resolve merge
This commit is contained in:
Ernie Park
@@ -1,3657 +0,0 @@
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/*
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html5doctor.com Reset Stylesheet
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v1.6.1
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Last Updated: 2010-09-17
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Author: Richard Clark - http://richclarkdesign.com
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Twitter: @rich_clark
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*/
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html, body, div, span, object, iframe,
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h1, h2, h3, div.wiki-wrapper div#wiki_panel input[type="button"], h4, h5, h6, p, blockquote, pre,
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abbr, address, cite, code,
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del, dfn, em, img, ins, kbd, q, samp,
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small, strong, sub, sup, var,
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b, i,
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dl, dt, dd, ol, ul, li,
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fieldset, form, label, legend,
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table, caption, tbody, tfoot, thead, tr, th, td,
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article, aside, canvas, details, figcaption, figure,
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footer, header, hgroup, menu, nav, section, summary,
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time, mark, audio, video {
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margin: 0;
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padding: 0;
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border: 0;
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outline: 0;
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font-size: 100%;
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vertical-align: baseline;
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background: transparent; }
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body {
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line-height: 1; }
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article, aside, details, figcaption, figure,
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footer, header, hgroup, menu, nav, section {
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display: block; }
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nav ul {
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list-style: none; }
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blockquote, q {
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quotes: none; }
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blockquote:before, blockquote:after,
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q:before, q:after {
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content: '';
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content: none; }
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a {
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margin: 0;
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padding: 0;
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font-size: 100%;
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vertical-align: baseline;
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background: transparent; }
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/* change colours to suit your needs */
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ins {
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background-color: #ff9;
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color: #000;
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text-decoration: none; }
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/* change colours to suit your needs */
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mark {
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background-color: #ff9;
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color: #000;
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font-style: italic;
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font-weight: bold; }
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del {
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text-decoration: line-through; }
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abbr[title], dfn[title] {
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border-bottom: 1px dotted;
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cursor: help; }
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table {
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border-collapse: collapse;
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border-spacing: 0; }
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/* change border colour to suit your needs */
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hr {
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display: block;
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height: 1px;
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border: 0;
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border-top: 1px solid #cccccc;
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margin: 1em 0;
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padding: 0; }
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input, select {
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vertical-align: middle; }
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@font-face {
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font-family: 'Droid Sans';
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font-style: normal;
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font-weight: normal;
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src: local("Droid Sans"), local("DroidSans"), url("http://themes.googleusercontent.com/static/fonts/droidsans/v3/s-BiyweUPV0v-yRb-cjciL3hpw3pgy2gAi-Ip7WPMi0.woff") format("woff"); }
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@font-face {
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font-family: 'Droid Sans';
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font-style: normal;
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font-weight: bold;
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src: local("Droid Sans Bold"), local("DroidSans-Bold"), url("http://themes.googleusercontent.com/static/fonts/droidsans/v3/EFpQQyG9GqCrobXxL-KRMXbFhgvWbfSbdVg11QabG8w.woff") format("woff"); }
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.clearfix:after, .topbar:after, div.book-wrapper section.book nav:after, div.wiki-wrapper section.wiki-body header:after, body.askbot .secondary-nav nav:after, html body div.header-wrapper header:after, html body div.header-wrapper header nav ul:after, html body section.main-content:after, html footer:after, div.course-wrapper section.course-content ol.vert-mod li:after, div.book-wrapper section.book nav ul:after, div.wiki-wrapper div#wiki_panel div#wiki_create_form:after, body.askbot footer .footer-wrapper:after {
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content: ".";
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display: block;
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height: 0;
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clear: both;
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visibility: hidden; }
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.wrapper, html body div.header-wrapper header, html body section.main-content, html footer, section.activation, body.askbot .secondary-nav nav, body.askbot footer .footer-wrapper {
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margin: 0 auto;
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max-width: 1400px;
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min-width: 810px;
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width: 100%;
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text-align: left; }
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.wrapper div.table-wrapper, html body div.header-wrapper header div.table-wrapper, html body section.main-content div.table-wrapper, html footer div.table-wrapper, section.activation div.table-wrapper, body.askbot .secondary-nav nav div.table-wrapper, body.askbot footer .footer-wrapper div.table-wrapper, .wrapper div.course-wrapper, html body div.header-wrapper header div.course-wrapper, html body section.main-content div.course-wrapper, html footer div.course-wrapper, section.activation div.course-wrapper, body.askbot .secondary-nav nav div.course-wrapper, body.askbot footer .footer-wrapper div.course-wrapper, .wrapper div.book-wrapper, html body div.header-wrapper header div.book-wrapper, html body section.main-content div.book-wrapper, html footer div.book-wrapper, section.activation div.book-wrapper, body.askbot .secondary-nav nav div.book-wrapper, body.askbot footer .footer-wrapper div.book-wrapper {
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display: table;
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width: 100%; }
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.button, input[type="submit"], input[type="button"], button {
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-webkit-box-shadow: inset 0 1px 0 #a2a2a2, 0 0 3px #cccccc;
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-moz-box-shadow: inset 0 1px 0 #a2a2a2, 0 0 3px #cccccc;
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-ms-box-shadow: inset 0 1px 0 #a2a2a2, 0 0 3px #cccccc;
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-o-box-shadow: inset 0 1px 0 #a2a2a2, 0 0 3px #cccccc;
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box-shadow: inset 0 1px 0 #a2a2a2, 0 0 3px #cccccc;
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background-color: #959595;
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background-image: -webkit-gradient(linear, left top, left bottom, color-stop(0%, #959595), color-stop(100%, #7b7b7b));
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background-image: -webkit-linear-gradient(top, #959595, #7b7b7b);
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background-image: -moz-linear-gradient(top, #959595, #7b7b7b);
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background-image: -ms-linear-gradient(top, #959595, #7b7b7b);
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background-image: -o-linear-gradient(top, #959595, #7b7b7b);
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background-image: linear-gradient(top, #959595, #7b7b7b);
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-webkit-border-radius: 3px;
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-moz-border-radius: 3px;
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-ms-border-radius: 3px;
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-o-border-radius: 3px;
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border-radius: 3px;
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border: 1px solid #6f6f6f;
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padding: 4px 8px;
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color: #fff;
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font: bold 14px "Droid Sans", "Lucida Grande", "Lucida Sans Unicode", "Lucida Sans", Geneva, Verdana, sans-serif;
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cursor: pointer;
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-webkit-font-smoothing: antialiased; }
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.button:hover, input[type="submit"]:hover, input[type="button"]:hover, button:hover, .button:focus, input[type="submit"]:focus, input[type="button"]:focus, button:focus {
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-webkit-box-shadow: inset 0 1px 0 #bbbbbb, 0 0 3px #cccccc;
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-moz-box-shadow: inset 0 1px 0 #bbbbbb, 0 0 3px #cccccc;
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-ms-box-shadow: inset 0 1px 0 #bbbbbb, 0 0 3px #cccccc;
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-o-box-shadow: inset 0 1px 0 #bbbbbb, 0 0 3px #cccccc;
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box-shadow: inset 0 1px 0 #bbbbbb, 0 0 3px #cccccc;
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background-color: #a2a2a2;
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background-image: -webkit-gradient(linear, left top, left bottom, color-stop(0%, #a2a2a2), color-stop(100%, #7b7b7b));
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background-image: -webkit-linear-gradient(top, #a2a2a2, #7b7b7b);
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background-image: -moz-linear-gradient(top, #a2a2a2, #7b7b7b);
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background-image: -ms-linear-gradient(top, #a2a2a2, #7b7b7b);
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background-image: -o-linear-gradient(top, #a2a2a2, #7b7b7b);
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background-image: linear-gradient(top, #a2a2a2, #7b7b7b);
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border: 1px solid #555555; }
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.content, div.course-wrapper section.course-content, div.book-wrapper section.book, div.wiki-wrapper section.wiki-body {
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-webkit-box-sizing: border-box;
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-moz-box-sizing: border-box;
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-ms-box-sizing: border-box;
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-o-box-sizing: border-box;
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box-sizing: border-box;
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display: table-cell;
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padding: 22.652px;
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vertical-align: top;
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width: 76.518%; }
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.sidebar, div.course-wrapper div#accordion, div.book-wrapper ul#booknav, div.wiki-wrapper div#wiki_panel, body.askbot .main-content .discussion-wrapper aside {
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-webkit-box-shadow: inset -1px 0 0 #f6f6f6;
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-moz-box-shadow: inset -1px 0 0 #f6f6f6;
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-ms-box-shadow: inset -1px 0 0 #f6f6f6;
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-o-box-shadow: inset -1px 0 0 #f6f6f6;
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box-shadow: inset -1px 0 0 #f6f6f6;
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-webkit-box-sizing: border-box;
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-moz-box-sizing: border-box;
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-ms-box-sizing: border-box;
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-o-box-sizing: border-box;
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box-sizing: border-box;
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background: #e3e3e3;
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border-right: 1px solid #d3d3d3;
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display: table-cell;
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font-family: "Droid Sans", "Lucida Grande", "Lucida Sans Unicode", "Lucida Sans", Geneva, Verdana, sans-serif;
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text-shadow: 0 1px 0 #f1f1f1;
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vertical-align: top;
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width: 23.482%;
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position: relative; }
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.sidebar h3, div.course-wrapper div#accordion h3, div.book-wrapper ul#booknav h3, div.wiki-wrapper div#wiki_panel h3, body.askbot .main-content .discussion-wrapper aside h3, .sidebar div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel .sidebar input[type="button"], div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input[type="button"], div.book-wrapper ul#booknav div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel div.book-wrapper ul#booknav input[type="button"], div.wiki-wrapper div#wiki_panel input[type="button"], body.askbot .main-content .discussion-wrapper aside div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel body.askbot .main-content .discussion-wrapper aside input[type="button"] {
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-webkit-box-shadow: 0 1px 0 #eeeeee;
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-moz-box-shadow: 0 1px 0 #eeeeee;
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-ms-box-shadow: 0 1px 0 #eeeeee;
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-o-box-shadow: 0 1px 0 #eeeeee;
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box-shadow: 0 1px 0 #eeeeee;
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background: none;
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border: none;
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border-bottom: 1px solid #d3d3d3;
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color: #000;
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font-weight: normal;
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margin: 0;
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overflow: hidden; }
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.sidebar h3 a, div.course-wrapper div#accordion h3 a, div.book-wrapper ul#booknav h3 a, div.wiki-wrapper div#wiki_panel h3 a, body.askbot .main-content .discussion-wrapper aside h3 a, .sidebar div.wiki-wrapper div#wiki_panel input[type="button"] a, div.wiki-wrapper div#wiki_panel .sidebar input[type="button"] a, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input[type="button"] a, div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input[type="button"] a, div.book-wrapper ul#booknav div.wiki-wrapper div#wiki_panel input[type="button"] a, div.wiki-wrapper div#wiki_panel div.book-wrapper ul#booknav input[type="button"] a, div.wiki-wrapper div#wiki_panel input[type="button"] a, body.askbot .main-content .discussion-wrapper aside div.wiki-wrapper div#wiki_panel input[type="button"] a, div.wiki-wrapper div#wiki_panel body.askbot .main-content .discussion-wrapper aside input[type="button"] a {
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-webkit-transition-property: all;
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-moz-transition-property: all;
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-ms-transition-property: all;
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-o-transition-property: all;
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transition-property: all;
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-webkit-transition-duration: 0.15s;
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-moz-transition-duration: 0.15s;
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-ms-transition-duration: 0.15s;
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-o-transition-duration: 0.15s;
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transition-duration: 0.15s;
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-webkit-transition-timing-function: ease-out;
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-moz-transition-timing-function: ease-out;
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-ms-transition-timing-function: ease-out;
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-o-transition-timing-function: ease-out;
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transition-timing-function: ease-out;
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-webkit-transition-delay: 0;
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-moz-transition-delay: 0;
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||||
-ms-transition-delay: 0;
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-o-transition-delay: 0;
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transition-delay: 0;
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color: #4d4d4d;
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display: block;
|
||||
font-size: 14px;
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padding: 7px 7px 7px 30px;
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text-decoration: none; }
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.sidebar h3 a:hover, div.course-wrapper div#accordion h3 a:hover, div.book-wrapper ul#booknav h3 a:hover, div.wiki-wrapper div#wiki_panel h3 a:hover, body.askbot .main-content .discussion-wrapper aside h3 a:hover, .sidebar div.wiki-wrapper div#wiki_panel input[type="button"] a:hover, div.wiki-wrapper div#wiki_panel .sidebar input[type="button"] a:hover, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input[type="button"] a:hover, div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input[type="button"] a:hover, div.book-wrapper ul#booknav div.wiki-wrapper div#wiki_panel input[type="button"] a:hover, div.wiki-wrapper div#wiki_panel div.book-wrapper ul#booknav input[type="button"] a:hover, div.wiki-wrapper div#wiki_panel input[type="button"] a:hover, body.askbot .main-content .discussion-wrapper aside div.wiki-wrapper div#wiki_panel input[type="button"] a:hover, div.wiki-wrapper div#wiki_panel body.askbot .main-content .discussion-wrapper aside input[type="button"] a:hover {
|
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-webkit-box-shadow: 0 1px 0 white;
|
||||
-moz-box-shadow: 0 1px 0 white;
|
||||
-ms-box-shadow: 0 1px 0 white;
|
||||
-o-box-shadow: 0 1px 0 white;
|
||||
box-shadow: 0 1px 0 white;
|
||||
background: #efefef; }
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.sidebar h3 span.ui-icon, div.course-wrapper div#accordion h3 span.ui-icon, div.book-wrapper ul#booknav h3 span.ui-icon, div.wiki-wrapper div#wiki_panel h3 span.ui-icon, body.askbot .main-content .discussion-wrapper aside h3 span.ui-icon, .sidebar div.wiki-wrapper div#wiki_panel input[type="button"] span.ui-icon, div.wiki-wrapper div#wiki_panel .sidebar input[type="button"] span.ui-icon, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input[type="button"] span.ui-icon, div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input[type="button"] span.ui-icon, div.book-wrapper ul#booknav div.wiki-wrapper div#wiki_panel input[type="button"] span.ui-icon, div.wiki-wrapper div#wiki_panel div.book-wrapper ul#booknav input[type="button"] span.ui-icon, div.wiki-wrapper div#wiki_panel input[type="button"] span.ui-icon, body.askbot .main-content .discussion-wrapper aside div.wiki-wrapper div#wiki_panel input[type="button"] span.ui-icon, div.wiki-wrapper div#wiki_panel body.askbot .main-content .discussion-wrapper aside input[type="button"] span.ui-icon {
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||||
background-image: url(images/ui-icons_454545_256x240.png); }
|
||||
.sidebar h3.active, div.course-wrapper div#accordion h3.active, div.book-wrapper ul#booknav h3.active, div.wiki-wrapper div#wiki_panel h3.active, body.askbot .main-content .discussion-wrapper aside h3.active, .sidebar div.course-wrapper div#accordion h3.ui-accordion-header.ui-state-active, div.course-wrapper div#accordion .sidebar h3.ui-accordion-header.ui-state-active, div.course-wrapper div#accordion h3.ui-accordion-header.ui-state-active, div.book-wrapper ul#booknav div.course-wrapper div#accordion h3.ui-accordion-header.ui-state-active, div.course-wrapper div#accordion div.book-wrapper ul#booknav h3.ui-accordion-header.ui-state-active, div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion h3.ui-accordion-header.ui-state-active, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel h3.ui-accordion-header.ui-state-active, body.askbot .main-content .discussion-wrapper aside div.course-wrapper div#accordion h3.ui-accordion-header.ui-state-active, div.course-wrapper div#accordion body.askbot .main-content .discussion-wrapper aside h3.ui-accordion-header.ui-state-active, .sidebar div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input.ui-accordion-header.ui-state-active[type="button"], div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel .sidebar input.ui-accordion-header.ui-state-active[type="button"], div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input.ui-accordion-header.ui-state-active[type="button"], div.book-wrapper ul#booknav div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input.ui-accordion-header.ui-state-active[type="button"], div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel div.book-wrapper ul#booknav input.ui-accordion-header.ui-state-active[type="button"], div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input.ui-accordion-header.ui-state-active[type="button"], body.askbot .main-content .discussion-wrapper aside div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input.ui-accordion-header.ui-state-active[type="button"], div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel body.askbot .main-content .discussion-wrapper aside input.ui-accordion-header.ui-state-active[type="button"], .sidebar div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input.ui-accordion-header.ui-state-active[type="button"], div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion .sidebar input.ui-accordion-header.ui-state-active[type="button"], div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input.ui-accordion-header.ui-state-active[type="button"], div.book-wrapper ul#booknav div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input.ui-accordion-header.ui-state-active[type="button"], div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion div.book-wrapper ul#booknav input.ui-accordion-header.ui-state-active[type="button"], div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input.ui-accordion-header.ui-state-active[type="button"], body.askbot .main-content .discussion-wrapper aside div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input.ui-accordion-header.ui-state-active[type="button"], div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion body.askbot .main-content .discussion-wrapper aside input.ui-accordion-header.ui-state-active[type="button"], .sidebar div.wiki-wrapper div#wiki_panel input.active[type="button"], div.wiki-wrapper div#wiki_panel .sidebar input.active[type="button"], div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input.active[type="button"], div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input.active[type="button"], div.book-wrapper ul#booknav div.wiki-wrapper div#wiki_panel input.active[type="button"], div.wiki-wrapper div#wiki_panel div.book-wrapper ul#booknav input.active[type="button"], div.wiki-wrapper div#wiki_panel input.active[type="button"], body.askbot .main-content .discussion-wrapper aside div.wiki-wrapper div#wiki_panel input.active[type="button"], div.wiki-wrapper div#wiki_panel body.askbot .main-content .discussion-wrapper aside input.active[type="button"] {
