysis has three steps. The first step is find",
|
||||
"operating point by using LS. First you analyze your large",
|
||||
"signal circuit and find the operating point.",
|
||||
"You have to do this, because remember,",
|
||||
"the small signal models depend on the operating point values.",
|
||||
"Remember the gain of our amplifier depended on the bias",
|
||||
"point. Second step is develop small",
|
||||
"signal models of elements. Second step is take each of the",
|
||||
"elements in your circuit and find their equivalent small",
|
||||
"circuit model for each of the elements.",
|
||||
"Third step is replace original elements with their small signal",
|
||||
"model elements. Third step is simply take the",
|
||||
"large elements and replace them with their small signal",
|
||||
"equivalent models. Then analyze resulting circuit,",
|
||||
"and that circuit will be a linear circuit.",
|
||||
"So let's do an example. I will just use the amplifier",
|
||||
"as an example of this method. And convince you that you are",
|
||||
"going to get the same expression at the end, but just so,",
|
||||
"so simply without even the smallest amount of grubby math.",
|
||||
"Three steps. The first step is to find the",
|
||||
"operating point using the large signal model.",
|
||||
"And let me just do that here. I get my V out =",
|
||||
"VS-K/2(VI-VT)^2 RL. Let me just write down that out",
|
||||
"here. Don't worry about copying that",
|
||||
"down. It is on the last page of your",
|
||||
"notes. The first step of the method",
|
||||
"simply applies the large signal model and finds out the behavior",
|
||||
"of that circuit to find out what the bias point values are.",
|
||||
"The second step is to develop the small signal model of my",
|
||||
"elements. How do I go about developing",
|
||||
"the small signal models of elements?",
|
||||
"Let's start with the MOSFET. The large signal model for the",
|
||||
"MOSFET looks like this.",
|
||||
"",
|
||||
"Here is my Vgs. This is my gate.",
|
||||
"This is my drain. This is my source.",
|
||||
"And I know my iDS to be K/2(Vgs-VT)^2.",
|
||||
"So this is the large signal model for the MOSFET,",
|
||||
"again in saturation. I am talking about all of these",
|
||||
"models are under the saturation discipline.",
|
||||
"So Vgs relates to iDS in the following way for the MOSFET.",
|
||||
"That is iDS, is K/2 and that is my square",
|
||||
"law relationship. So what is a corresponding",
|
||||
"small signal model? I go ahead and start with this.",
|
||||
"The corresponding small signal model simply says that iDS",
|
||||
"relates to Vgs in the following way.",
|
||||
"All I have to do is find a small signal equivalent where I",
|
||||
"need to find out, given a small change in the",
|
||||
"input Vgs, what is the small change in the iDS?",
|
||||
"So I can apply my standard trick to a much simpler",
|
||||
"expression here, which is iDS simply,",
|
||||
"I differentiate this function with respect to Vgs.",
|
||||
"",
|
||||
"So I don't completely eliminate the math here,",
|
||||
"but it is a much simpler problem here.",
|
||||
"At Vgs equals the bias point times small vgs.",
|
||||
"I can find the small change in iDS corresponding to a small",
|
||||
"change in the input using this expression.",
|
||||
"That gives me iDS as simply K(Vgs-VT) vgs.",
|
||||
"I call this gm, and I will tell you why in a",
|
||||
"second. So what does this expression",
|
||||
"say? This expression says that if I",
|
||||
"have a small change in Vgs then this will be my small change in",
|
||||
"iDS. Notice that the resulting small",
|
||||
"signal model is also a dependent current source.",
|
||||
"It is a voltage controlled dependent current source.",
|
||||
"So the output is the current, and it is a dependent current",
|
||||
"source and it depends on the input voltage.",
|
||||
"The good news is that notice that this one,",
|
||||
"this expression here gm is a constant related to the bias",
|
||||
"point values. Therefore, notice that the",
|
||||
"small signal model for the MOSFET in saturation,",
|
||||
"not surprisingly, is a linear voltage controlled",
|
||||
"current source according to the following expression.",
|
||||
"So iDS=gm Vgs. Gm is a representation for",
|
||||
"K(Vgs-VT) and is called a transconductance.",
|
||||
"It is called a transconductance because it, in some sense,",
|
||||
"deflects the conductance properties of this based on the",
|
||||
"input. So it is a transconductance.",
|
||||
"So this value is called Vgs. Therefore, I can build the",
|
||||
"small signal model as follows. Vgs is a voltage controlled",
|
||||
"current source and iDS is simply gm Vgs.",
|
||||
"So this is my gate, drain, source.",
|
||||
"",
|
||||
"So that is the small signal model for my MOSFET.",
|
||||
"As a next step what are the other elements in my circuit?",
|
||||
"Let's see. I have a voltage source and I",
|
||||
"have a resistor, so let me find out the",
|
||||
"corresponding small signal model for a DC supply VS.",
|
||||
"This is Page 7. I will do it mathematically for",
|
||||
"you, but often times it is always good to do a sanity check",
|
||||
"using intuition. Let me ask you,",
|
||||
"the large signal for a DC supply looks like this.",
|
||||
"",
|
||||
"The element law for a voltage source is VS equals some capital",
|
||||
"VS. It is a constant voltage.",
|
||||
"So what do you expect to be the small signal model for a voltage",
|
||||
"source? In other words,",
|
||||
"for a small change, suppose I have a small change",
|
||||
"in the current, by how much should the output",
|
||||
"VS change? It shouldn't change.",
|
||||
"It is a voltage source. So what does intuition tell you",
|
||||
"is a small signal model for the voltage source?",
|
||||
"A short. So the key here is that a",
|
||||
"voltage source behaves like a short circuit for small",
|
||||
"perturbations. In other words,",
|
||||
"if I change the current flowing through it by a small amount",
|
||||
"somehow, the output is still going to held at VS.",
|
||||
"In other words, small signals are simply going",
|
||||
"to scoot through this voltage source without having any impact",
|
||||
"whatsoever on the voltage. Or mathematically I could also",
|
||||
"do small vs is del by del IS of VS evaluated at IS equals some",
|
||||
"capital IS times small IS. And therefore VS equals zero.",
|
||||
"What that means is that the small signal model for my",
|
||||
"voltage source is simply a short circuit.",
|
||||
"",
|
||||
"So in a small circuit voltage sources appear like a short",
|
||||
"circuit. Finally, I have a resistor,",
|
||||
"my resistor R. Let me find out its",
|
||||
"corresponding small signal model.",
|
||||
"The large signal model looks like this R, VR,",
|
||||
"IR. And I know that VR is simply",
|
||||
"RIR. And to find the small signal",
|
||||
"equivalent I do del of IRR divided by del IR for IR",
|
||||
"calculated at some constant value times small IR.",
|
||||
"What I am looking to do is to find out what is the change in",
|
||||
"the voltage across R for a small perturbation in the current?",
|
||||
"Again, let me exhort you to rely on intuition to at least",
|
||||
"sanity check your answers. So what do you think this",
|
||||
"should look like? It's a resistor and I have a",
|
||||
"small change in the current, by what do you expect the",
|
||||
"voltage to change? Think about,",
|
||||
"for the next five seconds, what the small signal model for",
|
||||
"this should look like and then I will go ahead and write down the",
|
||||
"answer.",
|
||||
"",
|
||||
"So differentiating I simply get RIR.",
|
||||
"In other words, for a resistor the small signal",
|
||||
"model is the resistor itself.",
|
||||
"",
|
||||
"So what I have done so far, let me just take you through",
|
||||
"where we are right now, give you the big picture there.",
|
||||
"I began by suggesting that looking to find an even simpler",
|
||||
"way to do small signal analysis. I gave you an informal proof to",
|
||||
"show that if I had small signal element models for all of my",
|
||||
"elements, I could simply replace them in the circuit and then do",
|
||||
"a corresponding linear circuit analysis phase to get the result",
|
||||
"I am looking for. There are three steps to the",
|
||||
"method. As a first step we began by",
|
||||
"finding small signal models for each of our elements.",
|
||||
"For the nonlinear MOSFET the small signal model was a linear",
|
||||
"dependent current source. For a voltage source the",
|
||||
"corresponding small signal model was a short circuit.",
|
||||
"Again, that makes sense intuitively if I change the",
|
||||
"current through a voltage source by a small amount.",
|
||||
"By how much does the voltage change?",
|
||||
"It is a voltage source, silly.",
|
||||
"The voltage doesn't change. So the small signal V,",
|
||||
"the small change in the voltage is zero, and that is the same",
|
||||
"thing as a short circuit. For a resistor by how much does",
|
||||
"the voltage change if I change the current by a small amount?",
|
||||
"Well, it will change by R times the current change,",
|
||||
"and that is the property of a resistor, R.",
|
||||
"As a final step what I would like to do, on Page 8,",
|
||||
"I'd like to very quickly draw for you the small signal circuit",
|
||||
"and then analyze it. This is the large signal",
|
||||
"circuit. That is a large signal circuit.",
|
||||
"And let me draw the small signal circuit.",
|
||||
"And the method says simply pluck out, gouge out each of",
|
||||
"these elements. And simply replace each of",
|
||||
"these nasty nonlinear elements with the corresponding small",
|
||||
"signal linear equivalents. So let's do that.",
|
||||
"Remember, for the input you replace input with its small",
|
||||
"signal voltage because I am telling you that it's sourcing a",
|
||||
"small change in VI. So that is VI.",
|
||||
"And then I replace a short for VS.",
|
||||
"I replace an R for RL because it is an RL itself for the small",
|
||||
"signal model. And then for the dependent",
|
||||
"source, we discovered that the dependent source was a linear",
|
||||
"dependent source given where ids=gmvi.",
|
||||
"Remember, this was my small VO. Here you go.",
|
||||
"I have a small signal circuit here where I have simply created",
|
||||
"that by replacing each of the big elements by little",
|
||||
"rinky-dink elements. Now these are all linear",
|
||||
"elements so I can do a really simple linear analysis.",
|
||||
"What method shall we use? Well, this is so simple.",
|
||||
"I will just go ahead and use the node method.",
|
||||
"So applying the node method at the node with voltage VO,",
|
||||
"what I will do is the current going up, VO divided by RL",
|
||||
"equals the current going down iDS.",
|
||||
"And so the current going up is VO divided by RL and the current",
|
||||
"going down is -- Oops, I should have done this.",
|
||||
"The total current going out is zero, so the sum of these two is",
|
||||
"zero. That is my good old node method",
|
||||
"here. And I know that iDS is simply",
|
||||
"gmvi equals zero. So right there I have the",
|
||||
"relationship between VO and VI. So VO is simply minus gmviRL.",
|
||||
"And remember gm was simply K VI minus VT.",
|
||||
"",
|
||||
"We are done, OK?",
|
||||
"What have we here? I created a linear circuit",
|
||||
"which simply comprised small signal models for each of my big",
|
||||
"elements. And then I simply did a",
|
||||
"straightforward linear analysis using any one of the linear",
|
||||
"techniques I knew about. This is simple enough so I",
|
||||
"apply the node method. And I've got the equation at",
|
||||
"this node, simplified it and I directly got the answer.",
|
||||
"In one or two steps I directly gave you the output as a",
|
||||
"function of the input. It can't get any simpler.",
|
||||
"Thank you."
|
||||
]
|
||||
}
|
||||
@@ -1,1991 +0,0 @@
|
||||
{
|
||||
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|
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|
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|
||||
"text": [
|
||||
"Let's get started.",
|
||||
"",
|
||||
"Can you hear me back there? Loud and clear.",
|
||||
"OK. Let's get started.",
|
||||
"Before I begin, just a couple of announcements.",
|
||||
"Brad Buren is one of our students here and he needs a",
|
||||
"note-taker. It's a paid position.",
|
||||
"So if you are interested you can stop by after class and see",
|
||||
"him. He's sitting right here out",
|
||||
"there, OK? Second, just a reminder that",
|
||||
"6.002 does have prerequisites. And the prerequisites are 8.02",
|
||||
"and 18.03. So with that let me start off",
|
||||
"with the usual. Do a quick review of what we've",
|
||||
"done so far. So we started out life looking",
|
||||
"at the laws of physics and Maxwell's equations and so on.",
|
||||
"And those were way too hard so we said let's make life easy for",
|
||||
"ourselves. So we chose to play in this",
|
||||
"playground in which we said we shall adhere to the lumped",
|
||||
"matter discipline. OK?",
|
||||
"The LMD. So we are in that playground.",
|
||||
"So this entire course, and for that matter large parts",
|
||||
"of EECS are within that playground, within which the",
|
||||
"lumped matter discipline applies.",
|
||||
"So as soon as we jumped into the playground,",
|
||||
"the LMD playground, we could take Maxwell's",
|
||||
"equations and abstract them out into two very,",
|
||||
"very simple rules. And the very simple rules were",
|
||||
"KVL and KCL. KVL simply said that I can sum",
|
||||
"the voltages in any loop in a circuit and the result then",
|
||||
"would be zero. Similarly, I can sum the",
|
||||
"currents that enter or exit any node and the sum will also be",
|
||||
"zero. So what you can now do is,",
|
||||
"if you feel like, you can go around and brag.",
|
||||
"Oh, yeah, we use Maxwell's equations in everyday life and,",
|
||||
"yeah, it's good stuff. And the key is that this is",
|
||||
"really an encapsulation of Maxwell's equations within this",
|
||||
"playground that we are in. So I talked about the first",
|
||||
"method of circuit analysis in the last lecture.",
|
||||
"And that method simply took the, wrote KVL for all the",
|
||||
"loops, wrote KCL for all the nodes and wrote element vi",
|
||||
"relationships. And together gave you a big",
|
||||
"bunch of equations. And you sat down and grunged",
|
||||
"through the equations and you solved for branch voltages and",
|
||||
"currents. So we reviewed a second method",
|
||||
"of circuit analysis. And I'll simply call it circuit",
|
||||
"composition. The basic idea behind this",
|
||||
"method was to learn some simple rules of how resistors add and",
|
||||
"conductances add and so on and so forth and look at a circuit",
|
||||
"and simplify the circuit by making series simplifications",
|
||||
"when the resistors are in series and so on and so forth,",
|
||||
"and compose it and play around with it till we end up with the",
|
||||
"current, the voltages that we are looking for.",
|
||||
"This is the intuitive method. And so a section in Chapter 2,",
|
||||
"I believe, of the course notes discusses several examples using",
|
||||
"this method and attempts to make a little bit formal the",
|
||||
"intuitive approach that is applied in this method.",
|
||||
"So we then looked at the node method.",
|
||||
"And the node method was simply a particular way of applying KVL",
|
||||
"and KCL. Node method,",
|
||||
"remember? We took a ground node.",
|
||||
"Then we labeled the nodes of the remaining voltages with",
|
||||
"respect to that ground. Then we wrote KCL for each of",
|
||||
"the nodes. And when we wrote KCL for each",
|
||||
"of the nodes, remember, KVL was implicit in",
|
||||
"this expression that we used for each of the currents that were",
|
||||
"exiting each node. So if Ej was a node voltage,",
|
||||
"then Ej minus Ei multiplied by the conductance Gi was the",
|
||||
"current that was going through one of those,",
|
||||
"I should call it Gij. This is a conductance that",
|
||||
"connects nodes i and j. That gave us the KVL that fed",
|
||||
"into the same system. So these are three methods.",
|
||||
"The node method, by the way, is sort of the",
|
||||
"workhorse of the 6.002 industry. And for that matter for all of",
|
||||
"the circuits industry. When in doubt,",
|
||||
"apply the mode method, you'll be OK.",
|
||||
"That applies to linear circuits, nonlinear circuits,",
|
||||
"what have you. What I'm going to do today is",
|
||||
"go through two more methods. So notice that the first few",
|
||||
"lectures of this course, the first three lectures simply",
|
||||
"comprise transitioning you from the world of physics to the",
|
||||
"world of EECS. And then two lectures on giving",
|
||||
"you a bag of tricks. So we start you off with the",
|
||||
"sort of tools, your mallets and chisels and so",
|
||||
"on and so forth. And these five methods are your",
|
||||
"tools. We'll look at two methods",
|
||||
"today. One method is called the method",
|
||||
"of superposition and the second method is called the Thevenin",
|
||||
"method. And these methods apply only to",
|
||||
"linear circuits. So we look at the subset of",
|
||||
"circuits that are linear, and these two methods apply to",
|
||||
"only those circuits. These are methods that combined",
|
||||
"with intuition really enables you to solve very interesting",
|
||||
"circuits very, very quickly.",
|
||||
"So let me do an example using a usual node method.",
|
||||
"And then jump into introducing the superposition methods and",
|
||||
"Thevenin methods using that same example.",
|
||||
"So let me draw you an example circuit here.",
|
||||
"",
|
||||
"So, again, I'm using this example, I will use this example",
|
||||
"to introduce the method of superposition and the Thevenin",
|
||||
"method. So what I'm going to do is",
|
||||
"start off the usual way and analyze the circuit using a",
|
||||
"method that you know now, the node method.",
|
||||
"And what I'll do is write down the node equations for this by",
|
||||
"applying the node method. So if you recall the node",
|
||||
"method. I choose a ground node.",
|
||||
"I'm going to choose this node. It's got both the voltage",
|
||||
"source connected to it, and it's also got many other",
|
||||
"edges impinging on it. So I'm going to choose that as",
|
||||
"my ground node and I'm going to label the other nodes with their",
|
||||
"voltages. So this is an unknown.",
|
||||
"I'll label it as e. I guess we just have one",
|
||||
"unknown e. And I know the voltage of this",
|
||||
"node, and that is simply V. Since it's V,",
|
||||
"there's a voltage source between the ground node and that",
|
||||
"node. So what I can do next is that I",
|
||||
"can write down the node equation for this node and then go from",
|
||||
"there. So let me go ahead and do that.",
|
||||
"So let me sum up the currents going outside,",
|
||||
"going outwards. So I have e minus v divide by",
|
||||
"R1, I have e minus zero divide by R2, and I have minus i equals",
|
||||
"zero. This is a node equation.",
|
||||
"The first thing I want you to observe is that this equation is",
|
||||
"linear in V and i. What I mean by linear is that",
|
||||
"you don't see terms like Vi or V-squared and things like that.",
|
||||
"It's some constant times V plus some constant times i equals",
|
||||
"some other constant. So that's quite nice.",
|
||||
"So I'm going to rearrange the terms in the following manner.",
|
||||
"I'll move the known sources to the right-hand side and collect",
|
||||
"the coefficients of e on this side, so I get one by R1 plus",
|
||||
"one by R2 over here.",
|
||||
"",
|
||||
"So stare at this for a moment and notice again here I have e,",
|
||||
"my unknown node voltage, there is some constant",
|
||||
"multiplier, and that equals some function of V summed up with",
|
||||
"some function of i. And, again, notice that this is",
|
||||
"a linear combination of V and i. No multiplication terms and so",
|
||||
"on and so forth. This is a pretty standard form",
|
||||
"in which we will represent equations quite often.",
|
||||
"And just to label it, this is often labeled G as the",
|
||||
"conductance matrix. Of course this is e,",
|
||||
"our unknown node voltages, and this is a linear sum of",
|
||||
"sources. So this is a very standard way",
|
||||
"that we will represent equations.",
|
||||
"We did that last week as well, or rather on Tuesday where I",
|
||||
"took a conductance matrix, multiplied that by a column",
|
||||
"vector of unknown node voltages and equated that to some linear",
|
||||
"combination of my source voltages.",
|
||||
"The reason the circuit is linear is that I have only",
|
||||
"linear elements in the circuit. I don't have any nonlinear",
|
||||
"elements. And because of that I can",
|
||||
"rewrite this in the following manner.",
|
||||
"I'm just going to express e as a function of V and i and bring",
|
||||
"it over to this side. So it's some function of i.",
|
||||
"So I get R1 R2 divide by R1 plus R2.",
|
||||
"And I bring R1 R2 to this side. That's what I get.",
|
||||
"So stare at this for a few seconds, very common form.",
|
||||
"My unknown node voltage is equal to this stuff on the",
|
||||
"right-hand side. The stuff on the right-hand",
|
||||
"side has a term multiplying the source voltage V and some other",
|
||||
"term multiplying the current I. And if I were to put this in",
|
||||
"sort of symbol-like form my unknown node voltage is some",
|
||||
"constant times V1 plus some constant times,",
|
||||
"is of the form constant times the source current,",
|
||||
"constant times the source voltage and so on.",
|
||||
"The units of As and Vs are different because in this case A",
|
||||
"has no units because V is a voltage.",
|
||||
"And so is e. In this case V has units of",
|
||||
"resistance. So that V times i gives me a",
|
||||
"voltage. So stare at this equation for a",
|
||||
"few seconds and this should help us build up some insight that",
|
||||
"will allow us to write down the answer almost by inspection.",
|
||||
"I'm going to show you a method now, in a few minutes,",
|
||||
"which will allow you to write down the answer e just by",
|
||||
"starring at the circuit without having to go through node",
|
||||
"equations and so on. The more and more methods I",
|
||||
"teach you, the more you will be able to do a lot of this",
|
||||
"completely by yourselves. In this particular example it's",
|
||||
"a relatively simple circuit but these methods would be",
|
||||
"particularly useful when you have more complicated",
|
||||
"situations. But before I go on let me spend",
|
||||
"a few minutes pontificating on linearity.",
|
||||
"So that's a linear circuit. And this equation gives me the",
|
||||
"unknown node voltage e as a linear sum of source voltages",
|
||||
"and source currents. Linearity implies two",
|
||||
"properties, the property of homogeneity and also gives vice",
|
||||
"to the property of superposition.",
|
||||
"Let's do homogeneity first. What this says is if I have a",
|
||||
"circuit, some circuit and I feed it some sort of inputs,",
|
||||
"A, then let's say my output is S.",
|
||||
"If you're feeling hungry think of these as apples and the",
|
||||
"circuit converts them into applesauce.",
|
||||
"So what homogeneity says is that what I can do is if I take",
|
||||
"each of my apples and instead of feeding it an entire apple what",
|
||||
"if I give it three-quarters of an apple?",
|
||||
"Say I multiple all my inputs by some constant alpha,",
|
||||
"three-quarters. What that says is that at the",
|
||||
"output instead of getting one full bottle of applesauce I'm",
|
||||
"going to get three-quarters of a bottle of apple sauce.",
|
||||
"So if I proportionately reduce all the inputs and if this is a",
|
||||
"linear circuit then so shall my output be reduced in the same",
|
||||
"proportion. So that's homogeneity.",
|
||||
"Next, let's look at superposition.",
|
||||
"",
|
||||
"The property of superposition says the following.",
|
||||
"The same kind of circuit. If I feed it apples then I get",
|
||||
"applesauce. I take the same circuit,",
|
||||
"and this time around if I feed the circuit a different set of",
|
||||
"inputs, say blueberries. And let's say my output,",
|
||||
"oops, let me do it this way. So as my output I get blueberry",
|
||||
"sauce, if such exists. So apples applesauce,",
|
||||
"blueberries give me blueberry sauce.",
|
||||
"Then what I'm going to get if I mix up the two,",
|
||||
"so let's say I take my circuit, the same circuit with a set of",
|
||||
"inputs and in this example one output.",
|
||||
"Let's say I mix up my inputs and some of my inputs in the",
|
||||
"following way, here I feed an A1 plus B1 and",
|
||||
"here A2 plus B2 and so on then at the output I am going to get",
|
||||
"a mush of apple sauce and blueberry sauce.",
|
||||
"All this says is that if I apply just apples I get",
|
||||
"applesauce. If I apply just blueberries I",
|
||||
"get blueberry sauce. Then if I were to figure out",
|
||||
"how this blender would have worked had I fed in the",
|
||||
"combinations of apples and blueberries, then for the",
|
||||
"purposes of understanding that blender all I could have done",
|
||||
"was taken by two outputs and just mixed them up together",
|
||||
"myself and that's exactly what I'd get.",
|
||||
"So if I sum up the inputs my outputs would also be the sum of",
|
||||
"the outputs with the inputs applied by themselves.",
|
||||
"So let me take this here and munge around with hit for a few",
|
||||
"seconds and get something interesting out of it.",
|
||||
"So notice two inputs, two inputs, outputs.",
|
||||
"In your notes I've given you another template for the next",
|
||||
"set of scribbles I'm going to make here.",
|
||||
"So use the next set of templates on page three.",
|
||||
"What I'm going to do here is something very simple,",
|
||||
"set one output to zero and feed a voltage V1.",
|
||||
"So that's feed a voltage V1 and set the other output to zero.",
|
||||
"And let's say I get Y1 as an output.",
|
||||
"And in this case I set the first voltage to zero and feed a",
|
||||
"different voltage V2 on the second input.",
|
||||
"And let's say my output is Y2. This is just a particular",
|
||||
"application of the superposition principle I just outlined.",
|
||||
"Apply V1 set one output to zero.",
|
||||
"Apply V2 set the original output to zero.",
|
||||
"Then what I'm going to find is that the answer will simply look",
|
||||
"like this, just replace for As and Bs what I just did and we",
|
||||
"get V1 and zero here and we get zero and V2 here.",
|
||||
"And as my output I'm going to get exactly the sum Y1 plus Y2.",
|
||||
"This is simply a particular application of superposition",
|
||||
"where what I'm saying is the following.",
|
||||
"If you look at this circuit here effectively what have I",
|
||||
"done? Effectively what I've done is",
|
||||
"apply the voltage V1 on one input and a voltage V2 on the",
|
||||
"other input. V1 here.",
|
||||
"V2 here. And the output is Y1 plus Y2.",
|
||||
"What I'm saying is look backwards now.",
|
||||
"What I'm saying is that the whole components of the output",
|
||||
"Y1 plus Y2 could individually be derived in the following manner.",
|
||||
"I could get the component Y1 by simply applying one of the",
|
||||
"voltages and setting the other to zero.",
|
||||
"I can get the other component Y2 by setting yet another input",
|
||||
"to zero and applying the voltage V2 to get Y2.",
|
||||
"And sum then up and that's my answer.",
|
||||
"This will become a lot clearer with an example.",
|
||||
"Again, remember if I have a bunch of inputs applied to a",
|
||||
"circuit, V1, V2 and so on, and I get some output then what",
|
||||
"this is saying is that I can alternatively find out the",
|
||||
"answer by applying just one voltage, setting all the others",
|
||||
"to zero, measuring the output, apply a second voltage,",
|
||||
"set all inputs to zero, measure the output and sum of",
|
||||
"applesauce and blueberry sauce and there you get the answer.",
|
||||
"Let's do an example. And before we go into that I",
|
||||
"talked about setting voltage sources and current sources to",
|
||||
"zero. First of all,",
|
||||
"what does it mean to set a voltage source to zero?",
|
||||
"This is the same as this. Setting a voltage source to",
|
||||
"zero is simply replacing the voltage source with a short,",
|
||||
"and setting a current source to zero simply implies an open",
|
||||
"circuit. So when I say zero that source,",
|
||||
"if it's a voltage source short it, if it's a current source",
|
||||
"open it.",
|
||||
"",
|
||||
"I can take any two nodes in the world and measure the potential",
|
||||
"difference across them. So there may be some potential",
|
||||
"difference across these set by the circuit that I haven't shown",
|
||||
"you on this side. There might be some other",
|
||||
"circuit that is controlling the voltage of these two nodes.",
|
||||
"The same with the short. What's V going to be?",
|
||||
"But there is a V. It's zero.",
|
||||
"So that's method four, method of superposition.",
|
||||
"And this method says that the output of a circuit --",
|
||||
"",
|
||||
"Again, remember I'm focusing on linear circuits.",
|
||||
"Remember, I have this playground where LMD applies.",
|
||||
"And within that playground I'm playing in the south goal area.",
|
||||
"In the south goal area, in that subset of the",
|
||||
"playground circuits are linear. So in that part of the",
|
||||
"playground superposition applies because there circuits are",
|
||||
"linear. So the output of a circuit is",
|
||||
"determined by summing up the responses to each source acting",
|
||||
"alone.",
|
||||
"",
|
||||
"Now, in this statement here this source stands for",
|
||||
"independent source. I haven't talked about",
|
||||
"independent versus dependent sources.",
|
||||
"We'll talk about dependent sources a few weeks from today.",
|
||||
"And just so you don't get confused, for dependent sources",
|
||||
"you will be looking at Section 3.3.3 of your course notes to",
|
||||
"see how superposition works with dependent sources.",
|
||||
"But remember we haven't covered dependent sources yet.",
|
||||
"We will be covering them about two weeks from now.",
|
||||
"So let's go back to our example and apply the method of",
|
||||
"superposition to an example. So the method says sum up the",
|
||||
"outputs of each of the sub-circuits where I'm applying",
|
||||
"one source acting alone. So let me just do this here.",
|
||||
"Let me start with the circuit. And let me start with shutting",
|
||||
"I off. So I have voltage V --",
|
||||
"",
|
||||
"I have R2. And I'm shutting I off.",
|
||||
"So I have replaced this with an open circuit.",
|
||||
"So I is zero. Let me call the node voltage eV",
|
||||
"to reflect that component of the node voltage that arises due to",
|
||||
"V acting alone. And you should look at this",
|
||||
"pattern here and very quickly be able to write the answer for",
|
||||
"patterns like this voltage, the two resistors.",
|
||||
"That's called a resistive divider.",
|
||||
"It will appear again and again and again.",
|
||||
"And eV is simply V times R2 divided by R1 plus R2.",
|
||||
"That's still my ground node. So the voltage here is simply",
|
||||
"this voltage divided by the two resistors to give you the",
|
||||
"current multiplied by R2 to give you the voltage across this R.",
|
||||
"Remember this pattern. You apply voltage divider",
|
||||
"patterns probably more times than any other pattern that you",
|
||||
"might imagine. So that's with the V acting",
|
||||
"alone. Now, let me do I acting alone.",
|
||||
"So for I acting alone --",
|
||||
"",
|
||||
"And what I do this time around is replace this with a short,",
|
||||
"replace the voltage source to the short.",
|
||||
"And let me call this voltage eI for the component of the voltage",
|
||||
"due to the current I. And eI, in this case,",
|
||||
"is simply given by yet another pattern here,",
|
||||
"the current across a pair or resistors is simply the",
|
||||
"effective resistance multiplied by the current so it's i and the",
|
||||
"effective resistance is R1, R2 or R1 plus R2.",
|
||||
"That's eI. That's a component that node",
|
||||
"due to the current I. Now, so the method says that.",
|
||||
"Then take these components, sum them up and there you have",
|
||||
"the answer. So E is simply ev plus ei.",
|
||||
"The components of V and I acting alone,",
|
||||
"just simply V times R2 divided by R1 plus R2 plus R1,",
|
||||
"R2. There we go.",
|
||||
"Fortunately, the fates have been kind to us",
|
||||
"and the answer is the same as the answer we obtained with the",
|
||||
"node method. No surprise here.",
|
||||
"So this is actually an incredibly simple method.",
|
||||
"So you can take a very complex circuit.",
|
||||
"What have you really done here? You can take a very complex",
|
||||
"circuit and you can solve a very complex circuit by breaking it",
|
||||
"down into many simple individual sub problems.",
|
||||
"You will do this in EECS time and time and time again.",
|
||||
"Whether it's in software systems or hardware systems or",
|
||||
"what have you, you're often times building",
|
||||
"complicated systems. Remember doom on this side?",
|
||||
"And the way and when you put these things together,",
|
||||
"let's say a large software system, is you don't write the",
|
||||
"whole piece of software starting main and grunge down.",
|
||||
"You build a lot of little components and tie the",
|
||||
"components together. In the same manner here you",
|
||||
"take a big circuit and you find its behavior for each source",
|
||||
"acting alone. Lots of little inky dinky",
|
||||
"simple little circuits. And you will see examples in",
|
||||
"your homework where you're given a big circuit or because it set",
|
||||
"all the Is to zero and the other Vs to zero the whole circuit",
|
||||
"almost vanishes and all that you're left with is a little",
|
||||
"resistor or two. So this is the very,",
|
||||
"very powerful method. I'd like to do a little",
|
||||
"demonstration for you. And what I'm going to show you",
|
||||
"is the demo is a vat of water. Actually, I'll tell you what it",
|
||||
"is in a second. But assume it is salt water for",
|
||||
"now. I'll apply two voltages.",
|
||||
"In this case I'm going to apply a sinusoid.",
|
||||
"That's not very good. A sinusoid and a triangular",
|
||||
"wave. And what I'm going to do is",
|
||||
"measure the response at this site.",
|
||||
"Now, this is a vat of salt water.",
|
||||
"And I'm going to tell you it behaves like a linear system.",
|
||||
"If you view each little particle, or each little",
|
||||
"cubic-centimeter or whatever of water, it'll behave like little",
|
||||
"resistor. So this vat of salt water",
|
||||
"behaves like big distributed resistor in the following",
|
||||
"manner.",
|
||||
"",
|
||||
"And so on. This of this big mesh of little",
|
||||
"resistors, but it's all resistors.",
|
||||
"It's a linear circuit. So I'm going to apply two",
|
||||
"voltages, a triangular and a sinusoid, and we're going to",
|
||||
"observe the output. And what do you expect to see",
|
||||
"there? You will see the superposition",
|
||||
"of the two, which is you'll see a sinusoid.",
|
||||
"And then you'll see the jagged triangular thing articulating",
|
||||
"the sinusoid pattern. What I'm going to do right now,",
|
||||
"don't put any water yet. This is the vat of nothing",
|
||||
"right now. It's all empty.",
|
||||
"Can we show the screen on this side?",
|
||||
"The oscilloscope screen?",
|
||||
"",
|
||||
"OK. Oh, there you go.",
|
||||
"So this is the screen of the oscilloscope now.",
|
||||
"Notice that I have a sinusoid and I have a triangular wave and",
|
||||
"the output is zero. And the reason is there is",
|
||||
"nothing in this vat. It's empty.",
|
||||
"So previously when I taught this course I would get",
|
||||
"saltwater and pour saltwater. Then we discovered a much",
|
||||
"better source of water that conducted electricity like one",
|
||||
"real mean fluid. Cambridge water.",
|
||||
"It just works very pleasantly. It just conducts electricity",
|
||||
"like nothing at all. And I've been thinking of using",
|
||||
"Charles River water next time and see what happens,",
|
||||
"although there we'd probably get some biological organisms",
|
||||
"doing strange things at you. But go ahead.",
|
||||
"Our friendly demonstration expert, Lorenzo,",
|
||||
"will pour some water into the vat.",
|
||||
"And you should begin seeing the output being a superposition of",
|
||||
"the two. So as he pours,",
|
||||
"there you go, do you see that?",
|
||||
"So you do see the sinusoidal articulation and the jagged wave",
|
||||
"form. And just to have some more fun,",
|
||||
"what I can do is increase one of the voltages.",
|
||||
"And you'll see --",
|
||||
"",
|
||||
"Now you know what would have happened if I had used Charles",
|
||||
"River water. So my output keeps increasing",
|
||||
"as I increase the corresponding wave form.",
|
||||
"",
|
||||
"I could do this, this is fun.",
|
||||
"So let me pause there and go onto the next topic.",
|
||||
"So that little demonstration showed you that even something",
|
||||
"as simple as this physical entity vat of water behaves like",
|
||||
"a linear system, and we can model that linear",
|
||||
"system as a set of resistors. Unbeknownst to you,",
|
||||
"right now, in the past ten seconds I introduced a new",
|
||||
"concept. It's called subliminal",
|
||||
"advertising. So one of the things we do in",
|
||||
"EE a lot is model real systems. So often times if I wanted to",
|
||||
"look at the behavior of salt, behavior of a vat of water,",
|
||||
"I can model it as a set of resistors for certain kinds of",
|
||||
"activities. Just hold that thought for some",
|
||||
"time later in your careers. All right.",
|
||||
"That's method four, the superposition method.",
|
||||
"Remember, it is methods like this that will make your life",
|
||||
"really, really, really easy.",
|
||||
"If you find that you are having to do a lot of grunging homework",
|
||||
"or something, just step back and think",
|
||||
"superposition, think Thevenin or think",
|
||||
"composition rule. There must be a simpler way",
|
||||
"usually. Let's do the next method.",
|
||||
"This is called the Thevenin method.",
|
||||
"To derive this method let me start by applying superposition",
|
||||
"to some circuit. So let's say I have some",
|
||||
"arbitrary network N. Assume it's a linear network",
|
||||
"and the network has a whole bunch of goodies in it.",
|
||||
"It has a bunch of resistors, it has a bunch of voltage",
|
||||
"sources, and it has a bunch of current sources.",
|
||||
"Many current sources. Many voltage sources.",
|
||||
"Many resistors. Some jumbled voltage sources,",
|
||||
"current sources and resistors. And I look at two nodes in this",
|
||||
"network. Here are two nodes in the",
|
||||
"network, two points in the network were elements connect.",
|
||||
"I'm looking at those two nodes and all I want to do is the",
|
||||
"following. I want to figure out if I take",
|
||||
"a rinky-dinky little current source and apply it there,",
|
||||
"all I want to figure out is what is V and what is I.",
|
||||
"There is this mongo box out here, a black box of resistors,",
|
||||
"voltage source and current sources, too many to count.",
|
||||
"I pick two nodes, apply a current source,",
|
||||
"and all I care about is what is the voltage that I will measure",
|
||||
"by applying it here. Notice the current here will be",
|
||||
"I because the current here is I. And I apply it here.",
|
||||
"I want to measure what the voltage is.",
|
||||
"Now, with the insight you've obtained from superposition,",
|
||||
"you should be able to jump up and state the form of the",
|
||||
"answer. So by superposition we know the",
|
||||
"following. We know that the effect of the",
|
||||
"circuit will be the same as the sum of components being added",
|
||||
"up. Sum of component,",
|
||||
"sum of component, a bunch of components added up.",
|
||||
"Each component will be the response of one source acting",
|
||||
"alone. So if I can figure out the",
|
||||
"effect of one source acting alone and put that down here,",
|
||||
"and do the same thing for all the sources, that's what I will",
|
||||
"get. So for the source Vm it's a",
|
||||
"linear circuit. So I know that my answer is",
|
||||
"going to be, in the final answer is going to be a Vm term and",
|
||||
"it's going to be multiplied by some alpha M term.",
|
||||
"I know that. It's a linear circuit so I know",
|
||||
"that the answer shall have a term Vm multiplied by some",
|
||||
"constant. Simple, I know that.",
|
||||
"Similarly, the same is true for, oh, this is the term Vm.",
|
||||
"And what I can do is I can measure just this effect by",
|
||||
"setting all the other sources to zero.",
|
||||
"So I can set all the other current sources to zero and all",
|
||||
"voltage sources, except for this one,",
|
||||
"and I can get that answer. So, similarly,",
|
||||
"for every voltage source I am going to get a term.",
|
||||
"So for every single voltage source, M1, M2,",
|
||||
"M3 and so on I'm going to get such a term and they're all",
|
||||
"going to sum up. Similarly, I'm going to get a",
|
||||
"term for In. And I know there will be an In",
|
||||
"term, and I know it's going to be some constant beta",
|
||||
"multiplying In. In this example of ours here,",
|
||||
"in this example, remember alpha was this and",
|
||||
"beta was this constant here. There's some constant beta,",
|
||||
"some constant alpha. And because I have a whole",
|
||||
"bunch of current sources there's going to be such a term for each",
|
||||
"one of them. And each one of these terms,",
|
||||
"Vm, In will be the voltage I would see here if I set all the",
|
||||
"other Vms to zero and I set all the other current sources,",
|
||||
"except for that one to zero. What am I missing?",
|
||||
"Is that it? The response here,",
|
||||
"V here. Am I missing anything here?",
|
||||
"Is that it? Now, don't all yell at once.",
|
||||
"What am I missing? Current source i,",
|
||||
"exactly. So if I have a current source i",
|
||||
"then there's an effect of this current as well.",
|
||||
"And so I write down i there, too.",
|
||||
"It's going to be some constant multiplying I.",
|
||||
"And that constant is going to look like a resistor,",
|
||||
"right, because this circuit contains current sources,",
|
||||
"voltage sources and resistors. If I've shorted all my voltage",
|
||||
"sources and opened all my current sources,",
|
||||
"what's left in here? Just a whole caboodle full of",
|
||||
"Rs. It's just going to look like",
|
||||
"some resistance R. And that's what I get here.",
|
||||
"So this is what V is going to look like and that's a form.",
|
||||
"So let's take a look at these components.",
|
||||
"",
|
||||
"Let's focus on the easy part first.",
|
||||
"What does this look like? This component looks like an I,",
|
||||
"it looks like a current and has some resistance.",
|
||||
"What is that resistance given by?",
|
||||
"Supposing I gave you this network and this currency source",
|
||||
"and I asked you tell me R. How would you measure R?",
|
||||
"What you would do is open all the current sources,",
|
||||
"short all the voltage sources, put a ohmmeter in there and",
|
||||
"measure the resistance R. That's R.",
|
||||
"OK, so we understand this term. What about this term here?",
|
||||
"Can someone tell me the units of this term here,",
|
||||
"this big thing here? Voltage.",
|
||||
"This is a voltage. This is a voltage.",
|
||||
"iR is a voltage. So this does behave like a",
|
||||
"voltage. And it behaves like some",
|
||||
"voltage V. So notice that as far as this",
|
||||
"current I is concerned the rest of the universe looks like a",
|
||||
"resistor and a voltage source behaving in some manner.",
|
||||
"And let me just call it Vth for now, and you'll know why in a",
|
||||
"second.",
|
||||
"",
|
||||
"The voltage has a form, some voltage plus Ri.",
|
||||
"So, in other words, as far as this I is concerned",
|
||||
"this whole network here N full of all the nice stuff is",
|
||||
"indistinguishable to this I here.",
|
||||
"So my I is sitting out there injecting a current into two",
|
||||
"nodes. If I am i, I'm looking at this,",
|
||||
"this network looks no different than a voltage source in series",
|
||||
"with the resistor R. Notice that the equation for",
|
||||
"this simple circuit is this, so I is given by V minus Vth",
|
||||
"divided by R. Just remember.",
|
||||
"",
|
||||
"It's a circuit. In other words,",
|
||||
"Agarwal sitting here cannot tell the difference if I'm",
|
||||
"measuring the voltage here between a circuit that looks",
|
||||
"like a Vth in series to the resistor or this huge mess of",
|
||||
"voltage sources and current sources and so on.",
|
||||
"Now, we will talk about Vth and R.",
|
||||
"R is called the resistance of the network as seen from the",
|
||||
"port with all the sources shut off.",
|
||||
"And similarly Vth, what is Vth?",
|
||||
"Vth is the open circuit voltage.",
|
||||
"In other words, if I apply the voltage here",
|
||||
"this is the response of all the current sources and all the",
|
||||
"voltage sources acting together. So it's as if I took this out",
|
||||
"and simply measured my V here as if I didn't exist,",
|
||||
"correct? Because this is the component",
|
||||
"of i. So if I opened i and measured",
|
||||
"V, I would get that big term on the left-hand side.",
|
||||
"That's my Vth. So that inspires the next",
|
||||
"method called the Thevenin method.",
|
||||
"",
|
||||
"In this method what I'm going to do is take some circuit,",
|
||||
"I'm on Page 9, with a mess of stuff.",
|
||||
"It's a big mess of stuff. And if I care to look at its",
|
||||
"impact on something else that I add from the outside then as far",
|
||||
"as the outside world is concerned this is",
|
||||
"indistinguishable from a circuit that looks like this.",
|
||||
"",
|
||||
"So what I can do is if I want to figure out what's happening",
|
||||
"here then, for the purpose of my analysis, this simple network",
|
||||
"here with R and Vth becomes a surrogate for this entire mess.",
|
||||
"So for the purpose of finding out the behavior at this point,",
|
||||
"I can take this huge mess and replace it with its Thevenin",
|
||||
"surrogate or Thevenin equivalent.",
|
||||
"This is called the Thevenin equivalent of this big network.",
|
||||
"Let me do an example that will make the method completely",
|
||||
"clear. Again, remember in EECS,",
|
||||
"most of our lives are about how can we make things so simple as",
|
||||
"being able to be analyzed by inspection?",
|
||||
"And so this is a method that takes you further down that",
|
||||
"path. So let me use the same circuit",
|
||||
"that I've been using before, my voltage V,",
|
||||
"R1, R2. This is an R.",
|
||||
"I'm 55 minutes fast so we have another three or four minutes.",
|
||||
"So this is my circuit. And let's say all I care about",
|
||||
"is finding out i1. That's all I care about.",
|
||||
"And what I'm going to do is I'm going to box this up and see if",
|
||||
"I can replace that with its Thevenin equivalent.",
|
||||
"So I'm going to box that up.",
|
||||
"",
|
||||
"What I'm saying is that I'm going to box it up and replace",
|
||||
"it with this Thevenin equivalent.",
|
||||
"I don't know what Vth and R are at this point.",
|
||||
"I'm just calling it Rth for fun.",
|
||||
"I don't know what these two values are, but if I knew what",
|
||||
"these two values were I can determine I really trivially as",
|
||||
"follows. I can get i1 as simply V minus",
|
||||
"Vth divided by R1 plus Rth. So if I knew Vth and Rth,",
|
||||
"I can write down i1 by inspection in that manner.",
|
||||
"So next, finally, how do I get Vth and Rth?",
|
||||
"You get Rth by looking at this network and shutting off all the",
|
||||
"voltage sources and measuring the resistance there.",
|
||||
"So I short my voltage source, that's R1.",
|
||||
"Oops, wrong way. I need to look this way.",
|
||||
"So looking this way, that's what I get.",
|
||||
"So what's Rth? Rth is simply R2.",
|
||||
"So I have opened my current source.",
|
||||
"Similarly, for Vth, remember all I want to do is",
|
||||
"look at the two nodes, step back, put a voltmeter",
|
||||
"there, measure the voltage, that's my open circuit voltage.",
|
||||
"So the way I do it is I take the circuit and simply measure",
|
||||
"the voltage there. That's R2.",
|
||||
"That's my current capital I. And I simply want to measure",
|
||||
"the open circuit voltage here, which is what?",
|
||||
"Just simply if I stand back and I kind of gingerly measure the",
|
||||
"voltage here without disturbing anything, I simply get IR2.",
|
||||
"So Vth is IR2 and Rth is R2 and here is the formula for the",
|
||||
"current in this branch when I apply a voltage source and a",
|
||||
"resistor R1 to this little circuit here.",
|
||||
"OK, let's pause and let me summarize this in about ten",
|
||||
"seconds. I had this circuit here.",
|
||||
"I wanted to find out i1. So what I said I'd do is take",
|
||||
"this complicated mess, well, it's not a complicated",
|
||||
"mess but assume it is, and replace with it a",
|
||||
"resistance Rth got by turning off all the sources.",
|
||||
"And the voltage in series, Vth, which I get simply by",
|
||||
"pulling this thing out, taking my input,",
|
||||
"this part out and simply measuring the open circuit",
|
||||
"voltage out there, Vth.",
|
||||
"And then I replaced the whole network with this new network",
|
||||
"that they call the Thevenin network, and voila,",
|
||||
"I get the answer in a second."
|
||||
]
|
||||
}
|
||||
@@ -1,2141 +0,0 @@
|
||||
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],
|
||||
"text": [
|
||||
"",
|
||||
"OK. Good morning.",
|
||||
"",
|
||||
"In the last lecture I did a little demonstration for you",
|
||||
"where I showed you a pair of inverters.",
|
||||
"And showed you that the output of the first inverter looked",
|
||||
"weird, certainly not like anything we have seen thus far.",
|
||||
"It looked like a slow rising transition like this.",
|
||||
"And using that motivation we have begun our study of RC",
|
||||
"circuits. And in particular for today the",
|
||||
"lecture is titled \"Digital Circuit Speed\".",
|
||||
"We are going to look at the fundamentals of digital circuit",
|
||||
"speed. And it all boils down to an RC",
|
||||
"delay. By the end of the lecture,",
|
||||
"I am going to show you two numbers that you can look at a",
|
||||
"circuit and obtain by observation, multiply them out",
|
||||
"and you will get a good idea of the speed at which a circuit",
|
||||
"will run. It is pretty amazing.",
|
||||
"So as a quick review -- The relevant section for this",
|
||||
"is Chapter 10.4. As a review,",
|
||||
"we said to understand things like this we need to develop the",
|
||||
"foundations for RC circuits. And the example I covered was",
|
||||
"that of a very simple circuit that looked like this --",
|
||||
"An RC circuit of this form. And I also showed you that for",
|
||||
"an input of the form, input that steps from zero to",
|
||||
"VI at time T equal to zero. And assuming that the capacitor",
|
||||
"state at time T equals zero was zero.",
|
||||
"What this means is that the capacitor starts from rest,",
|
||||
"so at time T=0, oops, this is VI,",
|
||||
"I'm sorry. So we assume that the capacitor",
|
||||
"starts from rest. At time T=0 I apply a VI step,",
|
||||
"capital VI. And then I want to look at how",
|
||||
"the voltage across the capacitor behaves.",
|
||||
"And we did a bunch of analysis. And at the end of the day,",
|
||||
"in the final demo in the lecture last time I showed you",
|
||||
"that the capacitor would behave like this.",
|
||||
"It would start off at, oops.",
|
||||
"I am sorry. This should be,",
|
||||
"let's assume that started off at VO.",
|
||||
"We get a different equation for zero.",
|
||||
"So let's say the capacitor started off at VO,",
|
||||
"in which case VC at time T=0 is VO as expected.",
|
||||
"And we showed that the output would look something like this.",
|
||||
"After a long period of time this would come up to VI and",
|
||||
"this rise had a time constant of tau=RC.",
|
||||
"So we wrote the equation for this waveform.",
|
||||
"And this is the case when VI is greater than VO.",
|
||||
"I would like you to stare at the circuit and this result here",
|
||||
"to get more intuition on what is going on.",
|
||||
"At time T=0, VC starts off at VO as expected",
|
||||
"because I am telling you that is the case, that is initial",
|
||||
"condition. It starts off at VO.",
|
||||
"Then this one steps to VI. There is no infinite transition",
|
||||
"anywhere here, and so the capacitor holds its",
|
||||
"voltage at VO, at time T=0.",
|
||||
"And then the VI here, which is greater than VO,",
|
||||
"begins to charge the capacitor up, charge it through this",
|
||||
"resistor. And so therefore the capacitor",
|
||||
"charges up. After a long period of time,",
|
||||
"from the basic foundations of capacitors, we know that the",
|
||||
"capacitor appears like a long-term open circuit to DC.",
|
||||
"This is a DC voltage VI. So it appears like an open",
|
||||
"circuit. So after a long period of time",
|
||||
"VI appears at the end. And from here to here I have an",
|
||||
"exponential rise that is typified by an equation of the",
|
||||
"form -t/RC. This kind of waveform rising",
|
||||
"from a smaller value to a higher value is typified by this",
|
||||
"expression. We saw the expression when we",
|
||||
"developed the equations last time.",
|
||||
"On the other hand, if the input was such that VI",
|
||||
"was smaller than VO, so let's say VI was smaller",
|
||||
"than VO then what will happen is that the capacitor voltage would",
|
||||
"start off at VO, because I am telling you that",
|
||||
"is the initial condition, and would then decay in this",
|
||||
"manner to the final value of VI which is the input.",
|
||||
"Instead of going up this way it decays down to the final value",
|
||||
"applied to the circuit. Again, the time constant is RC.",
|
||||
"But this is typified by a form, this is exponential rise and",
|
||||
"this guy e^-t/RC is an exponential decay.",
|
||||
"The key thing to remember is that when you have RC circuits",
|
||||
"of this form, the waveforms that you get are",
|
||||
"either each of the e^-t/RC or 1-e^-t/RC.",
|
||||
"So you can now begin to see how waveforms such as that come",
|
||||
"about. We will do an example and sit",
|
||||
"down and compute the inverter delay.",
|
||||
"And notice that this waveform here is very typical or",
|
||||
"corresponds to this waveform that we see here.",
|
||||
"Here I am starting at VO. And assuming this axis starts",
|
||||
"off at zero, this one starts very close to zero and then",
|
||||
"rises up to some final value. So far I have reviewed some",
|
||||
"material for you that I covered the last time.",
|
||||
"As a second step, I would like to give you a much",
|
||||
"more intuitive approach -- -- that doesn't involve solving",
|
||||
"any differential equations. And the reason I do this is",
|
||||
"that most experienced circuit designers do not sit down and",
|
||||
"write differential equations each time they see an RC",
|
||||
"circuit. When you are starting out and",
|
||||
"you see an RC circuit, you say node method and you",
|
||||
"write the differential equation, but experienced people don't do",
|
||||
"that. They look at it and they can",
|
||||
"sketch the waveform out by inspection.",
|
||||
"And I will show you how to do that.",
|
||||
"It is indeed incredibly simple once I give you some intuition.",
|
||||
"Throughout the rest of this course, I will be showing you",
|
||||
"many such examples where initially I develop the",
|
||||
"foundations of stuff and then show you an intuitive approach",
|
||||
"that very quickly lets you either get the final answer or",
|
||||
"at least sanity check the answer that you have gotten.",
|
||||
"And this is how experienced circuit designers deal with",
|
||||
"stuff. How many people here have seen",
|
||||
"this movie Bend it Like Beckham? So you know this Beckham",
|
||||
"character doesn't think about how he is going to curve the",
|
||||
"ball. He just does it and it happens.",
|
||||
"He doesn't sit down writing differential equations to find",
|
||||
"out the projectile trajectory and all of that stuff.",
|
||||
"You just kind of do it. These series of intuitions I am",
|
||||
"going to give you is going to be in line with the Bend it Like",
|
||||
"Beckham kind of intuition. And this one in particular I",
|
||||
"would like to do in honor of one of your recitation instructions",
|
||||
"Professor David Perreault. And so this piece of intuition",
|
||||
"is going to be termed \"Practice it Like Perreault\".",
|
||||
"Watch what I do with the other names.",
|
||||
"Professor David Perreault is really a world expert in",
|
||||
"designing really incredible power supplies for very,",
|
||||
"very small chips and so on. He doesn't start writing",
|
||||
"differential equations to do this stuff.",
|
||||
"He looks at it and sketches it out.",
|
||||
"Let me show you how he would do this.",
|
||||
"Suppose I have my circuit like before, VI, R and C,",
|
||||
"and I am telling you that VC(0)=VO.",
|
||||
"And my input VI is a step that looks like this.",
|
||||
"VI is a step. How would Professor Perreault",
|
||||
"do this? Let's do it completely by",
|
||||
"intuition. No math here.",
|
||||
"All right. We know that I have told you",
|
||||
"that this guy starts off at VO. I am telling you that.",
|
||||
"You know it is going to start at VO.",
|
||||
"And there is no impulse or huge infinite transition,",
|
||||
"and so the capacitor starts off at VO.",
|
||||
"We also know from basic capacitor properties that after",
|
||||
"a long period of time, in the steady state,",
|
||||
"this is but a DC voltage. If you apply a DC and here is",
|
||||
"my capacitor. After a long period of time",
|
||||
"this guy is going to look like an open circuit.",
|
||||
"It is going to charge up to some value and then is going to",
|
||||
"look like an open circuit. Because if it didn't,",
|
||||
"you would keep charging it and its voltage would keep",
|
||||
"increasing. That doesn't happen,",
|
||||
"it looks like an open circuit. So it looks like an open",
|
||||
"circuit in the long run. The voltage across it must be",
|
||||
"capital VI. If I don't have current flowing",
|
||||
"in the circuit then the only way that can happen is --",
|
||||
"This open circuit. Capital VI appears across the",
|
||||
"capacitor. Well, after a long period of",
|
||||
"time I know that the output must look like this.",
|
||||
"In this case, I have assumed VI is greater",
|
||||
"than VO. So you have two points of your",
|
||||
"curve, VO and VI after a long period of time.",
|
||||
"And, as I told you earlier, with capacitors you get two",
|
||||
"kinds of curves. Two things.",
|
||||
"What you do is go zoop. There you go.",
|
||||
"You're done. And this has an exponential",
|
||||
"rise. This is with the form",
|
||||
"1-e^-t/RC. So we can write an equation for",
|
||||
"that as follows. VC we know has something to do",
|
||||
"with minus t/RC. This is of that form,",
|
||||
"so there has to be that term in there somewhere.",
|
||||
"And I start off with VO. At time T=0 this is one and",
|
||||
"this is one, so this term becomes a zero.",
|
||||
"At time T=0 that becomes a zero so I get VO here.",
|
||||
"I am going to make sure this stuff stays zero at time T=0,",
|
||||
"so I start off with VO. Now, as time wears on what",
|
||||
"happens here? This voltage here,",
|
||||
"VI-VO, if you look at this difference.",
|
||||
"That is exponentially decaying over time.",
|
||||
"And so therefore all I have to do here is write VI-VO.",
|
||||
"There is the answer. I know the form of the curve.",
|
||||
"I am just fitting an expression that meets this form.",
|
||||
"This starts off at VO. When time T=0 this second",
|
||||
"expression is zero and so it is VO.",
|
||||
"And this difference here decays down to zero.",
|
||||
"And this difference here, VI-VO is multiplied by this",
|
||||
"term here and that is what I get.",
|
||||
"And you can confirm this. At time T=0 this is zero.",
|
||||
"At time T infinity this goes to zero, this goes to zero leaving",
|
||||
"a one, and VO and minus VO cancel and I get a VI.",
|
||||
"Virtually any such simple voltage source,",
|
||||
"current source, resistor, capacitor,",
|
||||
"circuit for most inputs like steps and so on can be analyzed",
|
||||
"in this manner. Initial value,",
|
||||
"final value, it's simple.",
|
||||
"And just to show you that this is simple, I am going to label",
|
||||
"this expression this way. It is of the form 1-e^-t/RC.",
|
||||
"Just remember that. Now, by the same token,",
|
||||
"what if VI had been smaller than VO?",
|
||||
"Then that is simple, too.",
|
||||
"I would have had my VI being here.",
|
||||
"VI would have been here. And that is of the form.",
|
||||
"In this particular situation, here is my VI,",
|
||||
"my starting value and I do this.",
|
||||
"And just to label that, let me label that this way.",
|
||||
"I just told you that for RC circuits you go this way or you",
|
||||
"go this way. So it is down here.",
|
||||
"I get some kind of an exponential decay.",
|
||||
"And, like before, think of this one.",
|
||||
"This one has VI as a base value here.",
|
||||
"And the difference between the two is VO minus VI.",
|
||||
"And that difference decays. So I have a VI out here,",
|
||||
"and this difference decays so I get VO-VI and that decays in",
|
||||
"this form. So I get an exponential decay",
|
||||
"of this difference here. Just stare at it for a while",
|
||||
"longer. You should be able to just go",
|
||||
"and knock it off like this, just like Professor Perreault",
|
||||
"would. No differential equations.",
|
||||
"Just write it down by looking at the curve.",
|
||||
"Let's keep these two in mind, OK, these forms?",
|
||||
"One is the 1-e^-t/RC form and the e^-t/RC.",
|
||||
"Both have a time constant RC. Let me just make this a dashed",
|
||||
"line just to be on the safe side here.",
|
||||
"",
|
||||
"That is our first piece of intuition.",
|
||||
"And, as I pointed out before, in problems you face in life or",
|
||||
"in ones that we give you, feel free to use the intuitive",
|
||||
"method. Or what you can do is apply the",
|
||||
"mathematical method and then check your answer by using your",
|
||||
"intuition. What I would like to do next is",
|
||||
"apply what you have learned so far to figure out what we set",
|
||||
"out to figure out, which is the delay of my",
|
||||
"inverter. I had promised you that by the",
|
||||
"end of this lecture I was going to close the loop on that little",
|
||||
"demo. I was going to close the loop",
|
||||
"for you on this little circuit that we had looked at,",
|
||||
"one inverter driving another inverter.",
|
||||
"This was A, this was inverter X, and this was my node B.",
|
||||
"The green curve you see out there, the middle one has a",
|
||||
"transition shown up there. And what I am going to do next",
|
||||
"is use the results we have gotten so far to compute a",
|
||||
"number. We are going to compute a delay",
|
||||
"number both for a rising transition.",
|
||||
"We will call that delay DR for rising transition.",
|
||||
"And we will compute a delay for the falling transition DF.",
|
||||
"Remember, that this is the input that falls down sharply.",
|
||||
"The intermediate node B rises much more slowly.",
|
||||
"And because this rises much more slowly this guy here falls",
|
||||
"a little after this transition here, and so there is a delay.",
|
||||
"And I am going to apply what we have learned so far and do an",
|
||||
"example for you and figure out what that delay is.",
|
||||
"This is an absolute foundational calculation done in",
|
||||
"building digital circuits all the time.",
|
||||
"It is remarkable that something so simple is used in designing",
|
||||
"even the most complex of circuits to obtain very quick",
|
||||
"ideas of what my delay will look like when I have some subcircuit",
|
||||
"driving some other piece of subcircuit.",
|
||||
"Let me just draw a few equivalent circuits for you.",
|
||||
"The internal circuit looks like this.",
|
||||
"",
|
||||
"This is my inverter X, A, my node B.",
|
||||
"And notice that I have this capacitor CGS.",
|
||||
"Since I am interested in this node, let me show you that,",
|
||||
"this capacitor explicitly, it is because of this capacitor",
|
||||
"here that arises because of this MOSFET here between the gate and",
|
||||
"the source. And that capacitor gives rise",
|
||||
"to this RC thing that we are seeing.",
|
||||
"This is RL, this is RL, VS, VS.",
|
||||
"And let's say, just as up there,",
|
||||
"at time T=0 I get a transition like so, a falling transition",
|
||||
"from say 5 volts to 0 volts at the node A.",
|
||||
"This is VA here. That is shown up there.",
|
||||
"And VB --",
|
||||
"",
|
||||
"We had expected that VB would look like this.",
|
||||
"We expected VB to be instantaneous and looking like",
|
||||
"that, but instead because of the capacitor VB looks like this.",
|
||||
"And remember, again, this is of the form",
|
||||
"1-e^-t/RC. And we will write down the",
|
||||
"answers by inspection. From this let me draw the",
|
||||
"connection to circuit delay by showing you another little graph",
|
||||
"here t, VB, zero. And what I am going to show",
|
||||
"you, this is 5 volts. And so the output goes like",
|
||||
"this from close to zero to 5 volts.",
|
||||
"It is close to zero. Because, at least with the",
|
||||
"inverters we have been seeing in lab and so on,",
|
||||
"the RON for the inverter is very, very small compared RL.",
|
||||
"So it is virtually zero down here.",
|
||||
"And so what is the delay? I mentioned there are two",
|
||||
"delays of interest. One is the rising delay.",
|
||||
"That is the logical value at the end, if I wait a long enough",
|
||||
"period of time, is a logical one.",