|
||||
-webkit-box-shadow: none;
|
||||
-moz-box-shadow: none;
|
||||
-ms-box-shadow: none;
|
||||
-o-box-shadow: none;
|
||||
box-shadow: none;
|
||||
background: none;
|
||||
border: 0;
|
||||
border-bottom: 1px solid #bbb;
|
||||
color: #000;
|
||||
font-weight: bold; }
|
||||
.sidebar h3.active a, div.course-wrapper div#accordion h3.active a, div.book-wrapper ul#booknav h3.active a, div.wiki-wrapper div#wiki_panel h3.active a, body.askbot .main-content .discussion-wrapper aside h3.active a, .sidebar div.course-wrapper div#accordion h3.ui-accordion-header.ui-state-active a, div.course-wrapper div#accordion .sidebar h3.ui-accordion-header.ui-state-active a, div.course-wrapper div#accordion h3.ui-accordion-header.ui-state-active a, div.book-wrapper ul#booknav div.course-wrapper div#accordion h3.ui-accordion-header.ui-state-active a, div.course-wrapper div#accordion div.book-wrapper ul#booknav h3.ui-accordion-header.ui-state-active a, div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion h3.ui-accordion-header.ui-state-active a, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel h3.ui-accordion-header.ui-state-active a, body.askbot .main-content .discussion-wrapper aside div.course-wrapper div#accordion h3.ui-accordion-header.ui-state-active a, div.course-wrapper div#accordion body.askbot .main-content .discussion-wrapper aside h3.ui-accordion-header.ui-state-active a, .sidebar div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input.ui-accordion-header.ui-state-active[type="button"] a, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel .sidebar input.ui-accordion-header.ui-state-active[type="button"] a, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input.ui-accordion-header.ui-state-active[type="button"] a, div.book-wrapper ul#booknav div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input.ui-accordion-header.ui-state-active[type="button"] a, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel div.book-wrapper ul#booknav input.ui-accordion-header.ui-state-active[type="button"] a, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input.ui-accordion-header.ui-state-active[type="button"] a, body.askbot .main-content .discussion-wrapper aside div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input.ui-accordion-header.ui-state-active[type="button"] a, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel body.askbot .main-content .discussion-wrapper aside input.ui-accordion-header.ui-state-active[type="button"] a, .sidebar div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input.ui-accordion-header.ui-state-active[type="button"] a, div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion .sidebar input.ui-accordion-header.ui-state-active[type="button"] a, div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input.ui-accordion-header.ui-state-active[type="button"] a, div.book-wrapper ul#booknav div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input.ui-accordion-header.ui-state-active[type="button"] a, div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion div.book-wrapper ul#booknav input.ui-accordion-header.ui-state-active[type="button"] a, div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input.ui-accordion-header.ui-state-active[type="button"] a, body.askbot .main-content .discussion-wrapper aside div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input.ui-accordion-header.ui-state-active[type="button"] a, div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion body.askbot .main-content .discussion-wrapper aside input.ui-accordion-header.ui-state-active[type="button"] a, .sidebar div.wiki-wrapper div#wiki_panel input.active[type="button"] a, div.wiki-wrapper div#wiki_panel .sidebar input.active[type="button"] a, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input.active[type="button"] a, div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input.active[type="button"] a, div.book-wrapper ul#booknav div.wiki-wrapper div#wiki_panel input.active[type="button"] a, div.wiki-wrapper div#wiki_panel div.book-wrapper ul#booknav input.active[type="button"] a, div.wiki-wrapper div#wiki_panel input.active[type="button"] a, body.askbot .main-content .discussion-wrapper aside div.wiki-wrapper div#wiki_panel input.active[type="button"] a, div.wiki-wrapper div#wiki_panel body.askbot .main-content .discussion-wrapper aside input.active[type="button"] a {
|
||||
color: #000; }
|
||||
|
||||
.topbar, div.book-wrapper section.book nav, div.wiki-wrapper section.wiki-body header, body.askbot .secondary-nav nav {
|
||||
background: #F6EFD4;
|
||||
border-bottom: 1px solid #eddfaa;
|
||||
margin: -22.652px -22.652px 22.652px;
|
||||
font-size: 12px;
|
||||
text-shadow: 0 1px 0 #fff; }
|
||||
.topbar a, div.book-wrapper section.book nav a, div.wiki-wrapper section.wiki-body header a, body.askbot .secondary-nav nav a {
|
||||
text-transform: uppercase;
|
||||
color: #292309; }
|
||||
.topbar a:hover, div.book-wrapper section.book nav a:hover, div.wiki-wrapper section.wiki-body header a:hover, body.askbot .secondary-nav nav a:hover {
|
||||
color: #7e691a; }
|
||||
|
||||
h1 {
|
||||
font-size: 1.6em;
|
||||
margin: 20px 0 10px 0; }
|
||||
|
||||
h2 {
|
||||
font-size: 14px;
|
||||
font-weight: bold;
|
||||
letter-spacing: 1px;
|
||||
margin: 20px 0 10px 0;
|
||||
text-transform: uppercase; }
|
||||
|
||||
p {
|
||||
margin-bottom: 22.652px; }
|
||||
|
||||
em {
|
||||
font-style: italic;
|
||||
font-family: Georgia, serif; }
|
||||
|
||||
input[type="email"], input[type="number"], input[type="password"], input[type="search"], input[type="tel"], input[type="text"], input[type="url"], input[type="color"], input[type="date"], input[type="datetime"], input[type="datetime-local"], input[type="month"], input[type="time"], input[type="week"], textarea {
|
||||
-webkit-box-shadow: 0 -1px 0 white;
|
||||
-moz-box-shadow: 0 -1px 0 white;
|
||||
-ms-box-shadow: 0 -1px 0 white;
|
||||
-o-box-shadow: 0 -1px 0 white;
|
||||
box-shadow: 0 -1px 0 white;
|
||||
background-color: #eeeeee;
|
||||
background-image: -webkit-gradient(linear, left top, left bottom, color-stop(0%, #eeeeee), color-stop(100%, white));
|
||||
background-image: -webkit-linear-gradient(top, #eeeeee, white);
|
||||
background-image: -moz-linear-gradient(top, #eeeeee, white);
|
||||
background-image: -ms-linear-gradient(top, #eeeeee, white);
|
||||
background-image: -o-linear-gradient(top, #eeeeee, white);
|
||||
background-image: linear-gradient(top, #eeeeee, white);
|
||||
border: 1px solid #999;
|
||||
font: 14px "Droid Sans", "Lucida Grande", "Lucida Sans Unicode", "Lucida Sans", Geneva, Verdana, sans-serif;
|
||||
padding: 4px; }
|
||||
input[type="email"]:focus, input[type="number"]:focus, input[type="password"]:focus, input[type="search"]:focus, input[type="tel"]:focus, input[type="text"]:focus, input[type="url"]:focus, input[type="color"]:focus, input[type="date"]:focus, input[type="datetime"]:focus, input[type="datetime-local"]:focus, input[type="month"]:focus, input[type="time"]:focus, input[type="week"]:focus, textarea:focus {
|
||||
border-color: #993333; }
|
||||
|
||||
html {
|
||||
margin-top: 0; }
|
||||
html body {
|
||||
color: #333333;
|
||||
font: 14px "Droid Sans", "Lucida Grande", "Lucida Sans Unicode", "Lucida Sans", Geneva, Verdana, sans-serif;
|
||||
text-align: center;
|
||||
margin: 0;
|
||||
background: #f3f3f3; }
|
||||
html body div.header-wrapper {
|
||||
-webkit-box-shadow: inset 0 1px 0 #bf4040, 0 1px 1px #cccccc;
|
||||
-moz-box-shadow: inset 0 1px 0 #bf4040, 0 1px 1px #cccccc;
|
||||
-ms-box-shadow: inset 0 1px 0 #bf4040, 0 1px 1px #cccccc;
|
||||
-o-box-shadow: inset 0 1px 0 #bf4040, 0 1px 1px #cccccc;
|
||||
box-shadow: inset 0 1px 0 #bf4040, 0 1px 1px #cccccc;
|
||||
background-color: #ac3939;
|
||||
background-image: -webkit-gradient(linear, left top, left bottom, color-stop(0%, #ac3939), color-stop(100%, #862d2d));
|
||||
background-image: -webkit-linear-gradient(top, #ac3939, #862d2d);
|
||||
background-image: -moz-linear-gradient(top, #ac3939, #862d2d);
|
||||
background-image: -ms-linear-gradient(top, #ac3939, #862d2d);
|
||||
background-image: -o-linear-gradient(top, #ac3939, #862d2d);
|
||||
background-image: linear-gradient(top, #ac3939, #862d2d);
|
||||
border-bottom: 1px solid #732626; }
|
||||
html body div.header-wrapper header {
|
||||
-webkit-box-sizing: border-box;
|
||||
-moz-box-sizing: border-box;
|
||||
-ms-box-sizing: border-box;
|
||||
-o-box-sizing: border-box;
|
||||
box-sizing: border-box;
|
||||
padding: 0 22.652px; }
|
||||
html body div.header-wrapper header h1 {
|
||||
border-right: 1px solid #862d2d;
|
||||
font-size: 14px;
|
||||
font-weight: bold;
|
||||
margin: 0 2.024% 0 0;
|
||||
padding: 15px 2.024% 15px 0;
|
||||
display: block;
|
||||
float: left;
|
||||
color: #000;
|
||||
text-shadow: 0 1px 0 #bf4040; }
|
||||
html body div.header-wrapper header h1 em {
|
||||
display: -moz-inline-box;
|
||||
-moz-box-orient: vertical;
|
||||
display: inline-block;
|
||||
vertical-align: baseline;
|
||||
zoom: 1;
|
||||
*display: inline;
|
||||
*vertical-align: auto;
|
||||
padding-right: 22.652px; }
|
||||
html body div.header-wrapper header nav {
|
||||
float: left;
|
||||
display: block;
|
||||
margin: 0;
|
||||
text-shadow: 0 -1px 0 #732626; }
|
||||
html body div.header-wrapper header nav ul {
|
||||
display: inline-block;
|
||||
padding: 15px 0;
|
||||
margin: 0; }
|
||||
html body div.header-wrapper header nav ul li {
|
||||
margin-right: 22.652px;
|
||||
display: inline-block;
|
||||
margin-bottom: 0; }
|
||||
html body div.header-wrapper header nav ul li a {
|
||||
color: #fff; }
|
||||
html body div.header-wrapper header nav ul li a:hover {
|
||||
color: rgba(255, 255, 255, 0.7);
|
||||
background-color: none;
|
||||
text-decoration: none; }
|
||||
html body section.main-content {
|
||||
-webkit-box-shadow: 0 1px 0 white;
|
||||
-moz-box-shadow: 0 1px 0 white;
|
||||
-ms-box-shadow: 0 1px 0 white;
|
||||
-o-box-shadow: 0 1px 0 white;
|
||||
box-shadow: 0 1px 0 white;
|
||||
-webkit-box-sizing: border-box;
|
||||
-moz-box-sizing: border-box;
|
||||
-ms-box-sizing: border-box;
|
||||
-o-box-sizing: border-box;
|
||||
box-sizing: border-box;
|
||||
background: #fff;
|
||||
border: 1px solid #ccc;
|
||||
border-top: 0; }
|
||||
html body img {
|
||||
max-width: 100%;
|
||||
height: auto; }
|
||||
html footer {
|
||||
-webkit-box-sizing: border-box;
|
||||
-moz-box-sizing: border-box;
|
||||
-ms-box-sizing: border-box;
|
||||
-o-box-sizing: border-box;
|
||||
box-sizing: border-box;
|
||||
color: #777;
|
||||
margin-top: 22.652px;
|
||||
padding: 0 22.652px; }
|
||||
html footer p {
|
||||
float: left; }
|
||||
html footer p a {
|
||||
color: #444; }
|
||||
html footer ul {
|
||||
float: right; }
|
||||
html footer ul li {
|
||||
display: inline-block;
|
||||
margin-right: 20px; }
|
||||
html footer ul li a {
|
||||
color: #444; }
|
||||
|
||||
#lean_overlay {
|
||||
position: fixed;
|
||||
z-index: 100;
|
||||
top: 0px;
|
||||
left: 0px;
|
||||
height: 100%;
|
||||
width: 100%;
|
||||
background: #000;
|
||||
display: none; }
|
||||
|
||||
div.leanModal_box {
|
||||
-webkit-border-radius: 3px;
|
||||
-moz-border-radius: 3px;
|
||||
-ms-border-radius: 3px;
|
||||
-o-border-radius: 3px;
|
||||
border-radius: 3px;
|
||||
-webkit-box-shadow: 0 0 6px black;
|
||||
-moz-box-shadow: 0 0 6px black;
|
||||
-ms-box-shadow: 0 0 6px black;
|
||||
-o-box-shadow: 0 0 6px black;
|
||||
box-shadow: 0 0 6px black;
|
||||
-webkit-box-sizing: border-box;
|
||||
-moz-box-sizing: border-box;
|
||||
-ms-box-sizing: border-box;
|
||||
-o-box-sizing: border-box;
|
||||
box-sizing: border-box;
|
||||
display: none;
|
||||
border: none;
|
||||
max-width: 600px;
|
||||
background: #fff;
|
||||
padding: 45.304px; }
|
||||
div.leanModal_box h1 {
|
||||
font-size: 24px;
|
||||
margin-top: 0;
|
||||
font-family: "Oswald";
|
||||
padding-bottom: 22.652px;
|
||||
border-bottom: 1px solid #eee;
|
||||
margin-bottom: 22.652px; }
|
||||
div.leanModal_box form {
|
||||
text-align: left; }
|
||||
div.leanModal_box form div#enroll_error {
|
||||
padding-bottom: 22.652px;
|
||||
color: #DF8B2C;
|
||||
text-transform: uppercase;
|
||||
letter-spacing: 1px;
|
||||
font-weight: bold; }
|
||||
div.leanModal_box form ol li {
|
||||
margin-bottom: 22.652px;
|
||||
width: 48.988%;
|
||||
float: left; }
|
||||
div.leanModal_box form ol li:nth-child(odd) {
|
||||
margin-right: 2.024%; }
|
||||
div.leanModal_box form ol li.terms, div.leanModal_box form ol li.remember {
|
||||
float: none;
|
||||
width: auto;
|
||||
clear: both;
|
||||
padding-top: 22.652px;
|
||||
border-top: 1px solid #eee; }
|
||||
div.leanModal_box form ol li.honor-code {
|
||||
width: auto;
|
||||
float: none; }
|
||||
div.leanModal_box form ol li label {
|
||||
display: block;
|
||||
font-weight: bold; }
|
||||
div.leanModal_box form ol li input[type="email"], div.leanModal_box form ol li input[type="number"], div.leanModal_box form ol li input[type="password"], div.leanModal_box form ol li input[type="search"], div.leanModal_box form ol li input[type="tel"], div.leanModal_box form ol li input[type="text"], div.leanModal_box form ol li input[type="url"], div.leanModal_box form ol li input[type="color"], div.leanModal_box form ol li input[type="date"], div.leanModal_box form ol li input[type="datetime"], div.leanModal_box form ol li input[type="datetime-local"], div.leanModal_box form ol li input[type="month"], div.leanModal_box form ol li input[type="time"], div.leanModal_box form ol li input[type="week"], div.leanModal_box form ol li textarea {
|
||||
width: 100%;
|
||||
-webkit-box-sizing: border-box;
|
||||
-moz-box-sizing: border-box;
|
||||
-ms-box-sizing: border-box;
|
||||
-o-box-sizing: border-box;
|
||||
box-sizing: border-box; }
|
||||
div.leanModal_box form ol li input[type="checkbox"] {
|
||||
margin-right: 10px; }
|
||||
div.leanModal_box form input[type="button"] {
|
||||
border: 1px solid #691b1b;
|
||||
-webkit-border-radius: 3px;
|
||||
-moz-border-radius: 3px;
|
||||
-ms-border-radius: 3px;
|
||||
-o-border-radius: 3px;
|
||||
border-radius: 3px;
|
||||
-webkit-box-shadow: inset 0 1px 0 0 #bc5c5c;
|
||||
-moz-box-shadow: inset 0 1px 0 0 #bc5c5c;
|
||||
-ms-box-shadow: inset 0 1px 0 0 #bc5c5c;
|
||||
-o-box-shadow: inset 0 1px 0 0 #bc5c5c;
|
||||
box-shadow: inset 0 1px 0 0 #bc5c5c;
|
||||
color: white;
|
||||
display: inline;
|
||||
font-size: 11px;
|
||||
font-weight: bold;
|
||||
background-color: #993333;
|
||||
background-image: -webkit-gradient(linear, left top, left bottom, color-stop(0%, #993333), color-stop(100%, #761e1e));
|
||||
background-image: -webkit-linear-gradient(top, #993333, #761e1e);
|
||||
background-image: -moz-linear-gradient(top, #993333, #761e1e);
|
||||
background-image: -ms-linear-gradient(top, #993333, #761e1e);
|
||||
background-image: -o-linear-gradient(top, #993333, #761e1e);
|
||||
background-image: linear-gradient(top, #993333, #761e1e);
|
||||
padding: 6px 18px 7px;
|
||||
text-shadow: 0 1px 0 #5d1414;
|
||||
-webkit-background-clip: padding-box;
|
||||
font-size: 18px;
|
||||
padding: 11.326px; }
|
||||
div.leanModal_box form input[type="button"]:hover {
|
||||
-webkit-box-shadow: inset 0 1px 0 0 #a44141;
|
||||
-moz-box-shadow: inset 0 1px 0 0 #a44141;
|
||||
-ms-box-shadow: inset 0 1px 0 0 #a44141;
|
||||
-o-box-shadow: inset 0 1px 0 0 #a44141;
|
||||
box-shadow: inset 0 1px 0 0 #a44141;
|
||||
cursor: pointer;
|
||||
background-color: #823030;
|
||||
background-image: -webkit-gradient(linear, left top, left bottom, color-stop(0%, #823030), color-stop(100%, #691c1c));
|
||||
background-image: -webkit-linear-gradient(top, #823030, #691c1c);
|
||||
background-image: -moz-linear-gradient(top, #823030, #691c1c);
|
||||
background-image: -ms-linear-gradient(top, #823030, #691c1c);
|
||||
background-image: -o-linear-gradient(top, #823030, #691c1c);
|
||||
background-image: linear-gradient(top, #823030, #691c1c); }
|
||||
div.leanModal_box form input[type="button"]:active {
|
||||
border: 1px solid #691b1b;
|
||||
-webkit-box-shadow: inset 0 0 8px 4px #5c1919, inset 0 0 8px 4px #5c1919, 0 1px 1px 0 #eeeeee;
|
||||
-moz-box-shadow: inset 0 0 8px 4px #5c1919, inset 0 0 8px 4px #5c1919, 0 1px 1px 0 #eeeeee;
|
||||
-ms-box-shadow: inset 0 0 8px 4px #5c1919, inset 0 0 8px 4px #5c1919, 0 1px 1px 0 #eeeeee;
|
||||
-o-box-shadow: inset 0 0 8px 4px #5c1919, inset 0 0 8px 4px #5c1919, 0 1px 1px 0 #eeeeee;
|
||||
box-shadow: inset 0 0 8px 4px #5c1919, inset 0 0 8px 4px #5c1919, 0 1px 1px 0 #eeeeee; }
|
||||
div.leanModal_box div#login {
|
||||
min-width: 300px; }
|
||||
div.leanModal_box div#login ol li {
|
||||
width: auto;
|
||||
float: none; }
|
||||
div.leanModal_box div.lost-password {
|
||||
text-align: left;
|
||||
margin-top: 22.652px; }
|
||||
div.leanModal_box div.lost-password a {
|
||||
color: #999; }
|
||||
div.leanModal_box div.lost-password a:hover {
|
||||
color: #444; }
|
||||
|
||||
div#feedback_div form ol li {
|
||||
float: none;
|
||||
width: 100%; }
|
||||
div#feedback_div form ol li textarea#feedback_message {
|
||||
height: 100px; }
|
||||
|
||||
div.course-wrapper div#accordion div#open_close_accordion {
|
||||
position: absolute;
|
||||
right: 0px;
|
||||
width: 20px;
|
||||
height: 20px;
|
||||
background: #ccc;
|
||||
border: 1px solid black;
|
||||
right: -22px;
|
||||
top: 5px; }
|
||||
div.course-wrapper div#accordion h3, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input[type="button"] {
|
||||
overflow: hidden;
|
||||
margin: 0; }
|
||||
div.course-wrapper div#accordion h3:last-child, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input[type="button"]:last-child, div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input[type="button"]:last-child {
|
||||
-webkit-box-shadow: none;
|
||||
-moz-box-shadow: none;
|
||||
-ms-box-shadow: none;
|
||||
-o-box-shadow: none;
|
||||
box-shadow: none; }
|
||||
div.course-wrapper div#accordion h3.ui-accordion-header, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input.ui-accordion-header[type="button"], div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input.ui-accordion-header[type="button"] {
|
||||
color: #000; }
|
||||
div.course-wrapper div#accordion h3.ui-accordion-header a, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input.ui-accordion-header[type="button"] a, div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input.ui-accordion-header[type="button"] a {
|
||||
font-size: 14px;
|
||||
color: #4d4d4d; }
|
||||
div.course-wrapper div#accordion h3.ui-accordion-header.ui-state-hover, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input.ui-accordion-header.ui-state-hover[type="button"], div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input.ui-accordion-header.ui-state-hover[type="button"] {
|
||||
border: none;
|
||||
border-bottom: 1px solid #d3d3d3; }
|
||||
div.course-wrapper div#accordion ul.ui-accordion-content {
|
||||
-webkit-border-radius: 0;
|
||||
-moz-border-radius: 0;
|
||||
-ms-border-radius: 0;
|
||||
-o-border-radius: 0;
|
||||
border-radius: 0;
|
||||
-webkit-box-shadow: inset -1px 0 0 #e6e6e6;
|
||||
-moz-box-shadow: inset -1px 0 0 #e6e6e6;
|
||||
-ms-box-shadow: inset -1px 0 0 #e6e6e6;
|
||||
-o-box-shadow: inset -1px 0 0 #e6e6e6;
|
||||
box-shadow: inset -1px 0 0 #e6e6e6;
|
||||
background: #d6d6d6;
|
||||
border: none;
|
||||
border-bottom: 1px solid #c3c3c3;
|
||||
font-size: 12px;
|
||||
margin: 0;
|
||||
overflow: hidden; }
|
||||
div.course-wrapper div#accordion ul.ui-accordion-content li.active {
|
||||
font-weight: bold; }
|
||||
div.course-wrapper div#accordion ul.ui-accordion-content li a {
|
||||
text-decoration: none;
|
||||
margin-bottom: 22.652px;
|
||||
display: block; }
|
||||
div.course-wrapper div#accordion ul.ui-accordion-content li a:hover {
|
||||
color: #666; }
|
||||
div.course-wrapper div#accordion ul.ui-accordion-content li a p {
|
||||
margin-bottom: 0; }
|
||||
div.course-wrapper div#accordion ul.ui-accordion-content li a p.subtitle {
|
||||
color: #666; }
|
||||
div.course-wrapper section.course-content ol.vert-mod li {
|
||||
border-top: 1px solid #eee;
|
||||
border-bottom: 1px solid #eee;
|
||||
padding: 15px 0; }
|
||||
div.course-wrapper section.course-content ol.vert-mod li h2 {
|
||||
margin-top: 0;
|
||||
margin-bottom: 15px; }
|
||||
div.course-wrapper section.course-content ol.vert-mod li input[type="text"] {
|
||||
display: inline-block;
|
||||
margin: 8px 4px 4px 10px; }
|
||||
div.course-wrapper section.course-content ol.sequence-nav {
|
||||
margin-bottom: 22.652px; }
|
||||
div.course-wrapper section.course-content ol.sequence-nav li {
|
||||
border: none;
|
||||
cursor: pointer;
|
||||
display: table-cell;
|
||||
min-width: 30px;
|
||||
min-height: 30px;
|
||||
padding: 0 10px; }
|
||||
div.course-wrapper section.course-content div.video-wrapper {
|
||||
float: left;
|
||||
width: 640px;
|
||||
min-height: 620px; }
|
||||
div.course-wrapper section.course-content div.video-wrapper iframe#html5_player {
|
||||
border: none;
|
||||
display: none;
|
||||
height: 390px;
|
||||
width: 640px; }
|
||||
div.course-wrapper section.course-content div.video-wrapper section ul {
|
||||
display: inline-block; }
|
||||
div.course-wrapper section.course-content div.video-wrapper section ul li {
|
||||
margin-top: 5px;
|
||||
display: inline-block;
|
||||
cursor: pointer;
|
||||
border: 0;
|
||||
padding: 0; }
|
||||
div.course-wrapper section.course-content div.video-wrapper section ul li div:empty {
|
||||
display: none; }
|
||||
div.course-wrapper section.course-content div.video-wrapper section div#slider {
|
||||
margin: -14px 0 10px 60px; }
|
||||
div.course-wrapper section.course-content div.video-wrapper section div#vidtime {
|
||||
float: left; }
|
||||
div.course-wrapper section.course-content div.video-wrapper section div#video_speeds {
|
||||
float: right;
|
||||
cursor: pointer; }
|
||||
div.course-wrapper section.course-content div.video-wrapper section div#video_speeds span:hover {
|
||||
color: #993333; }
|
||||
div.course-wrapper section.course-content ol.subtitles {
|
||||
width: 220px;
|
||||
margin-left: 20px;
|
||||
float: left; }
|
||||
div.course-wrapper section.course-content ol.subtitles li {
|
||||
margin-bottom: 0px;
|
||||
cursor: pointer;
|
||||
border: 0;
|
||||
padding: 0;
|
||||
color: #666; }
|
||||
div.course-wrapper section.course-content ol.subtitles li.current {
|
||||
background-color: #f3f3f3;
|
||||
color: #333; }
|
||||
div.course-wrapper section.course-content ol.subtitles li:hover {
|
||||
color: #993333; }
|
||||
div.course-wrapper section.course-content ol.subtitles li div {
|
||||
margin-bottom: 8px; }
|
||||
div.course-wrapper section.course-content ol.subtitles li div:empty {
|
||||
margin-bottom: 0px; }
|
||||
|
||||
div.book-wrapper ul#booknav {
|
||||
-webkit-box-sizing: border-box;
|
||||
-moz-box-sizing: border-box;
|
||||
-ms-box-sizing: border-box;
|
||||
-o-box-sizing: border-box;
|
||||
box-sizing: border-box;
|
||||
padding: 22.652px; }
|
||||
div.book-wrapper ul#booknav li ul {
|
||||
background: none; }
|
||||
div.book-wrapper section.book nav ul li {
|
||||
padding: 15px; }
|
||||
div.book-wrapper section.book nav ul li.last {
|
||||
float: left; }
|
||||
div.book-wrapper section.book nav ul li.next {
|
||||
float: right; }
|
||||
div.book-wrapper section.book section.page img {
|
||||
border: 1px solid #dddddd;
|
||||
max-width: 100%;
|
||||
min-width: 100%; }
|
||||
|
||||
div.profile-wrapper {
|
||||
display: table; }
|
||||
div.profile-wrapper section.user-info {
|
||||
-webkit-box-sizing: border-box;
|
||||
-moz-box-sizing: border-box;
|
||||
-ms-box-sizing: border-box;
|
||||
-o-box-sizing: border-box;
|
||||
box-sizing: border-box;
|
||||
margin-right: 2.024%;
|
||||
padding: 22.652px;
|
||||
width: 48.988%;
|
||||
background: #e3e3e3;
|
||||
border-right: 1px solid #d3d3d3;
|
||||
text-shadow: 0 1px 0 #f6f6f6;
|
||||
display: table-cell; }
|
||||
div.profile-wrapper section.course-info {
|
||||
-webkit-box-sizing: border-box;
|
||||
-moz-box-sizing: border-box;
|
||||
-ms-box-sizing: border-box;
|
||||
-o-box-sizing: border-box;
|
||||
box-sizing: border-box;
|
||||
display: table-cell;
|
||||
padding: 22.652px;
|
||||
width: 48.988%; }
|
||||
div.profile-wrapper section.course-info ul li {
|
||||
display: inline-block;
|
||||
padding-right: 1em; }
|
||||
|
||||
form#wiki_revision label {
|
||||
display: block;
|
||||
margin-bottom: 7px; }
|
||||
form#wiki_revision textarea {
|
||||
-webkit-box-sizing: border-box;
|
||||
-moz-box-sizing: border-box;
|
||||
-ms-box-sizing: border-box;
|
||||
-o-box-sizing: border-box;
|
||||
box-sizing: border-box;
|
||||
margin-bottom: 20px;
|
||||
min-height: 300px;
|
||||
width: 100%; }
|
||||
form#wiki_revision input[type="text"] {
|
||||
width: 50%; }
|
||||
form#wiki_revision input[type="submit"] {
|
||||
display: block;
|
||||
margin-top: 20px; }
|
||||
|
||||
div.wiki-wrapper {
|
||||
display: table;
|
||||
width: 100%; }
|
||||
div.wiki-wrapper div#wiki_panel {
|
||||
overflow: auto; }
|
||||
div.wiki-wrapper div#wiki_panel input[type="button"] {
|
||||
color: #4d4d4d;
|
||||
-webkit-transition-property: all;
|
||||
-moz-transition-property: all;
|
||||
-ms-transition-property: all;
|
||||
-o-transition-property: all;
|
||||
transition-property: all;
|
||||
-webkit-transition-duration: 0.15s;
|
||||
-moz-transition-duration: 0.15s;
|
||||
-ms-transition-duration: 0.15s;
|
||||
-o-transition-duration: 0.15s;
|
||||
transition-duration: 0.15s;
|
||||
-webkit-transition-timing-function: ease-out;
|
||||
-moz-transition-timing-function: ease-out;
|
||||
-ms-transition-timing-function: ease-out;
|
||||
-o-transition-timing-function: ease-out;
|
||||
transition-timing-function: ease-out;
|
||||
-webkit-transition-delay: 0;
|
||||
-moz-transition-delay: 0;
|
||||
-ms-transition-delay: 0;
|
||||
-o-transition-delay: 0;
|
||||
transition-delay: 0;
|
||||
font-size: 14px;
|
||||
margin: 0 !important;
|
||||
padding: 7px 7px 7px 30px;
|
||||
text-align: left;
|
||||
width: 100%; }
|
||||
div.wiki-wrapper div#wiki_panel input[type="button"]:hover {
|
||||
-webkit-box-shadow: 0 1px 0 white;
|
||||
-moz-box-shadow: 0 1px 0 white;
|
||||
-ms-box-shadow: 0 1px 0 white;
|
||||
-o-box-shadow: 0 1px 0 white;
|
||||
box-shadow: 0 1px 0 white;
|
||||
background: #efefef; }
|
||||
div.wiki-wrapper div#wiki_panel ul li.create-article {
|
||||
position: relative; }
|
||||
div.wiki-wrapper div#wiki_panel ul li.create-article h3, div.wiki-wrapper div#wiki_panel ul li.create-article input[type="button"] {
|
||||
position: relative; }
|
||||
div.wiki-wrapper div#wiki_panel ul li.create-article h3:before, div.wiki-wrapper div#wiki_panel ul li.create-article input[type="button"]:before {
|
||||
background: blue url(images/ui-icons_454545_256x240.png) -32px -16px no-repeat;
|
||||
display: block;
|
||||
position: absolute;
|
||||
top: 0;
|
||||
right: 0;
|
||||
width: 16px;
|
||||
height: 16px; }
|
||||
div.wiki-wrapper div#wiki_panel ul li.create-article h3:hover:before, div.wiki-wrapper div#wiki_panel ul li.create-article input[type="button"]:hover:before {
|
||||
background-image: url(images/ui-icons_454545_256x240.png) -64px -16px no-repeat; }
|
||||
div.wiki-wrapper div#wiki_panel div#wiki_create_form {
|
||||
padding: 15px;
|
||||
background: #d6d6d6;
|
||||
border-bottom: 1px solid #bbb; }
|
||||
div.wiki-wrapper div#wiki_panel div#wiki_create_form input[type="text"] {
|
||||
margin-bottom: 6px;
|
||||
display: block;
|
||||
width: 100%;
|
||||
-webkit-box-sizing: border-box;
|
||||
-moz-box-sizing: border-box;
|
||||
-ms-box-sizing: border-box;
|
||||
-o-box-sizing: border-box;
|
||||
box-sizing: border-box; }
|
||||
div.wiki-wrapper div#wiki_panel div#wiki_create_form ul li {
|
||||
float: left; }
|
||||
div.wiki-wrapper div#wiki_panel div#wiki_create_form ul li#cancel {
|
||||
float: right;
|
||||
margin-top: 10px; }
|
||||
div.wiki-wrapper section.wiki-body header p {
|
||||
float: left;
|
||||
padding: 15px;
|
||||
margin-bottom: 0;
|
||||
color: #937b1f;
|
||||
line-height: 1em; }
|
||||
div.wiki-wrapper section.wiki-body header ul {
|
||||
float: right; }
|
||||
div.wiki-wrapper section.wiki-body header ul li {
|
||||
float: left; }
|
||||
div.wiki-wrapper section.wiki-body header ul li input[type="button"] {
|
||||
-webkit-box-shadow: inset 1px 0 0 #faf7e9;
|
||||
-moz-box-shadow: inset 1px 0 0 #faf7e9;
|
||||
-ms-box-shadow: inset 1px 0 0 #faf7e9;
|
||||
-o-box-shadow: inset 1px 0 0 #faf7e9;
|
||||
box-shadow: inset 1px 0 0 #faf7e9;
|
||||
-webkit-border-radius: 0;
|
||||
-moz-border-radius: 0;
|
||||
-ms-border-radius: 0;
|
||||
-o-border-radius: 0;
|
||||
border-radius: 0;
|
||||
-webkit-transition-property: all;
|
||||
-moz-transition-property: all;
|
||||
-ms-transition-property: all;
|
||||
-o-transition-property: all;
|
||||
transition-property: all;
|
||||
-webkit-transition-duration: 0.15s;
|
||||
-moz-transition-duration: 0.15s;
|
||||
-ms-transition-duration: 0.15s;
|
||||
-o-transition-duration: 0.15s;
|
||||
transition-duration: 0.15s;
|
||||
-webkit-transition-timing-function: ease-out;
|
||||
-moz-transition-timing-function: ease-out;
|
||||
-ms-transition-timing-function: ease-out;
|
||||
-o-transition-timing-function: ease-out;
|
||||
transition-timing-function: ease-out;
|
||||
-webkit-transition-delay: 0;
|
||||
-moz-transition-delay: 0;
|
||||
-ms-transition-delay: 0;
|
||||
-o-transition-delay: 0;
|
||||
transition-delay: 0;
|
||||
background: #f2e7bf;
|
||||
border: 0;
|
||||
border-left: 1px solid #e4d080;
|
||||
color: #292309;
|
||||
text-shadow: none;
|
||||
font-weight: normal;
|
||||
font-size: 12px;
|
||||
text-transform: uppercase;
|
||||
letter-spacing: 1px;
|
||||
padding: 15px;
|
||||
margin: 0; }
|
||||
div.wiki-wrapper section.wiki-body header ul li input[type="button"]:hover {
|
||||
background: none; }
|
||||
div.wiki-wrapper section.wiki-body h1.wiki-title {
|
||||
font-weight: bold;
|
||||
padding-bottom: 10px;
|
||||
margin-bottom: 20px;
|
||||
border-bottom: 1px solid #ccc; }
|
||||
div.wiki-wrapper section.wiki-body p {
|
||||
line-height: 1.6em; }
|
||||
|
||||
section.activation {
|
||||
-webkit-box-shadow: 0 1px 0 white;
|
||||
-moz-box-shadow: 0 1px 0 white;
|
||||
-ms-box-shadow: 0 1px 0 white;
|
||||
-o-box-shadow: 0 1px 0 white;
|
||||
box-shadow: 0 1px 0 white;
|
||||
-webkit-box-sizing: border-box;
|
||||
-moz-box-sizing: border-box;
|
||||
-ms-box-sizing: border-box;
|
||||
-o-box-sizing: border-box;
|
||||
box-sizing: border-box;
|
||||
background: #fff;
|
||||
border-top: 0;
|
||||
border: 1px solid #ccc;
|
||||
max-width: 600px;
|
||||
padding: 22.652px;
|
||||
margin-top: 22.652px; }
|
||||
|
||||
section.help.main-content {
|
||||
padding: 22.652px; }
|
||||
section.help.main-content p {
|
||||
max-width: 700px; }
|
||||
section.help.main-content dl {
|
||||
margin-bottom: 22.652px; }
|
||||
section.help.main-content dl dd, section.help.main-content dl dt {
|
||||
margin-bottom: 11.326px; }
|
||||
section.help.main-content dl dt {
|
||||
font-weight: bold; }
|
||||
|
||||
body.askbot .secondary-nav {
|
||||
margin: 0; }
|
||||
body.askbot .secondary-nav nav {
|
||||
-webkit-box-sizing: border-box;
|
||||
-moz-box-sizing: border-box;
|
||||
-ms-box-sizing: border-box;
|
||||
-o-box-sizing: border-box;
|
||||
box-sizing: border-box;
|
||||
border: 1px solid #eddfaa;
|
||||
border-top: 0;
|
||||
margin: 0 auto;
|
||||
padding: 22.652px; }
|
||||
body.askbot .secondary-nav nav div {
|
||||
float: left; }
|
||||
body.askbot .secondary-nav nav div.question-filter {
|
||||
font-size: 16px;
|
||||
margin-top: 4px;
|
||||
width: 31.984%; }
|
||||
body.askbot .secondary-nav nav div.question-filter ul {
|
||||
-webkit-border-radius: 35px;
|
||||
-moz-border-radius: 35px;
|
||||
-ms-border-radius: 35px;
|
||||
-o-border-radius: 35px;
|
||||
border-radius: 35px;
|
||||
background: #e4d080;
|
||||
display: inline;
|
||||
margin: 0 0 0 10px;
|
||||
padding: 5.663px 20px; }
|
||||
body.askbot .secondary-nav nav div.question-filter ul li {
|
||||
display: inline-block;
|
||||
list-style: none;
|
||||
margin-right: 10px; }
|
||||
body.askbot .secondary-nav nav div.question-filter ul li:last-child {
|
||||
margin-right: 0; }
|
||||
body.askbot .secondary-nav nav div.question-filter ul li a {
|
||||
text-transform: capitalize;
|
||||
text-shadow: none;
|
||||
font-size: 14px; }
|
||||
body.askbot .secondary-nav nav div.question-filter ul li a.on {
|
||||
font-weight: bold; }
|
||||
body.askbot .secondary-nav nav div.search-box {
|
||||
margin-left: 2%;
|
||||
text-align: right;
|
||||
width: 65.992%; }
|
||||
body.askbot .main-content .discussion-wrapper {
|
||||
display: table;
|
||||
width: 100%; }
|
||||
body.askbot .main-content .discussion-wrapper .discussion-content {
|
||||
-webkit-box-sizing: border-box;
|
||||
-moz-box-sizing: border-box;
|
||||
-ms-box-sizing: border-box;
|
||||
-o-box-sizing: border-box;
|
||||
box-sizing: border-box;
|
||||
display: table-cell;
|
||||
padding: 2.024%;
|
||||
vertical-align: top;
|
||||
width: 74.494%; }
|
||||
body.askbot .main-content .discussion-wrapper .discussion-content .order-sort {
|
||||
-webkit-border-radius: 35px;
|
||||
-moz-border-radius: 35px;
|
||||
-ms-border-radius: 35px;
|
||||
-o-border-radius: 35px;
|
||||
border-radius: 35px;
|
||||
background-color: #faf7e9;
|
||||
height: 30px;
|
||||
float: right;
|
||||
font-size: 16px;
|
||||
margin: 3px 0;
|
||||
padding: 0 20px; }
|
||||
body.askbot .main-content .discussion-wrapper .discussion-content .order-sort a {
|
||||
color: #a88d23; }
|
||||
body.askbot .main-content .discussion-wrapper .discussion-content .order-sort a:before {
|
||||
content: '|';
|
||||
color: #eddfaa;
|
||||
font-size: 22px; }
|
||||
body.askbot .main-content .discussion-wrapper .discussion-content .order-sort a:hover {
|
||||
text-decoration: none;
|
||||
color: #544611; }
|
||||
body.askbot .main-content .discussion-wrapper aside {
|
||||
width: 23.482%;
|
||||
padding: 2.024%; }
|
||||
body.askbot .main-content .discussion-wrapper aside h2 {
|
||||
font-size: 16px; }
|
||||
body.askbot .main-content .discussion-wrapper aside h3, body.askbot .main-content .discussion-wrapper aside div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel body.askbot .main-content .discussion-wrapper aside input[type="button"] {
|
||||
border-bottom: 0;
|
||||
box-shadow: none; }
|
||||
body.askbot .main-content .discussion-wrapper aside input[type="text"] {
|
||||
width: 68%; }
|
||||
body.askbot .main-content .discussion-wrapper aside #displayTagFilterControl {
|
||||
margin-top: 10px; }
|
||||
body.askbot footer {
|
||||
margin: 0 auto;
|
||||
padding: 0; }
|
||||
body.askbot footer .footer-wrapper {
|
||||
-webkit-box-shadow: 0 1px 0 white;
|
||||
-moz-box-shadow: 0 1px 0 white;
|
||||
-ms-box-shadow: 0 1px 0 white;
|
||||
-o-box-shadow: 0 1px 0 white;
|
||||
box-shadow: 0 1px 0 white;
|
||||
-webkit-box-sizing: border-box;
|
||||
-moz-box-sizing: border-box;
|
||||
-ms-box-sizing: border-box;
|
||||
-o-box-sizing: border-box;
|
||||
box-sizing: border-box;
|
||||
background-color: #000;
|
||||
border-top: 0;
|
||||
padding: 1.012%; }
|
||||
|
||||
.badges a {
|
||||
color: #763333;
|
||||
text-decoration: underline; }
|
||||
|
||||
.badge-context-toggle.active, div.course-wrapper div#accordion h3.badge-context-toggle.ui-accordion-header.ui-state-active, div.course-wrapper div#accordion div.wiki-wrapper div#wiki_panel input.badge-context-toggle.ui-accordion-header.ui-state-active[type="button"], div.wiki-wrapper div#wiki_panel div.course-wrapper div#accordion input.badge-context-toggle.ui-accordion-header.ui-state-active[type="button"] {
|
||||
cursor: pointer;
|
||||
text-decoration: underline; }
|
||||
|
||||
body.user-messages {
|
||||
margin-top: 2.4em; }
|
||||
|
||||
.notify {
|
||||
position: fixed;
|
||||
top: 0px;
|
||||
left: 0px;
|
||||
width: 100%;
|
||||
z-index: 100;
|
||||
padding: 0;
|
||||
text-align: center;
|
||||
background-color: #f5dd69;
|
||||
border-top: #fff 1px solid;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif; }
|
||||
.notify p.notification {
|
||||
margin-top: 6px;
|
||||
margin-bottom: 6px;
|
||||
font-size: 16px;
|
||||
color: #424242; }
|
||||
|
||||
#closeNotify {
|
||||
position: absolute;
|
||||
right: 5px;
|
||||
top: 7px;
|
||||
color: #735005;
|
||||
text-decoration: none;
|
||||
line-height: 18px;
|
||||
background: -6px -5px url(../images/sprites.png) no-repeat;
|
||||
cursor: pointer;
|
||||
width: 20px;
|
||||
height: 20px; }
|
||||
#closeNotify:hover {
|
||||
background: -26px -5px url(../images/sprites.png) no-repeat; }
|
||||
|
||||
#header {
|
||||
margin-top: 0px;
|
||||
background: #16160f;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif; }
|
||||
|
||||
/*.content-wrapper {
|
||||
width: 960px;
|
||||
margin: auto;
|
||||
position: relative; }*/
|
||||
#logo img {
|
||||
padding: 5px 0px 5px 0px;
|
||||
height: 75px;
|
||||
width: auto;
|
||||
float: left; }
|
||||
|
||||
#userToolsNav {
|
||||
height: 20px;
|
||||
padding-bottom: 5px; }
|
||||
#userToolsNav a {
|
||||
height: 35px;
|
||||
text-align: right;
|
||||
margin-left: 20px;
|
||||
text-decoration: underline;
|
||||
color: #d0e296;
|
||||
font-size: 16px; }
|
||||
#userToolsNav a:first-child {
|
||||
margin-left: 0; }
|
||||
#userToolsNav a#ab-responses {
|
||||
margin-left: 3px; }
|
||||
#userToolsNav .user-info, #userToolsNav .user-micro-info {
|
||||
color: #b5b593; }
|
||||
#userToolsNav a img {
|
||||
vertical-align: middle;
|
||||
margin-bottom: 2px; }
|
||||
#userToolsNav .user-info a {
|
||||
margin: 0;
|
||||
text-decoration: none; }
|
||||
|
||||
#metaNav {
|
||||
float: right; }
|
||||
#metaNav a {
|
||||
color: #e2e2ae;
|
||||
padding: 0px 0px 0px 35px;
|
||||
height: 25px;
|
||||
line-height: 30px;
|
||||
margin: 5px 0px 0px 10px;
|
||||
font-size: 18px;
|
||||
font-weight: 100;
|
||||
text-decoration: none;
|
||||
display: block;
|
||||
float: left; }
|
||||
#metaNav a:hover {
|
||||
text-decoration: underline; }
|
||||
#metaNav a.on {
|
||||
font-weight: bold;
|
||||
color: #FFF;
|
||||
text-decoration: none; }
|
||||
#metaNav a.special {
|
||||
font-size: 18px;
|
||||
color: #B02B2C;
|
||||
font-weight: bold;
|
||||
text-decoration: none; }
|
||||
#metaNav a.special:hover {
|
||||
text-decoration: underline; }
|
||||
#metaNav #navTags {
|
||||
background: -50px -5px url(../images/sprites.png) no-repeat; }
|
||||
#metaNav #navUsers {
|
||||
background: -125px -5px url(../images/sprites.png) no-repeat; }
|
||||
#metaNav #navBadges {
|
||||
background: -210px -5px url(../images/sprites.png) no-repeat; }
|
||||
|
||||
#searchBar {
|
||||
display: inline-block;
|
||||
background-color: #fff;
|
||||
width: 412px;
|
||||
border: 1px solid #c9c9b5;
|
||||
float: right;
|
||||
height: 42px;
|
||||
margin: 6px 0px 0px 15px; }
|
||||
#searchBar .searchInput, #searchBar .searchInputCancelable {
|
||||
font-size: 30px;
|
||||
height: 40px;
|
||||
font-weight: 300;
|
||||
background: #FFF;
|
||||
border: 0px;
|
||||
color: #484848;
|
||||
padding-left: 10px;
|
||||
font-family: Arial;
|
||||
vertical-align: middle; }
|
||||
#searchBar .searchInput {
|
||||
width: 352px; }
|
||||
#searchBar .searchInputCancelable {
|
||||
width: 317px; }
|
||||
#searchBar .logoutsearch {
|
||||
width: 337px; }
|
||||
#searchBar .searchBtn {
|
||||
font-size: 10px;
|
||||
color: #666;
|
||||
background-color: #eee;
|
||||
height: 42px;
|
||||
border: #FFF 1px solid;
|
||||
line-height: 22px;
|
||||
text-align: center;
|
||||
float: right;
|
||||
margin: 0px;
|
||||
width: 48px;
|
||||
background: -98px -36px url(../images/sprites.png) no-repeat;
|
||||
cursor: pointer; }
|
||||
#searchBar .searchBtn:hover {
|
||||
background: -146px -36px url(../images/sprites.png) no-repeat; }
|
||||
#searchBar .cancelSearchBtn {
|
||||
font-size: 30px;
|
||||
color: #ce8888;
|
||||
background: #fff;
|
||||
height: 42px;
|
||||
border: 0px;
|
||||
border-left: #deded0 1px solid;
|
||||
text-align: center;
|
||||
width: 35px;
|
||||
cursor: pointer; }
|
||||
#searchBar .cancelSearchBtn:hover {
|
||||
color: #d84040; }
|
||||
|
||||
body.anon #searchBar {
|
||||
width: 500px; }
|
||||
body.anon #searchBar .searchInput {
|
||||
width: 440px; }
|
||||
body.anon #searchBar .searchInputCancelable {
|
||||
width: 405px; }
|
||||
|
||||
#askButton {
|
||||
background: url(../images/bigbutton.png) repeat-x bottom;
|
||||
line-height: 44px;
|
||||
text-align: center;
|
||||
width: 200px;
|
||||
height: 42px;
|
||||
font-size: 23px;
|
||||
color: #4a757f;
|
||||
margin-top: 7px;
|
||||
float: right;
|
||||
text-transform: uppercase;
|
||||
border-radius: 5px;
|
||||
-ms-border-radius: 5px;
|
||||
-moz-border-radius: 5px;
|
||||
-webkit-border-radius: 5px;
|
||||
-khtml-border-radius: 5px;
|
||||
-webkit-box-shadow: 1px 1px 2px #636363;
|
||||
-moz-box-shadow: 1px 1px 2px #636363;
|
||||
box-shadow: 1px 1px 2px #636363; }
|
||||
#askButton:hover {
|
||||
text-decoration: none;
|
||||
background: url(../images/bigbutton.png) repeat-x top;
|
||||
text-shadow: 0px 1px 0px #c6d9dd;
|
||||
-moz-text-shadow: 0px 1px 0px #c6d9dd;
|
||||
-webkit-text-shadow: 0px 1px 0px #c6d9dd; }
|
||||
|
||||
/*#ContentLeft {
|
||||
width: 730px;
|
||||
float: left;
|
||||
position: relative;
|
||||
padding-bottom: 10px; }
|
||||
|
||||
#ContentRight {
|
||||
width: 200px;
|
||||
float: right;
|
||||
padding: 0 0px 10px 0px; }*/
|
||||
#ContentFull {
|
||||
float: left;
|
||||
width: 960px; }
|
||||
|
||||
.box {
|
||||
/*background: #fff;*/
|
||||
/*padding: 4px 0px 10px 0px;*/
|
||||
/*width: 200px;*/
|
||||
/*.inputs {
|
||||
#interestingTagInput, #ignoredTagInput {
|
||||
width: 153px;
|
||||
padding-left: 5px;
|
||||
border: #c9c9b5 1px solid;
|
||||
height: 25px; }
|
||||
#interestingTagAdd, #ignoredTagAdd {
|
||||
background: url(../images/small-button-blue.png) repeat-x top;
|
||||
border: 0;
|
||||
color: #4a757f;
|
||||
font-weight: bold;
|
||||
font-size: 12px;
|
||||
width: 30px;
|
||||
height: 27px;
|
||||
margin-top: -2px;
|
||||
cursor: pointer;
|
||||
border-radius: 4px;
|
||||
-ms-border-radius: 4px;
|
||||
-moz-border-radius: 4px;
|
||||
-webkit-border-radius: 4px;
|
||||
-khtml-border-radius: 4px;
|
||||
text-shadow: 0px 1px 0px #e6f6fa;
|
||||
-moz-text-shadow: 0px 1px 0px #e6f6fa;
|
||||
-webkit-text-shadow: 0px 1px 0px #e6f6fa;
|
||||
-webkit-box-shadow: 1px 1px 2px #808080;
|
||||
-moz-box-shadow: 1px 1px 2px #808080;
|
||||
box-shadow: 1px 1px 2px #808080; }
|
||||
#interestingTagAdd:hover, #ignoredTagAdd:hover {
|
||||
background: url(../images/small-button-blue.png) repeat-x bottom; } }*/ }
|
||||
.box p {
|
||||
margin-bottom: 4px; }
|
||||
.box p.info-box-follow-up-links {
|
||||
text-align: right;
|
||||
margin: 0; }
|
||||
.box h2 {
|
||||
padding-left: 0;
|
||||
/*background: #eceeeb;*/
|
||||
height: 30px;
|
||||
line-height: 30px;
|
||||
/*text-align: right;*/
|
||||
/*font-size: 18px !important;*/
|
||||
font-weight: normal;
|
||||
color: #656565;
|
||||
/*padding-right: 10px;*/
|
||||
/*margin-bottom: 10px;*/
|
||||
/*font-family: 'Yanone Kaffeesatz',sans-serif;*/ }
|
||||
.box h3, .box div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel .box input[type="button"] {
|
||||
/*color: #4a757f;*/
|
||||
/*font-size: 18px;*/
|
||||
text-align: left;
|
||||
font-weight: normal;
|
||||
/*font-family: 'Yanone Kaffeesatz',sans-serif;*/
|
||||
padding-left: 0px; }
|
||||
.box .contributorback {
|
||||
background: #eceeeb url(../images/contributorsback.png) no-repeat center left; }
|
||||
.box label {
|
||||
color: #707070;
|
||||
font-size: 15px;
|
||||
display: block;
|
||||
float: right;
|
||||
text-align: left;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif;
|
||||
width: 80px;
|
||||
margin-right: 18px; }
|
||||
.box #displayTagFilterControl label {
|
||||
width: 160px; }
|
||||
.box ul {
|
||||
margin-left: 22px; }
|
||||
.box li {
|
||||
list-style-type: disc;
|
||||
font-size: 13px;
|
||||
line-height: 20px;
|
||||
margin-bottom: 10px;
|
||||
color: #707070; }
|
||||
.box ul.tags {
|
||||
list-style: none;
|
||||
margin: 0;
|
||||
padding: 0;
|
||||
line-height: 170%;
|
||||
display: block; }
|
||||
.box #displayTagFilterControl p label {
|
||||
color: #707070;
|
||||
font-size: 15px; }
|
||||
.box img.gravatar {
|
||||
margin: 1px; }
|
||||
.box a.followed, .box a.follow {
|
||||
background: url(../images/medium-button.png) top repeat-x;
|
||||
height: 34px;
|
||||
line-height: 34px;
|
||||
text-align: center;
|
||||
border: 0;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif;
|
||||
color: #4a757f;
|
||||
font-weight: normal;
|
||||
font-size: 21px;
|
||||
margin-top: 3px;
|
||||
display: block;
|
||||
width: 120px;
|
||||
text-decoration: none;
|
||||
border-radius: 4px;
|
||||
-ms-border-radius: 4px;
|
||||
-moz-border-radius: 4px;
|
||||
-webkit-border-radius: 4px;
|
||||
-khtml-border-radius: 4px;
|
||||
-webkit-box-shadow: 1px 1px 2px #636363;
|
||||
-moz-box-shadow: 1px 1px 2px #636363;
|
||||
box-shadow: 1px 1px 2px #636363;
|
||||
margin: 0 auto;
|
||||
padding: 0; }
|
||||
.box a.followed:hover, .box a.follow:hover {
|
||||
text-decoration: none;
|
||||
background: url(../images/medium-button.png) bottom repeat-x;
|
||||
text-shadow: 0px 1px 0px #c6d9dd;
|
||||
-moz-text-shadow: 0px 1px 0px #c6d9dd;
|
||||
-webkit-text-shadow: 0px 1px 0px #c6d9dd; }
|
||||
.box a.followed div.unfollow {
|
||||
display: none; }
|
||||
.box a.followed:hover div {
|
||||
display: none; }
|
||||
.box a.followed:hover div.unfollow {
|
||||
display: inline;
|
||||
color: #a05736; }
|
||||
.box .favorite-number {
|
||||
padding: 5px 0 0 5px;
|
||||
font-size: 100%;
|
||||
font-family: Arial;
|
||||
font-weight: bold;
|
||||
color: #777;
|
||||
text-align: center; }
|
||||
.box .notify-sidebar #question-subscribe-sidebar {
|
||||
margin: 7px 0 0 3px; }
|
||||
|
||||
.statsWidget p {
|
||||
color: #707070;
|
||||
font-size: 16px;
|
||||
border-bottom: #cccccc 1px solid;
|
||||
font-size: 13px; }
|
||||
.statsWidget p strong {
|
||||
float: right;
|
||||
padding-right: 10px; }
|
||||
|
||||
.questions-related {
|
||||
word-wrap: break-word; }
|
||||
.questions-related p {
|
||||
line-height: 20px;
|
||||
padding: 4px 0px 4px 0px;
|
||||
font-size: 16px;
|
||||
font-weight: normal;
|
||||
border-bottom: #cccccc 1px solid; }
|
||||
.questions-related a {
|
||||
font-size: 13px; }
|
||||
|
||||
#tips li {
|
||||
color: #707070;
|
||||
font-size: 13px;
|
||||
list-style-image: url(../images/tips.png); }
|
||||
#tips a {
|
||||
font-size: 16px; }
|
||||
|
||||
#markdownHelp li {
|
||||
color: #707070;
|
||||
font-size: 13px; }
|
||||
#markdownHelp a {
|
||||
font-size: 16px; }
|
||||
|
||||
#questionCount {
|
||||
font-weight: bold;
|
||||
font-size: 23px;
|
||||
color: #7ea9b3;
|
||||
width: 200px;
|
||||
float: left;
|
||||
margin-bottom: 8px;
|
||||
padding-top: 6px;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif; }
|
||||
|
||||
#listSearchTags {
|
||||
float: left;
|
||||
margin-top: 3px;
|
||||
color: #707070;
|
||||
font-size: 16px;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif; }
|
||||
|
||||
ul#searchTags {
|
||||
margin-left: 10px;
|
||||
float: right;
|
||||
padding-top: 2px; }
|
||||
|
||||
.search-tips {
|
||||
font-size: 16px;
|
||||
line-height: 17px;
|
||||
color: #707070;
|
||||
margin: 5px 0 10px 0;
|
||||
padding: 0px;
|
||||
float: left;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif; }
|
||||
.search-tips a {
|
||||
text-decoration: underline;
|
||||
color: #1b79bd; }
|
||||
|
||||
#question-list {
|
||||
float: left;
|
||||
position: relative;
|
||||
background-color: #FFF;
|
||||
padding: 0;
|
||||
width: 100%; }
|
||||
|
||||
.short-summary {
|
||||
position: relative;
|
||||
filter: inherit;
|
||||
padding: 10px;
|
||||
border-bottom: 1px solid #DDDBCE;
|
||||
margin-bottom: 1px;
|
||||
overflow: hidden;
|
||||
width: 710px;
|
||||
float: left;
|
||||
background: url(../images/summary-background.png) repeat-x; }
|
||||
.short-summary h2 {
|
||||
font-size: 24px;
|
||||
font-weight: normal;
|
||||
line-height: 26px;
|
||||
padding-left: 0;
|
||||
margin-bottom: 6px;
|
||||
display: block;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif; }
|
||||
.short-summary a {
|
||||
color: #464646; }
|
||||
.short-summary .userinfo {
|
||||
text-align: right;
|
||||
line-height: 16px;
|
||||
font-family: Arial;
|
||||
padding-right: 4px; }
|
||||
.short-summary .userinfo .relativetime {
|
||||
font-size: 11px;
|
||||
clear: both;
|
||||
font-weight: normal;
|
||||
color: #555; }
|
||||
.short-summary span.anonymous {
|
||||
font-size: 11px;
|
||||
clear: both;
|
||||
font-weight: normal;
|
||||
color: #555; }
|
||||
.short-summary .userinfo a {
|
||||
font-weight: bold;
|
||||
font-size: 11px; }
|
||||
.short-summary .counts {
|
||||
float: right;
|
||||
margin: 4px 0 0 5px;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif; }
|
||||
.short-summary .counts .item-count {
|
||||
padding: 0px 5px 0px 5px;
|
||||
font-size: 25px;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif; }
|
||||
.short-summary .counts .votes div, .short-summary .counts .views div, .short-summary .counts .answers div, .short-summary .counts .favorites div {
|
||||
margin-top: 3px;
|
||||
font-size: 14px;
|
||||
line-height: 14px;
|
||||
color: #646464; }
|
||||
.short-summary .tags {
|
||||
margin-top: 0; }
|
||||
.short-summary .votes, .short-summary .answers, .short-summary .favorites, .short-summary .views {
|
||||
text-align: center;
|
||||
margin: 0 3px;
|
||||
padding: 8px 2px 0px 2px;
|
||||
width: 51px;
|
||||
float: right;
|
||||
height: 44px;
|
||||
border: #dbdbd4 1px solid; }
|
||||
.short-summary .votes {
|
||||
background: url(../images/vote-background.png) repeat-x; }
|
||||
.short-summary .answers {
|
||||
background: url(../images/answers-background.png) repeat-x; }
|
||||
.short-summary .views {
|
||||
background: url(../images/view-background.png) repeat-x; }
|
||||
.short-summary .no-votes .item-count {
|
||||
color: #b1b5b6; }
|
||||
.short-summary .some-votes .item-count {
|
||||
color: #4a757f; }
|
||||
.short-summary .no-answers .item-count {
|
||||
color: #b1b5b6; }
|
||||
.short-summary .some-answers .item-count {
|
||||
color: #eab243; }
|
||||
.short-summary .no-views .item-count {