|
||||
"Delay is simply defined as starting from here how long does",
|
||||
"this output take to get to a valid one?",
|
||||
"At what voltage here can I say that this transition corresponds",
|
||||
"to a logical one? At what voltage here can I say",
|
||||
"that that represents a valid one?",
|
||||
"Any ideas? Yes.",
|
||||
"It depends on the discipline, bingo.",
|
||||
"So it depends on the discipline.",
|
||||
"Now let's get more specific. Since it depends on the",
|
||||
"discipline, at what value based on something in the discipline",
|
||||
"can I say this thing is a logical one?",
|
||||
"This is an output remember. VOH, bingo.",
|
||||
"There is some VOH somewhere. And it takes some amount of",
|
||||
"time to get to a valid logical one output, ergo there is your",
|
||||
"delay. This is tR.",
|
||||
"And I call this the rising delay of the inverter X.",
|
||||
"It is interesting that the rising delay of inverter X,",
|
||||
"based on our model, depends on the parameters of",
|
||||
"this inverter and the parameters of whatever it is driving.",
|
||||
"So remember that the delay is not necessarily just the",
|
||||
"property of the inverter itself, but it depends on the context.",
|
||||
"If I stick my inverter before another inverter like this,",
|
||||
"it is the capacitance on that inverter by our model that tells",
|
||||
"me what the delay is going to look like, of course in addition",
|
||||
"to RL. And we will do the math in a",
|
||||
"few seconds. By the same token,",
|
||||
"if I had this wire connecting not to one inverter but going to",
|
||||
"ten other inverters, I expect to have a capacitance",
|
||||
"equal to ten times CGS. And so therefore this thing",
|
||||
"should rise even more slowly, correct?",
|
||||
"The more capacitance on here the slower it rises up.",
|
||||
"Simple. If I put more and more load on",
|
||||
"this line by putting more and more MOSFETs on that line,",
|
||||
"more and more inverters this will rise slower.",
|
||||
"In our example I just have one, so let's go ahead and compute",
|
||||
"the delay. This is called the rising delay",
|
||||
"of X. That says that for this node",
|
||||
"here to go from its output value to a valid one,",
|
||||
"which is VOH how long does it take?",
|
||||
"Notice that if this capacitor was zero then you would have",
|
||||
"seen an instantaneous transition.",
|
||||
"If you have an instantaneous transition then notice that the",
|
||||
"rising delay was zero. That was the model we had",
|
||||
"looked at up until learning about capacitors.",
|
||||
"So let's go ahead and compute the number.",
|
||||
"I can draw an equivalent circuit for computing a rising",
|
||||
"delay. The equivalent circuit for the",
|
||||
"rising delay looks like the following.",
|
||||
"The VS voltage source, with a resistor RL and a",
|
||||
"capacitor CGS, because when I turn this guy",
|
||||
"off, this guy has gone off, and so as far as the rise time",
|
||||
"of this node is concerned I can look at this circuit,",
|
||||
"ground through CGS through RL through VS back to ground.",
|
||||
"And just for simplicity, let me draw this in a form that",
|
||||
"we understand.",
|
||||
"",
|
||||
"CGS. Let me use this as my ground",
|
||||
"node. And this is the voltage VB.",
|
||||
"And this is RL. And V is simply VS once that",
|
||||
"transition happens. My other equations here,",
|
||||
"VI=VS. And what is VB(0)?",
|
||||
"VB(0) is at what value does this node start out?",
|
||||
"Notice that for simplicity here if this RON is much,",
|
||||
"much smaller than RL, then this node would be very",
|
||||
"close to ground. So I will just go ahead and say",
|
||||
"that VB at T=0 is approximately zero.",
|
||||
"And then what I want to find out is what does the value look",
|
||||
"like for time starting from zero and then going forward?",
|
||||
"Well, we have become experts at this now.",
|
||||
"",
|
||||
"Let's do the intuition here. Start off with zero.",
|
||||
"That's good. Because my initial value is",
|
||||
"zero, I start off here. What is the final value?",
|
||||
"After a long time, since this is a DC voltage,",
|
||||
"what would be the value at VB after a long time?",
|
||||
"Pardon? VS.",
|
||||
"If I wait long enough then it is going to be at VS.",
|
||||
"This is greater than the initial value,",
|
||||
"so we're done. That is my 1-e^-t/RC form.",
|
||||
"It took me three seconds there. It's pretty cool.",
|
||||
"We could add the expression for this.",
|
||||
"And the expression was I take my starting value,",
|
||||
"which is zero, and I add to that this",
|
||||
"difference VS and I multiply that by this form.",
|
||||
"There we go. And remember I get this from",
|
||||
"that rising form up here. V0=0, this is zero,",
|
||||
"so it is simply VI times that, and VI=VS.",
|
||||
"I really would like you to get this intuition.",
|
||||
"If I had two choices, one is that you understand the",
|
||||
"intuition and are able to sketch that versus in your sleep be",
|
||||
"able to solve the differential equation and get to the answer.",
|
||||
"I would much rather you get the intuition, if it is one or the",
|
||||
"other. It is very simple.",
|
||||
"Start off at zero, I go chuck, and boom,",
|
||||
"I get to VS and this is my 1-e^-t/RC form.",
|
||||
"I need to compute tR. And tR is the time that this",
|
||||
"takes to get to VOH.",
|
||||
"",
|
||||
"For what value of time, for what T, does VB reach VOH?",
|
||||
"I want to find tR. What's tR?",
|
||||
"From that equation, that simply tells me the",
|
||||
"trajectory of VB as a function of time.",
|
||||
"And so I need to find out what is T for which VB is VOH?",
|
||||
"I write VOH=VS (1-e^-t/RC). So after a rise time my output",
|
||||
"is going to be VOH. And so let me go ahead and find",
|
||||
"tR. Let's see.",
|
||||
"I bring this to this left-hand side and divide VOH by VS,",
|
||||
"and then I move things around and what I end up getting is",
|
||||
"-tR/RC and on the other side I get ln(1-VOH/VS).",
|
||||
"Divide VOH by VS, that is this,",
|
||||
"move this to the other side, and move e^-t/RC to this side.",
|
||||
"And take logarithms on both sides.",
|
||||
"This is what I get. tR is therefore -RLCGS",
|
||||
"ln(1-VOH/VS). That is my rise time.",
|
||||
"You can just do this by inspection.",
|
||||
"It is just so awfully simple. Just to give to some intuition",
|
||||
"with numbers and so on. Let's say that RL=1K,",
|
||||
"VS=5 volts, VOH=4 volts, CGS=0.1 pF.",
|
||||
"This happens so often that we often time call it \"puff\".",
|
||||
"0.1 puff. It is pF, it's called puff.",
|
||||
"If it is nF, I don't know why they didn't",
|
||||
"call it \"nuff\". They just call it nanofarads.",
|
||||
"TR for these numbers gets to be one times ten to the three times",
|
||||
"point one times ten to the minus twelve for pico-farads",
|
||||
"ln(1-4/5). And if you do the math you get",
|
||||
"this down to 0.16 nanoseconds. This means that if I had an",
|
||||
"inverter like that droving another inverter then my output",
|
||||
"transition would be delayed by 0.16 nanoseconds.",
|
||||
"Trust me, when Intel builds microprocessors or when Broadcom",
|
||||
"builds its cable modem chips, they have to do this one way or",
|
||||
"the other using a computer tool or by hand for virtually every",
|
||||
"little subcircuit in their chip. That is how you get the delays",
|
||||
"or some approximation thereof. What I want you also to do is,",
|
||||
"for no particular reason, I will just compute for you the",
|
||||
"following quantity RLCGS. The time constant of that",
|
||||
"circuit for no reason at all. I am just going to compute it",
|
||||
"and stick it here. And RLCGS 1 K times 1 pF is",
|
||||
"simply 0.1 nanoseconds. I am just writing it and",
|
||||
"sticking it there for no particular reason.",
|
||||
"The next step let's do the falling delay,",
|
||||
"DF. That is the rising delay.",
|
||||
"And, although I didn't show this to you in the demo,",
|
||||
"there is a corresponding delay of the fall time.",
|
||||
"It doesn't fall instantly, but rather it falls rather",
|
||||
"slowly. Let's draw the equivalent",
|
||||
"circuit for when the node X falls.",
|
||||
"Notice that in my inverters here, this node starts off being",
|
||||
"at VS. This is high.",
|
||||
"And this is going to fall because when I turn this",
|
||||
"transistor on it is going to pull this node to ground or it",
|
||||
"is going to fall down. And what is the equivalent",
|
||||
"circuit? The equivalent circuit is that",
|
||||
"ground through capacitor to this node.",
|
||||
"At this node I have RON connecting to ground and I have",
|
||||
"RL connecting to ground through VS.",
|
||||
"Let me draw that little circuit for you.",
|
||||
"Remember life begins and ends on storage elements,",
|
||||
"so I will draw them first. My storage element CGS.",
|
||||
"That is VB. And, as I said,",
|
||||
"this is node X, it goes from RON to ground,",
|
||||
"and it also goes through RL through VS to ground.",
|
||||
"And in this particular situation VB of zero for the",
|
||||
"following delay, VB starts off at VS so VB of",
|
||||
"zero is VS. And the final output I am not",
|
||||
"sure yet. What is the final value of the",
|
||||
"voltage at this node? I don't know that yet.",
|
||||
"I need to compute that. So what I will do is whenever",
|
||||
"you see something like this, a capacitor connecting to",
|
||||
"linear stuff, or a nonlinear element",
|
||||
"connecting to linear stuff. For no apparent reason you",
|
||||
"should at least think about what?",
|
||||
"Think Thevenin, exactly.",
|
||||
"And then see if you can use the Thevenin method to simplify your",
|
||||
"life. Capacitor, a bunch of stuff",
|
||||
"here, I need to find out the initial value.",
|
||||
"Oh, I know that. That is VS.",
|
||||
"Done. I need to find the final value",
|
||||
"using my intuitive method. For the final value,",
|
||||
"I could do it just by looking at this, but I wanted to throw",
|
||||
"in Thevenin. Hey, let me try to the Thevenin",
|
||||
"equivalent and see if that makes my life any easier.",
|
||||
"VTH. The Thevenin method says that",
|
||||
"you can replace this circuit here with a Thevenin equivalent",
|
||||
"of the sort for the purpose of determining what happens at this",
|
||||
"node given that that is linear.",
|
||||
"",
|
||||
"So I need to find out that for the purpose of determining what",
|
||||
"happens at the node X. I have to replace this with its",
|
||||
"Thevenin equivalent. And I now need to find out RTH",
|
||||
"and VTH. So I get RTH by looking in",
|
||||
"here, shorting this guy and looking at the resistance.",
|
||||
"So I look in like this, then I short this guy here and",
|
||||
"I get RL in parallel with RON because this one shorts to",
|
||||
"ground. So RTH is simply RL in parallel",
|
||||
"with RON. This is a convenient notation",
|
||||
"for RL being in parallel with RON.",
|
||||
"And you all know the value of that.",
|
||||
"It is another one of our very simple patterns like voltage",
|
||||
"divider and so on. Resistances in parallel can be",
|
||||
"computed as RL RON divided by RL plus RON.",
|
||||
"What is VTH? VTH is the open circuit voltage",
|
||||
"here. If I take out this capacitor,",
|
||||
"I want to find out what the voltage here is.",
|
||||
"Ah-ha, voltage divider. VS, the voltage divider here,",
|
||||
"RL and RON. I could write this down as VS",
|
||||
"times RON/(RL+RON). Remember you will see again and",
|
||||
"again and again and again in 6.002 or any circuit stuff that",
|
||||
"you do, you will see them all over Thevenin.",
|
||||
"Voltage dividers, current dividers,",
|
||||
"resistances in series, resistances in parallel,",
|
||||
"RC thing-a-ma-jigs like this. So if you just remember those",
|
||||
"10 to 15 intuitive patterns then you are pretty much set for",
|
||||
"life. It just comes on again and",
|
||||
"again and again. Parallel resistors.",
|
||||
"Voltage dividers. You should be able to write",
|
||||
"down a voltage divider in your sleep.",
|
||||
"So this is what I have. Let me now write down",
|
||||
"intuitively what I expect the node X to do just by inspection.",
|
||||
"Let's see. What is the initial value of",
|
||||
"the voltage across the capacitor, intuitive method?",
|
||||
"This is how Professor Perreault would do it, remember?",
|
||||
"He would start off by saying ah-ha, initial value is VS",
|
||||
"because I am told it is VS. I start off with VS.",
|
||||
"And so I start off here. What is the value after a long,",
|
||||
"long time based on this circuit here?",
|
||||
"V Thevenin. After a long time this is a DC",
|
||||
"voltage because that is a DC voltage.",
|
||||
"The capacitor looks like an open circuit after a long time.",
|
||||
"And VTH appears there so it is simply V Thevenin.",
|
||||
"",
|
||||
"And then when you see those two, boy, I love doing this,",
|
||||
"you go like this. That is the coolest part.",
|
||||
"And then I am done. It is so simple.",
|
||||
"Three seconds or less, I am able to tell you what the",
|
||||
"delay of an inverter is purely by intuition,",
|
||||
"completely intuitively. I mean I haven't done any",
|
||||
"solving. It is just by observation.",
|
||||
"Took this circuit, made my life easy,",
|
||||
"Thevenin, looked at RTH, VTH and then sketched it by",
|
||||
"inspection. Again, if you find that things",
|
||||
"are really, really, really simple don't be",
|
||||
"surprised. Once you get some conceptual",
|
||||
"understanding things are indeed very simple.",
|
||||
"You can eliminate a lot of math just by staring at things",
|
||||
"attempting to build up the intuition.",
|
||||
"As a next step what I can do is write down the expression for",
|
||||
"VB. And I write down the expression",
|
||||
"from a falling transition. How do I do it?",
|
||||
"What was it? What is the method?",
|
||||
"I take the lowest value of interest here.",
|
||||
"That is VTH. And then I add to that this",
|
||||
"difference decaying exponentially.",
|
||||
"And that difference is simply VS-VTH.",
|
||||
"And that decays exponentially. This form is the e^-t/RC form.",
|
||||
"And, boom, I am done. Many of you are wondering,",
|
||||
"Professor Agarwal, if life was so simple,",
|
||||
"why on earth did you have us mess around with those",
|
||||
"differential equations to get here?",
|
||||
"You show us differential equations and then you don't use",
|
||||
"them anymore. Well, that is a good question.",
|
||||
"The answer to that is that you need to understand the",
|
||||
"foundations. Once you understand the",
|
||||
"foundations you can find simplifying techniques to get to",
|
||||
"where you need to be, but you need to understand the",
|
||||
"foundations. You need to at least see why",
|
||||
"things are the way they are at least once.",
|
||||
"Understand the foundations and then find intuitive ways of",
|
||||
"getting your answers. So now my falling delay here",
|
||||
"is, I start off with VOS and I need to get all the way down to",
|
||||
"what value to compute. At some point here,",
|
||||
"this is a valid one, at some point VB becomes a",
|
||||
"valid zero for the output. And that is when I stop my tF",
|
||||
"block. What is the value here for this",
|
||||
"to be a valid zero? Don't all yell at once.",
|
||||
"VOL. I simply had to figure out what",
|
||||
"is the value of time, this is Page 7,",
|
||||
"for which this expression decays down to VOL.",
|
||||
"So it is VTH+(VS-VTH) e^-tF/RC. Then I simplify this.",
|
||||
"How do I do that? VOL-VTH.",
|
||||
"Then I divide that by VS-VTH. So VOL-VTH.",
|
||||
"Divide that by VS-VTH. Take logarithms on both sides",
|
||||
"and then multiply by RC. So I get tF is -RC log of that.",
|
||||
"This is R Thevenin and this is CGS.",
|
||||
"How did I get this? VOL-VTH divided by VS-VTH.",
|
||||
"Take logs on both sides. And then multiply throughout by",
|
||||
"-1/-RC and I get my tF. Done.",
|
||||
"Let's do it for the same set numbers, just that we add an RON",
|
||||
"of 10 ohms. I will do this for RON of 10",
|
||||
"ohms and compute the value for you.",
|
||||
"tF=-RTH. RTH is RON parallel RL.",
|
||||
"This is 10 ohms. That is 1K.",
|
||||
"So 10 ohms in parallel with 1K is approximately 10 ohms.",
|
||||
"So let me just use approximately 10 ohms.",
|
||||
"1 pF, that is RC times ln of VOL.",
|
||||
"Oh, I need to give you a VOL. Let's say my discipline has VOL",
|
||||
"being 1 volt. And so therefore I end up",
|
||||
"getting a VOL-VTH divided by VS-VTH.",
|
||||
"Since RON is much, much, much smaller than RL,",
|
||||
"since RON is 10 ohms and this is 1K, most of VS will drop",
|
||||
"across RL. This is a hundred times",
|
||||
"smaller. Compared to VOL,",
|
||||
"which is 1 volt, VTH is very,",
|
||||
"very small. VTH will be on the order of",
|
||||
"0.05, and so therefore I simply write down VOL here and say VTH",
|
||||
"is approximately zero, and I get VS-VTH.",
|
||||
"This is approximately 5. So let me just say this is",
|
||||
"approximately. And if you do it you will get",
|
||||
"1.6 pico-seconds. Again, just for fun,",
|
||||
"let me write the corresponding RC time constant for the",
|
||||
"circuit, which is RTHCGS. So RTH is approximately 10 ohms",
|
||||
"and CGS is 1 pF, so this is 1 picosecond.",
|
||||
"",
|
||||
"Now you will understand why I have been writing this time",
|
||||
"constant down. It turns out that the time",
|
||||
"constant is a very, very important number.",
|
||||
"So you see an RC circuit, and you compute its time",
|
||||
"constant for an RLC connection like this, it is the series",
|
||||
"resistance times the capacitor. The time constant is a very",
|
||||
"important number. And usually the circuit delays",
|
||||
"are in the neighborhood of the time constant value.",
|
||||
"In this case this is 1 pS. That is 1.6 pS.",
|
||||
"And in this case we had 0.1 nS and 0.16 nS.",
|
||||
"So the time constant itself is a good indicator of what your",
|
||||
"delays are going to be like. If you have no time,",
|
||||
"you are sloshing your cereal down in the morning and you need",
|
||||
"to know how long the delay of the inverter very quickly,",
|
||||
"you have three seconds. Just do the RC and that is a",
|
||||
"good first approximation. What I would like to do next in",
|
||||
"the last three or four minutes is set up a little demo for you",
|
||||
"for your recitation, and then your recitation will",
|
||||
"cover it.",
|
||||
"",
|
||||
"This is a true story. This really,",
|
||||
"really happened. In this West Coast school,",
|
||||
"which shall remain nameless, they had a chip,",
|
||||
"they built a chip. And the chip had a bunch of",
|
||||
"pins, as you might imagine. And the pin,",
|
||||
"as you have a trace on a board, a wire on a board there are",
|
||||
"some capacitance attached to wires, between the wire and",
|
||||
"ground. And that is a capacitor.",
|
||||
"And they just called it a load capacitance.",
|
||||
"It could have been 0.1 pF or 0.01 pF or something like that.",
|
||||
"What they found when they built this chip --",
|
||||
"What they found was that the voltage here they expected to",
|
||||
"look like this, this computer science",
|
||||
"abstraction and so on, zero to one transition,",
|
||||
"boom, it should look like this. But for the reasons we saw",
|
||||
"today the observed transition was much slower and looked like",
|
||||
"this. So the students said ah-ha,",
|
||||
"let's speed up this chip. We can speed up the chip by",
|
||||
"looking at the RL and RON of my driving inverters.",
|
||||
"And if I make RL small -- Notice if I make RL small my",
|
||||
"delay is small. If I make RON small my falling",
|
||||
"delay is small. So let's make really small RLs",
|
||||
"and RONs and let's all have fun. Unfortunately,",
|
||||
"what they observed was that by making RL and RON both small,",
|
||||
"the RC time constant small they expected to see a much sharper",
|
||||
"rise time. And this was the original.",
|
||||
"But what really happened was -- They expected this to get",
|
||||
"faster and kind of look like this, but what happened was",
|
||||
"disaster struck. What they observed was",
|
||||
"something like that. This is a real-life story.",
|
||||
"And so instead of getting something like this they go",
|
||||
"something like this. And why is that a problem?",
|
||||
"That is a problem because notice when I expect to be at a",
|
||||
"zero, I got some spikes that went higher than VIL into the",
|
||||
"forbidden region and did bad things to me.",
|
||||
"So let me show you a little demo and show you that that's",
|
||||
"exactly how the circuit is behaving.",
|
||||
"",
|
||||
"Notice that this is what I expect but this is what I see.",
|
||||
"Look at the purple curve here. Notice these spikes that are",
|
||||
"showing up there. This is true.",
|
||||
"They saw it happen. And why is this happening?",
|
||||
"It turns out that what was happening was that the two pins",
|
||||
"were next to each other. And I will show you a little",
|
||||
"demonstration here. Let's see if you can figure out",
|
||||
"why this was happening. Think of these as two pins and",
|
||||
"the pins are close together. I am just modeling the two pins",
|
||||
"with a role of wire. And what I am going to do is --",
|
||||
"",
|
||||
"I am going to separate the wires and keep them far apart.",
|
||||
"It is like keeping my pins far apart.",
|
||||
"Hey, guess what happened? Those nasty spikes went away.",
|
||||
"But then I cannot keep my pins 1 meter apart on a chip.",
|
||||
"Your laptops are going to look 20 yards long.",
|
||||
"You want the pins to be very close to each other so that you",
|
||||
"can have many pins on chips and therefore have very small",
|
||||
"systems. But then look,",
|
||||
"I get the spikes. Any idea why that is happening?",
|
||||
"Why is that when the pins are close together I get those",
|
||||
"spikes? Any ideas?",
|
||||
"Somewhat? We just learned about",
|
||||
"capacitors, so this must have to do with capacitors.",
|
||||
"There is this parasitic capacitor between the pins,",
|
||||
"exactly. Here is what is happening.",
|
||||
"Here is what I expect. I expect a nice square wave at",
|
||||
"the output. But instead I have a pin next",
|
||||
"to me. And I have a faster wave form",
|
||||
"driving it. And so therefore there is a",
|
||||
"parasitic capacitor here. And because of that I get",
|
||||
"something called \"crosstalk\". And the model for crosstalk is",
|
||||
"some resultant resistance with the parasitic capacitor and I",
|
||||
"get those spikes. And the 6.002 experts saw the",
|
||||
"solution. They said how do we fix this",
|
||||
"problem? 6.002 experts said the way we",
|
||||
"fix this problem if it is slow it may be better.",
|
||||
"Instead of having sharp transitions let me drive it with",
|
||||
"slower transitions. Let's switch to the demo again.",
|
||||
"You will see this in recitation, but I will show you",
|
||||
"the demo very quickly. I have a sharp transition of",
|
||||
"the input, which is that yellow thing out there.",
|
||||
"I am going to make the transition slower.",
|
||||
"Switch to a triangular wave. And you will notice the spikes",
|
||||
"go away. Oh, no.",
|
||||
"That is the wrong one. The other one.",
|
||||
"There you go. The moment I switch to a slower",
|
||||
"transition boom, the spikes go away.",
|
||||
"You want to switch back to square?",
|
||||
"There you go. The 6.002 experts saw the",
|
||||
"solution. Slower transitions.",
|
||||
"And you will do this example in detail in Section tomorrow.",
|
||||
"Thank you."
|
||||
]
|
||||
}
|
||||
@@ -1,2222 +0,0 @@
|
||||
{
|
||||
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"text": [
|
||||
"",
|
||||
"All right. Good morning all.",
|
||||
"Today we embark on another new chapter in what we do.",
|
||||
"And the topic is going to be --",
|
||||
"",
|
||||
"We will talk about this thing called an Operational Amplifier.",
|
||||
"Before I get into the lecture, I want to point out a couple of",
|
||||
"things. One is that you are going to",
|
||||
"hear about two big words in today's lecture.",
|
||||
"Two big and incredibly important words.",
|
||||
"And I want to mention those words to you right now so that",
|
||||
"when I come to them in lecture you can say OK,",
|
||||
"I better pay really close attention, these are important",
|
||||
"words. All right.",
|
||||
"One of them is abstraction. The second one is feedback.",
|
||||
"Two incredibly important concepts.",
|
||||
"Abstraction, you have been seeing a couple",
|
||||
"times during this course, once in the beginning where we",
|
||||
"abstracted out Maxwell's equations by focusing on a",
|
||||
"smaller playground and simply using KVL, KCL in place of those",
|
||||
"equations. A big abstraction.",
|
||||
"It turns out that almost all of EECS is based upon abstractions",
|
||||
"at various levels. In the first lecture,",
|
||||
"I also showed you the layer upon layer of abstraction that",
|
||||
"we built to be able to build interesting systems.",
|
||||
"The second big thing is feedback.",
|
||||
"And I am going to relate this to anti-lock breaks in cars.",
|
||||
"And so, you can wait and see how we do that.",
|
||||
"It's an incredibly important concept.",
|
||||
"Before we dive into the amplifier abstraction,",
|
||||
"let me first talk about something that you know.",
|
||||
"Start with something that you know and then lead up into the",
|
||||
"operational amplifier and its circuits.",
|
||||
"You know about the MOSFET amplifier.",
|
||||
"",
|
||||
"The MOSFET amplifier that you know about looked like this.",
|
||||
"It was based on a MOSFET.",
|
||||
"",
|
||||
"There was a VS supply. There was a vI input,",
|
||||
"a vO output and, as I said, a VS supply.",
|
||||
"So, this was a MOSFET circuit that you've seen before.",
|
||||
"One way of viewing this is that this circuit has three major",
|
||||
"ports. This here is the input port",
|
||||
"with voltage vI. This here, between the drain",
|
||||
"terminal and the ground, is the output port.",
|
||||
"I take the output between the drain terminal and ground.",
|
||||
"And, finally, we have a third port,",
|
||||
"which is this one. It is called the power port.",
|
||||
"I apply VS between this terminal here and the ground",
|
||||
"terminal. And that gives us the power",
|
||||
"port. This device here was a three",
|
||||
"port device. Input port or control port,",
|
||||
"output port and a power port. And so we looked at the circuit",
|
||||
"and did a whole bunch of analyses of it.",
|
||||
"Then what I can do at this point, now that you've seen",
|
||||
"this, it's often times interesting to think about",
|
||||
"abstracting this out into some kind of a building block.",
|
||||
"Much like in software, you write a procedure and you",
|
||||
"abstract out the internal details of the procedure in the",
|
||||
"procedure declaration and in the call that you make.",
|
||||
"In the same way, we can take this little device",
|
||||
"here and abstract that out into the following abstraction.",
|
||||
"",
|
||||
"We could abstract that out as a device that looks like this.",
|
||||
"",
|
||||
"I have my input port, I have my output port and I",
|
||||
"have my power port. So, I can apply VS here.",
|
||||
"Notice that I've taken these six terminals here,",
|
||||
"one, two, three, four, five and six,",
|
||||
"and put a box around it. And just exposed the terminals",
|
||||
"to you. And I need to tell you a little",
|
||||
"bit more about the internal properties, but suffice it to",
|
||||
"say that you can begin working with this little block.",
|
||||
"An even simpler version of this for many applications might just",
|
||||
"look like this, vI and vO where there is a",
|
||||
"ground that is shared among them that is implicit in this",
|
||||
"picture. And vI and vO can simply be the",
|
||||
"node voltages at these nodes. This is a progressively more",
|
||||
"abstract representation of this amplifier.",
|
||||
"What we can do is, provided we know,",
|
||||
"we can abstract out the relevant properties of this",
|
||||
"block and expose them outside. And the relevant properties",
|
||||
"might well be that, let's say here the properties",
|
||||
"may be that I in is always zero. I can also express to you the",
|
||||
"gain of this amplifier. I may also be able to tell you",
|
||||
"the Thevenin equivalent for the output.",
|
||||
"There are some properties that I can give you that will let you",
|
||||
"use this building block abstractly.",
|
||||
"Today, what we will do is introduce a powerful abstraction",
|
||||
"of a type of amplifier. This is called the operational",
|
||||
"amplifier or \"op amp\" for short. What I am going to do is give",
|
||||
"you a slightly more involved building block than the one I",
|
||||
"have shown you there. But suffice it to say that the",
|
||||
"idea is going to be the same. This building block looks like",
|
||||
"this. This building block has an",
|
||||
"input port. This building block also has a",
|
||||
"port in which to connect power or the power port.",
|
||||
"And the way I am going to connect power,",
|
||||
"I am going to connect a plus VS supply here.",
|
||||
"That is going to be my ground node.",
|
||||
"And I am going to connect a minus VS supply to this node",
|
||||
"here. So, these voltages are both VS.",
|
||||
"I want to apply a plus VS here and a negative VS out here.",
|
||||
"And I am going to take the output between the ground node",
|
||||
"and the output node of the operational amplifier and call",
|
||||
"that a vO. This is the output port.",
|
||||
"So, input port and output port and a power port.",
|
||||
"Think of this as a pattern where I have an input port",
|
||||
"across which I connect the input.",
|
||||
"I have a power port across which I connect a plus VS,",
|
||||
"minus VS supply, and then I take the output",
|
||||
"terminal and take a ground terminal, which is defined by",
|
||||
"external components of my circuitry, and use this as my",
|
||||
"reference node. Remember ground is just a",
|
||||
"reference node. I am going to use this as a",
|
||||
"reference node. These two are equal in",
|
||||
"magnitude. And take this as my output.",
|
||||
"And when I do something like this, I can build an even",
|
||||
"simpler, so this is an abstract differential input amplifier.",
|
||||
"In other words, this amplifier is going to",
|
||||
"amplify whatever I apply at the input.",
|
||||
"A slightly more abstract representation of this looks",
|
||||
"like this. vOUT and plus/minus vIN.",
|
||||
"This is a slightly more abstract representation where,",
|
||||
"remember, we are going to draw this again and again,",
|
||||
"maybe at least 38 or 39 times in this course.",
|
||||
"And, remember, each time you draw it,",
|
||||
"remember that there is an implicit power port,",
|
||||
"a plus/minus supply that is connected which we don't show.",
|
||||
"And I remember when I first learned about it a long time ago",
|
||||
"there was a confusion in me initially.",
|
||||
"How does this work? Where is the power coming from?",
|
||||
"Just remember that power comes from a plus/minus supply,",
|
||||
"and we just don't show that in this abstraction.",
|
||||
"Now, the details, a lot of details are in Chapter",
|
||||
"16 of your course notes. That's the reading for that.",
|
||||
"The other thing is that there are some other key properties of",
|
||||
"this amplifier. And let me discuss those very",
|
||||
"quickly. First of all,",
|
||||
"I can draw a circuit model for the amplifier.",
|
||||
"Make some room for myself here. And this is a circuit model for",
|
||||
"what we call the ideal operational amplifier.",
|
||||
"And the circuit model is going to look like this.",
|
||||
"This is an abstract device. And, in terms of analyzing how",
|
||||
"this behaves in a circuit, I am going to show you this",
|
||||
"abstract circuit that looks as follows.",
|
||||
"Some input v is applied at these two terminals here.",
|
||||
"And this terminal is called my v plus terminal and this is",
|
||||
"called my v minus terminal, so this corresponds to these",
|
||||
"two terminals. I am telling you that the",
|
||||
"current going in is going to be zero, so i plus is going to be",
|
||||
"zero and i minus is going to be zero.",
|
||||
"i plus is the current in here and i minus is the current into",
|
||||
"the v minus terminal, and both these currents are",
|
||||
"going to be zero in this device here.",
|
||||
"The output is going to look like this.",
|
||||
"Let me just call it vOUT to be consistent with this here.",
|
||||
"And taken with ground as my reference.",
|
||||
"The output is simply Av. In other words,",
|
||||
"what I am doing is I am going to model this as a device that",
|
||||
"has a dependent source at its output.",
|
||||
"And the dependent source here is a voltage controlled voltage",
|
||||
"source. It is a dependent source,",
|
||||
"it is a voltage controlled voltage source such that the",
|
||||
"output voltage is A times the voltage v across its input.",
|
||||
"This is actually very simple. Think of these three terminals",
|
||||
"I have shown you here. I applied input across these.",