|
||||
color: #b1b5b6; }
|
||||
.short-summary .some-views .item-count {
|
||||
color: #d33f00; }
|
||||
.short-summary .accepted .item-count {
|
||||
background: url(../images/accept.png) no-repeat top right;
|
||||
display: block;
|
||||
text-align: center;
|
||||
width: 40px;
|
||||
color: #eab243; }
|
||||
.short-summary .some-favorites .item-count {
|
||||
background: #338333;
|
||||
color: #d0f5a9; }
|
||||
.short-summary .no-favorites .item-count {
|
||||
background: #eab243;
|
||||
color: yellow; }
|
||||
|
||||
.evenMore {
|
||||
font-size: 13px;
|
||||
color: #707070;
|
||||
padding: 15px 0px 10px 0px;
|
||||
clear: both; }
|
||||
.evenMore a {
|
||||
text-decoration: underline;
|
||||
color: #1b79bd; }
|
||||
|
||||
.pager {
|
||||
margin-top: 10px;
|
||||
margin-bottom: 16px; }
|
||||
|
||||
.pagesize {
|
||||
margin-top: 10px;
|
||||
margin-bottom: 16px;
|
||||
float: right; }
|
||||
|
||||
.paginator {
|
||||
padding: 5px 0 10px 0;
|
||||
font-size: 13px;
|
||||
margin-bottom: 10px; }
|
||||
.paginator .prev a, .paginator .next a {
|
||||
background-color: #fff;
|
||||
color: #777;
|
||||
padding: 2px 4px 3px 4px; }
|
||||
.paginator .prev a:visited, .paginator .next a:visited {
|
||||
background-color: #fff;
|
||||
color: #777;
|
||||
padding: 2px 4px 3px 4px; }
|
||||
.paginator a {
|
||||
color: #7ea9b3; }
|
||||
.paginator .prev {
|
||||
margin-right: .5em; }
|
||||
.paginator .next {
|
||||
margin-left: .5em; }
|
||||
.paginator .page a {
|
||||
padding: .25em;
|
||||
background-color: #fff;
|
||||
margin: 0em .25em;
|
||||
color: #ff; }
|
||||
.paginator .page a:visited {
|
||||
padding: .25em;
|
||||
background-color: #fff;
|
||||
margin: 0em .25em;
|
||||
color: #ff; }
|
||||
.paginator .curr {
|
||||
padding: .25em;
|
||||
background-color: #fff;
|
||||
margin: 0em .25em;
|
||||
color: #ff;
|
||||
background-color: #8ebcc7;
|
||||
color: #fff;
|
||||
font-weight: bold; }
|
||||
.paginator .next a, .paginator .prev a {
|
||||
color: #7ea9b3; }
|
||||
.paginator .page a:hover, .paginator .curr a:hover, .paginator .prev a:hover, .paginator .next a:hover {
|
||||
color: #8C8C8C;
|
||||
background-color: #E1E1E1;
|
||||
text-decoration: none; }
|
||||
.paginator .text {
|
||||
color: #777;
|
||||
padding: .3em; }
|
||||
.paginator .paginator-container-left {
|
||||
padding: 5px 0 10px 0; }
|
||||
|
||||
.tag-size-1 {
|
||||
font-size: 12px; }
|
||||
|
||||
.tag-size-2 {
|
||||
font-size: 13px; }
|
||||
|
||||
.tag-size-3 {
|
||||
font-size: 14px; }
|
||||
|
||||
.tag-size-4 {
|
||||
font-size: 15px; }
|
||||
|
||||
.tag-size-5 {
|
||||
font-size: 16px; }
|
||||
|
||||
.tag-size-6 {
|
||||
font-size: 17px; }
|
||||
|
||||
.tag-size-7 {
|
||||
font-size: 18px; }
|
||||
|
||||
.tag-size-8 {
|
||||
font-size: 19px; }
|
||||
|
||||
.tag-size-9 {
|
||||
font-size: 20px; }
|
||||
|
||||
.tag-size-10 {
|
||||
font-size: 21px; }
|
||||
|
||||
ul.tags {
|
||||
list-style: none;
|
||||
margin: 0;
|
||||
padding: 0;
|
||||
line-height: 170%;
|
||||
display: block; }
|
||||
ul.tags.marked-tags {
|
||||
list-style: none;
|
||||
margin: 0;
|
||||
padding: 0;
|
||||
line-height: 170%;
|
||||
display: block; }
|
||||
ul#related-tags {
|
||||
list-style: none;
|
||||
margin: 0;
|
||||
padding: 0;
|
||||
line-height: 170%;
|
||||
display: block; }
|
||||
ul.tags li {
|
||||
float: left;
|
||||
display: block;
|
||||
margin: 0 8px 0 0;
|
||||
padding: 0;
|
||||
height: 20px; }
|
||||
|
||||
.wildcard-tags {
|
||||
clear: both; }
|
||||
|
||||
ul.tags.marked-tags li, .wildcard-tags ul.tags li {
|
||||
margin-bottom: 5px; }
|
||||
|
||||
#tagSelector div.inputs {
|
||||
clear: both;
|
||||
float: none;
|
||||
margin-bottom: 10px; }
|
||||
|
||||
.tags-page ul.tags li {
|
||||
width: 160px;
|
||||
margin: 5px; }
|
||||
|
||||
ul#ab-user-tags li {
|
||||
width: 160px;
|
||||
margin: 5px; }
|
||||
ul#related-tags li {
|
||||
margin: 0 5px 8px 0;
|
||||
float: left;
|
||||
clear: left; }
|
||||
|
||||
.tag-left {
|
||||
cursor: pointer;
|
||||
display: block;
|
||||
float: left;
|
||||
height: 17px;
|
||||
margin: 0 5px 0 0;
|
||||
padding: 0;
|
||||
-webkit-box-shadow: 0px 0px 5px #d3d6d7;
|
||||
-moz-box-shadow: 0px 0px 5px #d3d6d7;
|
||||
box-shadow: 0px 0px 5px #d3d6d7; }
|
||||
|
||||
.tag-right {
|
||||
background: #f3f6f6;
|
||||
border: #fff 1px solid;
|
||||
border-top: #fff 2px solid;
|
||||
outline: #cfdbdb 1px solid;
|
||||
display: block;
|
||||
float: left;
|
||||
height: 17px;
|
||||
line-height: 17px;
|
||||
font-weight: normal;
|
||||
font-size: 11px;
|
||||
padding: 0px 8px 0px 8px;
|
||||
text-decoration: none;
|
||||
text-align: center;
|
||||
white-space: nowrap;
|
||||
vertical-align: middle;
|
||||
font-family: Arial;
|
||||
color: #717179; }
|
||||
|
||||
.deletable-tag {
|
||||
margin-right: 3px;
|
||||
white-space: nowrap;
|
||||
border-top-right-radius: 4px;
|
||||
border-bottom-right-radius: 4px;
|
||||
-moz-border-radius-topright: 4px;
|
||||
-moz-border-radius-bottomright: 4px;
|
||||
-webkit-border-bottom-right-radius: 4px;
|
||||
-webkit-border-top-right-radius: 4px; }
|
||||
|
||||
.tags a.tag-right, .tags span.tag-right {
|
||||
color: #585858;
|
||||
text-decoration: none; }
|
||||
.tags a:hover {
|
||||
color: #1A1A1A; }
|
||||
|
||||
.users-page h1, .tags-page h1 {
|
||||
float: left; }
|
||||
|
||||
.main-page h1 {
|
||||
margin-right: 5px; }
|
||||
|
||||
.delete-icon {
|
||||
margin-top: -1px;
|
||||
float: left;
|
||||
height: 21px;
|
||||
width: 18px;
|
||||
display: block;
|
||||
line-height: 20px;
|
||||
text-align: center;
|
||||
background: #bbcdcd;
|
||||
cursor: default;
|
||||
color: #fff;
|
||||
border-top: #cfdbdb 1px solid;
|
||||
font-family: Arial;
|
||||
border-top-right-radius: 4px;
|
||||
border-bottom-right-radius: 4px;
|
||||
-moz-border-radius-topright: 4px;
|
||||
-moz-border-radius-bottomright: 4px;
|
||||
-webkit-border-bottom-right-radius: 4px;
|
||||
-webkit-border-top-right-radius: 4px;
|
||||
text-shadow: 0px 1px 0px #7ea0a0;
|
||||
-moz-text-shadow: 0px 1px 0px #7ea0a0;
|
||||
-webkit-text-shadow: 0px 1px 0px #7ea0a0; }
|
||||
.delete-icon:hover {
|
||||
background: #b32f2f; }
|
||||
|
||||
.tag-number {
|
||||
font-weight: normal;
|
||||
float: left;
|
||||
font-size: 16px;
|
||||
color: #5d5d5d; }
|
||||
|
||||
.badges .tag-number {
|
||||
float: none;
|
||||
display: inline;
|
||||
padding-right: 15px; }
|
||||
|
||||
.section-title {
|
||||
color: #7ea9b3;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif;
|
||||
font-weight: bold;
|
||||
font-size: 24px; }
|
||||
|
||||
#fmask {
|
||||
margin-bottom: 30px;
|
||||
width: 100%; }
|
||||
|
||||
#askFormBar {
|
||||
display: inline-block;
|
||||
padding: 4px 7px 5px 0px;
|
||||
margin-top: 0px; }
|
||||
#askFormBar p {
|
||||
margin: 0 0 5px 0;
|
||||
font-size: 14px;
|
||||
color: #525252;
|
||||
line-height: 1.4; }
|
||||
#askFormBar .questionTitleInput {
|
||||
font-size: 24px;
|
||||
line-height: 24px;
|
||||
height: 36px;
|
||||
margin: 0px;
|
||||
padding: 0px 0 0 5px;
|
||||
border: #cce6ec 3px solid;
|
||||
width: 725px; }
|
||||
|
||||
.ask-page div#question-list, .edit-question-page div#question-list {
|
||||
float: none;
|
||||
border-bottom: #f0f0ec 1px solid;
|
||||
float: left;
|
||||
margin-bottom: 10px; }
|
||||
|
||||
.ask-page div#question-list a, .edit-question-page div#question-list a {
|
||||
line-height: 30px; }
|
||||
|
||||
.ask-page div#question-list h2, .edit-question-page div#question-list h2 {
|
||||
font-size: 13px;
|
||||
padding-bottom: 0;
|
||||
color: #1b79bd;
|
||||
border-top: #f0f0ec 1px solid;
|
||||
border-left: #f0f0ec 1px solid;
|
||||
height: 30px;
|
||||
line-height: 30px;
|
||||
font-weight: normal; }
|
||||
|
||||
.ask-page div#question-list span, .edit-question-page div#question-list span {
|
||||
width: 28px;
|
||||
height: 26px;
|
||||
line-height: 26px;
|
||||
text-align: center;
|
||||
margin-right: 10px;
|
||||
float: left;
|
||||
display: block;
|
||||
color: #fff;
|
||||
background: #b8d0d5;
|
||||
border-radius: 3px;
|
||||
-ms-border-radius: 3px;
|
||||
-moz-border-radius: 3px;
|
||||
-webkit-border-radius: 3px;
|
||||
-khtml-border-radius: 3px; }
|
||||
|
||||
.ask-page label, .edit-question-page label {
|
||||
color: #525252;
|
||||
font-size: 13px; }
|
||||
|
||||
.ask-page #id_tags, .edit-question-page #id_tags {
|
||||
border: #cce6ec 3px solid;
|
||||
height: 25px;
|
||||
padding-left: 5px;
|
||||
width: 395px;
|
||||
font-size: 14px; }
|
||||
|
||||
.title-desc {
|
||||
color: #707070;
|
||||
font-size: 13px; }
|
||||
|
||||
#fmanswer input.submit, .ask-page input.submit, .edit-question-page input.submit {
|
||||
float: left;
|
||||
background: url(../images/medium-button.png) top repeat-x;
|
||||
height: 34px;
|
||||
border: 0;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif;
|
||||
color: #4a757f;
|
||||
font-weight: normal;
|
||||
font-size: 21px;
|
||||
margin-top: 3px;
|
||||
border-radius: 4px;
|
||||
-ms-border-radius: 4px;
|
||||
-moz-border-radius: 4px;
|
||||
-webkit-border-radius: 4px;
|
||||
-khtml-border-radius: 4px;
|
||||
-webkit-box-shadow: 1px 1px 2px #636363;
|
||||
-moz-box-shadow: 1px 1px 2px #636363;
|
||||
box-shadow: 1px 1px 2px #636363;
|
||||
margin-right: 7px; }
|
||||
|
||||
#fmanswer input.submit:hover, .ask-page input.submit:hover, .edit-question-page input.submit:hover {
|
||||
text-decoration: none;
|
||||
background: url(../images/medium-button.png) bottom repeat-x;
|
||||
text-shadow: 0px 1px 0px #c6d9dd;
|
||||
-moz-text-shadow: 0px 1px 0px #c6d9dd;
|
||||
-webkit-text-shadow: 0px 1px 0px #c6d9dd; }
|
||||
|
||||
#editor {
|
||||
font-size: 100%;
|
||||
min-height: 200px;
|
||||
line-height: 18px;
|
||||
margin: 0;
|
||||
border-left: #cce6ec 3px solid;
|
||||
border-bottom: #cce6ec 3px solid;
|
||||
border-right: #cce6ec 3px solid;
|
||||
border-top: 0;
|
||||
padding: 10px;
|
||||
margin-bottom: 10px;
|
||||
width: 710px; }
|
||||
|
||||
#id_title {
|
||||
width: 100%; }
|
||||
|
||||
.wmd-preview {
|
||||
margin: 3px 0 5px 0;
|
||||
padding: 6px;
|
||||
background-color: #F5F5F5;
|
||||
min-height: 20px;
|
||||
overflow: auto;
|
||||
font-size: 13px;
|
||||
font-family: Arial; }
|
||||
.wmd-preview p {
|
||||
margin-bottom: 14px;
|
||||
line-height: 1.4;
|
||||
font-size: 14px; }
|
||||
.wmd-preview pre {
|
||||
background-color: #E7F1F8; }
|
||||
.wmd-preview blockquote {
|
||||
background-color: #eee; }
|
||||
.wmd-preview IMG {
|
||||
max-width: 600px; }
|
||||
|
||||
.preview-toggle {
|
||||
width: 100%;
|
||||
color: #b6a475;
|
||||
text-align: left; }
|
||||
.preview-toggle span:hover {
|
||||
cursor: pointer; }
|
||||
|
||||
.after-editor {
|
||||
margin-top: 15px;
|
||||
margin-bottom: 15px; }
|
||||
|
||||
.checkbox {
|
||||
margin-left: 5px;
|
||||
font-weight: normal;
|
||||
cursor: help; }
|
||||
|
||||
.question-options {
|
||||
margin-top: 1px;
|
||||
color: #666;
|
||||
line-height: 13px;
|
||||
margin-bottom: 5px; }
|
||||
.question-options label {
|
||||
vertical-align: text-bottom; }
|
||||
|
||||
.edit-content-html {
|
||||
border-top: 1px dotted #D8D2A9;
|
||||
border-bottom: 1px dotted #D8D2A9;
|
||||
margin: 5px 0 5px 0; }
|
||||
|
||||
.edit-question-page, #fmedit, .wmd-preview {
|
||||
color: #525252; }
|
||||
|
||||
.edit-question-page #id_revision, #fmedit #id_revision, .wmd-preview #id_revision {
|
||||
font-size: 14px;
|
||||
margin-top: 5px;
|
||||
margin-bottom: 5px; }
|
||||
|
||||
.edit-question-page #id_title, #fmedit #id_title, .wmd-preview #id_title {
|
||||
font-size: 24px;
|
||||
line-height: 24px;
|
||||
height: 36px;
|
||||
margin: 0px;
|
||||
padding: 0px 0 0 5px;
|
||||
border: #cce6ec 3px solid;
|
||||
width: 725px;
|
||||
margin-bottom: 10px; }
|
||||
|
||||
.edit-question-page #id_summary, #fmedit #id_summary, .wmd-preview #id_summary {
|
||||
border: #cce6ec 3px solid;
|
||||
height: 25px;
|
||||
padding-left: 5px;
|
||||
width: 395px;
|
||||
font-size: 14px; }
|
||||
|
||||
.edit-question-page .title-desc, #fmedit .title-desc, .wmd-preview .title-desc {
|
||||
margin-bottom: 10px; }
|
||||
|
||||
.question-page h1 {
|
||||
padding-top: 0px;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif; }
|
||||
.question-page h1 a {
|
||||
color: #464646;
|
||||
font-size: 30px;
|
||||
font-weight: normal;
|
||||
line-height: 1; }
|
||||
.question-page p.rss {
|
||||
float: none;
|
||||
clear: both;
|
||||
padding: 3px 0 0 23px;
|
||||
font-size: 15px;
|
||||
width: 110px;
|
||||
background-position: center left;
|
||||
margin-left: 0px !important; }
|
||||
.question-page p.rss a {
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif;
|
||||
vertical-align: top; }
|
||||
.question-page .question-content {
|
||||
float: right;
|
||||
width: 682px;
|
||||
margin-bottom: 10px; }
|
||||
.question-page #question-table {
|
||||
float: left;
|
||||
border-top: #f0f0f0 1px solid;
|
||||
margin: 6px 0 6px 0;
|
||||
border-spacing: 0px;
|
||||
width: 670px;
|
||||
padding-right: 10px; }
|
||||
.question-page .answer-table {
|
||||
margin: 6px 0 6px 0;
|
||||
border-spacing: 0px;
|
||||
width: 670px;
|
||||
padding-right: 10px;
|
||||
margin-top: 0px;
|
||||
border-bottom: 1px solid #D4D4D4;
|
||||
float: right; }
|
||||
.question-page .answer-table td {
|
||||
width: 20px;
|
||||
vertical-align: top; }
|
||||
.question-page #question-table td {
|
||||
width: 20px;
|
||||
vertical-align: top; }
|
||||
.question-page .question-body, .question-page .answer-body {
|
||||
overflow: auto;
|
||||
margin-top: 10px;
|
||||
font-family: Arial;
|
||||
color: #4b4b4b; }
|
||||
.question-page .question-body p, .question-page .answer-body p {
|
||||
margin-bottom: 14px;
|
||||
line-height: 1.4;
|
||||
font-size: 14px;
|
||||
padding: 0px 5px 5px 0px; }
|
||||
.question-page .question-body a, .question-page .answer-body a {
|
||||
color: #1b79bd; }
|
||||
.question-page .question-body li, .question-page .answer-body li {
|
||||
margin-bottom: 7px; }
|
||||
.question-page .question-body IMG, .question-page .answer-body IMG {
|
||||
max-width: 600px; }
|
||||
.question-page .post-update-info-container {
|
||||
float: right;
|
||||
width: 175px; }
|
||||
.question-page .post-update-info {
|
||||
background: white url(../images/background-user-info.png) repeat-x bottom;
|
||||
float: right;
|
||||
font-size: 9px;
|
||||
font-family: Arial;
|
||||
width: 158px;
|
||||
padding: 4px;
|
||||
margin: 0px 0px 5px 5px;
|
||||
line-height: 14px;
|
||||
border-radius: 4px;
|
||||
-ms-border-radius: 4px;
|
||||
-moz-border-radius: 4px;
|
||||
-webkit-border-radius: 4px;
|
||||
-khtml-border-radius: 4px;
|
||||
-webkit-box-shadow: 0px 2px 1px #bfbfbf;
|
||||
-moz-box-shadow: 0px 2px 1px #bfbfbf;
|
||||
box-shadow: 0px 2px 1px #bfbfbf; }
|
||||
.question-page .post-update-info p {
|
||||
line-height: 13px;
|
||||
font-size: 11px;
|
||||
margin: 0 0 2px 1px;
|
||||
padding: 0; }
|
||||
.question-page .post-update-info a {
|
||||
color: #444; }
|
||||
.question-page .post-update-info .gravatar {
|
||||
float: left;
|
||||
margin-right: 4px; }
|
||||
.question-page .post-update-info p.tip {
|
||||
color: #444;
|
||||
line-height: 13px;
|
||||
font-size: 10px; }
|
||||
.question-page .post-controls {
|
||||
font-size: 11px;
|
||||
line-height: 12px;
|
||||
min-width: 200px;
|
||||
padding-left: 5px;
|
||||
text-align: right;
|
||||
clear: left;
|
||||
float: right;
|
||||
margin-top: 10px;
|
||||
margin-bottom: 8px; }
|
||||
.question-page .post-controls a {
|
||||
color: #777;
|
||||
padding: 0px 3px 3px 22px;
|
||||
cursor: pointer;
|
||||
border: none;
|
||||
font-size: 12px;
|
||||
font-family: Arial;
|
||||
text-decoration: none;
|
||||
height: 18px;
|
||||
display: block;
|
||||
float: right;
|
||||
line-height: 18px;
|
||||
margin-top: -2px;
|
||||
margin-left: 4px; }
|
||||
.question-page .post-controls a:hover {
|
||||
background-color: #f5f0c9;
|
||||
border-radius: 3px;
|
||||
-ms-border-radius: 3px;
|
||||
-moz-border-radius: 3px;
|
||||
-webkit-border-radius: 3px;
|
||||
-khtml-border-radius: 3px; }
|
||||
.question-page .post-controls .sep {
|
||||
color: #ccc;
|
||||
float: right;
|
||||
height: 18px;
|
||||
font-size: 18px; }
|
||||
.question-page .post-controls .question-delete {
|
||||
background: url(../images/delete.png) no-repeat center left;
|
||||
padding-left: 16px; }
|
||||
.question-page .answer-controls .question-delete {
|
||||
background: url(../images/delete.png) no-repeat center left;
|
||||
padding-left: 16px; }
|
||||
.question-page .post-controls .question-flag, .question-page .answer-controls .question-flag {
|
||||
background: url(../images/flag.png) no-repeat center left; }
|
||||
.question-page .post-controls .question-edit, .question-page .answer-controls .question-edit {
|
||||
background: url(../images/edit2.png) no-repeat center left; }
|
||||
.question-page .post-controls .question-retag, .question-page .answer-controls .question-retag {
|
||||
background: url(../images/retag.png) no-repeat center left; }
|
||||
.question-page .post-controls .question-close, .question-page .answer-controls .question-close {
|
||||
background: url(../images/close.png) no-repeat center left; }
|
||||
.question-page .post-controls .permant-link, .question-page .answer-controls .permant-link {
|
||||
background: url(../images/link.png) no-repeat center left; }
|
||||
.question-page .tabBar {
|
||||
width: 100%; }
|
||||
.question-page #questionCount {
|
||||
float: left;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif;
|
||||
line-height: 15px; }
|
||||
.question-page .question-img-upvote, .question-page .question-img-downvote, .question-page .answer-img-upvote, .question-page .answer-img-downvote {
|
||||
width: 25px;
|
||||
height: 20px;
|
||||
cursor: pointer; }
|
||||
.question-page .question-img-upvote, .question-page .answer-img-upvote {
|
||||
background: url(../images/vote-arrow-up-new.png) no-repeat; }
|
||||
.question-page .question-img-downvote, .question-page .answer-img-downvote {
|
||||
background: url(../images/vote-arrow-down-new.png) no-repeat; }
|
||||
.question-page .question-img-upvote:hover, .question-page .question-img-upvote.on {
|
||||
background: url(../images/vote-arrow-up-on-new.png) no-repeat; }
|
||||
.question-page .answer-img-upvote:hover, .question-page .answer-img-upvote.on {
|
||||
background: url(../images/vote-arrow-up-on-new.png) no-repeat; }
|
||||
.question-page .question-img-downvote:hover, .question-page .question-img-downvote.on {
|
||||
background: url(../images/vote-arrow-down-on-new.png) no-repeat; }
|
||||
.question-page .answer-img-downvote:hover, .question-page .answer-img-downvote.on {
|
||||
background: url(../images/vote-arrow-down-on-new.png) no-repeat; }
|
||||
.question-page #fmanswer_button {
|
||||
margin: 8px 0px; }
|
||||
.question-page .question-img-favorite:hover {
|
||||
background: url(../images/vote-favorite-on.png); }
|
||||
.question-page div.comments {
|
||||
padding: 0; }
|
||||
.question-page #comment-title {
|
||||
font-weight: bold;
|
||||
font-size: 23px;
|
||||
color: #7ea9b3;
|
||||
width: 200px;
|
||||
float: left;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif; }
|
||||
.question-page .comments {
|
||||
font-size: 12px;
|
||||
clear: both; }
|
||||
.question-page .comments div.controls {
|
||||
clear: both;
|
||||
float: left;
|
||||
width: 100%;
|
||||
margin: 3px 0 20px 5px; }
|
||||
.question-page .comments .controls a {
|
||||
color: #988e4c;
|
||||
padding: 0 3px 2px 22px;
|
||||
font-family: Arial;
|
||||
font-size: 13px;
|
||||
background: url(../images/comment.png) no-repeat center left; }
|
||||
.question-page .comments .controls a:hover {
|
||||
background-color: #f5f0c9;
|
||||
text-decoration: none; }
|
||||
.question-page .comments .button, .question-page .comments input[type="submit"], .question-page .comments input[type="button"], .question-page .comments button {
|
||||
color: #988e4c;
|
||||
font-size: 11px;
|
||||
padding: 3px;
|
||||
cursor: pointer; }
|
||||
.question-page .comments a {
|
||||
background-color: inherit;
|
||||
color: #1b79bd;
|
||||
padding: 0; }
|
||||
.question-page .comments form.post-comments {
|
||||
margin: 3px 26px 0 42px; }
|
||||
.question-page .comments form.post-comments textarea {
|
||||
font-size: 13px;
|
||||
line-height: 1.3; }
|
||||
.question-page .comments textarea {
|
||||
height: 42px;
|
||||
width: 100%;
|
||||
margin: 7px 0 5px 1px;
|
||||
font-family: Arial;
|
||||
outline: none;
|
||||
overflow: auto;
|
||||
font-size: 12px;
|
||||
line-height: 140%;
|
||||
padding-left: 2px;
|
||||
padding-top: 3px;
|
||||
border: #cce6ec 3px solid; }
|
||||
.question-page .comments input {
|
||||
margin-left: 10px;
|
||||
margin-top: 1px;
|
||||
vertical-align: top;
|
||||
width: 100px; }
|
||||
.question-page .comments button {
|
||||
background: url(../images/small-button-blue.png) repeat-x top;
|
||||
border: 0;
|
||||
color: #4a757f;
|
||||
font-family: Arial;
|
||||
font-size: 13px;
|
||||
width: 100px;
|
||||
font-weight: bold;
|
||||
height: 27px;
|
||||
line-height: 25px;
|
||||
margin-bottom: 5px;
|
||||
cursor: pointer;
|
||||
border-radius: 4px;
|
||||
-ms-border-radius: 4px;
|
||||
-moz-border-radius: 4px;
|
||||
-webkit-border-radius: 4px;
|
||||
-khtml-border-radius: 4px;
|
||||
text-shadow: 0px 1px 0px #e6f6fa;
|
||||
-moz-text-shadow: 0px 1px 0px #e6f6fa;
|
||||
-webkit-text-shadow: 0px 1px 0px #e6f6fa;
|
||||
-webkit-box-shadow: 1px 1px 2px #808080;
|
||||
-moz-box-shadow: 1px 1px 2px #808080;
|
||||
box-shadow: 1px 1px 2px #808080; }
|
||||
.question-page .comments button:hover {
|
||||
background: url(../images/small-button-blue.png) bottom repeat-x;
|
||||
text-shadow: 0px 1px 0px #c6d9dd;
|
||||
-moz-text-shadow: 0px 1px 0px #c6d9dd;
|
||||
-webkit-text-shadow: 0px 1px 0px #c6d9dd; }
|
||||
.question-page .comments .counter {
|
||||
display: inline-block;
|
||||
width: 245px;
|
||||
float: right;
|
||||
color: #b6a475 !important;
|
||||
vertical-align: top;
|
||||
font-family: Arial;
|
||||
float: right;
|
||||
text-align: right; }
|
||||
.question-page .comments .comment {
|
||||
border-bottom: 1px solid #edeeeb;
|
||||
clear: both;
|
||||
margin: 0;
|
||||
margin-top: 8px;
|
||||
padding-bottom: 4px;
|
||||
overflow: auto;
|
||||
font-family: Arial;
|
||||
font-size: 11px;
|
||||
min-height: 25px;
|
||||
background: white url(../images/comment-background.png) bottom repeat-x;
|
||||
border-radius: 5px;
|
||||
-ms-border-radius: 5px;
|
||||
-moz-border-radius: 5px;
|
||||
-webkit-border-radius: 5px;
|
||||
-khtml-border-radius: 5px; }
|
||||
.question-page .comments div.comment:hover {
|
||||
background-color: #efefef; }
|
||||
.question-page .comments a.author {
|
||||
background-color: inherit;
|
||||
color: #1b79bd;
|
||||
padding: 0; }
|
||||
.question-page .comments a.author:hover {
|
||||
text-decoration: underline; }
|
||||
.question-page .comments span.delete-icon {
|
||||
background: url(../images/close-small.png) no-repeat;
|
||||
border: 0;
|
||||
width: 14px;
|
||||
height: 14px; }
|
||||
.question-page .comments span.delete-icon:hover {
|
||||
border: #BC564B 2px solid;
|
||||
border-radius: 10px;
|
||||
-ms-border-radius: 10px;
|
||||
-moz-border-radius: 10px;
|
||||
-webkit-border-radius: 10px;
|
||||
-khtml-border-radius: 10px;
|
||||
margin: -3px 0px 0px -2px; }
|
||||
.question-page .comments .content, .question-page .comments div.course-wrapper section.course-content, div.course-wrapper .question-page .comments section.course-content, .question-page .comments div.book-wrapper section.book, div.book-wrapper .question-page .comments section.book, .question-page .comments div.wiki-wrapper section.wiki-body, div.wiki-wrapper .question-page .comments section.wiki-body {
|
||||
margin-bottom: 7px; }
|
||||
.question-page .comments .comment-votes {
|
||||
float: left;
|
||||
width: 37px;
|
||||
line-height: 130%;
|
||||
padding: 6px 5px 6px 3px; }
|
||||
.question-page .comments .comment-body {
|
||||
line-height: 1.3;
|
||||
margin: 3px 26px 0 46px;
|
||||
padding: 5px 3px;
|
||||
color: #666;
|
||||
font-size: 13px; }
|
||||
.question-page .comments .comment-body .edit {
|
||||
padding-left: 6px; }
|
||||
.question-page .comments .comment-body p {
|
||||
font-size: 13px;
|
||||
line-height: 1.3;
|
||||
margin-bottom: 3px;
|
||||
padding: 0; }
|
||||
.question-page .comments .comment-delete {
|
||||
float: right;
|
||||
width: 14px;
|
||||
line-height: 130%;
|
||||
padding: 8px 6px; }
|
||||
.question-page .comments .upvote {
|
||||
margin: 0px;
|
||||
padding-right: 17px;
|
||||
padding-top: 2px;
|
||||
text-align: right;
|
||||
height: 20px;
|
||||
font-size: 13px;
|
||||
font-weight: bold;
|
||||
color: #777; }
|
||||
.question-page .comments .upvote.upvoted {
|
||||
color: #d64000; }
|
||||
.question-page .comments .upvote.hover {
|
||||
background: url(../images/go-up-grey.png) no-repeat;
|
||||
background-position: right 1px; }
|
||||
.question-page .comments .upvote:hover {
|
||||
background: url(../images/go-up-orange.png) no-repeat;
|
||||
background-position: right 1px; }
|
||||
.question-page .comments .help-text {
|
||||
float: right;
|
||||
text-align: right;
|
||||
color: gray;
|
||||
margin-bottom: 0px;
|
||||
margin-top: 0px;
|
||||
line-height: 50%; }
|
||||
.question-page #questionTools {
|
||||
font-size: 22px;
|
||||
margin-top: 11px;
|
||||
text-align: left; }
|
||||
.question-page .question-status {
|
||||
margin-top: 10px;
|
||||
margin-bottom: 15px;
|
||||
padding: 20px;
|
||||
background-color: #fef7cc;
|
||||
text-align: center;
|
||||
border: #e1c04a 1px solid; }
|
||||
.question-page .question-status h3, .question-page .question-status div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel .question-page .question-status input[type="button"] {
|
||||
font-size: 20px;
|
||||
color: #707070;
|
||||
font-weight: normal; }
|
||||
.question-page .vote-buttons {
|
||||
float: left;
|
||||
text-align: center;
|
||||
padding-top: 2px;
|
||||
margin: 10px 10px 0px 3px; }
|
||||
.question-page .vote-buttons IMG {
|
||||
cursor: pointer; }
|
||||
.question-page .vote-number {
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif;
|
||||
padding: 0px 0 5px 0;
|
||||
font-size: 25px;
|
||||
font-weight: bold;
|
||||
color: #777; }
|
||||
.question-page .vote-buttons .notify-sidebar {
|
||||
text-align: left;
|
||||
width: 120px; }
|
||||
.question-page .vote-buttons .notify-sidebar label {
|
||||
vertical-align: top; }
|
||||
.question-page .tabBar-answer {
|
||||
margin-bottom: 15px;
|
||||
padding-left: 7px;
|
||||
width: 723px;
|
||||
margin-top: 10px; }
|
||||
.question-page .answer .vote-buttons {
|
||||
float: left; }
|
||||
.question-page .accepted-answer {
|
||||
background-color: #f7fecc;
|
||||
border-bottom-color: #9BD59B; }
|
||||
.question-page .accepted-answer .vote-buttons {
|
||||
width: 27px;
|
||||
margin-right: 10px;
|
||||
margin-top: 10px; }
|
||||
.question-page .answer .post-update-info a {
|
||||
color: #444444; }
|
||||
.question-page .answered {
|
||||
background: #CCC;
|
||||
color: #999; }
|
||||
.question-page .answered-accepted {
|
||||
background: #DCDCDC;
|
||||
color: #763333; }
|
||||
.question-page .answered-accepted strong {
|
||||
color: #E1E818; }
|
||||
.question-page .answered-by-owner {
|
||||
background: #F1F1FF; }
|
||||
.question-page .answered-by-owner .comments {
|
||||
background-color: #E6ECFF; }
|
||||
.question-page .answered-by-owner .comments .button, .question-page .answered-by-owner .comments input[type="submit"], .question-page .answered-by-owner .comments input[type="button"], .question-page .answered-by-owner .comments button {
|
||||
background-color: #E6ECFF; }
|
||||
.question-page .answered-by-owner .vote-buttons {
|
||||
margin-right: 10px; }
|
||||
.question-page .answer-img-accept:hover {
|
||||
background: url(../images/vote-accepted-on.png); }
|
||||
.question-page .answer-body a {
|
||||
color: #1b79bd; }
|
||||
.question-page .answer-body li {
|
||||
margin-bottom: 0.7em; }
|
||||
.question-page #fmanswer {
|
||||
color: #707070;
|
||||
line-height: 1.2;
|
||||
margin-top: 10px; }
|
||||
.question-page #fmanswer h2 {
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif;
|
||||
color: #7ea9b3;
|
||||
font-size: 24px; }
|
||||
.question-page #fmanswer label {
|
||||
font-size: 13px; }
|
||||
.question-page .message {
|
||||
padding: 5px;
|
||||
margin: 0px 0 10px 0; }
|
||||
|
||||
@media screen and (-webkit-min-device-pixel-ratio:0) {
|
||||
textarea {
|
||||
padding-left: 3px !important; } }
|
||||
.facebook-share.icon, .twitter-share.icon, .linkedin-share.icon, .identica-share.icon {
|
||||
background: url(../images/socialsprite.png) no-repeat;
|
||||
display: block;
|
||||
text-indent: -100em;
|
||||
height: 25px;
|
||||
width: 25px;
|
||||
margin-bottom: 3px; }
|
||||
|
||||
.facebook-share.icon:hover, .twitter-share.icon:hover, .linkedin-share.icon:hover, .identica-share.icon:hover {
|
||||
opacity: 0.8;
|
||||
filter: alpha(opacity=80); }
|
||||
|
||||
.facebook-share.icon {
|
||||
background-position: -26px 0px; }
|
||||
|
||||
.identica-share.icon {
|
||||
background-position: -78px 0px; }
|
||||
|
||||
.twitter-share.icon {
|
||||
margin-top: 10px;
|
||||
background-position: 0px 0px; }
|
||||
|
||||
.linkedin-share.icon {
|
||||
background-position: -52px 0px; }
|
||||
|
||||
.openid-signin, .meta, .users-page, .user-profile-edit-page {
|
||||
font-size: 13px;
|
||||
line-height: 1.3;
|
||||
color: #525252; }
|
||||
|
||||
.openid-signin p, .meta p, .users-page p, .user-profile-edit-page p {
|
||||
font-size: 13px;
|
||||
color: #707070;
|
||||
line-height: 1.3;
|
||||
font-family: Arial;
|
||||
color: #525252;
|
||||
margin-bottom: 12px; }
|
||||
|
||||
.openid-signin h2, .meta h2, .users-page h2, .user-profile-edit-page h2 {
|
||||
color: #525252;
|
||||
padding-left: 0px;
|
||||
font-size: 16px; }
|
||||
|
||||
.openid-signin form, .meta form, .users-page form, .user-profile-edit-page form, .user-profile-page form {
|
||||
margin-bottom: 15px; }
|
||||
|
||||
.openid-signin input[type="text"], .meta input[type="text"], .users-page input[type="text"], .user-profile-edit-page input[type="text"], .user-profile-page input[type="text"], .openid-signin input[type="password"], .meta input[type="password"], .users-page input[type="password"], .user-profile-edit-page input[type="password"], .user-profile-page input[type="password"], .openid-signin select, .meta select, .users-page select, .user-profile-edit-page select, .user-profile-page select {
|
||||
border: #cce6ec 3px solid;
|
||||
height: 25px;
|
||||
padding-left: 5px;
|
||||
width: 395px;
|
||||
font-size: 14px; }
|
||||
|
||||
.openid-signin select, .meta select, .users-page select, .user-profile-edit-page select, .user-profile-page select {
|
||||
width: 405px;
|
||||
height: 30px; }
|
||||
|
||||
.openid-signin textarea, .meta textarea, .users-page textarea, .user-profile-edit-page textarea, .user-profile-page textarea {
|
||||
border: #cce6ec 3px solid;
|
||||
padding-left: 5px;
|
||||
padding-top: 5px;
|
||||
width: 395px;
|
||||
font-size: 14px; }
|
||||
|
||||
.openid-signin input.submit, .meta input.submit, .users-page input.submit, .user-profile-edit-page input.submit, .user-profile-page input.submit {
|
||||
background: url(../images/small-button-blue.png) repeat-x top;
|
||||
border: 0;
|
||||
color: #4a757f;
|
||||
font-weight: bold;
|
||||
font-size: 13px;
|
||||
font-family: Arial;
|
||||
height: 26px;
|
||||
margin: 5px 0px;
|
||||
width: 100px;
|
||||
cursor: pointer;
|
||||
border-radius: 4px;
|
||||
-ms-border-radius: 4px;
|
||||
-moz-border-radius: 4px;
|
||||
-webkit-border-radius: 4px;
|
||||
-khtml-border-radius: 4px;
|
||||
text-shadow: 0px 1px 0px #e6f6fa;
|
||||
-moz-text-shadow: 0px 1px 0px #e6f6fa;
|
||||
-webkit-text-shadow: 0px 1px 0px #e6f6fa;
|
||||
-webkit-box-shadow: 1px 1px 2px #808080;
|
||||
-moz-box-shadow: 1px 1px 2px #808080;
|
||||
box-shadow: 1px 1px 2px #808080; }
|
||||
|
||||
.openid-signin input.submit:hover, .meta input.submit:hover, .users-page input.submit:hover, .user-profile-edit-page input.submit:hover, .user-profile-page input.submit:hover {
|
||||
background: url(../images/small-button-blue.png) repeat-x bottom;
|
||||
text-decoration: none; }
|
||||
|
||||
.openid-signin .cancel, .meta .cancel, .users-page .cancel, .user-profile-edit-page .cancel, .user-profile-page .cancel {
|
||||
background: url(../images/small-button-cancel.png) repeat-x top !important;
|
||||
color: #525252 !important; }
|
||||
|
||||
.openid-signin .cancel:hover, .meta .cancel:hover, .users-page .cancel:hover, .user-profile-edit-page .cancel:hover, .user-profile-page .cancel:hover {
|
||||
background: url(../images/small-button-cancel.png) repeat-x bottom !important; }
|
||||
|
||||
#email-input-fs, #local_login_buttons, #password-fs, #openid-fs {
|
||||
margin-top: 10px; }
|
||||
|
||||
#email-input-fs #id_email, #local_login_buttons #id_email, #password-fs #id_email, #openid-fs #id_email, #email-input-fs #id_username, #local_login_buttons #id_username, #password-fs #id_username, #openid-fs #id_username, #email-input-fs #id_password, #local_login_buttons #id_password, #password-fs #id_password, #openid-fs #id_password {
|
||||
font-size: 12px;
|
||||
line-height: 20px;
|
||||
height: 20px;
|
||||
margin: 0px;
|
||||
padding: 0px 0 0 5px;
|
||||
border: #cce6ec 3px solid;
|
||||
width: 200px; }
|
||||
|
||||
#email-input-fs .submit-b, #local_login_buttons .submit-b, #password-fs .submit-b, #openid-fs .submit-b {
|
||||
background: url(../images/small-button-blue.png) repeat-x top;
|
||||
border: 0;
|
||||
color: #4a757f;
|
||||
font-weight: bold;
|
||||
font-size: 13px;
|
||||
font-family: Arial;
|
||||
height: 24px;
|
||||
margin-top: -2px;
|
||||
padding-left: 10px;
|
||||
padding-right: 10px;
|
||||
cursor: pointer;
|
||||
border-radius: 4px;
|
||||
-ms-border-radius: 4px;
|
||||
-moz-border-radius: 4px;
|
||||
-webkit-border-radius: 4px;
|
||||
-khtml-border-radius: 4px;
|
||||
text-shadow: 0px 1px 0px #e6f6fa;
|
||||
-moz-text-shadow: 0px 1px 0px #e6f6fa;
|
||||
-webkit-text-shadow: 0px 1px 0px #e6f6fa;
|
||||
-webkit-box-shadow: 1px 1px 2px #808080;
|
||||
-moz-box-shadow: 1px 1px 2px #808080;
|
||||
box-shadow: 1px 1px 2px #808080; }
|
||||
|
||||
#email-input-fs .submit-b:hover, #local_login_buttons .submit-b:hover, #password-fs .submit-b:hover, #openid-fs .submit-b:hover {
|
||||
background: url(../images/small-button-blue.png) repeat-x bottom; }
|
||||
|
||||
.openid-input {
|
||||
background: url(../images/openid.gif) no-repeat;
|
||||
padding-left: 15px;
|
||||
cursor: pointer; }
|
||||
|
||||
.openid-login-input {
|
||||
background-position: center left;
|
||||
background: url(../images/openid.gif) no-repeat 0% 50%;
|
||||
padding: 5px 5px 5px 15px;
|
||||
cursor: pointer;
|
||||
font-family: Trebuchet MS;
|
||||
font-weight: 300;
|
||||
font-size: 150%;
|
||||
width: 500px; }
|
||||
|
||||
.openid-login-submit {
|
||||
height: 40px;
|
||||
width: 80px;
|
||||
line-height: 40px;
|
||||
cursor: pointer;
|
||||
border: 1px solid #777;
|
||||
font-weight: bold;
|
||||
font-size: 120%; }
|
||||
|
||||
.tabBar-user {
|
||||
width: 375px; }
|
||||
|
||||
.user {
|
||||
padding: 5px;
|
||||
line-height: 140%;
|
||||
width: 166px;
|
||||
border: #eee 1px solid;
|
||||
margin-bottom: 5px;
|
||||
border-radius: 3px;
|
||||
-ms-border-radius: 3px;
|
||||
-moz-border-radius: 3px;
|
||||
-webkit-border-radius: 3px;
|
||||
-khtml-border-radius: 3px; }
|
||||
.user .user-micro-info {
|
||||
color: #525252; }
|
||||
.user ul {
|
||||
margin: 0;
|
||||
list-style-type: none; }
|
||||
.user .thumb {
|
||||
clear: both;
|
||||
float: left;
|
||||
margin-right: 4px;
|
||||
display: inline; }
|
||||
|
||||
.tabBar-tags {
|
||||
width: 270px;
|
||||
margin-bottom: 15px; }
|
||||
|
||||
a.medal {
|
||||
font-size: 17px;
|
||||
line-height: 250%;
|
||||
margin-right: 5px;
|
||||
color: #333;
|
||||
text-decoration: none;
|
||||
background: url(../images/medala.gif) no-repeat;
|
||||
border-left: 1px solid #EEE;
|
||||
border-top: 1px solid #EEE;
|
||||
border-bottom: 1px solid #CCC;
|
||||
border-right: 1px solid #CCC;
|
||||
padding: 4px 12px 4px 6px; }
|
||||
a:hover.medal {
|
||||
color: #333;
|
||||
text-decoration: none;
|
||||
background: url(../images/medala_on.gif) no-repeat;
|
||||
border-left: 1px solid #E7E296;
|
||||
border-top: 1px solid #E7E296;
|
||||
border-bottom: 1px solid #D1CA3D;
|
||||
border-right: 1px solid #D1CA3D; }
|
||||
|
||||
#award-list .user {
|
||||
float: left;
|
||||
margin: 5px; }
|
||||
|
||||
.tabBar-profile {
|
||||
width: 100%;
|
||||
margin-bottom: 15px;
|
||||
float: left; }
|
||||
|
||||
.user-profile-page {
|
||||
font-size: 13px;
|
||||
color: #525252; }
|
||||
.user-profile-page p {
|
||||
font-size: 13px;
|
||||
line-height: 1.3;
|
||||
color: #525252; }
|
||||
.user-profile-page .avatar img {
|
||||
border: #eee 1px solid;
|
||||
padding: 5px; }
|
||||
.user-profile-page h2 {
|
||||
padding: 10px 0px 10px 0px;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif; }
|
||||
|
||||
.user-details {
|
||||
font-size: 13px; }
|
||||
.user-details h3, .user-details div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel .user-details input[type="button"] {
|
||||
font-size: 16px; }
|
||||
|
||||
.user-about {
|
||||
background-color: #EEEEEE;
|
||||
height: 200px;
|
||||
line-height: 20px;
|
||||
overflow: auto;
|
||||
padding: 10px;
|
||||
width: 90%; }
|
||||
.user-about p {
|
||||
font-size: 13px; }
|
||||
|
||||
.follow-toggle, .submit {
|
||||
border: 0 !important;
|
||||
color: #4a757f;
|
||||
font-weight: bold;
|
||||
font-size: 12px;
|
||||
height: 26px;
|
||||
line-height: 26px;
|
||||
margin-top: -2px;
|
||||
font-size: 15px;
|
||||
cursor: pointer;
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif;
|
||||
background: url(../images/small-button-blue.png) repeat-x top;
|
||||
border-radius: 4px;
|
||||
-ms-border-radius: 4px;
|
||||
-moz-border-radius: 4px;
|
||||
-webkit-border-radius: 4px;
|
||||
-khtml-border-radius: 4px;
|
||||
text-shadow: 0px 1px 0px #e6f6fa;
|
||||
-moz-text-shadow: 0px 1px 0px #e6f6fa;
|
||||
-webkit-text-shadow: 0px 1px 0px #e6f6fa;
|
||||
-webkit-box-shadow: 1px 1px 2px #808080;
|
||||
-moz-box-shadow: 1px 1px 2px #808080;
|
||||
box-shadow: 1px 1px 2px #808080; }
|
||||
|
||||
.follow-toggle:hover, .submit:hover {
|
||||
background: url(../images/small-button-blue.png) repeat-x bottom;
|
||||
text-decoration: none !important; }
|
||||
|
||||
.follow-toggle .follow {
|
||||
font-color: #000;
|
||||
font-style: normal; }
|
||||
.follow-toggle .unfollow div.unfollow-red {
|
||||
display: none; }
|
||||
.follow-toggle .unfollow:hover div.unfollow-red {
|
||||
display: inline;
|
||||
color: #fff;
|
||||
font-weight: bold;
|
||||
color: #A05736; }
|
||||
.follow-toggle .unfollow:hover div.unfollow-green {
|
||||
display: none; }
|
||||
|
||||
.count {
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif;
|
||||
font-size: 200%;
|
||||
font-weight: 700;
|
||||
color: #777777; }
|
||||
|
||||
.scoreNumber {
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif;
|
||||
font-size: 35px;
|
||||
font-weight: 800;
|
||||
color: #777;
|
||||
line-height: 40px;
|
||||
margin-top: 3px; }
|
||||
|
||||
.vote-count {
|
||||
font-family: Arial;
|
||||
font-size: 160%;
|
||||
font-weight: 700;
|
||||
color: #777; }
|
||||
|
||||
.answer-summary {
|
||||
display: block;
|
||||
clear: both;
|
||||
padding: 3px; }
|
||||
|
||||
.answer-votes {
|
||||
background-color: #EEEEEE;
|
||||
color: #555555;
|
||||
float: left;
|
||||
font-family: Arial;
|
||||
font-size: 15px;
|
||||
font-weight: bold;
|
||||
height: 17px;
|
||||
padding: 2px 4px 5px;
|
||||
text-align: center;
|
||||
text-decoration: none;
|
||||
width: 20px;
|
||||
margin-right: 10px;
|
||||
border-radius: 4px;
|
||||
-ms-border-radius: 4px;
|
||||
-moz-border-radius: 4px;
|
||||
-webkit-border-radius: 4px;
|
||||
-khtml-border-radius: 4px; }
|
||||
|
||||
.karma-summary {
|
||||
padding: 5px;
|
||||
font-size: 13px; }
|
||||
.karma-summary h3, .karma-summary div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel .karma-summary input[type="button"] {
|
||||
text-align: center;
|
||||
font-weight: bold;
|
||||
padding: 5px; }
|
||||
|
||||
.karma-diagram {
|
||||
width: 477px;
|
||||
height: 300px;
|
||||
float: left;
|
||||
margin-right: 10px; }
|
||||
|
||||
.karma-details {
|
||||
float: right;
|
||||
width: 450px;
|
||||
height: 250px;
|
||||
overflow-y: auto;
|
||||
word-wrap: break-word; }
|
||||
.karma-details p {
|
||||
margin-bottom: 10px; }
|
||||
|
||||
.karma-gained {
|
||||
font-weight: bold;
|
||||
background: #eee;
|
||||
width: 25px;
|
||||
margin-right: 5px;
|
||||
color: green;
|
||||
padding: 3px;
|
||||
display: block;
|
||||
float: left;
|
||||
text-align: center;
|
||||
border-radius: 3px;
|
||||
-ms-border-radius: 3px;
|
||||
-moz-border-radius: 3px;
|
||||
-webkit-border-radius: 3px;
|
||||
-khtml-border-radius: 3px; }
|
||||
|
||||
.karma-lost {
|
||||
font-weight: bold;
|
||||
background: #eee;
|
||||
width: 25px;
|
||||
color: red;
|
||||
padding: 3px;
|
||||
display: block;
|
||||
margin-right: 5px;
|
||||
float: left;
|
||||
text-align: center;
|
||||
border-radius: 3px;
|
||||
-ms-border-radius: 3px;
|
||||
-moz-border-radius: 3px;
|
||||
-webkit-border-radius: 3px;
|
||||
-khtml-border-radius: 3px; }
|
||||
|
||||
.submit-row {
|
||||
margin-bottom: 10px; }
|
||||
|
||||
.revision {
|
||||
margin: 10px 0 10px 0;
|
||||
font-size: 13px;
|
||||
color: #525252; }
|
||||
.revision p {
|
||||
font-size: 13px;
|
||||
line-height: 1.3;
|
||||
color: #525252; }
|
||||
.revision h3, .revision div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel .revision input[type="button"] {
|
||||
font-family: 'Yanone Kaffeesatz',sans-serif;
|
||||
font-size: 21px;
|
||||
padding-left: 0px; }
|
||||
.revision .header {
|
||||
background-color: #F5F5F5;
|
||||
padding: 5px;
|
||||
cursor: pointer; }
|
||||
.revision .author {
|
||||
background-color: #e9f3f5; }
|
||||
.revision .summary {
|
||||
padding: 5px 0 10px 0; }
|
||||
.revision .summary span {
|
||||
background-color: #fde785;
|
||||
padding: 6px;
|
||||
border-radius: 4px;
|
||||
-ms-border-radius: 4px;
|
||||
-moz-border-radius: 4px;
|
||||
-webkit-border-radius: 4px;
|
||||
-khtml-border-radius: 4px;
|
||||
display: inline;
|
||||
-webkit-box-shadow: 1px 1px 4px #cfb852;
|
||||
-moz-box-shadow: 1px 1px 4px #cfb852;
|
||||
box-shadow: 1px 1px 4px #cfb852; }
|
||||
.revision .answerbody {
|
||||
padding: 10px 0 5px 10px; }
|
||||
.revision .revision-mark {
|
||||
width: 150px;
|
||||
text-align: left;
|
||||
display: inline-block;
|
||||
font-size: 11px;
|
||||
overflow: hidden; }
|
||||
.revision .revision-mark .gravatar {
|
||||
float: left;
|
||||
margin-right: 4px;
|
||||
padding-top: 5px; }
|
||||
.revision .revision-number {
|
||||
font-size: 300%;
|
||||
font-weight: bold;
|
||||
font-family: sans-serif; }
|
||||
|
||||
del {
|
||||
color: #C34719; }
|
||||
del .post-tag {
|
||||
color: #C34719; }
|
||||
|
||||
ins {
|
||||
background-color: #E6F0A2; }
|
||||
ins .post-tag, ins p {
|
||||
background-color: #E6F0A2; }
|
||||
|
||||
.vote-notification {
|
||||
z-index: 1;
|
||||
cursor: pointer;
|
||||
display: none;
|
||||
position: absolute;
|
||||
font-family: Arial;
|
||||
font-size: 14px;
|
||||
font-weight: normal;
|
||||
color: white;
|
||||
background-color: #8e0000;
|
||||
text-align: center;
|
||||
padding-bottom: 10px;
|
||||
-webkit-box-shadow: 0px 2px 4px #370000;
|
||||
-moz-box-shadow: 0px 2px 4px #370000;
|
||||
box-shadow: 0px 2px 4px #370000;
|
||||
border-radius: 4px;
|
||||
-ms-border-radius: 4px;
|
||||
-moz-border-radius: 4px;
|
||||
-webkit-border-radius: 4px;
|
||||
-khtml-border-radius: 4px; }
|
||||
.vote-notification h3, .vote-notification div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel .vote-notification input[type="button"] {
|
||||
background: url(../images/notification.png) repeat-x top;
|
||||
padding: 10px 10px 10px 10px;
|
||||
font-size: 13px;
|
||||
margin-bottom: 5px;
|
||||
border-top: #8e0000 1px solid;
|
||||
color: #fff;
|
||||
font-weight: normal;
|
||||
border-top-right-radius: 4px;
|
||||
border-top-left-radius: 4px;
|
||||
-moz-border-radius-topright: 4px;
|
||||
-moz-border-radius-topleft: 4px;
|
||||
-webkit-border-top-left-radius: 4px;
|
||||
-webkit-border-top-right-radius: 4px; }
|
||||
.vote-notification a {
|
||||
color: #fb7321;
|
||||
text-decoration: underline;
|
||||
font-weight: bold; }
|
||||
|
||||
.footer-links {
|
||||
color: #EEE;
|
||||
text-align: left;
|
||||
width: 500px;
|
||||
float: left; }
|
||||
.footer-links a {
|
||||
color: #e7e8a8; }
|
||||
|
||||
.powered-link {
|
||||
width: 500px;
|
||||
float: left;
|
||||
text-align: left; }
|
||||
.powered-link a {
|
||||
color: #8ebcc7; }
|
||||
|
||||
.copyright {
|
||||
color: #616161;
|
||||
width: 450px;
|
||||
float: right;
|
||||
text-align: right; }
|
||||
.copyright a {
|
||||
color: #8ebcc7; }
|
||||
.copyright img.license-logo {
|
||||
margin: 6px 0px 20px 10px;
|
||||
float: right; }
|
||||
|
||||
.notify-me {
|
||||
float: left; }
|
||||
|
||||
span.text-counter {
|
||||
margin-right: 20px; }
|
||||
span.form-error {
|
||||
color: #990000;
|
||||
font-weight: normal;
|
||||
margin-left: 5px; }
|
||||
|
||||
p.form-item {
|
||||
margin: 0px; }
|
||||
|
||||
.deleted {
|
||||
background: #F4E7E7 none repeat scroll 0 0; }
|
||||
|
||||
.form-row {
|
||||
line-height: 25px; }
|
||||
|
||||
table.form-as-table {
|
||||
margin-top: 5px; }
|
||||
table.form-as-table ul {
|
||||
list-style-type: none;
|
||||
display: inline; }
|
||||
table.form-as-table li {
|
||||
display: inline; }
|
||||
table.form-as-table td {
|
||||
text-align: right; }
|
||||
table.form-as-table th {
|
||||
text-align: left;
|
||||
font-weight: normal; }
|
||||
table.ab-subscr-form, table.ab-tag-filter-form {
|
||||
width: 45em; }
|
||||
|
||||
.submit-row {
|
||||
line-height: 30px;
|
||||
padding-top: 10px;
|
||||
display: block;
|
||||
clear: both; }
|
||||
|
||||
.errors {
|
||||
line-height: 20px;
|
||||
color: red; }
|
||||
|
||||
.error {
|
||||
color: darkred;
|
||||
margin: 0;
|
||||
font-size: 10px; }
|
||||
|
||||
label.retag-error {
|
||||
color: darkred;
|
||||
padding-left: 5px;
|
||||
font-size: 10px; }
|
||||
|
||||
.fieldset {
|
||||
border: none;
|
||||
margin-top: 10px;
|
||||
padding: 10px; }
|
||||
|
||||
span.form-error {
|
||||
color: #990000;
|
||||
font-size: 90%;
|
||||
font-weight: normal;
|
||||
margin-left: 5px; }
|
||||
|
||||
.favorites-empty {
|
||||
width: 32px;
|
||||
height: 45px;
|
||||
float: left; }
|
||||
|
||||
.user-info-table {
|
||||
margin-bottom: 10px;
|
||||
border-spacing: 0; }
|
||||
|
||||
.user-stats-table .narrow {
|
||||
width: 660px; }
|
||||
|
||||
.narrow .summary h3, .narrow .summary div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel .narrow .summary input[type="button"] {
|
||||
padding: 0px;
|
||||
margin: 0px; }
|
||||
|
||||
.relativetime {
|
||||
font-weight: bold;
|
||||
text-decoration: none; }
|
||||
|
||||
.narrow .tags {
|
||||
float: left; }
|
||||
|
||||
.user-action-1 {
|
||||
font-weight: bold;
|
||||
color: #333; }
|
||||
|
||||
.user-action-2 {
|
||||
font-weight: bold;
|
||||
color: #CCC; }
|
||||
|
||||
.user-action-3, .user-action-4 {
|
||||
color: #333; }
|
||||
|
||||
.user-action-5, .user-action-6 {
|
||||
color: darkred; }
|
||||
|
||||
.user-action-7 {
|
||||
color: #333; }
|
||||
|
||||
.user-action-8 {
|
||||
padding: 3px;
|
||||
font-weight: bold;
|
||||
background-color: #CCC;
|
||||
color: #763333; }
|
||||
|
||||
.revision-summary {
|
||||
background-color: #FFFE9B;
|
||||
padding: 2px; }
|
||||
|
||||
.question-title-link a {
|
||||
font-weight: bold;
|
||||
color: #0077CC; }
|
||||
|
||||
.answer-title-link a {
|
||||
color: #333; }
|
||||
|
||||
.post-type-1 a, .post-type-3 a, .post-type-5 a {
|
||||
font-weight: bold; }
|
||||
|
||||
.post-type-2 a, .post-type-4 a, .post-type-6 a, .post-type-8 a {
|
||||
color: #333; }
|
||||
|
||||
.hilite, .hilite1 {
|
||||
background-color: #ff0; }
|
||||
|
||||
.hilite2 {
|
||||
background-color: #f0f; }
|
||||
|
||||
.hilite3 {
|
||||
background-color: #0ff; }
|
||||
|
||||
.gold, .badge1 {
|
||||
color: #FFCC00; }
|
||||
|
||||
.silver, .badge2 {
|
||||
color: #CCCCCC; }
|
||||
|
||||
.bronze, .badge3 {
|
||||
color: #CC9933; }
|
||||
|
||||
.score {
|
||||
font-weight: 800;
|
||||
color: #333; }
|
||||
|
||||
a.comment {
|
||||
background: #EEE;
|
||||
color: #993300;
|
||||
padding: 5px; }
|
||||
a.offensive {
|
||||
color: #999; }
|
||||
|
||||
.message h1 {
|
||||
padding-top: 0px;
|
||||
font-size: 15px; }
|
||||
.message p {
|
||||
margin-bottom: 0px; }
|
||||
|
||||
p.space-above {
|
||||
margin-top: 10px; }
|
||||
|
||||
.warning {
|
||||
color: red; }
|
||||
|
||||
button::-moz-focus-inner {
|
||||
padding: 0;
|
||||
border: none; }
|
||||
|
||||
.submit {
|
||||
cursor: pointer;
|
||||
background-color: #D4D0C8;
|
||||
height: 30px;
|
||||
border: 1px solid #777777;
|
||||
font-weight: bold;
|
||||
font-size: 120%; }
|
||||
.submit:hover {
|
||||
text-decoration: underline; }
|
||||
.submit.small {
|
||||
margin-right: 5px;
|
||||
height: 20px;
|
||||
font-weight: normal;
|
||||
font-size: 12px;
|
||||
padding: 1px 5px; }
|
||||
.submit.small:hover {
|
||||
text-decoration: none; }
|
||||
|
||||
.question-page a.submit {
|
||||
display: -moz-inline-stack;
|
||||
display: inline-block;
|
||||
line-height: 30px;
|
||||
padding: 0 5px;
|
||||
*display: inline; }
|
||||
|
||||
.noscript {
|
||||
position: fixed;
|
||||
top: 0px;
|
||||
left: 0px;
|
||||
width: 100%;
|
||||
z-index: 100;
|
||||
padding: 5px 0;
|
||||
text-align: center;
|
||||
font-family: sans-serif;
|
||||
font-size: 120%;
|
||||
font-weight: Bold;
|
||||
color: #FFFFFF;
|
||||
background-color: #AE0000; }
|
||||
|
||||
.big {
|
||||
font-size: 14px; }
|
||||
|
||||
.strong {
|
||||
font-weight: bold; }
|
||||
|
||||
.orange {
|
||||
color: #d64000;
|
||||
font-weight: bold; }
|
||||
|
||||
.grey {
|
||||
color: #808080; }
|
||||
|
||||
.about div {
|
||||
padding: 10px 5px 10px 5px;
|
||||
border-top: 1px dashed #aaaaaa; }
|
||||
|
||||
.highlight {
|
||||
background-color: #FFF8C6; }
|
||||
|
||||
.nomargin {
|
||||
margin: 0; }
|
||||
|
||||
.margin-bottom {
|
||||
margin-bottom: 10px; }
|
||||
|
||||
.margin-top {
|
||||
margin-top: 10px; }
|
||||
|
||||
.inline-block {
|
||||
display: inline-block; }
|
||||
|
||||
.action-status {
|
||||
margin: 0;
|
||||
border: none;
|
||||
text-align: center;
|
||||
line-height: 10px;
|
||||
font-size: 12px;
|
||||
padding: 0; }
|
||||
.action-status span {
|
||||
padding: 3px 5px 3px 5px;
|
||||
background-color: #fff380;
|
||||
font-weight: normal;
|
||||
-moz-border-radius: 5px;
|
||||
-khtml-border-radius: 5px;
|
||||
-webkit-border-radius: 5px; }
|
||||
|
||||
.list-table td {
|
||||
vertical-align: top; }
|
||||
|
||||
table.form-as-table .errorlist {
|
||||
display: block;
|
||||
margin: 0;
|
||||
padding: 0 0 0 5px;
|
||||
text-align: left;
|
||||
font-size: 10px;
|
||||
color: darkred; }
|
||||
table.form-as-table input {
|
||||
display: inline;
|
||||
margin-left: 4px; }
|
||||
table.form-as-table th {
|
||||
vertical-align: bottom;
|
||||
padding-bottom: 4px; }
|
||||
|
||||
.form-row-vertical {
|
||||
margin-top: 8px;
|
||||
display: block; }
|
||||
.form-row-vertical label {
|
||||
margin-bottom: 3px;
|
||||
display: block; }
|
||||
|
||||
.text-align-right {
|
||||
text-align: center; }
|
||||
|
||||
ul.form-horizontal-rows {
|
||||
list-style: none;
|
||||
margin: 0; }
|
||||
ul.form-horizontal-rows li {
|
||||
position: relative;
|
||||
height: 40px; }
|
||||
ul.form-horizontal-rows label {
|
||||
display: inline-block; }
|
||||
ul.form-horizontal-rows ul.errorlist {