|
||||
"And the output is going to be A times whatever I applied.",
|
||||
"And A is going to tend towards infinity.",
|
||||
"A is going to be huge. And specific values for A might",
|
||||
"be a hundred thousand or a million or things of that sort.",
|
||||
"Huge A in this abstract amplifier.",
|
||||
"In addition to that, the other properties are that",
|
||||
"it is going to have infinite input resistance.",
|
||||
"That means looking in this looks like an open circuit.",
|
||||
"The fact that this is open here implies the infinite input",
|
||||
"resistance across this port. What about the output here?",
|
||||
"Remember, this is a voltage source.",
|
||||
"And we have a zero output resistance, which means that no",
|
||||
"matter how the load affects this, as I apply a load this is",
|
||||
"going to behave like an ideal voltage source and keep holding",
|
||||
"the voltage constant based on whatever the function I",
|
||||
"establish here. And A is virtually infinite.",
|
||||
"Let me pause there for a few seconds and just dwell on this",
|
||||
"so you just understand what the basic device is.",
|
||||
"Following this basic definition, I am just going to",
|
||||
"build a whole bunch of fun little circuits.",
|
||||
"The analysis will be pretty straightforward,",
|
||||
"but this is a big conceptual leap here where there is some",
|
||||
"circuitry inside. Containing resistors,",
|
||||
"MOSFETs, a whole bunch of stuff in there.",
|
||||
"I am not telling you what is inside it.",
|
||||
"Much like I could build an abstract amplifier,",
|
||||
"I could put an abstract box around the amplifier you saw",
|
||||
"earlier, I want to put a box around some circuitry.",
|
||||
"I am not telling you what the circuitry is.",
|
||||
"And, if you are curious, you should look at page 581 of",
|
||||
"your course notes. There is an example solved.",
|
||||
"The example is for a differential amplifier.",
|
||||
"This is the small signal analysis chapter.",
|
||||
"That differential amplifier that's solved in that example is",
|
||||
"usually the first stage in an operational amplifier circuit.",
|
||||
"That differential amplifier is the first stage at the input.",
|
||||
"And that differential amplifier, as the name implies,",
|
||||
"amplifies not a single voltage but amplifies a differential",
|
||||
"voltage. Note that this guy amplifies",
|
||||
"the voltage difference between these two terminals.",
|
||||
"That's v here. And v is simply the same as v",
|
||||
"plus minus v minus. It's the node voltage here",
|
||||
"minus the node voltage here. That is what's amplified.",
|
||||
"It amplifies a difference. Therefore, it is called a",
|
||||
"difference amplifier or a differential amplifier.",
|
||||
"And so that input stage is what is inside the op amp.",
|
||||
"It's got a bunch of other circuitry like level shifters",
|
||||
"and so on. And at the output it has got a",
|
||||
"buffer. At at the output it has",
|
||||
"something that is reminiscent of the source follower circuit that",
|
||||
"you learned about in recitations, solved an example",
|
||||
"in the course notes and in your homework as well.",
|
||||
"And you solved a variant of the source follower on your quiz as",
|
||||
"well in problem two. So, a circuit that looks like",
|
||||
"that appears at the output. Remember, for the source",
|
||||
"follower, the resistance looking in from the output was very,",
|
||||
"very small. You have seen some of the",
|
||||
"pieces that go inside the amplifier, but we will deal with",
|
||||
"this as a building block and simply represent it using this",
|
||||
"abstract little circuit. To dwell on this a little",
|
||||
"longer, this little device here is the workhorse of the analog",
|
||||
"industry. Much like your primitive gate",
|
||||
"abstraction, your inverter and NAND gate and so on,",
|
||||
"much as your primitive inverter or NAND gate was from the",
|
||||
"foundations of the digital industry.",
|
||||
"Remember we learned how to build this little abstract",
|
||||
"device called a NAND gate or an inverter?",
|
||||
"We noticed that those form the foundations of very complicated",
|
||||
"microprocessors. Those were the building blocks",
|
||||
"of the digital industry. In the same way,",
|
||||
"this little beast here is the building block of the analog",
|
||||
"industry. Just to give you an analogy",
|
||||
"from software, think of this abstract little",
|
||||
"device as a library routine from a library of functions when you",
|
||||
"program in C++ or whatever. Can someone give me an example",
|
||||
"of an incredibly popular routine that we use all the time that",
|
||||
"may be called the workhorse of the software industry?",
|
||||
"Pardon? An abstraction,",
|
||||
"an abstract procedure. One example might be something",
|
||||
"like a printf. Printf is an abstract name for",
|
||||
"a procedure that goes and does something for you.",
|
||||
"It is amazing how we take the lowly printf for granted.",
|
||||
"I stick my printf into my program, it includes the",
|
||||
"standard IO library and it goes and prints a value.",
|
||||
"You won't believe how complicated the printf is.",
|
||||
"As you go into learning more advanced software subjects,",
|
||||
"implementing the printf is a nightmare.",
|
||||
"It is horrendously complicated. Just imagine.",
|
||||
"You give it a string and it has to go and print that on your",
|
||||
"terminal or on your Windows system or whatever.",
|
||||
"Think of the complicated steps it has to go through.",
|
||||
"But, as far as you're concerned, it's simple.",
|
||||
"Just print out something and you're done.",
|
||||
"The same way. Think of this as the printf of",
|
||||
"the analog business. It is really simple,",
|
||||
"and the analysis is going to be incredibly simple,",
|
||||
"it will be mind-bogglingly simple, but inside it,",
|
||||
"heavens forbid if you look inside it.",
|
||||
"Tell you what, go into to S-T-D-I-O dot in one",
|
||||
"of the library routines and just pore through printf.",
|
||||
"The world's worst horrendous macros are in there.",
|
||||
"I mean it is just nasty. The same way inside the op amp,",
|
||||
"it is nasty. You don't want to go there.",
|
||||
"Much like in your C programming in your classes,",
|
||||
"you were able to use printf without fully knowing how it was",
|
||||
"implemented. Probably some MIT god or some",
|
||||
"key graduate implemented it, but once it was implemented you",
|
||||
"just used it based on simple abstract rules as to how it",
|
||||
"behaved. You didn't have to know what",
|
||||
"was inside it to use it. The same way with the",
|
||||
"operational amplifier. So, just think of printf when",
|
||||
"you see this and just imagine how simple it is going to be to",
|
||||
"use it. You may think that I spend way",
|
||||
"too much time, ten minutes dwelling on this",
|
||||
"abstract concept, but I like to dwell on things",
|
||||
"that I think are incredibly important.",
|
||||
"The concept of abstraction is very important.",
|
||||
"And it's not just in software. The concept of abstraction",
|
||||
"pervades all of EECS. And if I were to give you a",
|
||||
"project to say go and ask every professor what is the one word",
|
||||
"that you think best describes all of EECS?",
|
||||
"Just pick one word. Go ask every single professor",
|
||||
"you know. What is a single word?",
|
||||
"If you were to characterize all of EECS with just one word,",
|
||||
"what might that word be? In my mind, it is the A word,",
|
||||
"abstraction. It is all over.",
|
||||
"If you do a grep on all the words used by all your",
|
||||
"professors in your four years here, I promise you the first",
|
||||
"one will be know. And the second one will be",
|
||||
"abstraction. Check it out.",
|
||||
"See if what I am saying is true or not.",
|
||||
"It is all over the place. In 6.001, how many times do you",
|
||||
"think the word abstraction was used in 6.001?",
|
||||
"It's all over the map. It's the A word all over.",
|
||||
"Imagine your shock when you see it being used in 002 because the",
|
||||
"same concept applies. We build more complicated",
|
||||
"systems by abstracting out the details of lesser objects,",
|
||||
"and then using those to build the more complicated systems.",
|
||||
"Abstraction is a very powerful mechanism of dealing with",
|
||||
"complexity. Next step is how do I go about",
|
||||
"using the op amp? Let me show you how it looks on",
|
||||
"a scope. What I am going to do is apply",
|
||||
"input to the op amp, I am going to look at the",
|
||||
"output, place the resistor RL to ground and look at the output.",
|
||||
"And here I am going to apply a plus VS and out here a minus VS.",
|
||||
"Again, remember that a plus VS simply looks like this and a",
|
||||
"minus VS simply looks like this. It's just an inverted VS",
|
||||
"applied here so I get a minus VS at this input.",
|
||||
"First of all, what I would like to do is as I",
|
||||
"change vIN, I am going to plot for you how vOUT looks.",
|
||||
"vIN and this is vO. I am going to plot vIN in terms",
|
||||
"of microvolts and vO in volts. vIN is going to have a very",
|
||||
"very small, the scale is going to be in microvolts because",
|
||||
"remember the gain of this is huge.",
|
||||
"It's on the order of ten to the sixth.",
|
||||
"It's huge. Small changes in vIN are going",
|
||||
"to cause massive changes in vO. I have a very fine scale on the",
|
||||
"X axis. What is going to happen if I",
|
||||
"somehow magically make vIN exactly zero?",
|
||||
"If I short these two terminals, if this was a completely ideal",
|
||||
"op amp, which it never is, if it's a completely ideal op",
|
||||
"amp, then my output should be zero.",
|
||||
"As I increase my vIN the output should be A times vIN.",
|
||||
"For some small value of vIN, small v, let's say one",
|
||||
"microvolt, the output should be one volt.",
|
||||
"A is a constant so this would look like a straight line.",
|
||||
"And let's say my supply voltages are 12 volts minus 12",
|
||||
"volts, if this were an ideal amplifier and I didn't have to",
|
||||
"worry about the supply, this would just go on extending",
|
||||
"forever. But I have a plus 12 volt",
|
||||
"supply and a minus 12 volt supply.",
|
||||
"My output cannot go past those limits.",
|
||||
"And so, therefore, my output kind of flattens out",
|
||||
"at these two points. And it is called hitting the",
|
||||
"rails. Output goes up and you hear a",
|
||||
"thunk sound and you hit the rails.",
|
||||
"When you play with op amps in your next lab,",
|
||||
"if you listen really, really carefully you may hear",
|
||||
"it. So, this saturates out.",
|
||||
"Not surprisingly, this region where the output",
|
||||
"saturates at the supply is called the saturation region.",
|
||||
"Remember, don't confuse it with-- It's not the same as your",
|
||||
"saturation in the MOSFET. It is a totally different",
|
||||
"thing. It is just happenstance that we",
|
||||
"call this saturation. And if you would like to think",
|
||||
"about it, you can think of it as the thunk region.",
|
||||
"That's probably more appropriate to distinguish it",
|
||||
"from the saturation region in the MOSFET.",
|
||||
"And, not surprisingly, this one is called the active",
|
||||
"region. And it is in this region that",
|
||||
"we use the op amp. Here it has hit the rails and",
|
||||
"is kind of dangling out there. It's not much use to us.",
|
||||
"It's in this active region that we use it because this is where",
|
||||
"the gain is seen. Now, it turns out that this is",
|
||||
"a very high gain device. It is very skittish.",
|
||||
"This gain is kind of a really funny thing.",
|
||||
"It's dependent on a bunch of factors.",
|
||||
"This could be temperature dependent.",
|
||||
"This gain here and this curve is just completely skittish.",
|
||||
"It could depend on temperature. It could depend on time of day.",
|
||||
"It could depend on what medication this amplifier is on.",
|
||||
"It could depend on its mood swings.",
|
||||
"Who knows what? This is kind of unstable.",
|
||||
"And A in particular is highly unstable.",
|
||||
"It is going to be big, that's for sure,",
|
||||
"but it could be ten to the six, on a rainy day it might be two",
|
||||
"times ten to the six. If it feeling sleepy it may be",
|
||||
"point five times ten to the sixth.",
|
||||
"It is big but I cannot rely on it.",
|
||||
"Let me show you an example. I want to show you this curve",
|
||||
"for this MOSFET, apply an input and plotting the",
|
||||
"output. What I will do is take a look",
|
||||
"at this curve. Then what I am going to do is",
|
||||
"use a heat gun to heat the op amp and you are going to see",
|
||||
"this vary all over the map. If you still remember last",
|
||||
"week, some of you may remember that from some place in a",
|
||||
"similar situation where the gm for the MOSFETs you were given",
|
||||
"was also dependent on temperature and stuff like that.",
|
||||
"It is a very common occurrence. And that is certainly the case",
|
||||
"for the MOSFET.",
|
||||
"",
|
||||
"Let's apply input. Let's do this.",
|
||||
"This is vIN versus vOUT for the amplifier.",
|
||||
"Notice that this is plus 12 volts, this is minus 12 volts.",
|
||||
"It is about two volts per division.",
|
||||
"This axis here is in microvolts, I believe.",
|
||||
"For a very small change, for a few tens of microvolts,",
|
||||
"I have an incredibly high gain. Notice that this has an",
|
||||
"incredibly high gain here. The gain is the slope of this",
|
||||
"line, almost a vertical line. What I am going to do next,",
|
||||
"is to have some fun, is I am going to heat the op",
|
||||
"amp. To show you that A is kind of",
|
||||
"really skittish and also the fact that it doesn't quite hit",
|
||||
"zero, it does all kinds of weird things, I am going to heat the",
|
||||
"op amp. And then let's take a look at",
|
||||
"how that curve fluctuates.",
|
||||
"",
|
||||
"What you saw there was that the op amp began to behave really",
|
||||
"weirdly as I heated it. Instead of doing this it",
|
||||
"sometimes did this really weirdly, like getting an offset",
|
||||
"from the center and so on. And it does a bunch of other",
|
||||
"weird things, but we won't go into those",
|
||||
"details. It's not relevant for this",
|
||||
"course. But the point is that the gain",
|
||||
"and the offset at the input are dependent on temperature.",
|
||||
"And we look for ways to make it less dependent on temperature.",
|
||||
"As the next step, what I would like to do is",
|
||||
"build a circuit. This is model equivalent of",
|
||||
"your Hello World program. We are going to use the printf",
|
||||
"and build a small program on the printf.",
|
||||
"You don't have to worry about how printf is implemented,",
|
||||
"just that we can build very highly interesting circuits with",
|
||||
"this horrendously complicated function based on a simple",
|
||||
"abstraction of the device. The circuit that we will build",
|
||||
"is called a noninverting amplifier.",
|
||||
"",
|
||||
"From now on, I am not going to show you the",
|
||||
"plus/minus VS. I am not going to show the",
|
||||
"power port, but it is in there. It's hidden under the",
|
||||
"abstraction layer. This is my op amp.",
|
||||
"And I am going to build the following circuit.",
|
||||
"This is my v plus and this is my v minus.",
|
||||
"What I am going to do is for the v plus I shall apply a vIN.",
|
||||
"Let me talk a little bit about ground as well.",
|
||||
"Ground is commonly taken as the point at which I connect my VS",
|
||||
"and minus VS supply. It is kind of at the midpoint.",
|
||||
"And if VS and minus VS are very carefully tuned then the output",
|
||||
"is also going to be at that same ground reference when the input",
|
||||
"is zero. So, the ground is defined as",
|
||||
"the point at which I connect my plus/minus VS supplies.",
|
||||
"I apply my vIN out here. Then what I am going to do,",
|
||||
"here is my output vO. I am going to have a resistive",
|
||||
"divider to ground here and label these R1 and R2.",
|
||||
"And what I am going to do here is feed this back to the input,",
|
||||
"to the v minus input. I am going to sample the",
|
||||
"voltage here and feed that into here.",
|
||||
"So, this is my abstract model and this is my Hello World",
|
||||
"program. What we are going to do is",
|
||||
"simply analyze how this little program behaves.",
|
||||
"So, my equivalent circuit model.",
|
||||
"The way to analyze these is after one or two of these",
|
||||
"examples, you will be able to directly analyze this just by",
|
||||
"looking at it, by inspection.",
|
||||
"But, much as we did for the other pieces,",
|
||||
"let me grunge through drawing the equivalent circuit and",
|
||||
"grinding through the analysis, and then show you the much",
|
||||
"simpler way of doing it. And even here,",
|
||||
"even with this grinding analysis, it is going to be",
|
||||
"pretty simple in any case. So, I will replace the op amp",
|
||||
"with its equivalent circuit model.",
|
||||
"Its equivalent circuit was v plus, v minus.",
|
||||
"",
|
||||
"So, that was the equivalent circuit model of the operational",
|
||||
"amplifier, just this piece. I draw that for you.",
|
||||
"Then what I am going to do is I connect my v in here.",
|
||||
"And, remember, I have an R1,",
|
||||
"R2 resistive divider here. And this one gets connected to",
|
||||
"this terminal there. I also know that i plus is",
|
||||
"zero. I also know that i minus is",
|
||||
"zero. All I've done is simply",
|
||||
"replaced the amplifier with its equivalent circuit.",
|
||||
"Let's go ahead and analyze that circuit now.",
|
||||
"Let's go ahead and analyze that circuit.",
|
||||
"And it's going to be pretty simple, actually.",
|
||||
"What I am going to show you is the hard way of doing it.",
|
||||
"I will show you a much easier way, but the hard way itself is",
|
||||
"pathetically easy. What I want to do is find vO in",
|
||||
"terms of vIN. And there will be a bunch of",
|
||||
"other factors thrown in, including things like R1 and",
|
||||
"R2, A and stuff like that. Let's go and analyze it.",
|
||||
"vO, let's look at that circuit. By the way, let me take 30",
|
||||
"seconds and make a little speech at this point.",
|
||||
"When you see circuits like this, and I saw this happen in",
|
||||
"quiz two as well, for some reason,",
|
||||
"when you see a new kind of circuit, don't completely go",
|
||||
"berserk or freeze or whatever. There is just no reason to.",
|
||||
"You know the node method. The node method is the",
|
||||
"workhorse of our business. When in doubt apply the node",
|
||||
"method. It will simply work.",
|
||||
"Don't freeze. Don't think oh,",
|
||||
"man, I need to apply a pattern that I know already.",
|
||||
"I must have seen this somewhere.",
|
||||
"When in doubt boom, apply the node method.",
|
||||
"This circuit here, all I have here is one unknown",
|
||||
"node voltage. I know the voltage of v plus,",
|
||||
"I need to compute the voltage vO.",
|
||||
"There are two unknowns, vO is an unknown and the",
|
||||
"voltage here at v minus is another unknown.",
|
||||
"This is a very simple circuit involving a dependent voltage",
|
||||
"controlled voltage source, and you need to find out vO and",
|
||||
"v minus using the node method. Just apply it.",
|
||||
"It's simple. Don't freeze.",
|
||||
"Just look at it and say I can do it and apply the node method.",
|
||||
"It will simply work. So, let's do that.",
|
||||
"What I can do here is vO is A times v plus minus v minus.",
|
||||
"This is actually really simple. And then, if I take v plus",
|
||||
"here, I know v plus is simply vIN so I will just make that",
|
||||
"substitution right away. So, v plus is simply vIN.",
|
||||
"What is v minus? v minus here is vO --",
|
||||
"",
|
||||
"What is v plus? I'm sorry, v minus.",
|
||||
"v minus is simply the voltage that is between R1 and R2.",
|
||||
"Notice that no current flows in to the v minus node.",
|
||||
"There is no current flowing in. Voltage at v minus is simply",
|
||||
"the voltage given by the resistive divider,",
|
||||
"which is vO times R2 divided by R1 plus R2.",
|
||||
"Stare at that for another second.",
|
||||
"The voltage at this node here is simply given by the resistive",
|
||||
"divider. Because no current is flowing",
|
||||
"in this direction. And no current flows in because",
|
||||
"I am telling you there is no current there based on my",
|
||||
"abstraction. I am telling you i minus is",
|
||||
"zero. That voltage is simply the",
|
||||
"voltage at this resistive divider.",
|
||||
"And so I can simplify it further and write this as vO.",
|
||||
"So I get, there is a one here. And I move this thing over to",
|
||||
"this side so I get one plus A times R2 divided by R1 plus R2.",
|
||||
"And that is equal to AvIN. And simplifying it some more,",
|
||||
"I get vO is AvIN divided by one plus AR2 divided by R1 plus R2.",
|
||||
"Notice how simple this is, and this is the hard method.",
|
||||
"All I have done is analyze the circuit using the basic circuit",
|
||||
"analysis principle that you learned the first week of the",
|
||||
"course, and I have the output for you.",
|
||||
"I just noted very carefully what the relationships were",
|
||||
"between the various elements in the abstraction.",
|
||||
"Notice here that I am told that A is extremely large.",
|
||||
"A is on the order of ten to the six and so on.",
|
||||
"And suppose it is the case that, let me write that down",
|
||||
"again. vO is AvIN, one plus AR2,",
|
||||
"R2. Suppose R1 and R2 are more or",
|
||||
"less comparable and A is ten to the six, it's a huge number,",
|
||||
"so this whole number is much, much greater than one.",
|
||||
"If it is much huger than one, what I can do is I can then",
|
||||
"write this as follows. I can say that this is more or",
|
||||
"less equal to AvIN divided by AR2 divided by R1 plus R2.",
|
||||
"I am ignoring the one here. As soon as I do that,",
|
||||
"notice I can cancel out A and I get vO to be approximately equal",
|
||||
"to vIN times R1 plus R2 divided by R2.",
|
||||
"Notice now that when the gain is very large the output is a",
|
||||
"function of the input multiplied by some number.",
|
||||
"The beauty of this thing here is that when A is very large,",
|
||||
"or this expression is very large, A cancels out and there",
|
||||
"is no A in this relationship. This means that even though the",
|
||||
"basic amplifier was very skittish, the output here",
|
||||
"relates to the input based on components that I have control",
|
||||
"over. These are soldiers in my army.",
|
||||
"I control them. So, to give you a sense of some",
|
||||
"numbers here, suppose A was ten to the six.",
|
||||
"And I choose R1 to be 9R. And R to be some R.",
|
||||
"Then vO is ten to the sixth vIN divided by one plus ten to the",
|
||||
"six R divided by 9R plus R. So, that is ten to the six vIN",
|
||||
"divided by one plus ten to the six divided by ten.",
|
||||
"All right. If I ignore the one here,",
|
||||
"the ten to the six and ten to the six cancel out,",
|
||||
"this ends up giving me 10vIN. So, I get a really nice",
|
||||
"amplifier whose output is simply ten times the input and",
|
||||
"determined solely by some resistor values.",
|
||||
"Let me show you another quick demo this time and show you the",
|
||||
"amplifier again, but with resistors connected",
|
||||
"like that. And then I show you that I want",
|
||||
"to heat the amplifier to the wazoo, the op amp to the wazoo,",
|
||||
"but vO is going to be absolutely rock solid.",
|
||||
"Let's try that out.",
|
||||
"",
|
||||
"This time around, this is the transfer function,",
|
||||
"the vO versus vIN. And notice that this time",
|
||||
"around I have similar scales on the X and Y axes,",
|
||||
"and this has a slope of 10. This is the point where the",
|
||||
"amplifier saturates at plus 12 volts, and this is minus 12",
|
||||
"volts, and this point here is a zero.",
|
||||
"So, this is vIN, vOUT, plus 12,",
|
||||
"minus 12 and this slope is 10. What I am going to do now is",
|
||||
"heat the op amp to the wazoo and this ain't going to change",
|
||||
"because it's my external resistors that control it",
|
||||
"independent of the value of A, provided A continues to be very",
|
||||
"large. I am just articulating the",
|
||||
"vOUT, vIN curve. And let me start heating the op",
|
||||
"amp.",
|
||||
"",
|
||||
"Notice that it's pretty stable. It doesn't change because it is",
|
||||
"independent of the amplifier values.",
|
||||
"What I have done now is by connecting these resistors in",
|
||||
"this way, I have a nice amplifier with a gain of ten.",
|
||||
"The question you may ask yourselves is why?",
|
||||
"There is this little sucker in there that wants to shoot things",
|
||||
"up by ten to the sixth. Wants to knock things off the",
|
||||
"one rail or the negative rail. Why is it that it's behaving",
|
||||
"like a docile lamb here and giving us a nice little factor",
|
||||
"of ten gain no matter what I do to it?",
|
||||
"Why is it doing that? What is the intuition behind",
|
||||
"it? I will draw something on the",
|
||||
"board, but for the next ten seconds I want you think about",
|
||||
"it. See if you can come up with",
|
||||
"some insight as to why is it doing that.",
|
||||
"Why is it exactly ten? Why isn't the ten to the sixth",
|
||||
"kind of killing me somehow? Why am I getting exactly ten no",
|
||||
"matter what happens? See if you can come up with",
|
||||
"some intuition and then I will show you how it works.",
|
||||
"I will redraw the circuit in the meantime.",
|
||||
"",
|
||||
"Let me see if I can give you some intuition.",
|
||||
"This is my circuit, and let's say this is R and",
|
||||
"this is R. As an example,",
|
||||
"let's assume that the input is 5 volts, vIN is 5 volts.",
|
||||
"If R and R are equal, what should the output be?",
|
||||
"It's R and R, so it's R1 plus R2 divided by",
|
||||
"R2, right? It's 2R divided by R,",
|
||||
"so it has a gain of two. My amplifier has a gain of two",
|
||||
"because R1 plus R2 divided by R2, which is my gain,",
|
||||
"is R plus R divided by R equals two.",
|
||||
"So, this will be 10 volts. If that is 10 volts this is",
|
||||
"going to be 5 volts, correct?",
|
||||
"This R and R, voltage divider,",
|
||||
"this is five, so I get 5 volts here.",
|
||||
"This is v plus. This is v minus.",
|
||||
"I get R and R, 5 volts here,",
|
||||
"that's how the circuit looks. Now let's understand what is",
|
||||
"going on. And listen very carefully.",
|
||||
"This is going to be a key insight that I hope you will",
|
||||
"carry with you for the rest of your lives.",
|
||||
"This is really, really key.",
|
||||
"What you are going to see is, I think, the third big ah-ha",
|
||||
"moment in 6.002. Like small signal analysis,",
|
||||
"like the frequency domain stuff we saw, I think this is the",
|
||||
"third big one in the next 30 or 40 seconds, things that are",
|
||||
"completely either not necessarily intuitive but are",
|
||||
"just spectacular in terms of what they can do for you.",
|
||||
"Let's see. Let's suppose that because I am",
|
||||
"heating it, let's suppose that A suddenly tends to increase.",
|
||||
"It wants to increase because I have heated it.",
|
||||
"A is saying I want to get out this mold here and starts to",
|
||||
"break through its shackles here. Let's say, as a Gedanken",
|
||||
"experiment, that it tries to shoot up this to 12 volts.",
|
||||
"It tries to push it up higher. This is just a Gedanken",
|
||||
"experiment. The up arrow says that the",
|
||||
"increase in A is trying to push up vO momentarily.",
|
||||
"Let's see what happens. It is trying to push up vO",
|
||||
"momentarily, so let's say this goes to 12 hypothetically.",
|
||||
"If that goes to 12, what should this volt node go",
|
||||
"to? Six, exactly.",
|
||||
"This goes to 6 volts. If that goes to six,",
|
||||
"what does v minus go to? 6 volts again.",
|
||||
"So, v minus goes to 6 volts. Now at the input I have 5 volts",
|
||||
"at v plus and 6 volts at v minus, so where should the",
|
||||
"output go? The output should go down",
|
||||
"because the voltage of the negative terminal is higher.",
|
||||
"And so the output is A times v plus minus v minus.",
|
||||
"And because this has gone down, this has gone up here it is",
|
||||
"going to try to pull the output down.",
|
||||
"That is going to pull the output down let's say to 9 volts",
|
||||
"or something. Cachunk, there is a big battle",
|
||||
"going on here. A has gone up,",
|
||||
"it has boosted it up to 12, but the moment that goes to 12,",
|
||||
"this goes to 6, this goes to 6,",
|
||||
"and the op amp output has to go down to 9 volts now because this",
|
||||
"input is higher here. If this goes to 9,",
|
||||
"this goes to 4.5. If that goes to 4.5,",
|
||||
"this goes to 4.5. What happens now?",
|
||||
"If this goes to 4.5, what happens?",
|
||||
"It wants to go back up. Can't it make up its mind?",
|
||||
"This guy wants to go back up now because v plus is higher",
|
||||
"than v minus. What am I seeing here?",
|
||||
"This whole circuit here behaves like my little son,",
|
||||
"my 9-year-old. If say do this,",
|
||||
"he wants to do the exact opposite.",
|
||||
"So, there is a trick in how you make them do things for you.",
|
||||
"Look at this. Because of this arrangement of",
|
||||
"the circuit when A tries to push the output up,",
|
||||
"the rest of the circuit tries to pull it back down to where it",
|
||||
"used to be. If the circuit tries not to",
|
||||
"follow the true path, the rest of the circuit tries",
|
||||
"to whack it into shape so it follows a true path.",
|
||||
"And what's happening is because, in this arrangement,",
|
||||
"I have fed back a portion of the output to the negative",
|
||||
"input. I have fed back some of the",
|
||||
"output to the negative input. And by providing this feedback",
|
||||
"of a portion of the output to the negative input,",
|
||||
"I have arranged it in a way that I have something called",
|
||||
"negative feedback. What negative feedback does is",
|
||||
"that if this wanted to go wild and crazy, the circuit provides",
|
||||
"it with some negative feedback like you just saw.",
|
||||
"Feedback, a big word. If you take a poll of all the",
|
||||
"EECS faculty, I suspect that feedback would",
|
||||
"rank at least as the ninth or tenth most important word in the",
|
||||
"EECS. If abstract is number one,",
|
||||
"I think this would rank like a nine or a ten or something.",
|
||||
"So, that's the reason why it worked.",
|
||||
"In the last couple of minutes, let me give you some insight,",
|
||||
"based on something that you know, on how feedback works.",
|
||||
"This is a road here. Let's look at anti lock breaks.",
|
||||
"This is my tire. And let's say I have a set of",
|
||||
"disk brakes here. As the car is moving forward,",
|
||||
"if I apply the brakes the tire stops rolling,",
|
||||
"but if I apply the breaks too hard it can lock up the tire and",
|
||||
"the whole car can skid. The way anti lock breaks work",
|
||||
"is as follows. There is a controller that sits",
|
||||
"here. And there is a little person",
|
||||
"looking at the wheel and seeing is it turning.",
|
||||
"So, this is a feedback. And it is saying is it turning?",
|
||||
"Yes. Or, is it not turning?",
|
||||
"No. All this person watching the",
|
||||
"tire is doing is saying is it turning or is it not turning.",
|
||||
"That is it. That is a negative feedback.",
|
||||
"And so, if it is no and if it is yes.",
|
||||
"If it is yes then what this does is it applies the brakes",
|
||||
"even more strongly. It is turning so I can apply",
|
||||
"more brakes. But if it says oops,",
|
||||
"it stopped turning, what it does is it simply",
|
||||
"releases, the controller releases the brakes.",
|
||||
"And when the controller releases the brakes this one",
|
||||
"tends to loosen up a little bit and the tire starts turning",
|
||||
"again. So, this way you are constantly",
|
||||
"keeping the tire in its region of critical friction so that it",
|
||||
"is constantly moving. And static friction applies to",
|
||||
"how hard you can brake and it doesn't start skidding.",
|
||||
"In fact, if you take your car out, and I don't say you do",
|
||||
"this. Let's say go onto the Charles",
|
||||
"River in the dead of winter and you drive on the lake and you",
|
||||
"slam your anti lock brakes on, on an icy patch,",
|
||||
"you will notice that there is a constant sound that looks like",
|
||||
"something is vibrating in there. That is exactly what is",
|
||||
"happening. Oops, the tire is locked.",
|
||||
"Release the brakes. The wheel is turning.",
|
||||
"Jam the brakes on. That is exactly what is",
|
||||
"happening. The same way as out there,",
|
||||
"you notice that oops, the output is going up,",
|
||||
"pull it down, oops, it's going down,",
|
||||
"pull it up. So, there is constant negative",
|
||||
"feedback that is keeping the output stable.",
|
||||
"A very important concept. And I will ask your recitation",
|
||||
"instructors to cover the very simple method that is on page 9."