|
||||
list-style: none;
|
||||
color: darkred;
|
||||
font-size: 10px;
|
||||
line-height: 10px;
|
||||
position: absolute;
|
||||
top: 2px;
|
||||
left: 180px;
|
||||
text-align: left;
|
||||
margin: 0; }
|
||||
ul.form-horizontal-rows ul.errorlist li {
|
||||
height: 10px; }
|
||||
ul.form-horizontal-rows label {
|
||||
position: absolute;
|
||||
left: 0px;
|
||||
bottom: 6px;
|
||||
margin: 0px;
|
||||
line-height: 12px;
|
||||
font-size: 12px; }
|
||||
ul.form-horizontal-rows li input {
|
||||
position: absolute;
|
||||
bottom: 0px;
|
||||
left: 180px;
|
||||
margin: 0px; }
|
||||
|
||||
.narrow .summary {
|
||||
float: left; }
|
||||
|
||||
.user-profile-tool-links {
|
||||
font-weight: bold;
|
||||
vertical-align: top; }
|
||||
|
||||
ul.post-tags {
|
||||
margin-left: 3px; }
|
||||
ul.post-tags li {
|
||||
margin-top: 4px;
|
||||
margin-bottom: 3px; }
|
||||
ul.post-retag {
|
||||
margin-bottom: 0px;
|
||||
margin-left: 5px; }
|
||||
|
||||
#question-controls .tags {
|
||||
margin: 0 0 3px 0; }
|
||||
|
||||
#tagSelector {
|
||||
padding-bottom: 2px;
|
||||
margin-bottom: 0; }
|
||||
|
||||
#related-tags {
|
||||
padding-left: 3px; }
|
||||
|
||||
#hideIgnoredTagsControl {
|
||||
margin: 5px 0 0 0; }
|
||||
#hideIgnoredTagsControl label {
|
||||
font-size: 12px;
|
||||
color: #666; }
|
||||
|
||||
#hideIgnoredTagsCb {
|
||||
margin: 0 2px 0 1px; }
|
||||
|
||||
#recaptcha_widget_div {
|
||||
width: 318px;
|
||||
float: left;
|
||||
clear: both; }
|
||||
|
||||
p.signup_p {
|
||||
margin: 20px 0px 0px 0px; }
|
||||
|
||||
.simple-subscribe-options ul {
|
||||
list-style: none;
|
||||
list-style-position: outside;
|
||||
margin: 0; }
|
||||
|
||||
.wmd-preview a {
|
||||
color: #1b79bd; }
|
||||
.wmd-preview li {
|
||||
margin-bottom: 7px;
|
||||
font-size: 14px; }
|
||||
|
||||
.search-result-summary {
|
||||
font-weight: bold;
|
||||
font-size: 18px;
|
||||
line-height: 22px;
|
||||
margin: 0px 0px 0px 0px;
|
||||
padding: 2px 0 0 0;
|
||||
float: left; }
|
||||
|
||||
.faq-rep-item {
|
||||
text-align: right;
|
||||
padding-right: 5px; }
|
||||
|
||||
.user-info-table .gravatar {
|
||||
margin: 0; }
|
||||
|
||||
#responses {
|
||||
clear: both;
|
||||
line-height: 18px;
|
||||
margin-bottom: 15px; }
|
||||
#responses div.face {
|
||||
float: left;
|
||||
text-align: center;
|
||||
width: 54px;
|
||||
padding: 3px;
|
||||
overflow: hidden; }
|
||||
|
||||
.response-parent {
|
||||
margin-top: 18px; }
|
||||
.response-parent strong {
|
||||
font-size: 20px; }
|
||||
|
||||
.re {
|
||||
min-height: 57px;
|
||||
clear: both;
|
||||
margin-top: 10px; }
|
||||
|
||||
#responses input {
|
||||
float: left; }
|
||||
|
||||
#re_tools {
|
||||
margin-bottom: 10px; }
|
||||
|
||||
#re_sections {
|
||||
margin-bottom: 6px; }
|
||||
#re_sections .on {
|
||||
font-weight: bold; }
|
||||
|
||||
.avatar-page ul {
|
||||
list-style: none; }
|
||||
.avatar-page li {
|
||||
display: inline; }
|
||||
|
||||
.user-profile-page .avatar p {
|
||||
margin-bottom: 0px; }
|
||||
.user-profile-page .tabBar a#stats {
|
||||
margin-left: 0; }
|
||||
.user-profile-page img.gravatar {
|
||||
margin: 2px 0 3px 0; }
|
||||
.user-profile-page h3, .user-profile-page div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel .user-profile-page input[type="button"] {
|
||||
padding: 0;
|
||||
margin-top: -3px; }
|
||||
|
||||
.userList {
|
||||
font-size: 13px; }
|
||||
|
||||
img.flag {
|
||||
border: 1px solid #eee;
|
||||
vertical-align: text-top; }
|
||||
|
||||
.main-page img.flag {
|
||||
vertical-align: text-bottom; }
|
||||
|
||||
a.edit {
|
||||
padding-left: 3px;
|
||||
color: #145bff; }
|
||||
|
||||
.str {
|
||||
color: #080; }
|
||||
|
||||
.kwd {
|
||||
color: #008; }
|
||||
|
||||
.com {
|
||||
color: #800; }
|
||||
|
||||
.typ {
|
||||
color: #606; }
|
||||
|
||||
.lit {
|
||||
color: #066; }
|
||||
|
||||
.pun {
|
||||
color: #660; }
|
||||
|
||||
.pln {
|
||||
color: #000; }
|
||||
|
||||
.tag {
|
||||
color: #008; }
|
||||
|
||||
.atn {
|
||||
color: #606; }
|
||||
|
||||
.atv {
|
||||
color: #080; }
|
||||
|
||||
.dec {
|
||||
color: #606; }
|
||||
|
||||
pre.prettyprint {
|
||||
clear: both;
|
||||
padding: 3px;
|
||||
border: 0px solid #888; }
|
||||
|
||||
@media print {
|
||||
.str {
|
||||
color: #060; }
|
||||
|
||||
.kwd {
|
||||
color: #006;
|
||||
font-weight: bold; }
|
||||
|
||||
.com {
|
||||
color: #600;
|
||||
font-style: italic; }
|
||||
|
||||
.typ {
|
||||
color: #404;
|
||||
font-weight: bold; }
|
||||
|
||||
.lit {
|
||||
color: #044; }
|
||||
|
||||
.pun {
|
||||
color: #440; }
|
||||
|
||||
.pln {
|
||||
color: #000; }
|
||||
|
||||
.tag {
|
||||
color: #006;
|
||||
font-weight: bold; }
|
||||
|
||||
.atn {
|
||||
color: #404; }
|
||||
|
||||
.atv {
|
||||
color: #060; } }
|
||||
/*
|
||||
----------------------------------------------------------------------------------------
|
||||
|
||||
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;
|
||||
|
||||
----------------------------------------------------------------------------------------
|
||||
*/
|
||||
h1 {
|
||||
clear: both; }
|
||||
|
||||
h2 {
|
||||
clear: both; }
|
||||
|
||||
h3, div.wiki-wrapper div#wiki_panel input[type="button"] {
|
||||
font-size: 1em;
|
||||
margin: 20px 0 5px 0;
|
||||
clear: both; }
|
||||
|
||||
a:link, a:visited {
|
||||
text-decoration: none; }
|
||||
|
||||
a:hover {
|
||||
text-decoration: underline; }
|
||||
|
||||
#wrapper {
|
||||
background: transparent url(images/css/page-vbg.jpg) repeat-y scroll 50% 0px;
|
||||
margin: 0 auto;
|
||||
width: 100%; }
|
||||
|
||||
#topWrapper {
|
||||
width: 100%;
|
||||
height: 100px;
|
||||
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;
|
||||
height: 20px;
|
||||
margin: 0 auto;
|
||||
text-align: center;
|
||||
width: 800px; }
|
||||
#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; }
|
||||
|
||||
#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; }
|
||||
|
||||
#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; }
|
||||
|
||||
#hide_acc {
|
||||
min-height: 600; }
|
||||
|
||||
#mainblock {
|
||||
border: 0;
|
||||
padding: 0;
|
||||
margin: 0;
|
||||
width: 200;
|
||||
min-height: 600px;
|
||||
margin-left: 276px;
|
||||
margin-right: 0px; }
|
||||
|
||||
.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; }
|
||||
7
css/marketing-ie.css
Normal file
7
css/marketing-ie.css
Normal file
@@ -0,0 +1,7 @@
|
||||
body {
|
||||
margin: 0;
|
||||
padding: 0; }
|
||||
|
||||
.wrapper, .subpage, section.copyright, section.tos, section.privacy-policy, section.honor-code, header.announcement div, section.index-content, footer {
|
||||
margin: 0;
|
||||
overflow: hidden; }
|
||||
53
fonts/Apache License Version 2.txt
Executable file
53
fonts/Apache License Version 2.txt
Executable file
@@ -0,0 +1,53 @@
|
||||
Apache License
|
||||
|
||||
Version 2.0, January 2004
|
||||
|
||||
http://www.apache.org/licenses/
|
||||
|
||||
TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
|
||||
|
||||
1. Definitions.
|
||||
|
||||
"License" shall mean the terms and conditions for use, reproduction, and distribution as defined by Sections 1 through 9 of this document.
|
||||
|
||||
"Licensor" shall mean the copyright owner or entity authorized by the copyright owner that is granting the License.
|
||||
|
||||
"Legal Entity" shall mean the union of the acting entity and all other entities that control, are controlled by, or are under common control with that entity. For the purposes of this definition, "control" means (i) the power, direct or indirect, to cause the direction or management of such entity, whether by contract or otherwise, or (ii) ownership of fifty percent (50%) or more of the outstanding shares, or (iii) beneficial ownership of such entity.
|
||||
|
||||
"You" (or "Your") shall mean an individual or Legal Entity exercising permissions granted by this License.
|
||||
|
||||
"Source" form shall mean the preferred form for making modifications, including but not limited to software source code, documentation source, and configuration files.
|
||||
|
||||
"Object" form shall mean any form resulting from mechanical transformation or translation of a Source form, including but not limited to compiled object code, generated documentation, and conversions to other media types.
|
||||
|
||||
"Work" shall mean the work of authorship, whether in Source or Object form, made available under the License, as indicated by a copyright notice that is included in or attached to the work (an example is provided in the Appendix below).
|
||||
|
||||
"Derivative Works" shall mean any work, whether in Source or Object form, that is based on (or derived from) the Work and for which the editorial revisions, annotations, elaborations, or other modifications represent, as a whole, an original work of authorship. For the purposes of this License, Derivative Works shall not include works that remain separable from, or merely link (or bind by name) to the interfaces of, the Work and Derivative Works thereof.
|
||||
|
||||
"Contribution" shall mean any work of authorship, including the original version of the Work and any modifications or additions to that Work or Derivative Works thereof, that is intentionally submitted to Licensor for inclusion in the Work by the copyright owner or by an individual or Legal Entity authorized to submit on behalf of the copyright owner. For the purposes of this definition, "submitted" means any form of electronic, verbal, or written communication sent to the Licensor or its representatives, including but not limited to communication on electronic mailing lists, source code control systems, and issue tracking systems that are managed by, or on behalf of, the Licensor for the purpose of discussing and improving the Work, but excluding communication that is conspicuously marked or otherwise designated in writing by the copyright owner as "Not a Contribution."
|
||||
|
||||
"Contributor" shall mean Licensor and any individual or Legal Entity on behalf of whom a Contribution has been received by Licensor and subsequently incorporated within the Work.
|
||||
|
||||
2. Grant of Copyright License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable copyright license to reproduce, prepare Derivative Works of, publicly display, publicly perform, sublicense, and distribute the Work and such Derivative Works in Source or Object form.
|
||||
|
||||
3. Grant of Patent License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable (except as stated in this section) patent license to make, have made, use, offer to sell, sell, import, and otherwise transfer the Work, where such license applies only to those patent claims licensable by such Contributor that are necessarily infringed by their Contribution(s) alone or by combination of their Contribution(s) with the Work to which such Contribution(s) was submitted. If You institute patent litigation against any entity (including a cross-claim or counterclaim in a lawsuit) alleging that the Work or a Contribution incorporated within the Work constitutes direct or contributory patent infringement, then any patent licenses granted to You under this License for that Work shall terminate as of the date such litigation is filed.
|
||||
|
||||
4. Redistribution. You may reproduce and distribute copies of the Work or Derivative Works thereof in any medium, with or without modifications, and in Source or Object form, provided that You meet the following conditions:
|
||||
|
||||
You must give any other recipients of the Work or Derivative Works a copy of this License; and
|
||||
|
||||
You must cause any modified files to carry prominent notices stating that You changed the files; and
|
||||
|
||||
You must retain, in the Source form of any Derivative Works that You distribute, all copyright, patent, trademark, and attribution notices from the Source form of the Work, excluding those notices that do not pertain to any part of the Derivative Works; and
|
||||
|
||||
If the Work includes a "NOTICE" text file as part of its distribution, then any Derivative Works that You distribute must include a readable copy of the attribution notices contained within such NOTICE file, excluding those notices that do not pertain to any part of the Derivative Works, in at least one of the following places: within a NOTICE text file distributed as part of the Derivative Works; within the Source form or documentation, if provided along with the Derivative Works; or, within a display generated by the Derivative Works, if and wherever such third-party notices normally appear. The contents of the NOTICE file are for informational purposes only and do not modify the License. You may add Your own attribution notices within Derivative Works that You distribute, alongside or as an addendum to the NOTICE text from the Work, provided that such additional attribution notices cannot be construed as modifying the License. You may add Your own copyright statement to Your modifications and may provide additional or different license terms and conditions for use, reproduction, or distribution of Your modifications, or for any such Derivative Works as a whole, provided Your use, reproduction, and distribution of the Work otherwise complies with the conditions stated in this License.
|
||||
|
||||
5. Submission of Contributions. Unless You explicitly state otherwise, any Contribution intentionally submitted for inclusion in the Work by You to the Licensor shall be under the terms and conditions of this License, without any additional terms or conditions. Notwithstanding the above, nothing herein shall supersede or modify the terms of any separate license agreement you may have executed with Licensor regarding such Contributions.
|
||||
|
||||
6. Trademarks. This License does not grant permission to use the trade names, trademarks, service marks, or product names of the Licensor, except as required for reasonable and customary use in describing the origin of the Work and reproducing the content of the NOTICE file.
|
||||
|
||||
7. Disclaimer of Warranty. Unless required by applicable law or agreed to in writing, Licensor provides the Work (and each Contributor provides its Contributions) on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied, including, without limitation, any warranties or conditions of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A PARTICULAR PURPOSE. You are solely responsible for determining the appropriateness of using or redistributing the Work and assume any risks associated with Your exercise of permissions under this License.
|
||||
|
||||
8. Limitation of Liability. In no event and under no legal theory, whether in tort (including negligence), contract, or otherwise, unless required by applicable law (such as deliberate and grossly negligent acts) or agreed to in writing, shall any Contributor be liable to You for damages, including any direct, indirect, special, incidental, or consequential damages of any character arising as a result of this License or out of the use or inability to use the Work (including but not limited to damages for loss of goodwill, work stoppage, computer failure or malfunction, or any and all other commercial damages or losses), even if such Contributor has been advised of the possibility of such damages.
|
||||
|
||||
9. Accepting Warranty or Additional Liability. While redistributing the Work or Derivative Works thereof, You may choose to offer, and charge a fee for, acceptance of support, warranty, indemnity, or other liability obligations and/or rights consistent with this License. However, in accepting such obligations, You may act only on Your own behalf and on Your sole responsibility, not on behalf of any other Contributor, and only if You agree to indemnify, defend, and hold each Contributor harmless for any liability incurred by, or claims asserted against, such Contributor by reason of your accepting any such warranty or additional liability.
|
||||
BIN
fonts/OpenSans-Bold-webfont.eot
Executable file
BIN
fonts/OpenSans-Bold-webfont.eot
Executable file
Binary file not shown.
146
fonts/OpenSans-Bold-webfont.svg
Executable file
146
fonts/OpenSans-Bold-webfont.svg
Executable file
@@ -0,0 +1,146 @@
|
||||
<?xml version="1.0" standalone="no"?>
|
||||
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd" >
|
||||
<svg xmlns="http://www.w3.org/2000/svg">
|
||||
<metadata>
|
||||
This is a custom SVG webfont generated by Font Squirrel.
|
||||
Copyright : Digitized data copyright 20102011 Google Corporation
|
||||
Foundry : Ascender Corporation
|
||||
Foundry URL : httpwwwascendercorpcom
|
||||
</metadata>
|
||||
<defs>
|
||||
<font id="OpenSansBold" horiz-adv-x="1169" >
|
||||
<font-face units-per-em="2048" ascent="1638" descent="-410" />
|
||||
<missing-glyph horiz-adv-x="532" />
|
||||
<glyph unicode=" " horiz-adv-x="532" />
|
||||
<glyph unicode="	" horiz-adv-x="532" />
|
||||
<glyph unicode=" " horiz-adv-x="532" />
|
||||
<glyph unicode="!" horiz-adv-x="586" d="M117 143q0 84 45 127t131 43q83 0 128.5 -44t45.5 -126q0 -79 -46 -124.5t-128 -45.5q-84 0 -130 44.5t-46 125.5zM121 1462h346l-51 -977h-244z" />
|
||||
<glyph unicode=""" horiz-adv-x="967" d="M133 1462h279l-41 -528h-197zM555 1462h279l-41 -528h-197z" />
|
||||
<glyph unicode="#" horiz-adv-x="1323" d="M45 406v206h277l47 232h-252v209h289l77 407h219l-77 -407h198l78 407h215l-78 -407h240v-209h-279l-47 -232h258v-206h-297l-77 -406h-220l78 406h-194l-76 -406h-215l74 406h-238zM539 612h196l47 232h-196z" />
|
||||
<glyph unicode="$" d="M88 1049q0 145 113.5 238.5t316.5 113.5v153h137v-149q229 -10 414 -92l-94 -234q-156 64 -320 78v-295q195 -75 277.5 -130t121 -121t38.5 -154q0 -159 -115 -255.5t-322 -115.5v-205h-137v201q-244 5 -428 86v264q87 -43 209.5 -76t218.5 -39v310l-67 26 q-198 78 -280.5 169.5t-82.5 226.5zM389 1049q0 -44 30.5 -72.5t98.5 -58.5v235q-129 -19 -129 -104zM655 324q136 23 136 118q0 42 -34 71t-102 60v-249z" />
|
||||
<glyph unicode="%" horiz-adv-x="1845" d="M63 1026q0 457 345 457q169 0 259.5 -118.5t90.5 -338.5q0 -230 -89 -345.5t-261 -115.5q-165 0 -255 118.5t-90 342.5zM315 1024q0 -127 22.5 -189.5t72.5 -62.5q96 0 96 252q0 250 -96 250q-50 0 -72.5 -61.5t-22.5 -188.5zM395 0l811 1462h240l-811 -1462h-240z M1087 442q0 457 345 457q169 0 259.5 -118.5t90.5 -338.5q0 -229 -89 -344.5t-261 -115.5q-165 0 -255 118.5t-90 341.5zM1339 440q0 -127 22.5 -189.5t72.5 -62.5q96 0 96 252q0 250 -96 250q-50 0 -72.5 -61.5t-22.5 -188.5z" />
|
||||
<glyph unicode="&" horiz-adv-x="1536" d="M82 395q0 137 60.5 233.5t207.5 180.5q-75 86 -109 164.5t-34 171.5q0 152 116.5 245t311.5 93q186 0 297.5 -86.5t111.5 -231.5q0 -119 -69 -217.5t-223 -187.5l284 -277q71 117 123 301h318q-36 -135 -99 -263.5t-143 -227.5l301 -293h-377l-115 113 q-191 -133 -432 -133q-244 0 -387 112t-143 303zM403 424q0 -86 64.5 -137t165.5 -51q126 0 227 61l-332 330q-58 -44 -91.5 -92t-33.5 -111zM489 1124q0 -88 95 -194q86 48 132 94.5t46 108.5q0 53 -36 83.5t-93 30.5q-67 0 -105.5 -32t-38.5 -91z" />
|
||||
<glyph unicode="'" horiz-adv-x="545" d="M133 1462h279l-41 -528h-197z" />
|
||||
<glyph unicode="(" horiz-adv-x="694" d="M82 561q0 265 77.5 496t223.5 405h250q-141 -193 -213 -424t-72 -475q0 -245 73.5 -473.5t209.5 -413.5h-248q-147 170 -224 397t-77 488z" />
|
||||
<glyph unicode=")" horiz-adv-x="694" d="M61 1462h250q147 -175 224 -406.5t77 -494.5t-77.5 -490t-223.5 -395h-248q135 184 209 412.5t74 474.5q0 244 -72 475t-213 424z" />
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67
js/cktsim.js
67
js/cktsim.js
@@ -44,6 +44,7 @@ cktsim = (function() {
|
||||
|
||||
this.devices = []; // list of devices
|
||||
this.device_map = new Array(); // map name -> device
|
||||
this.voltage_sources = []; // list of voltage sources
|
||||
|
||||
this.finalized = false;
|
||||
this.diddc = false;
|
||||
@@ -104,10 +105,14 @@ cktsim = (function() {
|
||||
var type = component[0];
|
||||
|
||||
// ignore wires, ground connections, scope probes and view info
|
||||
if (type == 'view' || type == 'w' || type == 'g' || type == 's' || type == 'L') continue;
|
||||
if (type == 'view' || type == 'w' || type == 'g' || type == 's' || type == 'L') {
|
||||
continue;
|
||||
}
|
||||
|
||||
var properties = component[2];
|
||||
var name = properties['name'];
|
||||
if (name==undefined || name=='')
|
||||
name = '_' + properties['_json_'].toString();
|
||||
|
||||
// convert node names to circuit indicies
|
||||
var connections = component[3];
|
||||
@@ -134,11 +139,9 @@ cktsim = (function() {
|
||||
else if (type == 'o') // op amp
|
||||
this.opamp(connections[0],connections[1],connections[2],properties['A'],name);
|
||||
else if (type == 'n') // n fet
|
||||
this.n(connections[0],connections[1],connections[2],
|
||||
properties['W/L'],name);
|
||||
this.n(connections[0],connections[1],connections[2],properties['W/L'],name);
|
||||
else if (type == 'p') // p fet
|
||||
this.p(connections[0],connections[1],connections[2],
|
||||
properties['W/L'],name);
|
||||
this.p(connections[0],connections[1],connections[2],properties['W/L'],name);
|
||||
}
|
||||
}
|
||||
|
||||
@@ -214,10 +217,16 @@ cktsim = (function() {
|
||||
this.diddc = true;
|
||||
// create solution dictionary
|
||||
var result = new Array();
|
||||
// capture node voltages
|
||||
for (var name in this.node_map) {
|
||||
var index = this.node_map[name];
|
||||
result[name] = (index == -1) ? 0 : this.solution[index];
|
||||
}
|
||||
// capture branch currents from voltage sources
|
||||
for (var i = this.voltage_sources.length - 1; i >= 0; --i) {
|
||||
var v = this.voltage_sources[i];
|
||||
result['I('+v.name+')'] = this.solution[v.branch];
|
||||
}
|
||||
return result;
|
||||
}
|
||||
}
|
||||
@@ -457,6 +466,12 @@ cktsim = (function() {
|
||||
var index = this.node_map[name];
|
||||
result[name] = (index == -1) ? 0 : response[index];
|
||||
}
|
||||
// capture branch currents from voltage sources
|
||||
for (var i = this.voltage_sources.length - 1; i >= 0; --i) {
|
||||
var v = this.voltage_sources[i];
|
||||
result['I('+v.name+')'] = response[v.branch];
|
||||
}
|
||||
|
||||
result['time'] = response[this.N];
|
||||
return result;
|
||||
}
|
||||
@@ -537,6 +552,7 @@ cktsim = (function() {
|
||||
Circuit.prototype.add_device = function(d,name) {
|
||||
// Add device to list of devices and to device map
|
||||
this.devices.push(d);
|
||||
d.name = name;
|
||||
if (name) {
|
||||
if (this.device_map[name] === undefined)
|
||||
this.device_map[name] = d;
|
||||
@@ -599,6 +615,7 @@ cktsim = (function() {
|
||||
Circuit.prototype.v = function(n1,n2,v,name) {
|
||||
var branch = this.node(undefined,T_CURRENT);
|
||||
var d = new VSource(n1,n2,branch,v);
|
||||
this.voltage_sources.push(d);
|
||||
return this.add_device(d, name);
|
||||
}
|
||||
|
||||
@@ -1029,9 +1046,11 @@ cktsim = (function() {
|
||||
///////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
// argument is a string describing the source's value (see comments for details)
|
||||
// source types: dc,step,square,triangle,sin,pulse,pwl,pwlr
|
||||
// source types: dc,step,square,triangle,sin,pulse,pwl,pwl_repeating
|
||||
|
||||
// returns an object with the following attributes:
|
||||
// fun -- name of source function
|
||||
// args -- list of argument values
|
||||
// value(t) -- compute source value at time t
|
||||
// inflection_point(t) -- compute time after t when a time point is needed
|
||||
// dc -- value at time 0
|
||||
@@ -1071,32 +1090,35 @@ cktsim = (function() {
|
||||
// post-processing for constant sources
|
||||
// dc(v)
|
||||
if (src.fun == 'dc') {
|
||||
var value = src.args[0];
|
||||
if (value === undefined) value = 0;
|
||||
src.value = function(t) { return value; } // closure
|
||||
var v = arg_value(src.args,0,0);
|
||||
src.args = [v];
|
||||
src.value = function(t) { return v; } // closure
|
||||
}
|
||||
|
||||
// post-processing for step sources
|
||||
// step(v_init,v_plateau,t_delay,t_rise,t_fall)
|
||||
// step(v_init,v_plateau,t_delay,t_rise)
|
||||
else if (src.fun == 'step') {
|
||||
var v1 = arg_value(src.args,0,0); // default init value: 0V
|
||||
var v2 = arg_value(src.args,1,1); // default plateau value: 1V
|
||||
var td = Math.max(0,arg_value(src.args,2,0)); // time step starts
|
||||
var tr = Math.abs(arg_value(src.args,3,1e-9)); // default rise time: 1ns
|
||||
src.args = [v1,v2,td,tr]; // remember any defaulted values
|
||||
pwl_source(src,[td,v1,td+tr,v2],false);
|
||||
}
|
||||
|
||||
// post-processing for square wave
|
||||
// square(v_init,v_plateau,t_period)
|
||||
// square(v_init,v_plateau,freq)
|
||||
else if (src.fun == 'square') {
|
||||
var v1 = arg_value(src.args,0,0); // default init value: 0V
|
||||
var v2 = arg_value(src.args,1,1); // default plateau value: 1V
|
||||
var freq = Math.abs(arg_value(src.args,2,1)); // default frequency: 1s
|
||||
var freq = Math.abs(arg_value(src.args,2,1)); // default frequency: 1Hz
|
||||
src.args = [v1,v2,freq]; // remember any defaulted values
|
||||
|
||||
var per = freq == 0 ? Infinity : 1/freq;
|
||||
var t_change = 0.01 * per; // rise and fall time
|
||||
var t_pw = 0.49 * per; // half the cycle minus rise and fall time
|
||||
pwl_source(src,[0,v1,t_change,v2,t_change+t_pw,v2,t_change+t_pw+t_change,v1,per,v1],true);
|
||||
pwl_source(src,[0,v1,t_change,v2,t_change+t_pw,
|
||||
v2,t_change+t_pw+t_change,v1,per,v1],true);
|
||||
}
|
||||
|
||||
// post-processing for triangle
|
||||
@@ -1105,6 +1127,7 @@ cktsim = (function() {
|
||||
var v1 = arg_value(src.args,0,0); // default init value: 0V
|
||||
var v2 = arg_value(src.args,1,1); // default plateau value: 1V
|
||||
var freq = Math.abs(arg_value(src.args,2,1)); // default frequency: 1s
|
||||
src.args = [v1,v2,freq]; // remember any defaulted values
|
||||
|
||||
var per = freq == 0 ? Infinity : 1/freq;
|
||||
pwl_source(src,[0,v1,per/2,v2,per,v1],true);
|
||||
@@ -1112,8 +1135,8 @@ cktsim = (function() {
|
||||
|
||||
// post-processing for pwl and pwlr sources
|
||||
// pwl[r](t1,v1,t2,v2,...)
|
||||
else if (src.fun == 'pwl' || src.fun == 'pwlr') {
|
||||
pwl_source(src,src.args,src.fun == 'pwlr');
|
||||
else if (src.fun == 'pwl' || src.fun == 'pwl_repeating') {
|
||||
pwl_source(src,src.args,src.fun == 'pwl_repeating');
|
||||
}
|
||||
|
||||
// post-processing for pulsed sources
|
||||
@@ -1122,18 +1145,18 @@ cktsim = (function() {
|
||||
var v1 = arg_value(src.args,0,0); // default init value: 0V
|
||||
var v2 = arg_value(src.args,1,1); // default plateau value: 1V
|
||||
var td = Math.max(0,arg_value(src.args,2,0)); // time pulse starts
|
||||
|
||||
var tr = Math.abs(arg_value(src.args,3,1e-9)); // default rise time: 1ns
|
||||
var tf = Math.abs(arg_value(src.args,4,1e-9)); // default rise time: 1ns
|
||||
var pw = Math.abs(arg_value(src.args,5,1e9)); // default pulse width: "infinite"
|
||||
var per = Math.abs(arg_value(src.args,6,1e9)); // default period: "infinite"
|
||||
src.args = [v1,v2,td,tr,tf,pw,per];
|
||||
|
||||
var t1 = td; // time when v1 -> v2 transition starts
|
||||
var t2 = t1 + tr; // time when v1 -> v2 transition ends
|
||||
var t3 = t2 + pw; // time when v2 -> v1 transition starts
|
||||
var t4 = t3 + tf; // time when v2 -> v1 transition ends
|
||||
|
||||
pwl_source(src,[t1,v1,t2,v2,t3,v2,t4,v1,per,v1],true);
|
||||
pwl_source(src,[t1,v1, t2,v2, t3,v2, t4,v1, per,v1],true);
|
||||
}
|
||||
|
||||
// post-processing for sinusoidal sources
|
||||
@@ -1144,16 +1167,14 @@ cktsim = (function() {
|
||||
var freq = Math.abs(arg_value(src.args,2,1)); // default frequency: 1Hz
|
||||
var td = Math.max(0,arg_value(src.args,3,0)); // default time delay: 0sec
|
||||
var phase = arg_value(src.args,4,0); // default phase offset: 0 degrees
|
||||
src.args = [voffset,va,freq,td,phase];
|
||||
|
||||
phase /= 360.0;
|
||||
|
||||
// return value of source at time t
|
||||
src.value = function(t) { // closure
|
||||
if (t < td) return voffset + va*Math.sin(2*Math.PI*phase);
|
||||
else {
|
||||
var val = voffset + va*Math.sin(2*Math.PI*(freq*(t - td) + phase));
|
||||
return val;
|
||||
}
|
||||
else return voffset + va*Math.sin(2*Math.PI*(freq*(t - td) + phase));
|
||||
}
|
||||
|
||||
// return time of next inflection point after time t
|
||||
@@ -1163,9 +1184,6 @@ cktsim = (function() {
|
||||
}
|
||||
}
|
||||
|
||||
// to do:
|
||||
// post-processing for piece-wise linear sources
|
||||
|
||||
// object has all the necessary info to compute the source value and inflection points
|
||||
src.dc = src.value(0); // DC value is value at time 0
|
||||
return src;
|
||||
@@ -1531,6 +1549,7 @@ cktsim = (function() {
|
||||
var module = {
|
||||
'Circuit': Circuit,
|
||||
'parse_number': parse_number,
|
||||
'parse_source': parse_source,
|
||||
}
|
||||
return module;
|
||||
}());
|
||||
|
||||
309
js/schematic.js
309
js/schematic.js
@@ -594,8 +594,9 @@ schematic = (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());
|
||||
var n = this.components.length;
|
||||
for (var i = 0; i < n; i++)
|
||||
json.push(this.components[i].json(i));
|
||||
|
||||
// capture the current view parameters
|
||||
json.push(['view',this.origin_x,this.origin_y,this.scale,
|
||||
@@ -932,6 +933,10 @@ schematic = (function() {
|
||||
// for each electrical node
|
||||
for (var location in this.connection_points)
|
||||
(this.connection_points[location])[0].display_voltage(c,temp);
|
||||
|
||||
// let components display branch current info if available
|
||||
for (var i = this.components.length - 1; i >= 0; --i)
|
||||
this.components[i].display_current(c,temp)
|
||||
}
|
||||
}
|
||||
|
||||
@@ -980,9 +985,6 @@ schematic = (function() {
|
||||
c.fillText(text,(x - this.origin_x) * this.scale,(y - this.origin_y) * this.scale);
|
||||
}
|
||||
|
||||
HTMLCanvasElement.prototype.totalOffset = function(){
|
||||
}
|
||||
|
||||
// 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
|
||||
@@ -1678,8 +1680,9 @@ schematic = (function() {
|
||||
return [vmin,vmax,1.0/scale];
|
||||
}
|
||||
|
||||
function engineering_notation(n,nplaces) {
|
||||
function engineering_notation(n,nplaces,trim) {
|
||||
if (n == 0) return("0");
|
||||
if (trim == undefined) trim = true;
|
||||
|
||||
var sign = n < 0 ? -1 : 1;
|
||||
var log10 = Math.log(sign*n)/Math.LN10;
|
||||
@@ -1694,8 +1697,10 @@ schematic = (function() {
|
||||
if (nplaces > 0) {
|
||||
endindex += nplaces + 1;
|
||||
if (endindex > mlen) endindex = mlen;
|
||||
while (mstring.charAt(endindex-1) == '0') endindex -= 1;
|
||||
if (mstring.charAt(endindex-1) == '.') endindex -= 1;
|
||||
if (trim) {
|
||||
while (mstring.charAt(endindex-1) == '0') endindex -= 1;
|
||||
if (mstring.charAt(endindex-1) == '.') endindex -= 1;
|
||||
}
|
||||
}
|
||||
if (endindex < mlen)
|
||||
mstring = mstring.substring(0,endindex);
|
||||
@@ -1717,6 +1722,9 @@ schematic = (function() {
|
||||
return n.toString();
|
||||
}
|
||||
|
||||
var grid_pattern = [1,2];
|
||||
var cursor_pattern = [5,5];
|
||||
|
||||
// x_values is an array of x coordinates for each of the plots
|
||||
// y_values is an array of [color, value_array], one entry for each plot
|
||||
Schematic.prototype.graph = function(x_values,y_values,x_legend,y_legend) {
|
||||
@@ -1727,7 +1735,6 @@ schematic = (function() {
|
||||
var right_margin = 25;
|
||||
var bottom_margin = 45;
|
||||
var tick_length = 5;
|
||||
var pattern = [1,2];
|
||||
|
||||
var w = pwidth + left_margin + right_margin;
|
||||
var h = pheight + top_margin + bottom_margin;
|
||||
@@ -1735,7 +1742,7 @@ schematic = (function() {
|
||||
var canvas = document.createElement('canvas');
|
||||
canvas.width = w;
|
||||
canvas.height = h;
|
||||
|
||||
|
||||
// the graph itself will be drawn here and this image will be copied
|
||||
// onto canvas, where it can be overlayed with mouse cursors, etc.
|
||||
var bg_image = document.createElement('canvas');
|
||||
@@ -1779,7 +1786,7 @@ schematic = (function() {
|
||||
c.moveTo(temp,top_margin);
|
||||
c.lineTo(temp,end);
|
||||
} else
|
||||
c.dashedLineTo(temp,top_margin,temp,end,pattern);
|
||||
c.dashedLineTo(temp,top_margin,temp,end,grid_pattern);
|
||||
c.stroke();
|
||||
|
||||
// tick mark
|
||||
@@ -1821,7 +1828,7 @@ schematic = (function() {
|
||||
c.moveTo(left_margin,temp);
|
||||
c.lineTo(left_margin + pwidth,temp);
|
||||
} else
|
||||
c.dashedLineTo(left_margin,temp,left_margin + pwidth,temp,pattern);
|
||||
c.dashedLineTo(left_margin,temp,left_margin + pwidth,temp,grid_pattern);
|
||||
c.stroke();
|
||||
|
||||
// tick mark
|
||||
@@ -1864,6 +1871,27 @@ schematic = (function() {
|
||||
c.fillText(y_legend,0,0);
|
||||
c.restore();
|
||||
|
||||
// save info need for interactions with the graph
|
||||
canvas.x_values = x_values;
|
||||
canvas.y_values = y_values;
|
||||
canvas.x_legend = x_legend;
|
||||
canvas.y_legend = y_legend;
|
||||
canvas.x_min = x_min;
|
||||
canvas.x_scale = x_scale;
|
||||
canvas.y_min = y_min;
|
||||
canvas.y_scale = y_scale;
|
||||
canvas.left_margin = left_margin;
|
||||
canvas.top_margin = top_margin;
|
||||
canvas.pwidth = pwidth;
|
||||
canvas.pheight = pheight;
|
||||
canvas.tick_length = tick_length;
|
||||
|
||||
canvas.cursor_x = undefined;
|
||||
canvas.sch = this;
|
||||
|
||||
// do something useful when user mouses over graph
|
||||
canvas.addEventListener('mousemove',graph_mouse_move,false);
|
||||
|
||||
// return our masterpiece
|
||||
redraw_plot(canvas);
|
||||
return canvas;
|
||||
@@ -1883,9 +1911,73 @@ schematic = (function() {
|
||||
return min;
|
||||
}
|
||||
|
||||
function redraw_plot(canvas) {
|
||||
var c = canvas.getContext('2d');
|
||||
c.drawImage(canvas.bg_image,0,0);
|
||||
function redraw_plot(graph) {
|
||||
var c = graph.getContext('2d');
|
||||
c.drawImage(graph.bg_image,0,0);
|
||||
|
||||
if (graph.cursor_x != undefined) {
|
||||
// draw dashed vertical marker that follows mouse
|
||||
var x = graph.left_margin + graph.cursor_x;
|
||||
var end_y = graph.top_margin + graph.pheight + graph.tick_length;
|
||||
c.strokeStyle = grid_style;
|
||||
c.lineWidth = 1;
|
||||
c.beginPath();
|
||||
c.dashedLineTo(x,graph.top_margin,x,end_y,cursor_pattern);
|
||||
c.stroke();
|
||||
|
||||
// add x label at bottom of marker
|
||||
var graph_x = graph.cursor_x/graph.x_scale + graph.x_min;
|
||||
c.font = '10pt sans-serif';
|
||||
c.textAlign = 'center';
|
||||
c.textBaseline = 'top';
|
||||
c.fillStyle = background_style;
|
||||
c.fillText('\u2588\u2588\u2588\u2588\u2588',x,end_y);
|
||||
c.fillStyle = normal_style;
|
||||
c.fillText(engineering_notation(graph_x,3,false),x,end_y);
|
||||
|
||||
// compute which points marker is between
|
||||
var x_values = graph.x_values;
|
||||
var len = x_values.length;
|
||||
var index = 0;
|
||||
while (index < len && graph_x >= x_values[index]) index += 1;
|
||||
var x1 = (index == 0) ? x_values[0] : x_values[index-1];
|
||||
var x2 = x_values[index];
|
||||
|
||||
// for each plot, interpolate and output value at intersection with marker
|
||||
c.textAlign = 'left';
|
||||
var tx = graph.left_margin + 4;
|
||||
var ty = graph.top_margin;
|
||||
for (var plot = 0; plot < graph.y_values.length; plot++) {
|
||||
var values = graph.y_values[plot][1];
|
||||
|
||||
// interpolate signal value at graph_x using values[index-1] and values[index]
|
||||
var y1 = (index == 0) ? values[0] : values[index-1];
|
||||
var y2 = values[index];
|
||||
var y = y1;
|
||||
if (graph_x != x1) y += (graph_x - x1)*(y2 - y1)/(x2 - x1);
|
||||
|
||||
// annotate plot with value of signal at marker
|
||||
c.fillStyle = element_style;
|
||||
c.fillText('\u2588\u2588\u2588\u2588\u2588',tx-3,ty);
|
||||
c.fillStyle = probe_colors_rgb[graph.y_values[plot][0]];
|
||||
c.fillText(engineering_notation(y,3,false),tx,ty);
|
||||
ty += 14;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
function graph_mouse_move(event) {
|
||||
if (!event) event = window.event;
|
||||
var g = (window.event) ? event.srcElement : event.target;
|
||||
|
||||
g.relMouseCoords(event);
|
||||
// not sure yet where the 3,-3 offset correction comes from (borders? padding?)
|
||||
var gx = g.mouse_x - g.left_margin - 3;
|
||||
var gy = g.pheight - (g.mouse_y - g.top_margin) + 3;
|
||||
if (gx >= 0 && gx <= g.pwidth && gy >=0 && gy <= g.pheight) g.cursor_x = gx;
|
||||
else g.cursor_x = undefined;
|
||||
|
||||
redraw_plot(g);
|
||||
}
|
||||
|
||||
///////////////////////////////////////////////////////////////////////////////
|
||||
@@ -2112,7 +2204,9 @@ schematic = (function() {
|
||||
this.connections = [];
|
||||
}
|
||||
|
||||
Component.prototype.json = function() {
|
||||
Component.prototype.json = function(index) {
|
||||
this.properties['_json_'] = index; // remember where we are in the JSON list
|
||||
|
||||
var props = {};
|
||||
for (var p in this.properties) props[p] = this.properties[p];
|
||||
|
||||
@@ -2343,7 +2437,9 @@ schematic = (function() {
|
||||
// make an <input> widget for each property
|
||||
var fields = new Array();
|
||||
for (var i in this.properties)
|
||||
fields[i] = build_input('text',10,this.properties[i]);
|
||||
// underscore at beginning of property name => system property
|
||||
if (i.charAt(0) != '_')
|
||||
fields[i] = build_input('text',10,this.properties[i]);
|
||||
|
||||
var content = build_table(fields);
|
||||
content.fields = fields;
|
||||
@@ -2383,6 +2479,10 @@ schematic = (function() {
|
||||
}
|
||||
}
|
||||
|
||||
// default behavior: nothing to display for DC analysis
|
||||
Component.prototype.display_current = function(c,vmap) {
|
||||
}
|
||||
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
// Connection point
|
||||
@@ -2507,7 +2607,7 @@ schematic = (function() {
|
||||
return '<Wire ('+this.x+','+this.y+') ('+(this.x+this.dx)+','+(this.y+this.dy)+')>';
|
||||
}
|
||||
|
||||
Wire.prototype.json = function() {
|
||||
Wire.prototype.json = function(index) {
|
||||
var json = ['w',[this.x, this.y, this.x+this.dx, this.y+this.dy]];
|
||||
return json;
|
||||
}
|
||||
@@ -3024,14 +3124,18 @@ schematic = (function() {
|
||||
//
|
||||
////////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
|
||||
function Source(x,y,rotation,name,type,value) {
|
||||
Component.call(this,type,x,y,rotation);
|
||||
this.properties['name'] = name;
|
||||
this.properties['value'] = value ? value : '1';
|
||||
if (value == undefined) value = 'dc(1)';
|
||||
this.properties['value'] = value;
|
||||
this.add_connection(0,0);
|
||||
this.add_connection(0,48);
|
||||
this.bounding_box = [-12,0,12,48];
|
||||
this.update_coords();
|
||||
|
||||
this.content = document.createElement('div'); // used by edit_properties
|
||||
}
|
||||
Source.prototype = new Component();
|
||||
Source.prototype.constructor = Source;
|
||||
@@ -3068,10 +3172,141 @@ schematic = (function() {
|
||||
this.draw_text(c,this.properties['value'],13,24,3,property_size);
|
||||
}
|
||||
|
||||
Source.prototype.clone = function(x,y) {
|
||||
return new Source(x,y,this.rotation,this.properties['name'],this.type,this.properties['value']);
|
||||
// map source function name to labels for each source parameter
|
||||
source_functions = {
|
||||
'dc': ['DC value'],
|
||||
|
||||
'step': ['Initial value',
|
||||
'Plateau value',
|
||||
'Delay until step (secs)',
|
||||
'Rise time (secs)'],
|
||||
|
||||
'square': ['Initial value',
|
||||
'Plateau value',
|
||||
'Frequency (Hz)'],
|
||||
|
||||
'triangle': ['Initial value',
|
||||
'Plateau value',
|
||||
'Frequency (Hz)'],
|
||||
|
||||
'pwl': ['Comma-separated list of alternating times and values'],
|
||||
|
||||
'pwl_repeating': ['Comma-separated list of alternating times and values'],
|
||||
|
||||
'pulse': ['Initial value',
|
||||
'Plateau value',
|
||||
'Delay until pulse (secs)',
|
||||
'Time for first transition (secs)',
|
||||
'Time for second transition (secs)',
|
||||
'Pulse width (secs)',
|
||||
'Period (secs)'],
|
||||
|
||||
'sin': ['Offset value',
|
||||
'Amplitude',
|
||||
'Frequency (Hz)',
|
||||
'Delay until sin starts (secs)',
|
||||
'Phase offset (degrees)'],
|
||||
}
|
||||
|
||||
// build property editor div
|
||||
Source.prototype.build_content = function(src) {
|
||||
// make an <input> widget for each property
|
||||
var fields = []
|
||||
fields['name'] = build_input('text',10,this.properties['name']);
|
||||
|
||||
if (src == undefined) {
|
||||
fields['value'] = this.properties['value'];
|
||||
} else {
|
||||
// fancy version: add select tag for source type
|
||||
var src_types = [];
|
||||
for (var t in source_functions) src_types.push(t);
|
||||
var type_select = build_select(src_types,src.fun);
|
||||
type_select.component = this;
|
||||
type_select.addEventListener('change',source_type_changed,false)
|
||||
fields['type'] = type_select;
|
||||
|
||||
if (src.fun == 'pwl' || src.run == 'pwl_repeating') {
|
||||
var v = '';
|
||||
var first = true;
|
||||
for (var i = 0; i < src.args.length; i++) {
|
||||
if (first) first = false;
|
||||
else v += ',';
|
||||
v += engineering_notation(src.args[i],3);
|
||||
if (i % 2 == 0) v += 's';
|
||||
}
|
||||
fields[source_functions[src.fun][0]] = build_input('text',30,v);
|
||||
} else {
|
||||
// followed separate input tag for each parameter
|
||||
var labels = source_functions[src.fun];
|
||||
for (var i = 0; i < labels.length; i++) {
|
||||
var v = engineering_notation(src.args[i],3);
|
||||
fields[labels[i]] = build_input('text',10,v);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
var div = this.content;
|
||||
if (div.hasChildNodes())
|
||||
div.removeChild(div.firstChild); // remove table of input fields
|
||||
div.appendChild(build_table(fields));
|
||||
div.fields = fields;
|
||||
div.component = this;
|
||||
return div;
|
||||
}
|
||||
|
||||
function source_type_changed(event) {
|
||||
if (!event) event = window.event;
|
||||
var select = (window.event) ? event.srcElement : event.target;
|
||||
|
||||
// see where to get source parameters from
|
||||
var type = select.options[select.selectedIndex].value;
|
||||
var src = undefined;
|
||||
if (this.src != undefined && type == this.src.fun)
|
||||
src = this.src;
|
||||
else if (typeof cktsim != 'undefined')
|
||||
src = cktsim.parse_source(type+'()');
|
||||
|
||||
select.component.build_content(src);
|
||||
}
|
||||
|
||||
Source.prototype.edit_properties = function(x,y) {
|
||||
if (this.near(x,y)) {
|
||||
this.src = undefined;
|
||||
if (typeof cktsim != 'undefined')
|
||||
this.src = cktsim.parse_source(this.properties['value']);
|
||||
var content = this.build_content(this.src);
|
||||
|
||||
this.sch.dialog('Edit Properties',content,function(content) {
|
||||
var c = content.component;
|
||||
var fields = content.fields;
|
||||
|
||||
var first = true;
|
||||
var value = '';
|
||||
for (var label in fields) {
|
||||
if (label == 'name')
|
||||
c.properties['name'] = fields['name'].value;
|
||||
else if (label == 'value') {
|
||||
// if unknown source type
|
||||
value = fields['value'].value;
|
||||
c.sch.redraw_background();
|
||||
return;
|
||||
} else if (label == 'type') {
|
||||
var select = fields['type'];
|
||||
value = select.options[select.selectedIndex].value + '(';
|
||||
} else {
|
||||
if (first) first = false;
|
||||
else value += ',';
|
||||
value += fields[label].value;
|
||||
}
|
||||
}
|
||||
c.properties['value'] = value + ')';
|
||||
c.sch.redraw_background();
|
||||
});
|
||||
return true;
|
||||
} else return false;
|
||||
}
|
||||
|
||||
|
||||
function VSource(x,y,rotation,name,value) {
|
||||
Source.call(this,x,y,rotation,name,'v',value);
|
||||
this.type = 'v';
|
||||
@@ -3081,6 +3316,32 @@ schematic = (function() {
|
||||
VSource.prototype.toString = Source.prototype.toString;
|
||||
VSource.prototype.draw = Source.prototype.draw;
|
||||
VSource.prototype.clone = Source.prototype.clone;
|
||||
VSource.prototype.build_content = Source.prototype.build_content;
|
||||
VSource.prototype.edit_properties = Source.prototype.edit_properties;
|
||||
|
||||
// display current for DC analysis
|
||||
VSource.prototype.display_current = function(c,vmap) {
|
||||
var name = this.properties['name'];
|
||||
var label = 'I(' + (name ? name : '_' + this.properties['_json_']) + ')';
|
||||
var v = vmap[label];
|
||||
if (v != undefined) {
|
||||
// first draw some solid blocks in the background
|
||||
c.globalAlpha = 0.85;
|
||||
this.draw_text(c,'\u2588\u2588\u2588',0,24,4,annotation_size,element_style);
|
||||
c.globalAlpha = 1.0;
|
||||
|
||||
// display the node voltage at this connection point
|
||||
var i = engineering_notation(v,2) + 'A';
|
||||
this.draw_text(c,i,0,24,4,annotation_size,annotation_style);
|
||||
|
||||
// only display each current once
|
||||
delete vmap[label];
|
||||
}
|
||||
}
|
||||
|
||||
VSource.prototype.clone = function(x,y) {
|
||||
return new VSource(x,y,this.rotation,this.properties['name'],this.properties['value']);
|
||||
}
|
||||
|
||||
function ISource(x,y,rotation,name,value) {
|
||||
Source.call(this,x,y,rotation,name,'i',value);
|
||||
@@ -3091,6 +3352,12 @@ schematic = (function() {
|
||||
ISource.prototype.toString = Source.prototype.toString;
|
||||
ISource.prototype.draw = Source.prototype.draw;
|
||||
ISource.prototype.clone = Source.prototype.clone;
|
||||
ISource.prototype.build_content = Source.prototype.build_content;
|
||||
ISource.prototype.edit_properties = Source.prototype.edit_properties;
|
||||
|
||||
ISource.prototype.clone = function(x,y) {
|
||||
return new ISource(x,y,this.rotation,this.properties['name'],this.properties['value']);
|
||||
}
|
||||
|
||||
///////////////////////////////////////////////////////////////////////////////
|
||||
//
|
||||
|
||||
BIN
labs/cjtlab.png
BIN
labs/cjtlab.png
Binary file not shown.