|
||||
]
|
||||
}
|
||||
@@ -1,1892 +0,0 @@
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|
||||
"text": [
|
||||
"",
|
||||
"All right. Let's get moving.",
|
||||
"Good morning.",
|
||||
"",
|
||||
"Today, if everything works out, we have some fun for you guys.",
|
||||
"I hope it works out. We'll see.",
|
||||
"What I am going to do today is a very major application of the",
|
||||
"frequency response and the frequency domain analysis of",
|
||||
"circuits. And this application area is",
|
||||
"called filters. The area of filters often times",
|
||||
"demands a full course or a couple of full courses all by",
|
||||
"itself. And filters are incredibly",
|
||||
"useful. They're used in virtually every",
|
||||
"electronic device in some form or another.",
|
||||
"They're used in radio tuners. We will show you a demo of that",
|
||||
"today. They're also used in your cell",
|
||||
"phones. Every single cell phone has a",
|
||||
"set of filters. So, for example,",
|
||||
"how do you pick a conversation? You pick a conversation by",
|
||||
"picking a certain frequency and grabbing data from there.",
|
||||
"They are also in wide area network wireless transmitters.",
|
||||
"Do we have an access point here?",
|
||||
"I don't see one, but you've seen wireless access",
|
||||
"points. Again, there they have filters",
|
||||
"in them. So, virtually every single",
|
||||
"electronic device contains a filter at some point or another.",
|
||||
"And so, today we will look at this major, major application of",
|
||||
"frequency domain analysis. Before we get into that,",
|
||||
"I'd like to do a bit of review. The readings for today",
|
||||
"correspond to Chapter 14.4.2, 14.5 and 15.2 in the course",
|
||||
"notes. All right.",
|
||||
"Let's start with the review. We looked at this circuit last",
|
||||
"Friday --",
|
||||
"",
|
||||
"-- where I said that for our analysis, we are going to focus",
|
||||
"on this small, small region of the playground.",
|
||||
"And what's special about this region of our playground is that",
|
||||
"I am going to focus on sinusoidal inputs.",
|
||||
"And, second, I am going to focus on the",
|
||||
"steady state response. How does the response look like",
|
||||
"if I wait a long, long time?",
|
||||
"And then we said that the full blown time domain analysis was",
|
||||
"hard. This was, remember,",
|
||||
"the agonizing approach? And then I taught you the",
|
||||
"impedance approach in the last lecture, which was blindingly",
|
||||
"simple. And, in that impedance",
|
||||
"approach, what we said we would do is --",
|
||||
"I will apply the approach right now and in seconds derive the",
|
||||
"result for you. But the basic idea was we said",
|
||||
"what we are going to do is assume that we are going to",
|
||||
"apply inputs of the form Vi e to the j omega t.",
|
||||
"Wherever you see a capital and a small, there is an implicate e",
|
||||
"to the j omega t next to it. I'm not showing you that.",
|
||||
"And what I showed last time, and the class before that was",
|
||||
"once you find out the amplitude --",
|
||||
"Once you find out the multiplier that multiplies e to",
|
||||
"the j omega t, it's a complex number,",
|
||||
"you have all the information you need.",
|
||||
"And once you have this, you can find out the time",
|
||||
"domain response by simply taking the modulus of that,",
|
||||
"or the amplitude and the phase of that to get the angle.",
|
||||
"And that gives you the time domain response.",
|
||||
"So, our focus has been on these quantities.",
|
||||
"The impedance method says what I am going to do is replace each",
|
||||
"of these by impedances. And then the corresponding",
|
||||
"impedance model looks like this.",
|
||||
"",
|
||||
"Instead of R, I replace that with ZR.",
|
||||
"And instead of the capacitor, I am going to replace that with",
|
||||
"ZC. And this is my Vc.",
|
||||
"ZR is simply R and ZC was going to be one divided by sC where s",
|
||||
"was simply a shorthand notation for j omega.",
|
||||
"Based on this, once I converted all my",
|
||||
"elements into impedances, I can go ahead and apply all",
|
||||
"the good-old linear analysis techniques.",
|
||||
"I will discuss a bunch of them today.",
|
||||
"As an example, I could analyze this using my",
|
||||
"simple voltage divider relationship.",
|
||||
"Vc is simply ZC divided by ZC plus ZR times Vi.",
|
||||
"And that, in turn, is, well, let's say I divide",
|
||||
"this by Vi so I can get the response relation,",
|
||||
"is ZC divided by ZC plus ZR. And ZC I know to be one by j",
|
||||
"omega C, plus R. And multiplying throughout by j",
|
||||
"omega C, I get one divided by one plus j omega CR.",
|
||||
"It's incredibly simple. This is simply called the",
|
||||
"frequency response. And it's a transfer function",
|
||||
"representing the relationship between the output complex",
|
||||
"amplitude with the input. We can also plot this.",
|
||||
"Notice that in our entire analysis we have not only",
|
||||
"assumed sinusoidal input, but we're also saying that let",
|
||||
"us look at this only in the steady state.",
|
||||
"So, we will wait for time to be really, really large,",
|
||||
"and then look at the response. And so, therefore,",
|
||||
"we will plot the response not as a function of time,",
|
||||
"but rather we are going to plot the response as a function of",
|
||||
"omega. What we are going to say is I",
|
||||
"am going to input a sinusoid and my output is going to be some",
|
||||
"other sinusoid. And since I'm waiting for a",
|
||||
"long time to look at the output, time doesn't make sense",
|
||||
"anymore. Rather, my free variable is",
|
||||
"going to be my frequency, so I am going to change the",
|
||||
"frequency of the input that I apply.",
|
||||
"And so, I am going to plot this as a function of omega.",
|
||||
"This represents a completely complimentary view of circuits,",
|
||||
"the time domain view and then there is a frequency domain",
|
||||
"view. The frequency domain view says",
|
||||
"how did this circuit behave as I apply sinusoids of differing",
|
||||
"frequencies? I can plot that relationship in",
|
||||
"a graph like this, and this relationship is simply",
|
||||
"given by a parameter edge the transfer function,",
|
||||
"it's a function of omega. And I can also plot the",
|
||||
"absolute value of that. And let's take a look at what",
|
||||
"it looks like. So, I can look at functions",
|
||||
"like this and very quickly plot the response.",
|
||||
"I am going to do a whole bunch of plots just by staring at",
|
||||
"circuits and staring at expressions like this.",
|
||||
"And you will see a number of them today.",
|
||||
"First of all, the way you plot these is look",
|
||||
"for the values where omega is very small and when omega is",
|
||||
"very large. When omega is very,",
|
||||
"very small this term goes away. And so, for very small values",
|
||||
"of omega the output is simply one.",
|
||||
"Vc by Vi is simply one. This part goes away.",
|
||||
"What happens when omega is very, very large?",
|
||||
"When omega is really large, this part dominates,",
|
||||
"is much greater than one. If I ignore one in relation to",
|
||||
"this guy and take the absolute value of that then I simply get",
|
||||
"one divided by omega CR when omega is very large.",
|
||||
"So, when omega is very large, I get a decay of the form one",
|
||||
"over omega CR. I know the value for small",
|
||||
"omega, and it looks like this for very large omega.",
|
||||
"And, if you plot it out, this is how it's going to look",
|
||||
"like. Let's stare at this form for a",
|
||||
"little while longer. And let's plot some properties",
|
||||
"off it. First of all,",
|
||||
"you notice something else. When omega CR equals one then,",
|
||||
"in other words, when omega equals one by RC,",
|
||||
"notice that the output is given by one plus j.",
|
||||
"And the absolute value of that is simply one divided the square",
|
||||
"root of two. So, in other words,",
|
||||
"when omega is one by RC -- When omega is one by CR then",
|
||||
"the output is one by square root two times its value when omega",
|
||||
"is very, very small. So, that is one little piece of",
|
||||
"information. If you look at the form of",
|
||||
"this, I would like you to stare at it for a few minutes and try",
|
||||
"to understand what this represents.",
|
||||
"This says that for very low frequencies the response is",
|
||||
"virtually the same as the input in amplitude.",
|
||||
"In other words, if I apply some very low",
|
||||
"frequency sinusoid of some amplitude then the output",
|
||||
"amplitude is going to be same as that amplitude.",
|
||||
"And that's a one. Now, it also says when I apply",
|
||||
"a very high frequency, at very high frequencies it",
|
||||
"decays. So, this graph which says I am",
|
||||
"going to pass low frequencies without any attenuation,",
|
||||
"without hammering it, but I am going to clobber high",
|
||||
"frequencies and give you a very low amplitude signal at the",
|
||||
"output but pass through, almost without attenuation,",
|
||||
"the input at low frequencies. And so this is an example of",
|
||||
"what is called a low pass filter or LPF.",
|
||||
"What this is saying is that this little circuit here acts",
|
||||
"like a low pass filter. It's a low pass filter because",
|
||||
"it passes low frequencies without attenuation but kills",
|
||||
"high frequencies. If I take some music,",
|
||||
"and you will do experiments with this in lab.",
|
||||
"When is lab three? People are doing lab three",
|
||||
"right now, right? Lab three is going on right now",
|
||||
"and early next week as well. And, in lab three,",
|
||||
"you will play with looking at the response to music of",
|
||||
"different types of filters. If apply some music here,",
|
||||
"you will see that the output will pass low frequencies but",
|
||||
"really attenuate high frequencies.",
|
||||
"You will hear a lot of the low sounding base and so on but",
|
||||
"attenuate a lot of the high frequencies.",
|
||||
"All right. The other thing that I",
|
||||
"encourage you to do is Websim has built in pages for a large",
|
||||
"number of such circuits. You can go in there and play",
|
||||
"with the values of RC, or L for that matter,",
|
||||
"for a variety of circuits. And, if you click on frequency",
|
||||
"response, you actually get both the amplitude response and the",
|
||||
"phase as well. You can play with various",
|
||||
"values of RLC and see how the frequency response looks like",
|
||||
"for each of the circuits. As a next step,",
|
||||
"what I would like to do is just give you a sense of how",
|
||||
"impedances combine. This won't be very surprising",
|
||||
"given that they behave just like resistors, but it's good to go",
|
||||
"through it nonetheless. Suppose, just to build some",
|
||||
"insight, suppose I had two resistors in series.",
|
||||
"All right. R1 and R2.",
|
||||
"And this was my A and B terminals respectively.",
|
||||
"And let's say the complex amplitude of the voltage was Vab",
|
||||
"across this. Then I could relate,",
|
||||
"let's say Iab was the current, I can relate these resistances.",
|
||||
"Or, I could relate Vab and Iab as follows.",
|
||||
"Simply Vab divided by Iab equals R1 plus R2.",
|
||||
"I know that. And the same thing applies to R",
|
||||
"viewed as an impedance. It's still impedance R,",
|
||||
"and so this one still goes ahead and applies.",
|
||||
"The second thing I can try is the circuit of this form.",
|
||||
"A, B, and I have an R1 and an L in this case.",
|
||||
"And what I can do is, in the impedance model,",
|
||||
"I can view this as an impedance of value j omega L.",
|
||||
"And I can also combine them to get the impedance between A and",
|
||||
"B. Much as I got a resistance",
|
||||
"between A and B, I can get an impedance between",
|
||||
"A and B as Vab divided by Iab. And that will be given by ZR1",
|
||||
"plus ZL, and that is simply R1 plus j omega L.",
|
||||
"Similarly, I can do an even more complicated circuit.",
|
||||
"So, resistance. And here I have a capacitor in",
|
||||
"series with the resistance, and then I apply inductor to",
|
||||
"it. This is A, B,",
|
||||
"Iab and plus, minus Vab.",
|
||||
"And let me call this R1 and let me call this R2 and this is C",
|
||||
"and L. I can go about combining these",
|
||||
"in much the same manner that I combine my resistances in the",
|
||||
"series parallel simplifications. I can define an impedance Zab",
|
||||
"between the A and B terminals as ZR1 plus Z of this combination,",
|
||||
"impedance of this combination, which is simply impedance of C",
|
||||
"and that of R2 in parallel with each other.",
|
||||
"I get Zc in parallel with ZR2. Notice that this notation",
|
||||
"simply says that look at the impedance of the capacitor in",
|
||||
"parallel with a resistor. And then, finally,",
|
||||
"I add to that the series impedance of the inductor ZL.",
|
||||
"Exactly as you would have done for resistances,",
|
||||
"if all of these resistances you would have said R of this piece",
|
||||
"plus the R of the parallel combination plus the R of",
|
||||
"whatever was here. This time around we have",
|
||||
"impedances. And replacing this with the",
|
||||
"values, this is R1. I know for ZL it's j omega L.",
|
||||
"And so, for ZL, parallel ZR2 it is given by",
|
||||
"ZCZR2 divided by ZC plus ZR2, which is simply R1 here and j",
|
||||
"omega L. And let me just substitute the",
|
||||
"values here. I know that ZR2 is simply R2,",
|
||||
"ZC is one by j omega C, and then one by j omega C plus",
|
||||
"R2. And I can go ahead and simplify",
|
||||
"that further and get my impedance Zab.",
|
||||
"Notice how simple analysis has become.",
|
||||
"Using this technique, using the impedance method",
|
||||
"we've managed to convert our analysis from solving",
|
||||
"differential equations to going back to algebra.",
|
||||
"A large part of what we do in circuits is see how we can get",
|
||||
"back to really simple algebra and try to be clever about how",
|
||||
"we do things. So, this is as far as analysis",
|
||||
"is concerned. In the next five minutes,",
|
||||
"I want to give you some insight into how you can build different",
|
||||
"kinds of impedances.",
|
||||
"",
|
||||
"And I won't go into too much detail but give some insight",
|
||||
"into how you can get a sense for the kind of filters you want to",
|
||||
"design. Or, at the very least,",
|
||||
"given a filter, how can you very quickly get",
|
||||
"some insight into what kind of filter it is,",
|
||||
"how it performs, what its frequency response is",
|
||||
"and so on. And, this time around,",
|
||||
"this piece of intuition will be in honor of Umans.",
|
||||
"And back to our Bend it Like Beckham series,",
|
||||
"I call this \"Unleash it like Umans\".",
|
||||
"What experts in the field do is they don't go about sitting",
|
||||
"around writing differential equations, but rather use a lot",
|
||||
"of insight into how to solve these things.",
|
||||
"And so in honor of Umans, I will label this unleash it",
|
||||
"like Umans. Let's get some insight into how",
|
||||
"the response of various elements look like.",
|
||||
"Let's take, for example, I have some impedance Z.",
|
||||
"Let's say this could be a resistor, it could be an",
|
||||
"inductor or it could be a capacitor.",
|
||||
"Let's take a look at what the frequency response of just these",
|
||||
"elements look like. In other words,",
|
||||
"what are the frequency dependents of Z itself?",
|
||||
"Let me just plot the impedance of each of these elements as a",
|
||||
"function of frequency. Let me just take the absolute",
|
||||
"value of their impedance. Notice that it's a complex",
|
||||
"number. For the inductor it's j omega",
|
||||
"L. And let me take the absolute",
|
||||
"value omega L in that case and plot it for you.",
|
||||
"And use that to develop some insight.",
|
||||
"Let's do a simple case first. If Z is a resistance of value R",
|
||||
"then no matter what the frequency my value is going to",
|
||||
"be R. If I have an inductor of value",
|
||||
"L then the impedance is going to look like j omega L,",
|
||||
"and so I am going to omega L for that.",
|
||||
"And the dependence of that simply says that for low omega",
|
||||
"the impedance is very small. For omega zero the impedance is",
|
||||
"zero and it increases linearly with omega.",
|
||||
"So, it's omega L for the inductor.",
|
||||
"Impedance increases linerally as I increase the frequency.",
|
||||
"What about for the capacitor? For the capacitor,",
|
||||
"the impedance is one divided by j omega C.",
|
||||
"And so, therefore, I get the dependence being",
|
||||
"related to omega C. Which says that for very high",
|
||||
"frequencies impedance is very low, but for very low",
|
||||
"frequencies the impedance is very high and I get a behavior",
|
||||
"pattern that looks something like this.",
|
||||
"It goes as one by omega C. As omega is very large,",
|
||||
"my impedance is very small. If omega is very small,",
|
||||
"my impedance goes towards that of an open circuit.",
|
||||
"This is not surprising. You've known this before,",
|
||||
"right? That a capacitor behaves like",
|
||||
"an open circuit for DC. An inductor behaves like a",
|
||||
"short circuit for DC. Notice that zero frequency here",
|
||||
"corresponds to DC. The capacitor looks like an",
|
||||
"open circuit for DC, very high impedance.",
|
||||
"The inductor looks like a short circuit for DC,",
|
||||
"very low impedance. And the opposite is true at",
|
||||
"very high frequencies. While R is a constant",
|
||||
"throughout. Let's use this to build some",
|
||||
"insight into how our circuits might look.",
|
||||
"Let me do this example.",
|
||||
"",
|
||||
"Let's say I have a Vi and I measure the response across the",
|
||||
"resistor.",
|
||||
"",
|
||||
"So, I measure Vr divided by Vi and take the absolute value and",
|
||||
"take a look at how it's going to look like.",
|
||||
"I want you to stare at this for me and help me with what the",
|
||||
"response is going to look like. Let's take incredibly high",
|
||||
"frequencies. At very high frequencies,",
|
||||
"this has a very high frequency, what do the capacitor look like",
|
||||
"to very high frequencies? Is it an open or is it a short?",
|
||||
"A short circuit. At very high frequencies the",
|
||||
"capacitor looks like a short circuit.",
|
||||
"Then Vi simply appears across the resistor,",
|
||||
"which means that at very high frequencies the output is very",
|
||||
"close to the input. At very low frequencies what",
|
||||
"happens? At very low frequencies the",
|
||||
"capacitor looks like an open circuit.",
|
||||
"If this looks like an open circuit then very little voltage",
|
||||
"will drop across this resistor here because most of it is going",
|
||||
"to drop across the capacitor. What is going to happen is,",
|
||||
"for very low values, I am going to be looking at",
|
||||
"something out here. And, because of that,",
|
||||
"my response looks like this. And this is of a different form",
|
||||
"than the one you saw earlier. In this case,",
|
||||
"I pass high frequencies but attenuate low frequencies.",
|
||||
"Not surprisingly, this is called a high pass",
|
||||
"filter.",
|
||||
"",
|
||||
"You need to begin to be able to think about capacitors and",
|
||||
"inductors in terms of their high and low frequency properties.",
|
||||
"And, if you develop that intuition, once you develop the",
|
||||
"intuition about capacitors and inductors and their frequency",
|
||||
"relationship, that will be a big step forward",
|
||||
"in 002. If you get that insight,",
|
||||
"you will go a long way in terms of knowing how to tackle",
|
||||
"problems and being able to quickly sketch responses.",
|
||||
"Yes.",
|
||||
"",
|
||||
"In the case of, if we get something like j",
|
||||
"omega L, what you can do is take the limit as omega goes to zero.",
|
||||
"If it is omega L then notice that it is going to start",
|
||||
"linear. And, on the other hand,",
|
||||
"if when you get very high frequencies, for example,",
|
||||
"if you get one by something omega C then this is a",
|
||||
"hyperbolic relationship, so it is going to go ahead",
|
||||
"looking like this. So, you can take a look at a",
|
||||
"lot of these functions at their very low values and see how they",
|
||||
"look like at that point. All right.",
|
||||
"The next one I would like to draw for you is something that",
|
||||
"looks like this.",
|
||||
"",
|
||||
"Let's say, for example, I have an inductor L and a",
|
||||
"resistor R and I want to see what that looks like.",
|
||||
"In this particular example, I have H, take the absolute",
|
||||
"value. So, what is this going to look",
|
||||
"like? I am going to look at the value",
|
||||
"across the resistor here. Here what I am going to find is",
|
||||
"that at very low frequencies this guy is a short circuit.",
|
||||
"Since this guy is a short circuit, all the voltage drops",
|
||||
"across the resistor so it's going to look like this.",
|
||||
"And, at very high frequencies, what I am going to find is that",
|
||||
"the inductor is going to appear like an open circuit.",
|
||||
"And so, therefore, all the voltage is going to",
|
||||
"pretty much drop across the inductor.",
|
||||
"It will be R divided by something plus omega L.",
|
||||
"So, at high frequencies this guy is going to taper off to",
|
||||
"zero and is going to look like this.",
|
||||
"And this is back to my low pass filter.",
|
||||
"Just to go back to a question asked earlier,",
|
||||
"how do you know what this looks like?",
|
||||
"I can very quickly write down the expression for H of j omega.",
|
||||
"This is simply going to be R divided by R plus if this is VR.",
|
||||
"VR is simply R divided by one by j omega C.",
|
||||
"I multiply it out by j omega C in the numerator and the",
|
||||
"denominator. I'm going to find j omega C",
|
||||
"here and I am going to get one by j omega C here.",
|
||||
"And what is going to happen with something like this is that",
|
||||
"as omega becomes very small then I am going to ignore this.",
|
||||
"When omega becomes very small, I can ignore this with respect",
|
||||
"to one, and I get R j omega C. Given that, is what I've drawn",
|
||||
"here correct or wrong? This goes away with respect to",
|
||||
"one. I am left with R j omega C,",
|
||||
"right? For very low frequencies.",
|
||||
"Given what I have drawn here, is that correct or is that",
|
||||
"wrong? Well, it's hard to say.",
|
||||
"For very, very low frequencies it starts out being linear",
|
||||
"because it's an omega relationship,",
|
||||
"and then it goes up like this and then goes out there.",
|
||||
"Let me go onto another example. Let me do another example here",
|
||||
"which is something like -- I need to make sure I don't",
|
||||
"make a mistake here. If I get R j omega C by R j",
|
||||
"omega C, you know what, this ends up being a first",
|
||||
"order system, and so is going to look like",
|
||||
"this. I blew it there.",
|
||||
"Back to this system here. If I have an L and an R and I",
|
||||
"look at this equation to look at what happens across L,",
|
||||
"you can plot that again. And for very low frequencies it",
|
||||
"is going to be zero amplitude here and for very high",
|
||||
"frequencies this is going to be an open circuit,",
|
||||
"and so the response is going to look something like this.",
|
||||
"That's going to end up being your high pass filter.",
|
||||
"As another example, I would like to do a series RLC",
|
||||
"circuit --",
|
||||
"",
|
||||
"-- and try to get you some sense of what that output looks",
|
||||
"like. Let's use our intuition and",
|
||||
"first write down what this looks like and then go and do some",
|
||||
"math and see if the math corresponds to what our",
|
||||
"intuition tells us. I want to plot Vr with respect",
|
||||
"to Vi. I want to plot it there.",
|
||||
"For something like this, what happens at very low",
|
||||
"frequencies? We are just looking to get",
|
||||
"very, very crudely what this graph is going to look like.",
|
||||
"Very, very crudely what this graph is going to look like.",
|
||||
"Given that I am taking the voltage across VR,",
|
||||
"what happens at very low frequencies?",
|
||||
"At incredibly low frequencies, the inductor looks like a short",
|
||||
"circuit, but the capacitor looks like open circuit.",
|
||||
"An open circuit in series with a short circuit that ends up",
|
||||
"looking like an open circuit. And so, therefore,",
|
||||
"all my voltage falls across VR. Now, what happens at very high",
|
||||
"frequencies? At very high frequencies the",
|
||||
"capacitor looks like a short. But the inductor looks like an",
|
||||
"open circuit now for very high frequencies, correct?",
|
||||
"Just remember, capacitor is short for high",
|
||||
"frequencies inductor open for high frequencies.",
|
||||
"So, this ends up having a very high impedance.",
|
||||
"At very high frequencies this guy has a very high impedance.",
|
||||
"And, because of that, for a high value of frequency,",
|
||||
"I end up going in that manner. This behavior has the effect of",
|
||||
"the capacitor here. And for very high frequencies I",
|
||||
"get the effect of the inductor. And so this means that I have",
|
||||
"very low values for low frequencies, very low values for",
|
||||
"high frequencies. And, as the frequency",
|
||||
"increases, I do something like this.",
|
||||
"I keep building up, then the inductor begins to",
|
||||
"play a role, and then I taper off again.",
|
||||
"This kind of a filter where I kill low and high frequencies",
|
||||
"and pass intermediate frequencies is called a band",
|
||||
"pass filter, BPF. This means that it passes",
|
||||
"frequencies in some band. Let's get some more insight on",
|
||||
"this by writing down the equations.",
|
||||
"So, Vr divided by Vi is simply R.",
|
||||
"Using the impedance relation it is R divided by j omega L plus",
|
||||
"one divided by j omega C plus R. I am going to use this equation",
|
||||
"later, so let me stash it away on my stack and put a little",
|
||||
"notation there. I am going to multiply",
|
||||
"throughout by j omega C. And what I end up getting is j",
|
||||
"omega RC divided by one plus R j omega RC, and then here,",
|
||||
"I get j times j is minus one, so I get minus omega squared.",
|
||||
"Let me rewrite it this way. I get minus omega squared.",
|
||||
"So, j j is minus one, omega times omega is omega",
|
||||
"squared, and then I get an LC. That's what I end up getting.",
|
||||
"And if I take the absolute value here, I end up getting,",
|
||||
"back to your complex algebra, the square root of this real",
|
||||
"value squared plus imaginary value squared.",
|
||||
"So, one minus omega squared LC plus omega RC squared.",
|
||||
"This is from, you can look it up in your",
|
||||
"complex algebra appendix in the course notes.",
|
||||
"It's simply omega RC here, then square of the real value",
|
||||
"plus the square of the imaginary value, and take the square root",
|
||||
"of that. By staring at this,",
|
||||
"you can notice that you realize a really important property.",
|
||||
"When omega equals LC. I'm sorry.",
|
||||
"When omega equals one divided by LC, what happens?",
|
||||
"Sorry, square root of LC. When omega is one divided by",
|
||||
"square root of LC then omega squared times LC becomes one.",
|
||||
"When this is true then this becomes one, and one and one",
|
||||
"cancel out. And, not only that,",
|
||||
"when these cancel out, these two cancel out at that",
|
||||
"point, so I end up getting a one, which means that when omega",
|
||||
"equals omega nought equals one by square root of LC and I end",
|
||||
"up getting a value that is one. It's pretty amazing.",
|
||||
"Which means that if I drive this at omega nought,",
|
||||
"if my sinusoid has a frequency omega nought where omega nought",
|
||||
"is one by square root of LC, if I'm sitting here and this is",
|
||||
"a black box on the right-hand side, and I drive this at a",
|
||||
"frequency omega nought equals one divided by square root of",
|
||||
"LC, what does this entire circuit look like to me?",
|
||||
"I'm sitting there, the black box here.",
|
||||
"I'm driving it at omega nought equals one by square root of LC",
|
||||
"at that frequency. What does that circuit look",
|
||||
"like? Yes.",
|
||||
"It looks like a resistor. It's pretty amazing.",
|
||||
"It means that even though I have an L and a C here,",
|
||||
"if I happen to drive this at omega nought then the circuit",
|
||||
"looks purely resistive and it seems to give me the same input",
|
||||
"appearing at the output. In other words,",
|
||||
"the effect of these two cancels out.",
|
||||
"And that aspect is called driving the circuit at its",
|
||||
"resonance point. Resonance is when you're",
|
||||
"driving the circuit at omega nought equals one by a square",
|
||||
"root of LC.",
|
||||
"",
|
||||
"I will very quickly sketch for you a couple of other ways of",
|
||||
"looking at circuits. Supposing I looked at this",
|
||||
"value here, Vlc, I looked at the value across",
|
||||
"the inductor and the capacitor, what will the frequency",
|
||||
"response look like? I am looking at the voltage",
|
||||
"across the inductor and the capacitor in series.",
|
||||
"Let's see. Let's go back to our usual",
|
||||
"mantra. Think about Steve Umans when",
|
||||
"you do this. What would he do?",
|
||||
"He would say ah-ha, at very low frequencies the",
|
||||
"capacitor is going to look like an open circuit.",
|
||||
"In my voltage divider, I am measuring the voltage",
|
||||
"across an open circuit, so the entire Vi must drop",
|
||||
"across the inductor and capacitor.",
|
||||
"Similarly, at very high frequencies the inductor looks",
|
||||
"like an open circuit now, so it looks like this.",
|
||||
"At very high frequencies inductor is an open circuit.",
|
||||
"And, again, I'm looking at the voltage divider across the near",
|
||||
"infinite resistance, impedance, so I get a high",
|
||||
"value here as well. Well, in the middle the value",
|
||||
"dips and I get something like this.",
|
||||
"So, this thing is called a band stop filter.",
|
||||
"Here I can nail any specific frequency, as long as the",
|
||||
"frequency falls in roughly that regime.",
|
||||
"Yet another example.",
|
||||
"",
|
||||
"The reason I'm working on so many examples is that to",
|
||||
"experts, a large part of what they do is look at a circuit and",
|
||||
"boom, give a rough form of how it looks like.",
|
||||
"That can get you half the way there in most of what you're",
|
||||
"going to do. How did this look like?",
|
||||
"If I take the voltage Vo versus Vi, let's take a look.",
|
||||
"At very low frequencies, the inductor looks like a short",
|
||||
"circuit, correct? I am talking the voltage across",
|
||||
"a short circuit, so it looks like this.",
|
||||
"At very high frequencies, I am taking a voltage across a",
|
||||
"parallel combination, but the capacitor is now a",
|
||||
"short circuit. So, that looks like a",
|
||||
"capacitor. This looks like an inductor out",
|
||||
"here and this is a capacitor holding sway here.",
|
||||
"And so, somewhere in the middle it goes up and comes down like",
|
||||
"that. So, it's a band pass filter.",
|
||||
"What is amazing is that you can take fairly complicated",
|
||||
"circuits, and just by doing a quick analysis of what happens",
|
||||
"at very low frequencies, what happens at very high",
|
||||
"frequencies, you can roughly sketch the response.",
|
||||
"And then what you should do, in addition to that,",
|
||||
"is if it's a second order circuit, just assume that it's",
|
||||
"going to do something interesting at its resonance",
|
||||
"frequency, at omega nought equals one by square root of LC.",
|
||||
"Something interesting is going to happen.",
|
||||
"Check it out. And for circuits that are first",
|
||||
"order, RC or RL, the important number is the",
|
||||
"time constant RC. Usually, when you're driving it",
|
||||
"at one by RC, omega equals one by RC then",
|
||||
"what happens is that you often times end up getting a value",
|
||||
"that is one by square root two times the input value in the",
|
||||
"circuits we looked at here. Next, what I am going to do is",
|
||||
"talk about a major, major application of filters.",
|
||||
"And that is an AM receiver. Let me do Radios 101 for 30",
|
||||
"seconds. These guys have an antenna.",
|
||||
"You take a ground here. You pick up a signal at your",
|
||||
"antenna. There is an implied ground as",
|
||||
"well. And what you do,",
|
||||
"as a first step, is you begin processing the",
|
||||
"signal now. What we place right there is a",
|
||||
"little filter that looks like this.",
|
||||
"It is a inductor and a capacitor in parallel.",
|
||||
"And this capacitor is really your tuner that you can tune to",
|
||||
"radio frequencies. And then what you have here is",
|
||||
"a bunch of other processing and end up with your speaker.",
|
||||
"And the processing that happens here is you have a demodulator,",
|
||||
"you have an amplifier and a bunch of other things that let's",
|
||||
"not worry about them for now. What we do here is the antenna",
|
||||
"picks up a signal. So, in some sense,",
|
||||
"this part of the circuit here is your source.",
|
||||
"I could replace it with its Thevenin equivalent as follows.",
|
||||
"",
|
||||
"So, the front end of your radio looks like a Vi,",
|
||||
"R, L and a C. Where have you seen this",
|
||||
"before? Right there.",
|
||||
"That's the front end of radios. Let me tell you why I need a",
|
||||
"band pass filter in a radio out here.",
|
||||
"The way life works is as follows.",
|
||||
"I have my frequency. Let me do this not in radians",
|
||||
"but in kilohertz for now, and let me plot your radio",
|
||||
"signal strength. In the Boston area,",
|
||||
"the signals go between 540 kilohertz and they go all the",
|
||||
"way to 1600 kilohertz. In some areas we have begun to",
|
||||
"use the 1700 extra band as well for some new stations.",
|
||||
"This is the frequency range of interest.",
|
||||
"If you look at your radio tuner, you will see 540",
|
||||
"kilohertz all the way up to 1600 and you can tune your AM radio.",
|
||||
"The way it works is that each station is given 10 kilohertz of",
|
||||
"spectrum here. And so, this is at 1000",
|
||||
"kilohertz, 1010 kilohertz and so on.",
|
||||
"And each station transmits its signal in plus or minus 5",
|
||||
"kilohertz around that point. And this station transmits it",
|
||||
"here and this station transmits it here and so on.",
|
||||
"This is 1030. This guy is WBZ News Radio",
|
||||
"1030, for those of you who listen to it.",
|
||||
"What happens is that at 10 kilohertz, each station gets 10",
|
||||
"kilohertz, and so WBZ transmits in the 10 kilohertz around 1030.",
|
||||
"Notice that each of these signals transmitted by radio",
|
||||
"stations happen within small bands.",
|
||||
"Now, you will learn a lot more about modulation and how do you",
|
||||
"get a signal to go in a small band and all that stuff.",
|
||||
"You will learn about that in 6.003.",
|
||||
"For now, don't worry about how I did all of this.",
|
||||
"How do you listen to that station?",
|
||||
"The way you listen to that station is you put a low pass",
|
||||
"filter here. You put a low pass filter that",
|
||||
"does the following. Let's say I want to hear WBZ",
|
||||
"1030.",
|
||||
"",
|
||||
"If I pass this entire signal through that filter.",
|
||||
"And if I arrange to have the omega nought of my filter at",
|
||||
"1030. If I can arrange to have the",
|
||||
"omega nought at 1030 then this is the response of my filter.",
|
||||
"And I am going to pick out this guy and cut out everything else.",
|
||||
"I am just going to get this.",
|
||||
"",
|
||||
"Let's listen to the station for some time.",
|
||||
"",
|
||||
"So, you can see I can tune to the station WBUL."
|
||||
]
|
||||
}
|
||||
@@ -1,1352 +0,0 @@
|
||||
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"text": [
|
||||
"All right, good morning. So today, we are going to talk about what is both a basic device",
|
||||
"in itself, the amplifier, and it also serves as a real key example of both nonlinear analysis",
|
||||
"and small signal analysis.",
|
||||
"So, today, dependent sources and amplifiers. So, let me first spend a few seconds just",
|
||||
"pointing out to you some of the key points from our previous lectures. I also want to",
|
||||
"point out that each chapter in the course notes has a summary at the end of it.",
|
||||
"And if you take a quick scan of the summary at the end of each chapter, it highlights",
|
||||
"the major takeaway points from each chapter. It stresses what's important, and if you have",
|
||||
"to remember a few things, what are those things to remember? So, to quickly review, we talked",
|
||||
"about a few primitive elements: resistors, voltage sources, and so on.",
|
||||
"And by now, you should have the facility to play around with these device elements. And",
|
||||
"then we talked about the Node method, and this is kind of the workhorse of 6.002. When",
|
||||
"in doubt, use the Node method.",
|
||||
"OK, and this will work both for linear circuits and nonlinear circuits. OK, so if you see",
|
||||
"a problem, or if you see a situation in real life that requires analysis, then as a first",
|
||||
"step, you should try to think of whether you could apply some of the key intuitive shortcut",
|
||||
"methods, superposition.",
|
||||
"One of my favorites, the Thevenin method, the Norton method, or the method that involves",
|
||||
"composition, that is very quickly analyzing circuits that have resistors in series and",
|
||||
"parallel. OK, so if you can apply one of these quick, intuitive, shortcut methods, go do",
|
||||
"so.",
|
||||
"If you can't, then usually you can resort to the Node method irrespective of whether",
|
||||
"the circuit is linear or nonlinear. So the last week was focused on the nonlinear method",
|
||||
"or nonlinear circuits, and we spent the first lecture talking about a straightforward application",
|
||||
"of the Node method, which gave us a bunch of nonlinear equations that we had to solve.",
|
||||
"In the last lecture, we talked about the small signal trick. What we said is if you look",
|
||||
"at the whole space of nonlinear circuits, then within that space, if we focus on small",
|
||||
"variations, small perturbations about an operating point, then even the behavior of nonlinear",
|
||||
"circuits in that small regime would be linear.",
|
||||
"So small signal method. And as an example, I showed you how I could take a highly nonlinear",
|
||||
"device like the garage door opener LED, and using that, build a pretty nice transmitter",
|
||||
"that would transmit music.",
|
||||
"And as long as we kept the signal small, and operated the device in a region where its",
|
||||
"transfer curve was relatively smooth, and I biased, or set the operating point appropriately,",
|
||||
"I would get a linear, small signal response.",
|
||||
"OK. So today, we're going to do a couple things. We're going to look at dependent sources.",
|
||||
"And the reading for this is section 2.6 of your course notes. And, the dependent source",
|
||||
"will be a new element in your tool chest.",
|
||||
"We will also do amplifiers, and amplifiers are in section 7.1 and section 7.2 of your",
|
||||
"course notes. So, before I begin with dependent sources, I'm just a huge believer in motivating",
|
||||
"things with real world examples.",
|
||||
"OK, so let me start by motivating: why we need an amplifier? Why do we need to do things",
|
||||
"like this? Or why do we even bother? And, spend a few minutes really getting you to",
|
||||
"appreciate that amplification is fundamental.",
|
||||
"OK, it's as foundational to life as high fat potato chips and stuff like that. So, let's",
|
||||
"do some basic examples here. So first, let me talk about, why do we need to amplify signals.",
|
||||
"Why amplify? Why do we care about building an amplifier? So, an amplifier, think of a",
|
||||
"little box, and apply some sort of small input.",
|
||||
"And I get a larger output. In this example, this may be a voltage with a swing of 10 mV,",
|
||||
"and in this case, the output might be another voltage with a swing of, say, 100 mV. And",
|
||||
"commonly, the amplifier, in addition to an input and an output, input port and output",
|
||||
"port, may also contain the power port, OK, so that I can apply a power supply to the",
|
||||
"amplifier because commonly as an amplifier signal, I'm looking for a power gain as well,",
|
||||
"an increase in the power provided by the output.",
|
||||
"So, that's an abstract definition of an amplifier, and let's take a look at an example of why",
|
||||
"we may need this. So let's say I have a small, useful signal, and let's say the signal has",
|
||||
"1 mV peak to peak.",
|
||||
"And, I'm looking to transmit the signal over a wire to some other point. But let's say",
|
||||
"that in this environment, I get a bunch of noise that is in a noisy environment. And",
|
||||
"in this environment, let's assume that some noise may get superimposed.",
|
||||
"And if I have a 1 mV signal, and 10 mV of noise, then what I end up with at the output",
|
||||
"is something that looks like this. And it's really hard to distinguish my 1 mV signal",
|
||||
"from that large amount of noise.",
|
||||
"On the other hand, if I do the following, if I took the signal and passed the signal",
|
||||
"to an amplifier, and I amplified the signal to be a much larger version of the same signal,",
|
||||
"let's say in this particular situation 100 mV peak to peak signal.",
|
||||
"OK, so I magnified the signal by a factor of 100. OK, let's say it's a linear amplifier,",
|
||||
"I linearly amplified signal to be 100 mV, then in that case, if I had a noise on top",
|
||||
"of this, it's going to be less discernible.",
|
||||
"The signal will look like this.",
|
||||
"OK, my 10 mV noise would add on to it. But, this is still pretty decent. I can still recognize",
|
||||
"the input. And so, this is one application of amplification. If I need to send something",
|
||||
"from point A to point B as an analog signal, then an amplified signal is less prone to",
|
||||
"noise attacks than a small signal.",
|
||||
"Not surprisingly, a large number of devices that are used in everyday life have amplifiers",
|
||||
"built into them. So, get a little cell phone, and virtually every single cell phone contains",
|
||||
"an amplifier. By the way, this is an all digital cell phone.",
|
||||
"It's a Kyocera, I forget the number now. It's completely digital. OK, although they say",
|
||||
"it's completely digital, it turns out that a significant fraction of the circuitry is",
|
||||
"analog, in particular, so digital is sort of a marketing term to say that there's something",
|
||||
"special about this.",
|
||||
"But remember, there's a bunch of analog stuff. So, here's my little antenna from the cell",
|
||||
"phone. OK, and typically the first thing that happens to a signal as it comes out of the",
|
||||
"antenna in your cell phone is, look at cell phone circuits, or cell phone systems would",
|
||||
"be something that looks like this, OK, this, and may have a label LNA.",
|
||||
"If someone were to take a guess at what LNA might stand for? What's that? Linear amplifier.",
|
||||
"That's pretty good. So that's LNA. Close enough. A is correct. It's amplifier. What does L",
|
||||
"and N stand for? Low noise.",
|
||||
"OK, so this stands for low noise amplifier. So, I get a really rinky dinky small signal",
|
||||
"here, and then the low noise amplifier amplifies a signal. And in real cell phones, and for",
|
||||
"that matter, in your 802.11b, or 802.11a, or 802.11g wireless cards, same thing.",
|
||||
"Antenna, low noise amplifier, and then you may have a bunch of processing. And commonly,",
|
||||
"you have a bunch of analog processing. And then, you convert the analog to a digital",
|
||||
"signal. OK, I recall last week I asked somebody in class here, how would we transmit the signal",
|
||||
"from point A to point B without it being impacted way too much by noise, and he said, oh, go",
|
||||
"digital.",
|
||||
"Good point. OK, so if I go digital, I can transfer the signal without noise being a",
|
||||
"real factor. But the analog to digital converters need the signal strengths to be a given value",
|
||||
"before it can chop it up into digital levels.",
|
||||
"OK, so an amplifier is very fundamental. OK, and so in this case, what may be a signal",
|
||||
"of a few tens of microvolts to be amplified to some large enough value that it can be",
|
||||
"further processed. So, that's application of amplification in the analog domain.",
|
||||
"Let me talk about amplification in the digital domain. So, that's in the analog domain. This",
|
||||
"amplification is in the domain that I have both analog and digital. OK, and now let me",
|
||||
"talk about amplification in the digital domain, OK? I'm going to argue that amplification",
|
||||
"is absolutely foundational to the digital domain.",
|
||||
"OK, the digital abstraction would not occur if I did not have basic amplification. OK,",
|
||||
"and the next minute and 37 seconds I will prove that to you, OK? So, let's do so. So,",
|
||||
"let's suppose I have a very simple digital system, and the system simply contains a pair",
|
||||
"of inverters.",
|
||||
"So, if I send a one here, it's a zero here and a one here, which is a very simple, trivial,",
|
||||
"digital system. And here's the input. Here's the output. And we said that for digital systems",
|
||||
"of this sort to work, they have to follow a static discipline.",
|
||||
"OK, our signals and our circuits must follow a discipline for them all to work together.",
|
||||
"And, the discipline we described comprised of signals adhering to certain voltage thresholds",
|
||||
"so that all the components in the system could agree on what comprised a zero, and what comprised",
|
||||
"a one, OK? So the way we did that was we said that you would have a threshold called VIH,",
|
||||
"V input high, and another threshold called VIL, V input low.",
|
||||
"OK, and we said that this circuit must recognize signals that are higher than VIH, 3 V for",
|
||||
"example as a one, and simultaneously, any signal that has a voltage level less than",
|
||||
"VIL, say, two volts, should be recognized as a zero.",
|
||||
"That was the input constraint. On the output, it had a similar set of constraints, where",
|
||||
"we had tougher constraints on devices, where we said that the output had to satisfy a output",
|
||||
"low constraint, output high constraint.",
|
||||
"What this said is that for this circuit to be called a good digital circuit that satisfies",
|
||||
"the static discipline, signals that were ones here should be recognized as such. And if",
|
||||
"I am producing a one as an output, then the signal level should be higher than VOH.",
|
||||
"Similarly, if the signal's a zero, then it should be less than VOL. So as an example,",
|
||||
"this may be 2 V, this may be 3 V, and this may be 4 V, and this may be 1 V. OK, so input,",
|
||||
"I should recognize 2 V and less as a zero, but at the output I have to produce a very,",
|
||||
"very low value, 1 V.",
|
||||
"So, I have some noise margin. So as an example, say if I made a plot of the input/output,",
|
||||
"so I get my VIL here and VIH here. This is time. This would comprise a valid digital",
|
||||
"signal: zero, one, zero, one, and so on.",
|
||||
"OK, now, I had a tougher set of constraints at the output. I would have VOL, VOH. So,",
|
||||
"at the output, OK, I'm required to stretch the ones and zeros to be further apart from",
|
||||
"each other so that I get noise margin, and the corresponding signal for our little circuit",
|
||||
"there would look like so.",
|
||||
"Right, if this is a valid input, then this would be the corresponding, valid output.",
|
||||
"OK, and need I say more? OK, you can see that, intuitively, look, there's amplification happening",
|
||||
"here, and the reason is that VOL is chosen to be less than VIL, and VOH is higher than",
|
||||
"VIH.",
|
||||
"So therefore, the signal has to be stretched. The signal has to be amplified. OK, and what's",
|
||||
"the minimum amplification needed for the system to work? The minimum amplification is if I",
|
||||
"had a signal that looked like this.",
|
||||
"OK, that barely skimmed the VIL, VIH level. OK, so if signal were this high peak to peak,",
|
||||
"VIH minus VIL, and what's the absolute minimum signal at the output? It would look something",
|
||||
"like this. OK, barely skimming VOL and VOH, OK, so the corresponding output level would",
|
||||
"be VOH minus VOL.",
|
||||
"OK, so this is the absolute minimum amplification that my digital circuit has to provide. OK,",
|
||||
"and notice, VOH is larger than VIH. VOL is smaller than VIL. Therefore, this quantity",
|
||||
"needs to be greater than one.",
|
||||
"OK, so I've shown you both a simple, graphical, intuitive explanation, and this is a slightly",
|
||||
"more formal proof that even the digital circuit really requires to have amplification built",
|
||||
"into it, if it is to satisfy valid static disciplines.",
|
||||
"Yes? Yes. The question is, is that the same as gain? Good question. Yes, the term amplification",
|
||||
"has many, many variants. You could say gain. You could say amplification. You could say",
|
||||
"increase in signal strength, and so on and so forth.",
|
||||
"And in fact, when talking about low noise amplifiers, people sometimes talk about having",
|
||||
"the low noise, high gain amplifier at the input stage. OK, so let me pause there in",
|
||||
"terms of motivation. So, I believe I've motivated every which way: pure analog, analog/digital,",
|
||||
"and digital.",
|
||||
"OK, so I've covered every single base here. And so, we need amplification. OK, so let's",
|
||||
"look at how to build a fundamental, primitive device called the amplifier. Before we do",
|
||||
"that, however, let me take a quick detour.",
|
||||
"It will be convenient for me, as I show you how to build an amplifier, to introduce a",
|
||||
"new device, a new element, called the dependent source. OK, let me introduce a new device",
|
||||
"for your arsenal of devices, along with resistors, You learned about a MOSFET, a switch, voltage",
|
||||
"source, current source, and now a dependent source.",
|
||||
"So, a dependent source looks like this, OK, has an output port, and has a control port.",
|
||||
"So, a dependent source in its simplest form has two ports: an input port and an output",
|
||||
"port. Remember, a port is a convenient pairing of terminals, and I apply signals to such",
|
||||
"terminal pairs.",
|
||||
"But this is a abstract diagram for a dependent source, and to get a little bit more specific,",
|
||||
"let me show you an example of a dependent source. So, let's say, here's my input, and",
|
||||
"I label the terminal variables for the input.",
|
||||
"VC is the voltage applied to the input, and IC is the current into this terminal here.",
|
||||
"And, here is the symbol for the dependent source. Much like a current source or a voltage",
|
||||
"source has a circle around it, the corresponding symbol for a dependent source is like so.",
|
||||
"So this example, for instance, is a dependent, current source. I can apply the corresponding",
|
||||
"output variables, I0, OK, and I can say that the current, I, is some function. In this",
|
||||
"example, I've designed the example that the current through the current source, I, is",
|
||||
"some function of the input voltage or the control voltage, VC.",
|
||||
"OK, so notice that the current through a current source, the current through this current source,",
|
||||
"I, is some function of another variable. OK, in this example, it's the voltage across its",
|
||||
"control port.",
|
||||
"Not surprisingly, this device is called a voltage controlled current source -- -- or",
|
||||
"a VCCS. So, in like manner I can also devise other forms of sources. You can think of this",
|
||||
"is a device where a voltage controls an output current.",
|
||||
"You can think of all other combinations, current controlling current, voltage controlling voltage,",
|
||||
"current controlling voltage, and so on. So, another example, I give you another dependent",
|
||||
"source, and in this situation, my output current is controlled by an input current, VC.",
|
||||
"IC rather. And I claim that I for this one is some function of a current, IC. OK, it's",
|
||||
"another dependent source where the output current for its output port is related to",
|
||||
"the current, IC. And, this is a current controlled current source.",
|
||||
"OK, it's a current controlled current source. And, if I had lots of time on my hands, and",
|
||||
"I was wanting to kill time, I'd sit around drawing for you, other types of dependent",
|
||||
"sources. I would draw for you a current controlled voltage sourced, and I could also draw for",
|
||||
"you a voltage controlled voltage source.",
|
||||
"OK, so that's an abstract diagram for such a source. And so, let's do a few examples",
|
||||
"involving elements like this. To begin, just so you can build up your intuition, let me",
|
||||
"start by doing a very simple circuit, involving an independent current source, OK, just so we can relate back to what we've",
|
||||
"been doing so far.",
|
||||
"So, let's say I have some resistor, and I have a standard current source with current",
|
||||
"I nought. This is an independent current source. Remember the circle? And, some resistor, R,",
|
||||
"and let's say I care about the voltage across the resistor.",
|
||||
"OK, so I have a current I nought flowing through it. So, I can very quickly write down VR as,",
|
||||
"simply, I0 R. OK, it's the drop across the resistor when a current I nought flows through",
|
||||
"it. OK, so this is what you've been used to doing.",
|
||||
"Correspondingly, I can do an example with a dependent current source. And, as an example,",
|
||||
"I'll use a voltage controlled current source. OK, a voltage controlled current source is",
|
||||
"a dependent current source whose output current depends on the voltage applied at the control",
|
||||
"port of the current source.",
|
||||
"So let me build a little circuit. OK, so here's my current. And let's say it's VC IC for the",
|
||||
"control port, and similarly, let's say my current I here is some function of the control",
|
||||
"port voltage. And let's say, to be specific, there is some K over VC, some function.",
|
||||
"OK, there are a variety of dependent sources that can be built, and here's a hypothetical",
|
||||
"device where the output current is mathematically related to the input in the following manner.",
|
||||
"So, let me build a circuit of the following form.",
|
||||
"So, let's add the resistor, R, and here's my circuit, OK? And, as before, let me look",
|
||||
"to figuring out what VR is. So, notice that I have to supply some voltage at the input",
|
||||
"so that the output can depend on the input because right now I don't know what the input",
|
||||
"here.",
|
||||
"So what I'll do is let me apply VR over here. OK, so let me make this connection. OK, let",
|
||||
"me make the connection from here to here. What I've done is I've applied VR at the control",
|
||||
"port of the dependent current source.",
|
||||
"OK, and I often draw a circuit like this. This looks pretty messy. I will often draw",
|
||||
"the circuit like so: R, VR. OK, short form circuit drawing would look like this. This",
|
||||
"is a complete drawing that I show you the explicit connections of the control port,",
|
||||
"but oftentimes, when the control port does not have any other impact in the circuit,",
|
||||
"you can eliminate, don't explicitly show the control port.",
|
||||
"Rather, you can simply show the dependence of the output current on whatever circuit",
|
||||
"variable you have in mind. So, you can draw the diamond like this, and see its current",
|
||||
"is some function of VR. VR in this is case is K divided by VR, OK? OK, so let's go ahead and analyze this little",
|
||||
"circuit here, and look at what this might give us.",
|
||||
"Our goal, as before, is to find out the value, VR. So, in this case, let's apply the Node",
|
||||
"method to this node, and sum the currents into that node to be zero. OK, so sum the",
|
||||
"currents going into that node to be zero.",
|
||||
"The current going down is simply VR divided by R. OK, and that is equal to the current",
|
||||
"that is going out of the node. And so that is equal to F of VR. And I know that F of",
|
||||
"VR is given by K divided by VR.",
|
||||
"OK, a simple application of the Node method. So then, I collect VR's on the left hand side,",
|
||||
"and I get VR squared is K times R, OK, and VR is simply the square root of KR. There",
|
||||
"you go: I'm done. OK, I've gone ahead an applied the Node method to this, and when have to",
|
||||
"figure out the current here, I simply reflect the fact that it depends on VR like so, and",
|
||||
"I just go ahead and solve the circuit.",
|
||||
"Remember, the workhorse of the circuit industry, the Node method, when in doubt, apply it.",
|
||||
"It simply works. And notice, this is a nonlinear circuit. OK, the dependence is nonlinear,",
|
||||
"and I get the response like so.",
|
||||
"So, to plug in some numbers, supposing K was 10 to the minus 3 amperes per volt, and R",
|
||||
"was one kilo ohm, then I can plug the numbers in and the kilo here cancels with the 10 to",
|
||||
"the minus 3, and I get VR equals 1 V.",
|
||||
"OK, this simply says, if I build a circuit like this, then this voltage here will be",
|
||||
"1 V. So, again, as long as you remember that the dependent source is simply another little",
|
||||
"circuit element, OK, and you usually draw just the output port for dependent sources,",
|
||||
"and reflect the way that the control affects the current, that'll suffice, and you get,",
|
||||
"through the application of the Node method, the variable you're interested in.",
|
||||
"Let's do another example,",
|
||||
"OK, of another fun current source, a voltage controlled current source, and look at it",
|
||||
"this way. So, let's say I have a resistor, and I have a current source, a resistor, RL,",
|
||||
"and this goes to some, I apply a VS here.",
|
||||
"Remember this short form notation; that's simply applying a supply VS between that node",
|
||||
"and the ground. OK, and let us say the current IV through the device is some function of",
|
||||
"the current at its control port.",
|
||||
"OK, so I'm not going to show you that. But remember that the device already looks like",
|
||||
"this, that there is a control port here. I'm not showing that to you. And let us say that",
|
||||
"I apply some voltage, VI, to the input port.",
|
||||
"The reason we often don't show the input port is for many practical dependent sources, the",
|
||||
"input has no other effect on the circuit. So, for example, in this case, the input has",
|
||||
"infinite resistance looking in.",
|
||||
"So therefore, if I apply a VI here, it doesn't draw any current from VI. I simply apply the",
|
||||
"voltage, VI. It doesn't affect the circuit in any other way except in terms of how it",
|
||||
"controls the current ID.",
|
||||
"So let's say the current ID is some function of VI because VI is applied at the control",
|
||||
"port. OK, and as I pointed out before, I oftentimes, just for clarity, just to show this dependent",
|
||||
"source explicitly.",
|
||||
"OK, so let's work the example. So as I said, I'm going to choose ID to be F of VI, and",
|
||||
"let's pick some specific parameters here. Let's say it's K by two VI minus one, both",
|
||||
"squared. OK, and let's say this is true for VI less than equal to one volt.",
|
||||
"And let us also say that ID equals zero for VI less than one volt. OK, it's a dependent",
|
||||
"source, and it can have various forms of dependences on the input. And, I just picked an example",
|
||||
"of some hypothetical, or as yet, hypothetical dependent source, the current through which",
|
||||
"is related to the input using a square law relation, VI minus one all squared as long",
|
||||
"as VI is greater than one.",
|
||||
"And if VI is less than one, then the current is simply zero, it shuts off. So, I can go",
|
||||
"ahead and apply. So, let's say I want to find out V0 versus VI. So, I care about finding",
|
||||
"out V0. V0 is the voltage of this node with respect to ground.",
|
||||
"OK, so it's a slightly more complicated circuit than you saw up here, than you saw up there.",
|
||||
"So, let's go ahead and do this example. Start by applying the workhorse of the circuits",
|
||||
"business, the Node method, and let's start with doing this for VI.",
|
||||
"Let's first do it for VI greater than one, notice the behavior of this is different for",
|
||||
"different ranges of VI. So let's first do it for VI greater than or equal to one and",
|
||||
"apply the Node method. Node method says sum the currents going into this node; we know",
|
||||
"the voltage at this node.",
|
||||
"It's VI. We know the voltage at this node. It's VS. OK, the only unknown is V nought.",
|
||||
"And so, let's go ahead and write the node equations for that node. So, the current going",
|
||||
"up, let me simply equate the current going up to the current that has been supplied by",
|
||||
"this particular node here.",
|
||||
"And, that should equate that the two of them should sum to zero, the current going up plus",
|
||||
"the current going down should sum to zero. So, I get V0 minus VS divided by R. That's",
|
||||
"the current going up.",
|
||||
"Plus, the current going down must sum to zero, plus ID must sum to zero. And ID is going",
|
||||
"to be K divided by two VI minus one all squared. That must equal zero. Straightforward application",
|
||||
"of Node method, current going up plus the current going down at this node should equal",
|
||||
"zero because the total current leaving the node must be zero, OK? So I can go ahead and",
|
||||
"simplify this, multiply it throughout by, I call this RL here.",
|
||||
"So, multiply it throughout by RL, and move all of this to the other side, so I get VS",
|
||||
"divided by RL, multiply it throughout by RL. I get VS at this side. I take this term to",
|
||||
"the other side. This becomes a minus.",
|
||||
"RL multiplies here, so I get KRL. That's the expression I get. V nought is VS minus KRL",
|
||||
"divided by two times VI minus one all squared. Let me put a box around this because I will",
|
||||
"be referring to this more times in 6.002 for a variety of reasons than probably any other",
|
||||
"equation on Earth.",
|
||||
"OK, this is the first time you saw it. You saw it here. OK, mark it down. You'll smile",
|
||||
"every other time you look at it in quizzes, and you will find out why this comes up very",
|
||||
"often in 6.002. So, I'll just give you a few seconds to savor this big moment in your 6.002",
|
||||
"life.",
|
||||
"All right, OK, so it's pretty simple actually. I mean, there's really not much. A lot of",
|
||||
"this stuff is just a plain old, simple application of the Node method, and things just fall out.",
|
||||
"It's just so simple.",
|
||||
"So, the V nought, I apply the Node method, I get V nought for this nonlinear circuit.",
|
||||
"I can also it for VI less than one. For VI less than one, when VI is less than one, what",
|
||||
"happens? ID is zero. OK, since ID is zero, think of this as an open circuit.",
|
||||
"OK, so there's no voltage drop across RL. And, this voltage V nought is equal to VS.",
|
||||
"So, I like to see things in pictures. I'm not an equations kind of person. I'm much",
|
||||
"more of a graphical person.",
|
||||
"So, let me draw a little graph to show how V nought, to see the form of V nought, and",
|
||||
"then let's study that little system a little bit more carefully. So, this is page seven,",
|
||||
"and we plot V nought versus VI for you.",
|
||||
"And let's take a look at how this really simple circuit looks. This has got nothing. It's",
|
||||
"got an RL resistor connected to a supply, and a dependent current source, and I apply",
|
||||
"some voltage VI at the input.",
|
||||
"It's a very, very simple circuit. So, let's see. So as long as VI is less than one, the output stays at VS. OK, that makes intuitive",
|
||||
"sense, right? As long as the current here is zero, this is like an open circuit here.",
|
||||
"If this is an open circuit, then effectively, V nought is simply the voltage VS. V nought",
|
||||
"simply appears here. If you want to grunge through KVL and KCL, go ahead. VS minus RL",
|
||||
"times the current is V nought, and the current is zero so it's, yes.",
|
||||
"So, this is simply VS. When VI goes above one volt, fun stuff begins to happen. OK,",
|
||||
"when V nought goes above one volt, then this equation applies because VI is greater than",
|
||||
"one. This equation applies.",
|
||||
"And, when VI is a one, one minus one is zero. This term cancels out, so this is VS. OK,",
|
||||
"phew! So, I start off here. As VI increases, what happens now? As VI increases, this term",
|
||||
"here becomes increasingly negative, OK, subtracting from VS.",
|
||||
"OK, so I get some behavior like this. V nought begins to drop. And it makes intuitive sense,",
|
||||
"right? As ID begins to increase, the voltage here will begin to drop because I'm drawing",
|
||||
"more and more current through RL.",
|
||||
"I'm dropping more and more across RL. So more and more drops across RL, so V nought begins",
|
||||
"to drop too. So, it looks something like this. I'll show you a little demo, but my claim",
|
||||
"is that you have just seen an amplifier.",
|
||||
"Whoa. You just saw an amplifier. So, I snuck an amplifier by you, OK? So, I just snuck an amplifier past you. I'll show",
|
||||
"you why in a second. So, let's take a look at this waveform here. Let's not worry about",
|
||||
"what happens way down here.",
|
||||
"We'll talk about that a little later. But, look at this curve here. I claim there is",
|
||||
"amplification in the following sense. Focus on some change in the input voltage, delta",
|
||||
"VI, OK, and for that change in input voltage, I get some change in the output voltage.",
|
||||
"OK, for some change in the input voltage, delta VI, I get some change in the output",
|
||||
"voltage. And guess what? In this, at least the way I have drawn it, delta V nought divided",
|
||||
"by delta VI, if I can find regions of the curve where this is greater than one, then",
|
||||
"I have amplification.",
|
||||
"OK, so what's that saying? What that's saying is that if I apply some voltage here, OK,",
|
||||
"and I change that voltage by a small amount from, let's say, 2 V to 2.1. OK, I am going",
|
||||
"to find the output voltage.",
|
||||
"Let's say I go from 2 V to 2.1 here. OK, abstractly out there, I might have an output that goes",
|
||||
"from three to, let's say, two V perhaps. OK, so for a 0.1 change here, I'm going to get",
|
||||
"a bigger drop here, so from 3 V to 2 V, giving me an amplification in this little circuit.",
|
||||
"OK, so we'll see this again and again, and you'll really understand it. So, I have a",
|
||||
"small change in the input, and I have a corresponding larger change in the output. So, I've shown",
|
||||
"you an amplifier.",
|
||||
"I haven't shown you a linear amplifier. There's an extra charge for that. OK, that'll happen",
|
||||
"later. OK, all I've shown you so far is an amplifier, and this happens to be a crummy",
|
||||
"amplifier. It's a nonlinear amplifier because, notice, this is not linear.",
|
||||
"It's a nice little curve, and so it's not linear. But, I promised you an amplifier,",
|
||||
"and I'm cheap, and that's all you get for now. OK, we'll see linear stuff later, but",
|
||||
"for now, I have a little amplifier.",
|
||||
"So, let's do some real numbers, and plot some numbers down, and also look at a demo. So,",
|
||||
"let's do an example. Let's say VS is 10 V, that the K is two milliamps per V squared,",
|
||||
"and let's say RL is five kilo-ohms, OK? So, let me substitute these values into that equation,",
|
||||
"and I get V nought is, VS is ten.",
|
||||
"So, it's ten minus, KRL divided by two. So, K is two milliamps. Two milliamps times five",
|
||||
"kilo-ohms is ten divided by two gives me five, and VI minus one squared. That's what I have.",
|
||||
"I just plug in a bunch of numbers, and that's what I get.",
|
||||
"So, what I'll do is let me just do a little table for you, and plot using real numbers,",
|
||||
"simply plot those values for you.",
|
||||
"So when VI is zero, my current is zero, and I get - oh, that equation doesn't apply, by",
|
||||
"the way; that applies when VI is greater than one. Ok. So as long as VI is less than one,",
|
||||
"my output is simply VS, the output is simply ten volts.",
|
||||
"Ok, so all the way up to one, my output V is - all the units are all volts - that's",
|
||||
"what I get.",
|
||||
"I come down to 2, I plug in two for VI, 2 minus 1 is a 1. So it's 1 squared. 5 times",
|
||||
"1 squared is five. And 10 minus 5 is 5. I get 5 out here.",
|
||||
"Ok? And then, I can go and do the math. If it's 2.1, I get 4 volts here. And 2.2, I get",
|
||||
"2.8. And so on. Ok, notice that the .1 volt change here resulted in a - go up a .1 change",
|
||||
"here results in a minus 1 volt change there. So input went up by .1 volts, my output...",
|
||||
"kerplunked down by one whole volt.",
|
||||
"Ok, so a small change here resulted in a bigger change there. And that's the amplification",
|
||||
"that I am claiming here.",
|
||||
"Ok? So. Let me show you a small demo of a small device that I built involving such a",
|
||||
"dependent source.",
|
||||
"Let's do it here.",
|
||||
"Ok. So on my s axis, here is VI. And VO is on my y axis. And focus on this little point",
|
||||
"here.",
|
||||
"Ok? Right now my VI is zero. And so therefore that's my output. I will gradually increase",
|
||||
"VI, we're going to watch the output and see how it behaves. Pretty much like the little",
|
||||
"graph I drew for you.",
|
||||
"So I'm increasing VI. Ok, notice that invitially the current source is off, the dependent source",
|
||||
"is off, so I move straight down. Ok, nothing happens. Until I hit a value at which the",
|
||||
"the current source begins to come on. And then I begin to see a drop in the output as",
|
||||
"the current source begins to conduct current.",
|
||||
"So you see that as I increase the voltage VI, boom! You see the huge drop.",
|
||||
"Ok, notice that for a small change, I'm now getting a big drop in the output. Ok?",
|
||||
"So let's pause here for a second, and in the last couple of minutes, I want to cover one",
|
||||
"last point.",
|
||||
"Notice that the curve I've shown you up there looks like the curve up here: it goes kaboom!",
|
||||
"and drops according to come kind of formulation that I've shown you here.",
|
||||
"In the last couple of minutes, let me discuss a small point that's a practical issue.",
|
||||
"In the curve that I showed you, in the mathematics that I gave you, if you just go by the math.",
|
||||
"So what I'm about to show you will differentiate a mathematician from an electrical engineer.",
|
||||
"Mathematicians would have taken the curve, and reported it like this. This is zero. Mathematically, that equation says that starting",
|
||||
"here, this current simply goes down. But if I told you this device that I have here, this",
|
||||
"dependent source is a practical dependent source, a device that I have physically built,",
|
||||
"and I also say that it's a passive device. In other words, it cannot produce power. It's",
|
||||
"like a little resistor. It doesn't produce power. It's a passive device.",
|
||||
"So if it's a passive device, if I tell you that, then you'll say, Something doesn't make",
|
||||
"sense here. Mathematically, it says it should look like this. But what's special about a",
|
||||
"point down here? The point down here says the output has gone negative. This is zero",
|
||||
"here. The output has gone negative. And my current source is still supplying a current.",
|
||||
"Ok, so up here, the voltage across the device is positive, and it's supplying a current,",
|
||||
"so it's consuming power like a resistor. Like all bad little resistors do, they burn power.",
|
||||
"So here, on the other hand, my output is going to be negative, but it's still sitting there",
|
||||
"sinking current. Ok, because VO is negative, but my current is still in the same direction,",
|
||||
"what has now happened is the device has begun to supply power.",
|
||||
"So mathematically, this curve says the device has begun to supply power.",
|
||||
"It turns out it's not a practical device, it's a passive device. So it cannot go here.",
|
||||
"So what happens is that somewhere along here, our model breaks down. The equation I've shown",
|
||||
"you for the current source, where is it?",
|
||||
"This model breaks down.",
|
||||
"When V0 becomes very small, the model breaks down and it no longer behaves like a current",
|
||||
"source.",
|
||||
"It begins to behave more and more like a resistor. And what happens realistically, is that the",
|
||||
"output goes down and then kind of becomes a zero-hugging line. I'll show you that in",
|
||||
"a second.",
|
||||
"And it doesn't - for this particular device it doesn't really go down here.",
|
||||
"Let me just show you that part. So notice for that device, mathematically, just by that",
|
||||
"model, it should have just gone through the floor and it points through to the corridor",
|
||||
"below, but this is a prcatical device.",
|
||||
"So notice that the model breaks down. And that's what begins to happen.",
|
||||
"Ok, the device stops behaving like a dependent current source, rather it behaves like some",
|
||||
"corny old resistor or something like that and saturates out. Ok."
|
||||
]
|
||||
}
|
||||
@@ -1,1538 +0,0 @@
|
||||
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|
||||
"text": [
|
||||
"",
|
||||
"I will be replacing Professor Agarwal today because he is",
|
||||
"away. I am one of the recitation",
|
||||
"instructors for those of you who have not seen me.",
|
||||
"We will talk today about a neat application of RC networks and",
|
||||
"expand those to application in MOS memory systems.",
|
||||
"To connect with everything, we will get back to the basic",
|
||||
"circuit that we have been discussing so far.",
|
||||
"And you recall the circuit that we have been studying,",
|
||||
"the canonical RC with an input voltage function of t.",
|
||||
"And we had specified that we solved this problem for the case",
|
||||
"of a step input or a condition in which a t=0.",
|
||||
"At t greater or equal to zero vI is equal to some capital VI",
|
||||
"value that for now on is constant.",
|
||||
"And the other condition that we discussed was the value of the",
|
||||
"voltage on the capacitor that would exist at time t=0.",
|
||||
"Let's call that vc(0). And in general there is some",
|
||||
"finite value here. It can be zero or it can be",
|
||||
"different from zero. Given that, we learned how to",
|
||||
"write down directly, without messing around with",
|
||||
"differential equations, the answer for the voltage on",
|
||||
"the capacitor vc(t), let me define also my vc right",
|
||||
"here, is equal to VI, the final value,",
|
||||
"plus vc(0), the initial value on the capacitor,",
|
||||
"minus the final value, e^-t/RC.",
|
||||
"This is our standard equation to which we plug in,",
|
||||
"and it's either a rising exponential if VI is larger than",
|
||||
"VC or a decaying exponential if VI is a smaller value than VC.",
|
||||
"This should all be familiar. And, again, as pointed out in",
|
||||
"the notes, the reading for today is 10.3 and for the new material",
|
||||
"you should look at Chapter 11 where we discuss memory.",
|
||||
"This is where we stood as of last time.",
|
||||
"Now, I would like to discuss a little bit more about the",
|
||||
"storage of charge in capacitors. And how we can take advantage",
|
||||
"of that for storing logic state. One of the things that I am",
|
||||
"sure you must be aware of is that one of the perhaps most",
|
||||
"massively produced chips is actually the so-called DRAM",
|
||||
"which you find in every PC and every computer that exists",
|
||||
"anywhere. This DRAM is dynamic random",
|
||||
"access memory in which we can store a state and come back and",
|
||||
"look at it at any time later, provided we don't power off our",
|
||||
"machine. The logic state in the basic",
|
||||
"memory elements, of which instead there are",
|
||||
"close to 1 giga elements per chip, are stored on capacitors.",
|
||||
"And so we will play a little bit with that concept today.",
|
||||
"And, although we're not going to discuss the specific example",
|
||||
"of the DRAM, the basic elements of the DRAM you will see",
|
||||
"actually in a demo shortly. So that's the general response",
|
||||
"of this network that I have here to an input VI that happens at",
|
||||
"t=0. Now, the one thing that you",
|
||||
"recognize immediately is that it really doesn't matter what the",
|
||||
"value of VI was for t less than zero.",
|
||||
"What really counts is the value of VI at t=0.",
|
||||
"And that's the value that we're interested in.",
|
||||
"Now, there is an implicit statement in that.",
|
||||
"And that statement is that somehow that network appears",
|
||||
"like this at t=0. So, there has to be some switch",
|
||||
"there, and you will see that, that basically starts my",
|
||||
"condition to that at t=0. And so the history of VI really",
|
||||
"doesn't matter. The response following that",
|
||||
"equation that we have there will depend on the initial value",
|
||||
"which is vc(0) here. Now that is the voltage on the",
|
||||
"capacitor at that time. And then assuming that VI is a",
|
||||
"value that is larger than vc(0) will have a rising exponential",
|
||||
"that will come to this value. And this is the time constant",
|
||||
"RC and this is time. So, the capacitor starts with",
|
||||
"some voltage here and goes to a new voltage that is imposed by",
|
||||
"the input for time greater than zero.",
|
||||
"We can define at any one time, say this time,",
|
||||
"this time, this time, this time the state of the",
|
||||
"capacitor. The state.",
|
||||
"What is the state of the capacitor?",
|
||||
"The state is the summary of all inputs that are relevant to",
|
||||
"predicting the future. If I know the state of the",
|
||||
"capacitor this time, I can predict what it is going",
|
||||
"to go given a response VI here in the future.",
|
||||
"So, predicts the future. Now, what is the state variable",
|
||||
"on the capacitor? What is actually stored on the",
|
||||
"capacitor? You can say,",
|
||||
"well, what is stored is voltage.",
|
||||
"The real physical quantity that is stored is the charge q which",
|
||||
"is for linear capacitors related to the voltage,",
|
||||
"let me actually write it correctly, vc like this.",
|
||||
"So, the real state variable is this.",
|
||||
"",
|
||||
"But for a linear capacitor, since there is one-to-one",
|
||||
"relationship between the two, v is also a state variable.",
|
||||
"OK, so let's then go back to our original circuit.",
|
||||
"What we have is --",
|
||||
"",
|
||||
"-- vc(t), so that's the future value of the voltage on the",
|
||||
"capacitor, is a function of vc(0), the initial value and the",
|
||||
"variable input now in the future time.",
|
||||
"And for the case of vI(t) being constant VI for t greater or",
|
||||
"equal than zero we have the equation that we just described.",
|
||||
"Nothing new.",
|
||||
"",
|
||||
"All the past inputs to the capacitor for time t less or",
|
||||
"equal to zero is summarized in this value.",
|
||||
"And vi being constant the future is predicted from that.",
|
||||
"So, that's the concept of the state.",
|
||||
"There is an initial state on the capacitor.",
|
||||
"And then there is a final state that will be reached when",
|
||||
"equilibrium actually is achieved.",
|
||||
"There is a fair amount of discussion in the text,",
|
||||
"and we don't go in great detail here, but it is both convenient",
|
||||
"for analysis and also it's interesting in many cases to",
|
||||
"look at the response of a linear network for two different",
|
||||
"conditions. So, we're interested in two",
|
||||
"cases. One is the so-called zero state",
|
||||
"response. Now, what is the zero state",
|
||||
"response? It's the response to a",
|
||||
"condition in which we impose an input and impose also the",
|
||||
"condition that the initial value, initial state of the",
|
||||
"capacitor is zero. So then we ask how does it",
|
||||
"respond to vi(t)? So, starting with a capacitor",
|
||||
"at zero state what is the response?",
|
||||
"It allows us to decouple the initial conditions from the",
|
||||
"response to the input. Now, you will see that this is",
|
||||
"actually very useful. The second condition to which",
|
||||
"we're also very interested is the so-called zero input",
|
||||
"response. What is that?",
|
||||
"That is vi(t)=0. Now, it's the condition under",
|
||||
"which there is no input. vi(t)=0.",
|
||||
"The question here is how does it relax?",
|
||||
"We're starting with an initial state.",
|
||||
"So, how this state relaxes out in the circuit.",
|
||||
"Now, the zero state response, this one here is Z so called SR",
|
||||
"for our case, which I will write like this,",
|
||||
"vC, ZSR is simply a rising exponential.",
|
||||
"We start from zero and we go to VI.",
|
||||
"So, it's VI-VI e^-t/RC. So, that's the ZSR.",
|
||||
"The ZIR, the zero input response is like this.",
|
||||
"It's the decay of the initial voltage on the capacitor to zero",
|
||||
"or to equilibrium. Starting from vC(0) we're",
|
||||
"decaying like this. Now, do you see something",
|
||||
"that's rather obvious from what's on the board in terms of",
|
||||
"ZIR and ZSR and the final complete answer which is there?",
|
||||
"",
|
||||
"They are specific cases, but how do they relate to the",
|
||||
"full answer? It's the sum.",
|
||||
"It's the superposition of the two.",
|
||||
"What basically we see here -- And that's actually a general",
|
||||
"statement, is that vC = vC,ZSR + vC,ZIR.",
|
||||
"Now, you may say this is trivial because we started from",
|
||||
"that, ended back in that from some very simple observations.",
|
||||
"However, we are not always solving networks for responses",
|
||||
"that are steps. The input voltage may be a",
|
||||
"ramp. We did that in recitation.",
|
||||
"Or, it could be an impulse. Or, it can be a more",
|
||||
"complicated function. Having this observation in",
|
||||
"place actually allows us to solve the problem rather neatly.",
|
||||
"If I have time at the end, I might come back to this.",
|
||||
"So, this is the same equation as I started with,",
|
||||
"arrived at from a principle of superposition of two different",
|
||||
"solutions. One application of state which",
|
||||
"can be, since we have energy storage element here,",
|
||||
"the capacitor, which can be stored on the",
|
||||
"capacitor is in memory. And you may ask,",
|
||||
"so why do we need a memory node to perform logic?",
|
||||
"Well, there are cases in which a result depends on previous",
|
||||
"results. So, a computation proceeds in",
|
||||
"time. In order to do that,",
|
||||
"we need to store intermediate results and proceed forward.",
|
||||
"One good example is if you're doing a continuous summation,",
|
||||
"say, on your calculator, you keep putting things in the",
|
||||
"memory. The M+ button,",
|
||||
"right? And you keep adding a series of",
|
||||
"numbers. Every time we store the sum of",
|
||||
"the previous operation we add another number and so on.",
|
||||
"Clearly we need some way of storing state.",
|
||||
"For a complete computing system, we need combinational",
|
||||
"logic and we need memory. In fact, these are the two",
|
||||
"basic elements that are essential for any kind of",
|
||||
"computing system. We need to remember",
|
||||
"intermediate results. We need to remember transient",
|
||||
"inputs. And that's the role that all",
|
||||
"these enormous amount of memory that comes to play in computers",
|
||||
"is doing. The basic memory abstraction is",
|
||||
"as follows.",
|
||||
"",
|
||||
"Imagine a block which needs to be populated by transistor,",
|
||||
"resistor, capacitor, whatever elements.",
|
||||
"And it has a control input, which we will call the store.",
|
||||
"It has a state input that we will call dIN and has an output",
|
||||
"dOUT. When we're telling this",
|
||||
"element, OK, now it's time to store, it looks at the input dIN",
|
||||
"and stores it for, in principle,",
|
||||
"an infinite amount of time. If we were to make a drawing of",
|
||||
"this, of what this looks like, let's suppose,",
|
||||
"let me do all this in one axis. So, time moves this way.",
|
||||
"Let's suppose that we have an input dIN that looks like this,",
|
||||
"and the store command comes in the form of a logic.",
|
||||
"Let's actually suggest here this is logic one,",
|
||||
"this is logic zero. And, although this is not",
|
||||
"absolutely necessary, let's also define that the",
|
||||
"store command comes in the form of a logic one at this store",
|
||||
"input. Store, let's say,",
|
||||
"looks like this.",
|
||||
"",
|
||||
"What does the output look like then in this particular case?",
|
||||
"Assuming that the output was dOUT, the stored element was",
|
||||
"zero prior to the store, then the output would look like",
|
||||
"this. This is dOUT.",
|
||||
"As you can see, it would remember the one that",
|
||||
"it saw at this point. In fact, it would do that",
|
||||
"irrespective of what was stored in this memory cell.",
|
||||
"For example, suppose it was storing one and",
|
||||
"the output didn't change, it's still one.",
|
||||
"If it was storing a zero, it would flip to a one.",
|
||||
"If we had another store, let's say here,",
|
||||
"then what happens? Then it would go back down to",
|
||||
"zero because now we sampled an input that is zero and we",
|
||||
"flipped the state. That's what a memory --",
|
||||
"",
|
||||
"-- element or cell would do for us.",
|
||||
"It would remember the output state.",
|
||||
"And, not only that, but in principle it should be",
|
||||
"undisturbable. In other words,",
|
||||
"I may do something to this dOUT but it should not flip the",
|
||||
"state. And that comes about quite a",
|
||||
"bit. Because in actual integrated",
|
||||
"circuit memory there is lots and lots and lots of nearest",
|
||||
"neighbors to this cell which, when they're flipped,",
|
||||
"have a cross-coupling to the cell.",
|
||||
"The cell must be designed robust enough that it doesn't",
|
||||
"flip, that no coupling actually occurs.",
|
||||
"All right. Now we're going to try to apply",
|
||||
"what we've learned so far to invent a basic memory element.",
|
||||
"And, believe it or not, this is the key to the DRAM.",
|
||||
"",
|
||||
"Let's implement this in a circuit.",
|
||||
"",
|
||||
"Suppose I have a switch here like this.",
|
||||
"",
|
||||
"And I will put a capacitor. I take my dOUT here.",
|
||||
"This is dIN. And the switch is operated by a",
|
||||
"command here that we will call store.",
|
||||
"When store is one it goes up. When store is zero it is down",
|
||||
"here. That's capacitor C.",
|
||||
"This is the storage node.",
|
||||
"",
|
||||
"What are we actually storing in this case?",
|
||||
"Let's suppose that this voltage here is 5 volts.",
|
||||
"I flip the switch up to one and I flip it back down to zero.",
|
||||
"What's the voltage in this capacitor here?",
|
||||
"5 volts. Now the capacitor is at 5",
|
||||
"volts, I put dIN to ground, flip the switch back up and",
|
||||
"then back down to its known storing condition.",
|
||||
"What's the voltage in the capacitor?",
|
||||
"It's zero, exactly. So, it does store the value of",
|
||||
"the voltage that it saw, five or zero,",
|
||||
"high and low. It stores it because it stores",
|
||||
"charge. That's actually the physical",
|
||||
"quantity that's stored. It's manifested as a voltage,",
|
||||
"which we see. All right.",
|
||||
"Now, is this, oh, before I move from here.",
|
||||
"What is the basic cell in a DRAM, one that you go out and",
|
||||
"buy by the billions of cells? It's actually this.",
|
||||
"The only difference is that this switch here is replaced",
|
||||
"with a MOSFET.",
|
||||
"",
|
||||
"And that's all it is. So, a MOSFET plays the role of",
|
||||
"the switch. When the gate is high this is a",
|
||||
"resistor and connects the input to the capacitor.",
|
||||
"And when the gate voltage is below the threshold voltage this",
|
||||
"is an open, as we've seen, and it isolates the transistor",
|
||||
"from the output. So, that's the basic memory",
|
||||
"element.",
|
||||
"",
|
||||
"And, as I said, it's the key to a DRAM.",
|
||||
"OK. Now let's consider a little bit",
|
||||
"the conditions of operation of this thing.",
|
||||
"Let me draw the circuit in two conditions.",
|
||||
"One in which it is storing, one in which it is sampling and",
|
||||
"one in which it is storing. Not to redraw this thing.",
|
||||
"Assuming that I have a MOSFET there, I would have the on",
|
||||
"resistance in place here when store=1.",
|
||||
"Now, in principle, the output is connected to --",
|
||||
"",
|
||||
"-- some load resistance. We'll talk a little bit more",
|
||||
"about this load resistance in a minute.",
|
||||
"This is the situation when we are at store=1 situation.",
|
||||
"For example, let's suppose that dIN is 5",
|
||||
"volts. Now, what is the situation for",
|
||||
"store=0? It's very simple.",
|
||||
"We have the capacitor C and dOUT and here we have a",
|
||||
"resistance. The switch is open.",
|
||||
"This is store=0 condition. What we have in this case is we",
|
||||
"have a problem similar to what I was discussing earlier.",
|
||||
"It is a ZIR, if you like,",
|
||||
"situation. And this you can think of as a",
|
||||
"ZSR if we're starting with zero charge on the capacitor,",
|
||||
"but I'm interested in this part.",
|
||||
"In this case, I am starting with a vC(0)=5",
|
||||
"volts. And I'm asking myself how long",
|
||||
"will this cell hold the value? And, in fact,",
|
||||
"that is actually what happens in a dynamic RAM.",
|
||||
"The value on the capacitor is not stored forever.",
|
||||
"In fact, that's why we call it dynamic because we have to come",
|
||||
"back and restore it every once in a while.",
|
||||
"For how long are we going to store the charge?",
|
||||
"What's the response of vc for t greater than zero after the",
|
||||
"switch flicked? It's very simple.",
|
||||
"It's vc is equal to 5 volts e to the minus t over RC,",
|
||||
"right? That's the response.",
|
||||
"We have a decay. And applying to the things we",
|
||||
"know. We start from 5 volts,",
|
||||
"let's say here, I have a decay going down",
|
||||
"towards zero, at some point we are going to",
|
||||
"cross the threshold for high. The only period in which I have",
|
||||
"a valid output, if the capacitor was storing a",
|
||||
"one, is this period here. This is the only period in",
|
||||
"which I have valid stored one because, once I go beyond",
|
||||
"capital T here, I have crossed the legal limit,",
|
||||
"threshold for discriminating a high output.",
|
||||
"And from then on the output is no longer valid.",
|
||||
"So, this memory is good provided time is less than",
|
||||
"capital T. It's not a case in which the",
|
||||
"capacitor can hold charge forever.",
|
||||
"In fact, we can calculate, that is we can solve for T in",
|
||||
"this particular case. It's in your notes.",
|
||||
"Nothing really profound. T is equal to minus RC log VOH",
|
||||
"over 5 volts. So, this is basically what the",
|
||||
"response is going to be. Now, there is an implicit",
|
||||
"assumption here, which is that the store pulse",
|
||||
"width is much, much larger than RON C.",
|
||||
"In other words, when we want to store a one",
|
||||
"here starting from zero, we better charge it all the way",
|
||||
"up to 5 volts in the time that our switch is connected here.",
|
||||
"And what is the relevant time constant?",
|
||||
"It's going to be the RON C. In fact, it's actually the RON",
|
||||
"parallel RL with C. But typically RON is much,",
|
||||
"much less than RL so we don't have to worry about that.",
|
||||
"Dominant time constant is RON C.",
|
||||
"So, provided these things are happening, we have a memory.",
|
||||
"Now, we can try to improve things a little bit.",
|
||||
"We see here that we will have a decay to an invalid state in",
|
||||
"time T. How can we improve things?",
|
||||
"One way to improve things are the buffer.",
|
||||
"Here is our memory element again.",
|
||||
"Here is the capacitor. This is the storing node.",
|
||||
"Now I am going to put the buffering effect.",
|
||||
"I am going to put two buffers here.",
|
||||
"Two invertors, I should say,",
|
||||
"because if I am storing a one here I want to be able to see a",
|
||||
"one here as well. And, in this case,",
|
||||
"what I am looking at is the RIN of the buffer.",
|
||||
"And, in principle, I have out here the RL.",
|
||||
"Now, this is better because if RIN is much larger than RL then",
|
||||
"the time T, in this case, is much larger than the case",
|
||||
"without buffer. So, we buffer the effect of VL.",
|
||||
"This could be one of these neat circuits we saw in recitation",
|
||||
"like a source faller, for example,",
|
||||
"or it can be just an inverter in which case you just see the",
|
||||
"input of a transistor. So, now this condition can be",
|
||||
"satisfied. Let me give you some cases",
|
||||
"which are some numbers that are typical for a dynamic RAM.",
|
||||
"Typical times we're talking about is RIN on order of 1",
|
||||
"gigaohm and storage node capacitor on order of 1",
|
||||
"femtofarad to one picofarad. Now, if you can do the math in",
|
||||
"your head, which is just multiplication,",
|
||||
"you will see that the time constant, the RC is between 1",
|
||||
"millisecond to 1 microsecond. And for DRAMs,",
|
||||
"actually, we try to be in the order of milliseconds.",
|
||||
"These are the times we're talking about.",
|
||||
"If I have this kind of circuit, somehow there has got to be",
|
||||
"additional circuitry that comes back, samples the voltage here",
|
||||
"and restores it. And that is actually what is",
|
||||
"happening in a DRAM. And my laptop is working there",
|
||||
"and its DRAM keeps getting refreshed every,",
|
||||
"say, millisecond or whatever the condition is.",
|
||||
"But, in our case, we are going to do a slightly",
|
||||
"different case in which we will create a static memory.",
|
||||
"Let's actually look at, first of all,",
|
||||
"the case of the discharge. Pay attention to,",
|
||||
"let me actually break the loop here.",
|
||||
"This is my capacitor. This is a resistor that is in",
|
||||
"series with a capacitor like you see here.",
|
||||
"Actually, I am going to keep that resistor in series with the",
|
||||
"capacitor, even in this case, because I have it for my second",
|
||||
"part of my example. I charge the capacitor to 5",
|
||||
"volts. And you can see here this",
|
||||
"lights up, I hope everybody can see it, proportional to the",
|
||||
"voltage that I have here. From here on it's all logic",
|
||||
"levels. So, the intensity of light here",
|
||||
"will always be the same. It's either lit or it's not",
|
||||
"lit. Right now I am charging the",
|
||||
"capacitor. In fact, let's see.",
|
||||
"Maybe I can discharge the capacitor first.",
|
||||
"",
|
||||
"Here the capacitor is discharged.",
|
||||
"As you can see, the input is zero,",
|
||||
"the output is a one, and then the output of this",
|
||||
"inverter here is a one. I have two inverters in series.",
|
||||
"And I am going to charge the capacitor.",
|
||||
"I charged it to 5 volts and this lit up, this is off of",
|
||||
"course, that's an inverter, this is a valid zero,",
|
||||
"produce a valid one. And now I am going to take the",
|
||||
"input out. As you can see it's stored.",
|
||||
"In fact, we have to wait for a very long time.",
|
||||
"We don't have enough time to wait for this to discharge,",
|
||||
"so instead what I am going to do now is I am going to add also",
|
||||
"the resistor. Now I am going to flip the",
|
||||
"resistor in parallel with the capacitor to imitate what",
|
||||
"happens when we have an input resistance.",
|
||||
"You saw that there was a discharge of the capacitor.",
|
||||
"This input level went down. Voltage here flipped over to a",
|
||||
"one. Let me do it again now with a",
|
||||
"resistor in place. Storing charge on the",
|
||||
"capacitor. That's the store command.",
|
||||
"Now, don't store. I have less,",
|
||||
"about a second. The element here is 20,000",
|
||||
"microfarads and 100 ohms which gives me a time constant of two",
|
||||
"seconds. Assuming a VOC of the order of,",
|
||||
"let's say, I don't know what it is for this case,",
|
||||
"2.5, the log would be about 0.5, so it cuts basically the",
|
||||
"time to about one. So, it lasts about one second,",
|
||||
"if my math is all correct. It's actually a little longer",
|
||||
"than a second, excuse me, but the point is",
|
||||
"that the charge is gone. Now, notice,",
|
||||
"however, that there is something I can do here,",
|
||||
"which is that suppose I take the switch or a switch and bring",
|
||||
"it back and provide a path from the output to the input here.",
|
||||
"And this switch is open when this is closed and closed when",
|
||||
"this is open. So, this basically is the",
|
||||
"compliment of store. What I am doing now is I put a",
|
||||
"charge here, it produces a valid one at this point,",
|
||||
"and then I am feeding this valid one back to the input.",
|
||||
"As you can see, this will now allow me,",
|
||||
"even though I have a high resistance, to store the value",
|
||||
"for a long time. In this case,",
|
||||
"what I am going to do is I am going to connect the output,",
|
||||
"as you can see here. And I have my resistor in.",
|
||||
"And I am storing zero here, storing 5 volts.",
|
||||
"Now I am going to flip the switch.",
|
||||
"Basically, I mean the don't store, don't look case.",
|
||||
"You notice this dims a little bit.",
|
||||
"Sorry. No, I want the resistor in.",
|
||||
"",
|
||||
"There. Yes.",
|
||||
"OK, so the output remain value. This dimmed a little bit but",
|
||||
"the output has remained OK. All right.",
|
||||
"So, we've provided a feedback. Now we've created a static",
|
||||
"memory. This will hold charge for as",
|
||||
"long as the circuit is powered up.",
|
||||
"Now, there is still one little problem that I have with this",
|
||||
"kind of configuration. And that is if I disturb this",
|
||||
"output the charge may, the state may change.",
|
||||
"So, for example, let's say that I have --",
|
||||
"I disturbed it by coming close to it, so let's charge it again.",
|
||||
"",
|
||||
"OK. I flipped the switch.",
|
||||
"I flipped the state from the output.",
|
||||
"That is an invalid condition. I shouldn't be able to do that.",
|
||||
"How do I avoid that? How can I avoid this problem",
|
||||
"that you just saw?",
|
||||
"",
|
||||
"Well, I need yet another buffer.",
|
||||
"The answer is in your notes. If I don't take the output here",
|
||||
"but rather take the output here, or if I don't want an inverted",
|
||||
"output, if I don't want an inverted output,",
|
||||
"I could put yet another element there.",
|
||||
"Then the situation would be fine.",
|
||||
"In this case, let me do it again.",
|
||||
"Charge.",
|
||||
"",
|
||||
"Why isn't this lit?",
|
||||
"",
|
||||
"A bad one?",
|
||||
"",
|
||||
"Now, of course we disturbed the input.",
|
||||
"Now, of course I can do anything I want here.",
|
||||
"Nothing happens, but you may say this is a",
|
||||
"trivial case because this is already zero.",
|
||||
"So, I am going to change the state.",
|
||||
"Here's is the changed state. See.",
|
||||
"I can show this. Nothing happens up there.",
|
||||
"So, this is an interesting situation in which I am",
|
||||
"buffering the output so that the output does not feed back to the",
|
||||
"input. And, by and large,",
|
||||
"in designing circuits this is something that we do.",
|
||||
"Now, in the remaining three minutes there is an example that",
|
||||
"we have. Can we put the laptop here?",
|
||||
"",
|
||||
"OK, so here is an example of how memory can be put together",
|
||||
"now to create something a little bit more complicated.",
|
||||
"And you can see the memory cells that we were discussing",
|
||||
"here. There's four of them,",
|
||||
"so this is a four bit memory. There is a decoder at the",
|
||||
"beginning here which decodes the address of each cell,",
|
||||
"so the input here will tell me which cell I need to address.",
|
||||
"Let's look at the truth table. This is the truth table for the",
|
||||
"decoder. As you can see,",
|
||||
"depending on the address that I have here, this is zero,",
|
||||
"one, two and three in a binary system, only A,",
|
||||
"B, C or D is up, is high.",
|
||||
"Which means that this end operation here only allows the",
|
||||
"input that is presented to all of the cells,",
|
||||
"what is going through the AND gate here to appear at the",
|
||||
"output. If, for example,",
|
||||
"we have a one, zero, the only end input that",
|
||||
"is going to be high is going to be this one.",
|
||||
"And that means the only cell that will look at the input when",
|
||||
"the store comes up is going to be this one here.",
|
||||
"At that point it will store whatever is on the input cell",
|
||||
"because that's an AND operation. That is a simple example of a",
|
||||
"memory. And following that simple",
|
||||
"arrangement you can build incredibly large memory systems.",
|
||||
"So, that's all I had for today. And I will see you on Tuesday."
|
||||
]
|
||||
}
|
||||
@@ -1,2063 +0,0 @@
|
||||
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"text": [
|
||||
"All right. Good morning.",
|
||||
"Good morning. So, we have some fun stuff for",
|
||||
"today's lecture, and as far as the final is",
|
||||
"concerned and so on, I'd like you to forget about",
|
||||
"anything we do today, absolutely.",
|
||||
"So, get your mind to become a blank, and forget anything you",
|
||||
"hear in today's lecture. So, what I'm going to show you",
|
||||
"today will hopefully completely blow your minds.",
|
||||
"And I'm not talking about controlled substances or",
|
||||
"anything. So what I'm going to do is show",
|
||||
"you a few things that behave completely and spectacularly",
|
||||
"differently than how you expect them to.",
|
||||
"And, today's lecture is appropriately called --",
|
||||
"",
|
||||
"OK. So, we're going to violate the",
|
||||
"abstraction barrier here, and do some fun things.",
|
||||
"And, the important thing to realize is that in all of 6.002,",
|
||||
"we have, after all, based on some assumptions we",
|
||||
"made at the beginning of the course like lumped matter",
|
||||
"discipline and so on, we have landed ourselves in",
|
||||
"this playground called the playground of 6.002.",
|
||||
"And, within that playground, certain ground rules apply.",
|
||||
"OK, and our entire course depended on those assumptions",
|
||||
"being true. So, for example,",
|
||||
"the first assumption we made that brought us from Maxwell's",
|
||||
"equations to the lumped matter discipline was,",
|
||||
"or rather the circuit abstraction, was a lumped matter",
|
||||
"discipline. And there were three tenets of",
|
||||
"the lumped matter discipline. One is that the rate of change",
|
||||
"of flux was going to be zero within our circuits,",
|
||||
"not inside elements, but in the circuit itself,",
|
||||
"and second, the dq by dt was going to be zero outside the",
|
||||
"elements, and third, something we did not dwell upon",
|
||||
"in the course, but it's certainly present in",
|
||||
"the course notes is that the speeds of signals that we are",
|
||||
"going to consider are going to be much slower than the speed of",
|
||||
"light. OK, so we're going to be",
|
||||
"working in a realm where we are going to be well slower than the",
|
||||
"speed of light. OK, so starting with that,",
|
||||
"let me walk you through some examples and some fun stuff.",
|
||||
"So, the first case is called the Double Take.",
|
||||
"So, let me sketch out a small little circuit for you,",
|
||||
"and take a look at the expected behavior, and then show you what",
|
||||
"really happens in real life. So, the first case,",
|
||||
"I have a voltage source, and what I'm going to do is",
|
||||
"make a transition from a zero to a one.",
|
||||
"Think of it as a step input, and through a Thevenin like",
|
||||
"resistance, I want to feed it to a circuit.",
|
||||
"The circuit will go to an inverter.",
|
||||
"This node goes to an inverter, and goes through some other",
|
||||
"circuits within our own design here.",
|
||||
"So, again, remember, a step input here,",
|
||||
"and this input goes through a Thevenin like resistance,",
|
||||
"or is applied to some other circuit elements.",
|
||||
"So, if I apply a step here, what do you expect?",
|
||||
"You expect that, so let me call that VI,",
|
||||
"and let me call that Vo. So, if I plot VI as a function",
|
||||
"of time, and let's say this step input happens at t=0.",
|
||||
"So let's say this is t=0 here, and let's say this is a 5V",
|
||||
"step. So, I expect that this input",
|
||||
"here is going to go to, VI here, is going to go to 5V",
|
||||
"at t=0. What do I expect at Vo?",
|
||||
"At Vo, based on our circuit abstraction, I get a step input",
|
||||
"here. I should get a step of some",
|
||||
"magnitude here, depending on what's connected",
|
||||
"in this direction. And let's simply say that",
|
||||
"what's connected here is an inverter, and maybe other",
|
||||
"inverters at the other side. So essentially,",
|
||||
"as far as this node is concerned, it's got some wires",
|
||||
"connected to it. And at the end of the wires,",
|
||||
"it has an open circuit, an open circuit,",
|
||||
"for example, like the gate input of this",
|
||||
"inverter. So what do you expect at V",
|
||||
"nought? A step input here,",
|
||||
"and at V nought I see an open circuit.",
|
||||
"OK, so I expect the same step at V nought: 5V.",
|
||||
"So, that's what we've prepared you for, OK?",
|
||||
"But, the fun thing that we're going to see,",
|
||||
"so this is what you expect, and I'll show you a little demo",
|
||||
"that is going to show you something very different.",
|
||||
"What you're going to see is not this.",
|
||||
"OK, you're not going to be seeing that.",
|
||||
"Rather, I'm going to show you something that looks like this.",
|
||||
"",
|
||||
"So, at t=0, I do see Vo looking like a step, and approximately",
|
||||
"halfway through, decides, ah,",
|
||||
"well never mind, and flattens out,",
|
||||
"OK, then says, oh, OK, and zoom,",
|
||||
"it goes back up to 5V. So, it sort of does a bit of a",
|
||||
"double take up there saying, hey, what's going on here?",
|
||||
"And zoom, jumps up to 5V, and then it's five as you",
|
||||
"expect. OK, so this is some finite",
|
||||
"amount of time that looks like that.",
|
||||
"OK, so try to understand what's going on.",
|
||||
"So let me show you a quick little demo.",
|
||||
"So that's the input VI. OK, so that's the input VI that",
|
||||
"you expect, and I won't do anything to my circuit at this",
|
||||
"point. And, go ahead.",
|
||||
"So, let's see what happens now. There you go.",
|
||||
"So now, I'm showing you the output here at Vo.",
|
||||
"So at VI, there's a nice little step, and at Vo,",
|
||||
"notice that I get something that behaves like this.",
|
||||
"OK, and I promise you, nothing we've taught you in",
|
||||
"6.002 prepares you for this. OK, and as I mentioned at the",
|
||||
"beginning of this lecture, it would behoove you to forget",
|
||||
"about everything you learn in today's lecture for the next two",
|
||||
"weeks at least. So what's going on here?",
|
||||
"Any ideas? Anybody?",
|
||||
"Any thoughts? So what's up with my circuit",
|
||||
"here? It says, oh,",
|
||||
"OK, a step. It starts off and says,",
|
||||
"oh, never mind, and then meanders along at 2.5V",
|
||||
"and then says oh, step, yes, I remember,",
|
||||
"and then boom, it jumps up to 5V.",
|
||||
"So, any theories? Any guesses?",
|
||||
"Any wild guesses? OK, so let me draw you a little",
|
||||
"bit more of a detailed circuit, and see if you can explain",
|
||||
"what's going on here. So, the circuit that I've drawn",
|
||||
"there is not quite the circuit I have at least in terms of my",
|
||||
"wires. So, what I have is something",
|
||||
"that looks like this, VI, and this is going to step",
|
||||
"to 5V. I do have a resistance,",
|
||||
"R. This is Vo, this does go to an",
|
||||
"inverter. But what is also happening is",
|
||||
"that I have a long wire. OK, you see this guy here?",
|
||||
"We had one of our union folks stretch out along the floor",
|
||||
"here. We have a really long wire that",
|
||||
"connects to the Vo node, and there's also a long",
|
||||
"corresponding ground. So, this wire is a coaxial",
|
||||
"cable that is used for Ethernet and such like.",
|
||||
"It's got a core that carries a signal, and around the core is",
|
||||
"shielding that is the ground. OK, so that goes a long way,",
|
||||
"and at the end, it is open.",
|
||||
"OK, it's an open circuit at the end.",
|
||||
"I haven't connected anything out there: open circuit.",
|
||||
"So, you know, something's happening here",
|
||||
"that's making the circuit behave like this.",
|
||||
"So, this is VI. At Vo --",
|
||||
"",
|
||||
"So at Vo I'm getting this funny behavior.",
|
||||
"OK, so does anybody want to take the next piece of clues",
|
||||
"here, does anybody want to take a stab at guessing what might be",
|
||||
"going on here? Yes?",
|
||||
"Ah, we have a shill in the audience here.",
|
||||
"So, the theory is that the step here, think of it as an",
|
||||
"electromagnetic pulse that goes from zero to five,",
|
||||
"and things in real life don't travel instantaneously.",
|
||||
"So, there's something with a wave that flies down,",
|
||||
"and the wave goes to the end, flips, and then comes back,",
|
||||
"and then establishes the full voltage here.",
|
||||
"So that is indeed at the root of what's going on.",
|
||||
"And let me put it in layman's terms and then describe the",
|
||||
"details of what's going on here. OK, so the way to view what's",
|
||||
"going on is that I have this long wire.",
|
||||
"OK, in the very first lecture, I started off by saying wires",
|
||||
"are ideal. OK, ideal wires are such that I",
|
||||
"can transmit signals on them. Wires are small so that the",
|
||||
"propagation time of signals is inconsequential compared to the",
|
||||
"rise times and fall times of the signals of interest.",
|
||||
"By having this really long cable here, I have clearly",
|
||||
"violated that assumption, which is the wires are really,",
|
||||
"really long here. OK, and so I somehow need to",
|
||||
"model what the wire is doing to my circuit when I don't have a",
|
||||
"small wire. So what actually happens,",
|
||||
"the way to view it is the following.",
|
||||
"So, although this is a wire, to understand the mechanics of",
|
||||
"what's going on, I really have to model it much",
|
||||
"more accurately, OK?",
|
||||
"And, the way to model a wire like this is that notice that",
|
||||
"every small element of a wire has associated with it some",
|
||||
"inductance. OK, so let's take a small",
|
||||
"segment of the coax cable here. The coax cable is a small core",
|
||||
"surrounded by a metallic shield. OK, that's a ground.",
|
||||
"And so, when I have a wire surrounded by a metallic shield,",
|
||||
"that also has the capacitance, OK, inductance and capacitance.",
|
||||
"So this small segment can be modeled as a really small",
|
||||
"inductance, and a really tiny capacitance.",
|
||||
"Similarly, the next segment can be modeled as a tiny inductance",
|
||||
"and a capacitance. There is also a resistance",
|
||||
"here, but let's assume that the resistance is zero for our",
|
||||
"model, and also the parallel resistance is also infinity.",
|
||||
"OK, so it's an inductor, capacitor, and really the",
|
||||
"situation that I have is not a pair of ideal wires,",
|
||||
"but really a really, really small inductance,",
|
||||
"and a small capacitance in parallel.",
|
||||
"So, it's more of a set of distributed elements that I have",
|
||||
"here. Notice that in my lump circuit",
|
||||
"abstraction, when we talked about the RLC model for the wire",
|
||||
"between two inverters, we lumped it.",
|
||||
"We lumped this thing into a model that looked like this.",
|
||||
"OK, we lumped the resistance into a source resistance.",
|
||||
"We lumped all the inductors into a lumped inductor.",
|
||||
"We lumped all the capacitances into a lumped capacitance.",
|
||||
"OK, but in this situation, I can do this when the signal",
|
||||
"speeds of interest are much, much, much slower than the",
|
||||
"speed of light than the propagation speeds of",
|
||||
"electromagnetic signals. In this case,",
|
||||
"that is not quite true. And so, therefore,",
|
||||
"we have to model it much more exactly.",
|
||||
"We need to see what's going on. So, what's happening here is",
|
||||
"that at t=0, I get this step. So, think of that as a pulse of",
|
||||
"energy, and the instant it comes here, and instantaneously this",
|
||||
"guy looks like a voltage divider, OK?",
|
||||
"I've chosen my resistance, R, here to match the",
|
||||
"instantaneous impedance looking in, which is also R.",
|
||||
"I've arranged it to be that way.",
|
||||
"So, instantaneously, the point at which the pulse",
|
||||
"appears at this point, looking down here looks like",
|
||||
"another resistor to this pulse. OK, therefore,",
|
||||
"when I start out, I start out going up and",
|
||||
"pausing at 2.5 because instantaneously,",
|
||||
"this looks like a resistance, R.",
|
||||
"So instantaneously, it's a voltage divider,",
|
||||
"R, and so it's 2.5 here, instantaneously.",
|
||||
"OK, then what happens? Then those little pulse",
|
||||
"propagates down. What does it mean for a pulse",
|
||||
"of energy to propagate down? Well, it begins sending a",
|
||||
"current through the inductor, begins charging up the",
|
||||
"capacitor, current here, so that's what I mean by saying",
|
||||
"that the pulse of energy goes down.",
|
||||
"OK, it's a step that sends current to the inductor and",
|
||||
"charges of the capacitors, and that wave front moves out",
|
||||
"here and comes all the way here. What happens there?",
|
||||
"Well, think about it. Supposing you stand here,",
|
||||
"and you hold a long string in your hand somehow,",
|
||||
"and just do this Gedanken experiment.",
|
||||
"It's not easy to do. And so, let's say you somehow",
|
||||
"have the long string that you're holding onto,",
|
||||
"and the string on the other side is not connected to",
|
||||
"anything. OK, just imagine this",
|
||||
"experiment. OK, and what you do is you",
|
||||
"suddenly raise the string up at your end by about a foot.",
|
||||
"What are you going to see happen?",
|
||||
"So instantaneously, the string is up here,",
|
||||
"but the rest of the string is down a foot below.",
|
||||
"And then you see this wave propagate down the string,",
|
||||
"right? So here's a string.",
|
||||
"I lift this thing, and you see this wave propagate",
|
||||
"all the way down, the one foot wave propagate all",
|
||||
"the way down until you come here.",
|
||||
"What happens here? So, out here,",
|
||||
"the string is down here, the wave propagates out here",
|
||||
"and pulls it up to one. And then what?",
|
||||
"There's nothing connected there, so the string is zipped",
|
||||
"up, but it's got the energy. OK, where does energy go?",
|
||||
"Well, it continues going up, and sends a wave back.",
|
||||
"OK, so just think of a string that you pull up like this and",
|
||||
"propagates down, boom, hits the other end,",
|
||||
"reverses, and comes back at me. OK, you can look at a",
|
||||
"complementary situation, not the same as this,",
|
||||
"but complementary by taking a string, tying it to a door,",
|
||||
"and lifting it up. It's not the same situation.",
|
||||
"It's a complementary situation where it's tied down.",
|
||||
"Tying down a string is tantamount to shorting the ends",
|
||||
"here. OK, in that case what you'll",
|
||||
"see happen: as the wave goes down, at the end the string",
|
||||
"can't move, so the wave goes and flips around and comes back.",
|
||||
"Try it out at home. Take a long piece of string,",
|
||||
"tie it up there, do this, OK?",
|
||||
"And you'll see the wave go out, flip, and then come back at",
|
||||
"you. So, if your friends see you",
|
||||
"tying a long piece of string doing this, hopefully they won't",
|
||||
"think you're nuts or something. OK, so the same way here:",
|
||||
"this thing flies down, OK, there's no way to dissipate",
|
||||
"the energy here, so this thing continues up.",
|
||||
"And then, what I'm going to see happen is the wave move back.",
|
||||
"OK, the wave begins to move back, and that's another 2.5V,",
|
||||
"resulting in a net 5V at this terminal.",
|
||||
"That wave begins to blast back, OK, and then when it comes back",
|
||||
"here, after some amount of time, it raises this to 5V,",
|
||||
"and that's what you see happen here.",
|
||||
"So, this is a wave going down, and then after a time,",
|
||||
"2t, it goes back up to 5V. That's a return wave.",
|
||||
"It's 2t because to get down here is t seconds,",
|
||||
"and then t seconds to come back, which is why we have 2t.",
|
||||
"OK, that is why you see that pulse at 2.5.",
|
||||
"OK, so I'd like to show you a few more things here.",
|
||||
"Clearly we don't want that in our circuits.",
|
||||
"Could someone tell me what problem would happen if my",
|
||||
"signals looked like this in my digital circuits?",
|
||||
"Instead of being nice little steps, if there was a little",
|
||||
"thing in the middle and then a step, what's the problem with",
|
||||
"signals like this? In digital circuits,",
|
||||
"what did it violate? Yeah?",
|
||||
"Exactly. This little sucker here is",
|
||||
"meandering out in the forbidden region for all of 2T.",
|
||||
"Can't do that. OK, can't have that.",
|
||||
"Well, so we need to fix the problem because this is real",
|
||||
"life. OK, but what if you and your",
|
||||
"buddy were signaling each other but using digital signals from",
|
||||
"one dorm room to another maybe a few hundred feet down?",
|
||||
"Your circuit isn't going to work because the signal's going",
|
||||
"to meander around in the forbidden region for some time.",
|
||||
"So, any ideas what might you do?",
|
||||
"Yeah? Put a resistor on the end.",
|
||||
"OK, trick the circuit. So, what you can do,",
|
||||
"and I'm going to show you a little demo here,",
|
||||
"what you can do is the reason I got this wave propagating back,",
|
||||
"was that there was nothing to absorb the energy.",
|
||||
"So instead, what if I put another resistor here,",
|
||||
"R? So, as far as a burst of energy",
|
||||
"is concerned, it says, oh,",
|
||||
"yeah, it just looks the same. It's R, and goes and dissipates",
|
||||
"in this resistor, R, and guess what?",
|
||||
"I don't have any wave going back, and I'm done.",
|
||||
"So, what I'm going to find, then, is that out here,",
|
||||
"this goes up to 5V, but out here,",
|
||||
"I will have a signal that starts out and goes up to 2.5,",
|
||||
"and that's it. OK, I lift it up,",
|
||||
"it goes down, it goes to 2.5 because in the",
|
||||
"lumped model that you've been dealing with,",
|
||||
"it's a resistor R, a resistor R to ground,",
|
||||
"and you're taking the connection here or here.",
|
||||
"So, it's your standard lumped model, your voltage resistive",
|
||||
"divider, and it just simply works.",
|
||||
"Yeah, that's it. So, this is the end of the",
|
||||
"cable. OK, if somehow you could watch",
|
||||
"this and that at the same time, so what I'm going to do,",
|
||||
"and this is a resistor, R, I'm just going to plug it",
|
||||
"in. OK, if the fates are smiling at",
|
||||
"me, what should you see there? What should happen is that the",
|
||||
"second jump from 2.5 to 5 should simply go away.",
|
||||
"It should just go to 2.5. Let's try that.",
|
||||
"There you go. I take it out,",
|
||||
"it jumps back up. OK, so all I've done here is",
|
||||
"put in a resistor at the end, and I'm still measuring the",
|
||||
"voltage here. So, that's one solution.",
|
||||
"One solution is to put a resistor here.",
|
||||
"So, I absorb the energy, and the resistance has to be",
|
||||
"equal to the instantaneous impedance looking in.",
|
||||
"And the instantaneous impedance, for many of these",
|
||||
"cables is 50 ohms. It's called a characteristic",
|
||||
"impedance. OK, you'll learn a lot more",
|
||||
"about it if you take 6.014. That course starts out with",
|
||||
"assuming that things are distributed in that matter.",
|
||||
"OK, so if you want to design multi-gigahertz chips,",
|
||||
"it turns out that if you have signals that are traveling",
|
||||
"around at edge speeds in the 0.1-1 nanosecond range,",
|
||||
"remember, light travels roughly one nanosecond a foot.",
|
||||
"And if the signals are roughly of interest are 0.1 nanoseconds,",
|
||||
"then if the chips are one inch in size, right there,",
|
||||
"the propagation speed of a signal across a chip is 0.1",
|
||||
"nanoseconds. OK, so today,",
|
||||
"we have to deal with these issues and try to figure out",
|
||||
"what to do about them. OK, so that's one solution that",
|
||||
"somebody pointed out. There is a second solution.",
|
||||
"Anybody else have a second solution for me?",
|
||||
"And then there's a third solution, too.",
|
||||
"So it's OK. You can give me either the",
|
||||
"second or the third solution. It doesn't matter.",
|
||||
"Anybody? You have two to choose from,",
|
||||
"come on. Yeah?",
|
||||
"You can do that, yeah.",
|
||||
"So we could define the problem away by saying this transition",
|
||||
"is such that my high is below 2.5.",
|
||||
"So, once it goes above 2.5, who cares what it does?",
|
||||
"That's a good point. That's solution number four,",
|
||||
"and that works. OK, so I still need two and",
|
||||
"three. Put a diode in there?",
|
||||
"Yeah, I guess you could. If the diode had the same kind",
|
||||
"of impedance looking in, it kind of may work.",
|
||||
"That's solution 4.2. I'm still waiting for solution",
|
||||
"two and three. Pardon?",
|
||||
"Cut off the cable? Exactly.",
|
||||
"So, the solution says, work on a different problem.",
|
||||
"And that is solution number two.",
|
||||
"OK, so the idea is, the root of all evil,",
|
||||
"this long wire, which is why I had this thing",
|
||||
"here. So instead, if I had short",
|
||||
"wires, then what will happen is if it's a very small wire,",
|
||||
"it'll look like this. And the wire's small enough.",
|
||||
"I will see an itty-bitty thingamajig out there,",
|
||||
"but not a whole lot. By the way, the fun thing is",
|
||||
"that you can actually calculate the speed of light,",
|
||||
"the experiment I just showed you.",
|
||||
"Can we put that up again? No, the big one.",
|
||||
"So, in the experiment that I showed you, this distance was",
|
||||
"about 500 nanoseconds, OK?",
|
||||
"This distance was 500 nanoseconds this time interval.",
|
||||
"The length of this cable is about 500 feet,",
|
||||
"somewhere around 500 feet. So you can figure out the speed",
|
||||
"of light. What's the speed of light?",
|
||||
"So, this is about 500 nanoseconds, and this cable is",
|
||||
"roughly 500 feet. What's the speed of light?",
|
||||
"Roughly a foot per nanosecond. So, would you believe that in",
|
||||
"6.002 we've figured out the speed of light from a simple",
|
||||
"experiment? All right, so let's do the next",
|
||||
"experiment now. Let's take out the long cable,",
|
||||
"and connect a short cable instead.",
|
||||
"So, what I'm going to do is disconnect the long cable,",
|
||||
"and instead, connect a small cable.",
|
||||
"It's still relatively long, but much shorter than the 500",
|
||||
"foot cable. So what you should see happen",
|
||||
"now is that the little step should not be this big,",
|
||||
"but much, much smaller. So, take a look up there.",
|
||||
"There you go. OK, so with this thingamajig,",
|
||||
"the little blip there is very small.",
|
||||
"And of course, if I make it even smaller,",
|
||||
"then that can virtually vanish. OK, so that is solution number",
|
||||
"two. So, we've done one,",
|
||||
"two, four, 4.2. So, what's solution number",
|
||||
"three? One more solution.",
|
||||
"Pardon? So, another solution we",
|
||||
"mentioned is we change this resistance.",
|
||||
"and that will work, if I make this very,",
|
||||
"very low, then I'll get much closer to 5V here.",
|
||||
"Yeah, that's a possibility. That's solution six I guess.",
|
||||
"So what was solution number three?",
|
||||
"And you all should be able to solve this.",
|
||||
"You guys know the answer. OK, you folks should be able to",
|
||||
"solve this. Yes?",
|
||||
"Ah, clock. So, what I can do is just as",
|
||||
"was pointed out, that I leveraged my abstraction",
|
||||
"by changing my VOH and VIH thresholds.",
|
||||
"So that'll work. The alternative thing is to use",
|
||||
"a clock. A clock is a distinguished",
|
||||
"signal that I send around in my digital circuit,",
|
||||
"OK? So all I do is if I arrange it",
|
||||
"such that my clock doesn't happen in this vicinity,",
|
||||
"but rather, my clock happens late enough, then I'm going to",
|
||||
"sample and look at my signals only on the rising and falling",
|
||||
"edges of the clock, in which case I won't be",
|
||||
"looking at the signal, but the signal is doing weird",
|
||||
"things. OK, so a decent clock would",
|
||||
"also solve the problem. OK, any last minute questions",
|
||||
"before we go onto the next one? OK, the next problem that we're",
|
||||
"going to look at is titled the Double Dip.",
|
||||
"OK, so what I'm going to do here is our Vs power supply,",
|
||||
"and what I'm going to do is feed the power supply to an",
|
||||
"inverter. OK, so we've been doing this",
|
||||
"all along; Vs, I feed the supply to an",
|
||||
"inverter. And what I'm also going to do",
|
||||
"is, so this is ground, and I'm going to feed it to,",
|
||||
"so feed the power supply connection to a couple of",
|
||||
"inverters. OK, and what I'm going to do is",
|
||||
"apply some sort of a signal to this inverter,",
|
||||
"and I'm going to observe, and I'm going to look at this",
|
||||
"signal here. So, the abstraction should tell",
|
||||
"you that here's a power supply. This is 5V, or whatever the",
|
||||
"supply voltage is to these two inverters.",
|
||||
"That should be fine, and feed some sort of input to",
|
||||
"this inverter, OK, and the output here should",
|
||||
"be simply determined by this input.",
|
||||
"This signal can have absolutely no bearing on this output.",
|
||||
"OK, and let's look at that and actually confirm it.",
|
||||
"So, I build a circuit like this, and we look at this",
|
||||
"output, and initially there should not be any,",
|
||||
"it should simply work fine. OK, so it should work now,",
|
||||
"right? OK.",
|
||||
"So what you have here, this input here is the input",
|
||||
"that I'm feeding to this inverter.",
|
||||
"That is a straight line. Is that the power supply?",
|
||||
"It doesn't matter? OK, so I believe this is the,",
|
||||
"we'll check in a few minutes, but I suspect this is the power",
|
||||
"supply, and this guy here is the output looking here.",
|
||||
"So, the green one is the look here part.",
|
||||
"So, there must have been a one-to-zero transition here,",
|
||||
"and that's all fine. So, so far, so good.",
|
||||
"OK, no problem so far. Now what I'm going to do is I'm",
|
||||
"going to do something to the circuit that as far as",
|
||||
"abstraction is concerned, it doesn't show up on the",
|
||||
"circuit. OK, it's below the abstraction",
|
||||
"layer. OK, I'm going to do something,",
|
||||
"and suddenly, some things are going to",
|
||||
"happen. Look up there.",
|
||||
"The circuit hasn't changed. It's the same circuit.",
|
||||
"I've done nothing to the circuit.",
|
||||
"OK, look at the green output. I've done nothing to the",
|
||||
"circuit that is visible here. OK, it's below the radar screen",
|
||||
"here. It's below the abstraction",
|
||||
"barrier. But, look at the disaster here.",
|
||||
"OK, in particular, the spikes going up are not so",
|
||||
"much of a problem. Because of the static",
|
||||
"discipline, if I am at five or six or seven,",
|
||||
"it doesn't matter as long as I am higher than VOH.",
|
||||
"So as long as I'm higher than VOH I don't have a problem.",
|
||||
"But the problems are these repeated dips.",
|
||||
"OK, the dips are a problem here, which is why I labeled",
|
||||
"this experiment the Double Dip. OK, the dips are bad because if",
|
||||
"they are large enough, they can then group the output",
|
||||
"down into the forbidden region, or worse yet,",
|
||||
"make it look like a zero. OK, so you're not prepared for",
|
||||
"this. So what I'm going to do is tell",
|
||||
"you what I did to the circuit, and then ask you to help me",
|
||||
"figure it out. So all I did was applied a load",
|
||||
"resistance to this, I think of 50 ohms or some RL.",
|
||||
"I just applied a load resistor. And this inverter here,",
|
||||
"I believe, is a CMOS inverter that looks, OK?",
|
||||
"So I have this input applied to this inverter,",
|
||||
"and all I did is I applied an RL load here.",
|
||||
"And notice that the load here should not really change what's",
|
||||
"happening if this is an ideal inverter, OK,",
|
||||
"the load here should simply draw some current but really",
|
||||
"should not change any other property.",
|
||||
"OK, so just remember, what's the signal doing?",
|
||||
"The signal is high. This guy turns on,",
|
||||
"and current flows like this. So, let's say I had some sort",
|
||||
"of a capacitor here. This charges like this,",
|
||||
"and when it's slow, the PFET is on,",
|
||||
"and current flows through here down here.",
|
||||
"And then when this goes high, this guy goes off,",
|
||||
"and this guy turns on. OK, so the current flows out",
|
||||
"this way and this charges through this guy.",
|
||||
"When I turn it off, the P fret turns on and draws",
|
||||
"current from the top. OK, so do we have any theories",
|
||||
"as to why I'm getting that messy stuff, the dips and the spikes,",
|
||||
"on the output of this inverter? So why does this inverter care",
|
||||
"what the load of this inverter is?",
|
||||
"I mean, who cares? So, put your thinking caps on.",
|
||||
"Any theories? You guys did pretty well with",
|
||||
"the previous one. And this is much easier,",
|
||||
"actually. Need a better power supply;",
|
||||
"OK, so what I'm going to do is I'm going to replace the power",
|
||||
"supply, and instead, use a much bigger power supply",
|
||||
"at 5V. A big, mongo power supply that",
|
||||
"can supply 100 amps, and guess what,",
|
||||
"I've made the changes, but guess what,",
|
||||
"I still see the spikes. Good try, but it didn't work",
|
||||
"out. Good try, good try.",
|
||||
"What next? Any other solutions?",
|
||||
"Yes? So dips are because of the",
|
||||
"resistance, and the spikes are because of the inductance?",
|
||||
"You're half correct. So, which one is it?",
|
||||
"So, dips are because of resistances, and spikes are",
|
||||
"because of inductances. You're half correct.",
|
||||
"It turns out that both the dips and the spikes are because of",
|
||||
"inductances. OK, but be that as it may,",
|
||||
"let me give you the next clue here, and then see if you can",
|
||||
"come closer to the answer. So, what I've done here is I've",
|
||||
"made this wire really, really long.",
|
||||
"OK, it's a really long wire, OK, but it's a thick wire,",
|
||||
"so it's a long, long, thick wire.",
|
||||
"So it's not the resistance. It's really,",
|
||||
"really thick and mongo, and it's a long wire,",
|
||||
"so a signal wire above a ground plane behaves like an inductor.",
|
||||
"And so here, it has the capacitance to,",
|
||||
"but in this case it's inductance.",
|
||||
"It's inductance here. So, I'll give you another ten",
|
||||
"seconds to think about it and then tell you the answer.",
|
||||
"But despite the inductance here, it turns out if I take out",
|
||||
"this resistor, the problem goes away.",
|
||||
"Look, I take out the resistor, the problem goes away.",
|
||||
"Yes, there is an inductor here. OK, I take out this resistor,",
|
||||
"problem goes away. I put the resistor back in,",
|
||||
"boom. Yes?",
|
||||
"OK, pretty good. That's 86 points.",
|
||||
"So here's what's going on. There's an inductor here,",
|
||||
"and when I put a 50 ohm resistor here,",
|
||||
"I put this resistor. When the PFET turns on,",
|
||||
"it draws a current. OK, it's going to draw a",
|
||||
"current. It draws a current;",
|
||||
"remember that across an inductor, I have a drop.",
|
||||
"And the drop relates to the di/dt.",
|
||||
"Remember, for a capacitor, the current is Cdv/dt.",
|
||||
"For the inductor, the voltage across the inductor",
|
||||
"is Ldi/dt. So, if di/dt,",
|
||||
"from switching a large current through the inductor every",
|
||||
"cycle, OK, big di/dt, di/dt is large.",
|
||||
"I've made it large by having a very small RL,",
|
||||
"so, you know, pulling a big current through",
|
||||
"every few, whatever, every cycle,",
|
||||
"and then stopping it. And so therefore,",
|
||||
"I'm getting these big drops across this inductor that relate",
|
||||
"to Ldi/dt. In other words,",
|
||||
"the power supply here is fine. While you guys were watching,",
|
||||
"I switched to the huge, mongo power supply,",
|
||||
"and so this voltage is fine. But then this voltage after the",
|
||||
"wire is the problem. So, this voltage here doesn't",
|
||||
"look like this anymore. Rather, it has spikes that go",
|
||||
"down, for example, and when I switch the other",
|
||||
"way, they go up. OK, so therefore,",
|
||||
"what I end up having here is big spikes on this power supply.",
|
||||
"And when this guy's power supply goes wacko,",
|
||||
"then I see the spikes on its output as well.",
|
||||
"OK, so what are the solutions for that?",
|
||||
"Any solutions here? What can I do to fix the",
|
||||
"problem? Pardon?",
|
||||
"Stop using the, exactly.",
|
||||
"When in doubt, do something else.",
|
||||
"Build a different design. So what I could do is this is",
|
||||
"pretty dumb, using a long wire. And so, no, but trust me,",
|
||||
"oftentimes you go to the store room and they give you a big",
|
||||
"roll of wire, and you're too lazy to cut a",
|
||||
"piece out. Use the whole roll,",
|
||||
"and use the two ends, and connect it in,",
|
||||
"OK? So, if I had a much shorter",
|
||||
"piece of wire, then that can solve my problem.",
|
||||
"But again, remember, what's small to you may not be",
|
||||
"small to the circuit. OK, so let's say,",
|
||||
"for example, I'm Intel, and I'm building a",
|
||||
"10 GHz Pentium 6 processor. OK, it's 0.1 nanosecond is my",
|
||||
"cycle time. There, even a small,",
|
||||
"itty bitty wire can be a real problem.",
|
||||
"OK, and so therefore, distributing power throughout a",
|
||||
"one inch chip that's clocking at 10 GHz is a really,",
|
||||
"really hard problem. And our own David Perreault,",
|
||||
"who is doing one of our sections, is one of the world's",
|
||||
"experts in this field. Distributing power,",
|
||||
"something as simple as, how do I get 1V in a stable",
|
||||
"manner to every single device on my chip?",
|
||||
"It's a hard problem. OK, so now, you have to begin",
|
||||
"feeding your power supply connections much like RC",
|
||||
"circuits, OK, and you have to solve some hard",
|
||||
"problems to be able to simply distribute power decently",
|
||||
"throughout your circuit. So, what else can I do?",
|
||||
"Yeah? Say it again?",
|
||||
"Ah, I can do that. I could use different wires to",
|
||||
"connect each of the inverters. That's a good point.",
|
||||
"So here, the coupling happens because I connect the two",
|
||||
"inverters way out here. So instead, I use a different",
|
||||
"cable. I hadn't thought of that.",
|
||||
"That's a creative solution. OK, so in fact,",
|
||||
"if you build a chip, so we built this chip called",
|
||||
"RAW in our group, and it has on the order of 10",
|
||||
"million gates. And this chip we built with",
|
||||
"IBM's technology, and it turns out that you don't",
|
||||
"send power supply in through a pin and then connect that 1.5V",
|
||||
"supply to all your gates. What you do is from that pin,",
|
||||
"you then build special power supply buffering trees.",
|
||||
"And each tree, each leaf of the tree drives a",
|
||||
"subcircuit. In other words,",
|
||||
"if this is a chip, you have lots and lots of gates",
|
||||
"throughout your chip. What you do not do is bring in",
|
||||
"a power supply like this, and then connect.",
|
||||
"You don't do that. That's the worst possible thing",
|
||||
"you can do. It's an absolute disaster for",
|
||||
"the reason just brought up. OK, so instead what you do is",
|
||||
"divide up the chip into, say, four quadrants.",
|
||||
"OK, in our case, we have 16 quadrants.",
|
||||
"And then what you do is from this point, you take one wire",
|
||||
"that goes to this quadrant, one wire that comes here,",
|
||||
"one here, and one here, so that you're getting the",
|
||||
"power supply very close to the source, and you have different",
|
||||
"connections going to each quadrant so that switching in",
|
||||
"this quadrant will not affect this guy because of the",
|
||||
"inductance of this lead here. OK, and if you hadn't taken",
|
||||
"6.002, you'd have been arguing with IBM, I don't want 16 wires.",
|
||||
"I want just one wire. OK, so there are other",
|
||||
"solutions, of course. There's a couple more solution.",
|
||||
"One is that what you can do is part of the problem here is that",
|
||||
"all my transitions are really, really sharp.",
|
||||
"OK, so di/dt is very, very large.",
|
||||
"So, there's a whole new technique in design of digital",
|
||||
"and analog circuits, which talks about,",
|
||||
"maybe I should call it waveform engineering, OK,",
|
||||
"or edge engineering. OK, it's also called edge",
|
||||
"smoothing. The idea is that rather than",
|
||||
"have very sharp edges in your circuit, you try to have",
|
||||
"smoother edges. And when you have smoother",
|
||||
"edges, OK, then your di/dt is now going to be less.",
|
||||
"It's not going to be very, very high.",
|
||||
"Rather, your delta I is spread out over a longer period of",
|
||||
"time. Of course, that means the",
|
||||
"circuits may have to run a little slower,",
|
||||
"but that can also solve the problem.",
|
||||
"And in fact, that same smoothing of the",
|
||||
"waveforms was also the solution you saw in the capacitive",
|
||||
"coupling we saw a month and a half ago.",
|
||||
"And let me show you the demo, and then close up.",
|
||||
"Not working? OK, that's OK.",
|
||||
"It doesn't matter. So if you remember the demo",
|
||||
"from the lecture about a month and a half ago in capacitors,",
|
||||
"I talked about a chip with two pins, and there was this",
|
||||
"capacitive coupling between the pins.",
|
||||
"And because of this, if this waveform is switching,",
|
||||
"then because of this coupling, you will end up getting,",
|
||||
"if this is the signal here, you will end up getting spikes",
|
||||
"on this pin because of the signaling of the other pin.",
|
||||
"And that's good old capacitive coupling.",
|
||||
"OK, and to eliminate this, what you can do is much like",
|
||||
"with the inductance system, if you, rather than having",
|
||||
"sharp transitions on this pin, if you have smooth transitions",
|
||||
"that look like this, then what you can do is you'll",
|
||||
"now spread delta V from here to here over a longer delta T.",
|
||||
"OK, delta T has become longer, and because of that,",
|
||||
"you end up getting much better behavior, and you don't end up",
|
||||
"getting these spikes. So therefore,",
|
||||
"if you want to build really, really fast circuits,",
|
||||
"you have to be really careful. You can build fast circuits,",
|
||||
"but watch out for them fast edges.",
|
||||
"OK, fast edges are nasty. They kill you.",
|
||||
"That's something to remember as you build the next generation of",
|
||||
"circuits. Well, thank you all.",
|
||||
"I had a blast, and I hope you guys had fun",
|
||||
"too. Thank you."
|
||||
]
|
||||
}
|
||||
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user