|
Before Width: | Height: | Size: 6.4 KiB |
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
||||
"text": []
|
||||
}
|
||||
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
||||
"text": []
|
||||
}
|
||||
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
||||
"text": []
|
||||
}
|
||||
@@ -1,515 +0,0 @@
|
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|
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|
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|
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
],
|
||||
"text": [
|
||||
"INSTRUCTOR: Based on the previous method or the",
|
||||
"previous property that you saw for linear circuits, we are",
|
||||
"now ready to define the superposition method for",
|
||||
"circuit analysis.",
|
||||
"Note that the superposition method",
|
||||
"applies to linear circuits.",
|
||||
"And again, to refresh your memory, remember, we are in",
|
||||
"the EECS playground that we got into by adhering to the",
|
||||
"lumped matter discipline.",
|
||||
"And within that, we looked at the node method and the KVL",
|
||||
"KCL method that applies all over the EECS playground.",
|
||||
"And then what we'll now do is look at some methods that will",
|
||||
"apply to only a region of this playground where linear",
|
||||
"circuits reside.",
|
||||
"So the first of these methods is the superposition method.",
|
||||
"And again, it applies to linear circuits.",
|
||||
"So the method is very simple and inspired by the",
|
||||
"superposition property that we studied for linear circuits.",
|
||||
"So the method simply says this.",
|
||||
"You first find the responses of the circuit to each source",
|
||||
"acting alone.",
|
||||
"Think of this as a divide and conquer method where you take",
|
||||
"your entire circuit, and you find the responses of the",
|
||||
"circuit to each source acting alone.",
|
||||
"You turn off all the sources, and you find the response to",
|
||||
"each source acting alone.",
|
||||
"Then what you do is simply sum those individual responses.",
|
||||
"Note that this technique applies to",
|
||||
"independent sources only.",
|
||||
"So if I have a linear circuit, then this technique applies to",
|
||||
"independent sources only.",
|
||||
"Now we will look at what happens when you have",
|
||||
"dependent sources and so on in later lectures.",
|
||||
"OK, let's move ahead.",
|
||||
"The first step was find the response of the circuit to",
|
||||
"each source acting alone.",
|
||||
"But what does it mean for each source to act alone?",
|
||||
"What it means is that you turn off all the other sources.",
|
||||
"So for example, suppose we are focused on a",
|
||||
"voltage source here.",
|
||||
"What does it mean to turn off this voltage source?",
|
||||
"In other words, if I want to set this voltage to 0, what",
|
||||
"does it mean in terms of my circuit?",
|
||||
"So in terms of my circuit, what this means is that I am",
|
||||
"going to short the source.",
|
||||
"So what you do is you short the source, and you end up",
|
||||
"with a short circuit here.",
|
||||
"And that is my voltage source having been set to 0.",
|
||||
"And so I take all my voltage sources in the circuit and",
|
||||
"simply short them out.",
|
||||
"And this would be making each of the sources to act alone.",
|
||||
"OK, next let's look at a current source and see what it",
|
||||
"means to set a current source to 0.",
|
||||
"So in this case, what you do is much as you set a voltage",
|
||||
"source to 0 by shorting it out, you set the current",
|
||||
"source to 0 by open-circuiting it like so.",
|
||||
"So you create an open circuit in place of the current",
|
||||
"source, and that's what it means to set a",
|
||||
"current source to zero.",
|
||||
"OK, so now we are ready to go try out an example using the",
|
||||
"method of superposition.",
|
||||
"And again, remember the method of superposition has",
|
||||
"two parts to it.",
|
||||
"In the first part, you find the responses of the circuit",
|
||||
"to each source acting alone.",
|
||||
"And then second, you sum up the partial responses.",
|
||||
"So let's go back to our old faithful example.",
|
||||
"In this example, we have two sources, a voltage source and",
|
||||
"a current source.",
|
||||
"And let's say our goal is to find the node voltage e taken",
|
||||
"with respect to this ground.",
|
||||
"And we are going to use the superposition",
|
||||
"method to do the circuit.",
|
||||
"So I showed the circuit on the right-hand corner here.",
|
||||
"And notice that e is the node voltage that I",
|
||||
"need to figure out.",
|
||||
"So by the superposition method, I have two steps.",
|
||||
"My first step is find the responses of the circuit to",
|
||||
"each source acting alone.",
|
||||
"So what I'm going to do is let me start with finding the",
|
||||
"response of the circuit to the voltage source acting alone.",
|
||||
"So what do I do to get a subcircuit in which the",
|
||||
"voltage source is acting alone?",
|
||||
"So I want you to think about this and try to figure out",
|
||||
"what the resulting subcircuit is going to look like.",
|
||||
"I'll give you a few seconds to do that before I do it myself.",
|
||||
"All right.",
|
||||
"This is the subcircuit.",
|
||||
"And what I've done here is I've had to turn the current",
|
||||
"source off.",
|
||||
"So notice that out here I create an open circuit, and",
|
||||
"that is the result of my current source",
|
||||
"being turned off.",
|
||||
"And this is my usual ground node.",
|
||||
"And let me call this node voltage with the voltage",
|
||||
"source acting alone as ev. So ev is the partial response of",
|
||||
"the circuit to the voltage source acting alone.",
|
||||
"Now how do we go about solving for ev?",
|
||||
"Notice that we have a known pattern here.",
|
||||
"We have a voltage source connected to a pair of",
|
||||
"resistors, R1 and R2.",
|
||||
"And ev is simply the voltage across R2.",
|
||||
"Now this is a known pattern.",
|
||||
"So one thing you should keep in mind is that in circuits",
|
||||
"and electronics, we use patterns a lot.",
|
||||
"Whenever we see a pattern, we can directly go and write down",
|
||||
"the what the outward response is going to look like.",
|
||||
"What I'm going to do is throughout this course, as you",
|
||||
"we more and more patterns, I am going to alert",
|
||||
"you to these patterns.",
|
||||
"So right here is a voltage divider pattern.",
|
||||
"So for the voltage divider pattern, I can write down ev",
|
||||
"as being some fraction of the source voltage v. But the",
|
||||
"divider action is simply R2 divide by R2 plus R2.",
|
||||
"So it is simply the voltage across R2, and that is given",
|
||||
"by R2 divide by R1 plus R2.",
|
||||
"And this is a known pattern that you will find very",
|
||||
"helpful as you analyze circuits very quickly.",
|
||||
"Next let's look at I acting alone.",
|
||||
"Before we do that, what do we have so far?",
|
||||
"Again, recall, this is the circuit we",
|
||||
"are trying to analyze.",
|
||||
"We are trying to get the node voltage e.",
|
||||
"And so far we have computed the partial voltage ev due to",
|
||||
"the voltage source acting alone.",
|
||||
"As the next step-- again, this is still step one of the",
|
||||
"superposition method--",
|
||||
"let's look at the partial response of the circuit due to",
|
||||
"the current acting alone.",
|
||||
"To get the response for the current acting alone, I need",
|
||||
"to build a circuit in which the voltage",
|
||||
"source is turned off.",
|
||||
"I'll let you think for a couple of seconds as to what",
|
||||
"the circuit will look like before I draw it out for you.",
|
||||
"OK, let's go ahead.",
|
||||
"So to turn off this voltage source, all I have to do is",
|
||||
"replace it with a short circuit like so.",
|
||||
"So notice that I have replaced the voltage source with a",
|
||||
"short circuit, and I've left the current source in place.",
|
||||
"I have my ground node here.",
|
||||
"And notice that my goal is to find the partial voltage eI",
|
||||
"that is a result of the current source acting alone.",
|
||||
"So notice that I have a second pattern here.",
|
||||
"And in this case, this is a current divider pattern.",
|
||||
"Actually, this is a even simpler pattern.",
|
||||
"I simply have a current that is flowing",
|
||||
"into a pair of resistors.",
|
||||
"OK, so I have a current, I, that is flowing into a pair of",
|
||||
"resistors, R1 and R2.",
|
||||
"And so I can compute the voltage across the pair of",
|
||||
"resistors very straightforwardly.",
|
||||
"So eI is simply the resistance times the current.",
|
||||
"And the resistance of a paralel pair of resistors is",
|
||||
"simply R1 R2 divide by R1 plus R2 times the current I.",
|
||||
"OK, so now I have computed both ev and eI, the two",
|
||||
"partial voltages with each of the voltages acting alone.",
|
||||
"And now I am ready for step two of the",
|
||||
"superposition method.",
|
||||
"And the step two of the superposition method simply",
|
||||
"says that you sum the two partial voltages, ev and eI.",
|
||||
"So my resulting voltage e is simply the sum of the two",
|
||||
"partial voltages ev and eI.",
|
||||
"And I have those as R2 divide by R1 plus R2 times v. And I",
|
||||
"sum that to eI.",
|
||||
"And eI is R1 R2 divide by R1 plus R2 times I. And",
|
||||
"there you have it.",
|
||||
"Not surprisingly, this expression here is identical",
|
||||
"to the expression that you obtained by using the node",
|
||||
"method in the previous lecture."
|
||||
]
|
||||
}
|
||||
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
||||
"text": []
|
||||
}
|
||||
@@ -1,1907 +0,0 @@
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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."
|
||||
]
|
||||
}
|
||||
@@ -1,194 +0,0 @@
|
||||
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"text": [
|
||||
"SPEAKER 1: Before we begin the course, I wanted to cover a",
|
||||
"few administrative details.",
|
||||
"First of all, this course does have prerequisites.",
|
||||
"To do well in the course, you must have a advanced placement",
|
||||
"or AP-level understanding of electricity and",
|
||||
"magnetism in physics.",
|
||||
"And these are at the level of MIT 8.02 course, which you",
|
||||
"might check out on MIT OpenCourseWare.",
|
||||
"It's also useful for you to have a basic knowledge of",
|
||||
"solving simple differential equations.",
|
||||
"Now, they will cover how to solve some simple equations in",
|
||||
"this course.",
|
||||
"But if you come in with a knowledge of solving simple",
|
||||
"differential equations, that will be extremely helpful.",
|
||||
"There is a textbook for this course, it is \"Foundations of",
|
||||
"Analog and Digital Electronic Circuits\" by Agarwal and Lang.",
|
||||
"You can obtain a copy from Amazon if you like.",
|
||||
"The book is not required, but certainly useful.",
|
||||
"We will make available parts of the textbook in an",
|
||||
"electronic form on our course site as well.",
|
||||
"I want to draw special attention to some of the",
|
||||
"underlined readings from this book in your course at a",
|
||||
"glance handout.",
|
||||
"This handout tells you what is going to happen",
|
||||
"weekly in this course.",
|
||||
"It also tells you week by week what are the readings that we",
|
||||
"recommend that you do.",
|
||||
"We really recommend that you at least skim through the",
|
||||
"material that is assigned as reading.",
|
||||
"Now, the underlying readings are particularly important, as",
|
||||
"they stress intuition in how you solve circuits and",
|
||||
"electronics problems.",
|
||||
"Now in addition to the various forms of 6.002x material that",
|
||||
"we will share with you, such as video lectures, interactive",
|
||||
"exercises, and so on, that we will have several forms of",
|
||||
"assessment.",
|
||||
"We will give you weekly homeworks and laboratories.",
|
||||
"These homeworks and laboratories must be completed",
|
||||
"by the deadline indicated on the assignment, and we will",
|
||||
"assign both homeworks and labs each week.",
|
||||
"Now the video lectures and the exercises and so on are for",
|
||||
"you to learn the material.",
|
||||
"Your performance in the course will be assessed",
|
||||
"using several methods.",
|
||||
"One is, you will be assessed on homeworks, and those will",
|
||||
"count for 15% of your grade.",
|
||||
"And we will have about 10 homeworks.",
|
||||
"There will be laboratories, again around 10 laboratories,",
|
||||
"and they also count for 15% of your grade.",
|
||||
"There will be a mid-term, which will count for 30%, and",
|
||||
"a final, which will count for 40%.",
|
||||
"Now, we will give you instructions on how to do the",
|
||||
"midterm and the final in the course bulletin board that you",
|
||||
"should be watching constantly.",
|
||||
"We urge you to collaborate, if you have other friends taking",
|
||||
"the course, on your lecture videos and on the",
|
||||
"exercises and so on.",
|
||||
"And you are also free to, and encouraged to, collaborate in",
|
||||
"discussing high-level concepts and materials in this course.",
|
||||
"However, the assessed materials, such as homeworks,",
|
||||
"labs, midterms and final exams, must be",
|
||||
"done on your own."
|
||||
]
|
||||
}
|
||||
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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."
|
||||
]
|
||||
}
|
||||
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
||||
"text": []
|
||||
}
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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."
|
||||
]
|
||||
}
|
||||
@@ -1,5 +0,0 @@
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||||
{
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"start": [],
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"end": [],
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"text": []
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}
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@@ -1,5 +0,0 @@
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{
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"start": [],
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2893875,
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2897354,
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2915891,
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|
||||
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||||
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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."
|
||||
]
|
||||
}
|
||||
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
||||
"text": []
|
||||
}
|
||||
@@ -1,71 +0,0 @@
|
||||
{
|
||||
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|
||||
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|
||||
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||||
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||||
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|
||||
"text": [
|
||||
"SPEAKER 1: 6.002x is an extraordinarily fun course.",
|
||||
"This course is the first course in an EE or an EECS",
|
||||
"curriculum at MIT.",
|
||||
"This course will help you make the big jump",
|
||||
"from physics to EECS.",
|
||||
"You will learn, what, all kinds of fun",
|
||||
"things in this course.",
|
||||
"So, for example, you will learn what's behind this.",
|
||||
"What's behind the iPhone.",
|
||||
"What are some of the foundational technologies and",
|
||||
"cool ideas that drive this and many other fun",
|
||||
"things in our lives?",
|
||||
"Very useful things in our lives as well, that have",
|
||||
"really been able to improve the productivity of all of",
|
||||
"humankind over the past many, many decades.",
|
||||
"This course also forms the foundations of",
|
||||
"devices like this.",
|
||||
"This is a chip photo of Intel's 22",
|
||||
"nanometer multicore processor.",
|
||||
"And you will learn about some basic technologies that are",
|
||||
"used in building devices such as this as well."
|
||||
]
|
||||
}
|
||||
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
||||
"text": []
|
||||
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|
||||
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||||
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|
||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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|
||||
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|
||||
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||||
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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."
|
||||
]
|
||||
}
|
||||
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
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"text": []
|
||||
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"text": [
|
||||
"PROFESSOR: In the previous segment, we saw that circuits",
|
||||
"composed of linear elements were, themselves, linear.",
|
||||
"In this segment, we will see that linear circuits or linear",
|
||||
"systems can be analyzed with extremely powerful techniques.",
|
||||
"We will study two of these properties of circuits,",
|
||||
"homogeneity and superposition, in this segment.",
|
||||
"Let's start by studying the property of homogeneity.",
|
||||
"So what does homogeneity mean?",
|
||||
"Supposing we have a system with a bunch of inputs one",
|
||||
"output here.",
|
||||
"And let's say the inputs are x1, x2, and so on.",
|
||||
"And for these xes let's say the corresponding output is y.",
|
||||
"Let me add a little cartoon here, just to",
|
||||
"make it easy to follow.",
|
||||
"As they say, a picture is worth 1,000 words.",
|
||||
"So let's say, if you have apple as an input and you get",
|
||||
"a different kind of apple as an output, then let's look at",
|
||||
"what the property of homogeneity says.",
|
||||
"If I take the same system and if I",
|
||||
"multiply each of the inputs--",
|
||||
"x1, x2, and the old output, y-- if I multiply each of the",
|
||||
"inputs with some constant, alpha, then the property of",
|
||||
"homogeneity says that the output will also be multiplied",
|
||||
"by the same value, alpha.",
|
||||
"So this is the homogeneity property.",
|
||||
"And in terms of our picture, if you have an Apple and you",
|
||||
"took a fraction of the apple out, then your output would",
|
||||
"also have the same fraction of the apple out.",
|
||||
"So this is the homogeneity property.",
|
||||
"Next let's look at another extremely powerful technique,",
|
||||
"superposition.",
|
||||
"Now superposition is a property of linear circuits,",
|
||||
"and let's first understand what this property means.",
|
||||
"So supposing I have a system here.",
|
||||
"And what I'll do is I'll apply two sets of",
|
||||
"inputs to the system.",
|
||||
"So in the first set, let's say I apply the a set of inputs,",
|
||||
"x1a, x2a, and so on.",
|
||||
"And let's say that that gives rise to the a set of outputs.",
|
||||
"And then if I take the same system--",
|
||||
"just to make it clear, let me mark it as s.",
|
||||
"If I take the same system and I apply a b set of inputs--",
|
||||
"so x1b, x2b, and so on--",
|
||||
"and if I get a corresponding output, yb, then what can we",
|
||||
"say about the resulting system?",
|
||||
"And just to make it very clear, going back to our",
|
||||
"pictures and cartoons here, let's say the a set of inputs",
|
||||
"corresponds to apples, a for apples.",
|
||||
"And the b set of inputs goes on to blueberries.",
|
||||
"So jokingly here, if I feed a bunch of apples to the system",
|
||||
"and I get applesauce at the output, and on the other hand,",
|
||||
"if I feed a bunch of blueberries to the system and",
|
||||
"I get blueberry sauce at the output, then let's do some fun",
|
||||
"stuff here.",
|
||||
"Suppose I take the same system and I feed through the system",
|
||||
"the sum of both of these inputs.",
|
||||
"In other words, if I feed it x1a, x2a, and so on, and I add",
|
||||
"to each corresponding input the b set of inputs, so I get",
|
||||
"x1b here and x2b here-- so notice that this is here, and",
|
||||
"the b set of inputs is here.",
|
||||
"So notice that all I've done is I've added up",
|
||||
"corresponding inputs.",
|
||||
"What superposition tells me is that my outputs will be a sum",
|
||||
"of the corresponding inputs.",
|
||||
"In other words, if I had ya with the a set of inputs",
|
||||
"alone, and I had yb with the b set of inputs alone, then if I",
|
||||
"sum the corresponding inputs, the a and the b inputs, then",
|
||||
"my output will be a sum of the corresponding outputs as well.",
|
||||
"And again, jokingly, if I feed apples and blueberries to the",
|
||||
"input, then in this case, jokingly again, maybe I get",
|
||||
"mixed fruit jam.",
|
||||
"How does this yield something interesting for us?",
|
||||
"Let me do a specific example of the property of",
|
||||
"superposition and see how this will yield a very interesting",
|
||||
"technique to analyze linear circuits.",
|
||||
"Again, remember, both the homogeneity and superposition",
|
||||
"property applies to linear circuits.",
|
||||
"So let me take a specific instance of",
|
||||
"superposition here.",
|
||||
"And so I take some system, a linear system, and let's say I",
|
||||
"have two inputs that I apply, v1 and v2.",
|
||||
"And let's say my goal is to find out what the output is.",
|
||||
"What I want to show you is that, by the method of",
|
||||
"superposition, I can use a divide and conquer technique.",
|
||||
"What I can do is I can take the same system and I can set",
|
||||
"the v2 output to 0 and apply just the v1.",
|
||||
"And I measure the corresponding output, y1.",
|
||||
"So y1 here is the partial output, given that I have",
|
||||
"applied a v1 alone.",
|
||||
"Similarly, I take the same system and in this case,",
|
||||
"second time around, I set v1 to 0, and I apply v2 alone.",
|
||||
"And then let's say I get y2 as my output",
|
||||
"with v2 acting alone.",
|
||||
"Then here is something very interesting.",
|
||||
"So by superposition from a previous example, recall that",
|
||||
"if I took one set of inputs and a second set of inputs and",
|
||||
"I summed up the corresponding values, then superposition",
|
||||
"said my output would be a sum of the individual outputs with",
|
||||
"just each of those applied alone.",
|
||||
"In other words, if I show the v1 as 0 and then if I sum to",
|
||||
"that the second set of inputs, 0 and v2 from here, so that",
|
||||
"this got applied here and the first set of inputs got",
|
||||
"applied here, then what superposition would say is",
|
||||
"that my output would be a sum of the two partial outputs.",
|
||||
"In other words, y1 would come from here and y2 would be the",
|
||||
"same as the y2 with the v2 applied alone.",
|
||||
"So this is an extremely powerful idea.",
|
||||
"So to recap, what have I done here?",
|
||||
"I have used a method of superposition to apply a set",
|
||||
"of inputs in the following way.",
|
||||
"I started by saying that I have a circuit and I want to",
|
||||
"apply v1 and v2 to it and compute the output.",
|
||||
"Now rather than trying to solve the circuit by applying",
|
||||
"both v1 and v2, what I did was I broke it up into two",
|
||||
"sub-problems. In the first sub-problem, what I did was I",
|
||||
"applied v1 alone and set v2 to 0, and then in the second",
|
||||
"sub-problem, I applied v2 alone and I set v1 to be 0.",
|
||||
"And I computed the two partial outputs, y1 and y2.",
|
||||
"The method of superposition then says that if I took the",
|
||||
"two corresponding sets of inputs and summed them up,",
|
||||
"then my output would be a sum of the two partial outputs.",
|
||||
"Notice that at the input here, if you look at these two",
|
||||
"inputs, the v1 plus 0 is simply the v1, v2 plus 0 is",
|
||||
"simply v2, which is the same as what I have here.",
|
||||
"So in other words, I was able to solve the circuit that",
|
||||
"contained v1 and v2 as inputs by applying just v1 alone and",
|
||||
"then v2 alone, and then by summing up the two",
|
||||
"corresponding outputs.",
|
||||
"This will yield an incredibly powerful method for us called",
|
||||
"the method of superposition."
|
||||
]
|
||||
}
|
||||
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
||||
"text": []
|
||||
}
|
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@@ -1,533 +0,0 @@
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"text": [
|
||||
"ANANT AGARWAL: So let me give you an example of a bunch of",
|
||||
"interesting lumped elements and then show you a couple of",
|
||||
"really nasty lumped elements.",
|
||||
"LORENZO: I'm going to switch to the other one.",
|
||||
"I made a mistake.",
|
||||
"ANANT AGARWAL: So what you see out here, so we characterize",
|
||||
"lumped elements by the vi characteristics, OK?",
|
||||
"You apply a voltage, measure the current, So what I can do",
|
||||
"is I can plot i here and v here and see",
|
||||
"what it looks like.",
|
||||
"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 the constant, I get a straight line.",
|
||||
"That's the i-axis, the v-axis, and this is a 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.",
|
||||
"I change the value r because it's a variable resistor, and",
|
||||
"it changes slope because my r is different.",
|
||||
"Next, let me go to--",
|
||||
"LORENZO: Fixed.",
|
||||
"ANANT AGARWAL: --a fixed resistor, and this guy here on",
|
||||
"the screen to your left, I guess, 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--",
|
||||
"i, v. If my voltage goes across, that Zener diode goes",
|
||||
"up slightly, the current shoots up.",
|
||||
"But if the voltage becomes negative, I don't have any",
|
||||
"current flowing through it until the voltage passes some",
|
||||
"threshold, at which point my current begins to build up.",
|
||||
"So you can increase voltage a little bit, and you 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--",
|
||||
"i, v. If the voltage across the diode becomes positive,",
|
||||
"around 0.6 volts or thereabout, the current begins",
|
||||
"to shoot up.",
|
||||
"But if the voltage is below that threshold of 0.6, 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.",
|
||||
"Next example is a thermistor.",
|
||||
"A thermistor is a resistor whose resistance varies with",
|
||||
"temperature, OK?",
|
||||
"So this is a very expensive little drier, hair drier.",
|
||||
"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.",
|
||||
"As it cools down--",
|
||||
"let me cool it down.",
|
||||
"So you can see it's coming down.",
|
||||
"I can zap it again.",
|
||||
"[TURNS ON DRYER]",
|
||||
"ANANT AGARWAL: I could do this all day.",
|
||||
"This is so much fun.",
|
||||
"[LAUGHTER]",
|
||||
"ANANT AGARWAL: OK, so that's a another",
|
||||
"interesting lumped element.",
|
||||
"As the temperature rises, its resistance changes.",
|
||||
"LORENZO: Photo.",
|
||||
"ANANT AGARWAL: Next thing is called a photoresistor.",
|
||||
"It's a resistor.",
|
||||
"It used to be a resistor, Lorenzo?",
|
||||
"LORENZO: Yeah.",
|
||||
"OK, that's fine.",
|
||||
"ANANT AGARWAL: So this is a photoresistor.",
|
||||
"And notice that it almost behaves like an open circuit.",
|
||||
"Well, 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 photoresistor.",
|
||||
"LORENZO: Now, we go to the--",
|
||||
"ANANT AGARWAL: So now I'm going to show you a battery.",
|
||||
"Notice, we didn't talk about batteries before.",
|
||||
"I'll show you a battery.",
|
||||
"So before we show a battery, just think in your own minds,",
|
||||
"what should the iv characteristic of a",
|
||||
"battery look like?",
|
||||
"i, v, a battery supplies a constant voltage.",
|
||||
"You know, your little cell, your double A",
|
||||
"battery, 1.5 volts?",
|
||||
"So think about what the iv characteristic of a battery",
|
||||
"should look like for three seconds before",
|
||||
"I show it to you.",
|
||||
"And so I show it, Lorenzo.",
|
||||
"It's a straight line.",
|
||||
"This is a good battery.",
|
||||
"It's a straight vertical line, which says that the voltage is",
|
||||
"1.5 volts or thereabouts no matter",
|
||||
"what current it supplies.",
|
||||
"As an ideal voltage source, it as a fixed voltage v no matter",
|
||||
"what the current going through it is.",
|
||||
"Now I'll show you a dud, a bad battery.",
|
||||
"And this is what the bad battery looks like.",
|
||||
"So many of you had a your car batteries die on you, and when",
|
||||
"you go to the store, they check your batteries.",
|
||||
"They use exactly this principle, that dead batteries",
|
||||
"have resistance.",
|
||||
"Whenever you see slopes here, you're thinking of resistance,",
|
||||
"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 we need to end with a bulb.",
|
||||
"And what you'll see is that a bulb is simply--",
|
||||
"behaves like a resistor.",
|
||||
"It's 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'll deal with a lot more set of lumped elements--",
|
||||
"switches, MOFETs, capacitors, inductors, a bunch",
|
||||
"of other fun stuff.",
|
||||
"But before we do that, what I wanted to tell you is that",
|
||||
"don't go berserk on this abstraction binge, OK?",
|
||||
"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've already had this tacit handshake, which said",
|
||||
"that we'll follow the discipline, OK?",
|
||||
"Even after we follow the discipline, there are ranges",
|
||||
"to how well physical elements can behave like",
|
||||
"ideal lumped elements.",
|
||||
"For example, what I'm going to do is show you as a resistor.",
|
||||
"And it's going to look like a resistor, and I'm going to",
|
||||
"keep the voltage around it.",
|
||||
"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'll say,",
|
||||
"oh yeah, the curve will keep extending",
|
||||
"until I reach infinity.",
|
||||
"But this is a practical resistor, so, you know.",
|
||||
"The people out here, you're going to have to cover your",
|
||||
"eyes or something.",
|
||||
"So your abstraction can predict that.",
|
||||
"It says the current is an amp.",
|
||||
"It can predict the heat, light, or the smell.",
|
||||
"Because in the laboratory, when you get the smell, you",
|
||||
"know what somebody has just done.",
|
||||
"They blown the resistor.",
|
||||
"So that's one example of a lumped",
|
||||
"abstraction breaking down.",
|
||||
"So if I really believe in my own BS, anything's a lumped",
|
||||
"element, so here's a pickle.",
|
||||
"[LAUGHTER]",
|
||||
"ANANT AGARWAL: A pickle's a lumped element.",
|
||||
"I can treat it as a lumped resistor.",
|
||||
"But this is a very interesting lumped resistor.",
|
||||
"[LAUGHTER]",
|
||||
"ANANT AGARWAL: Don't try this at home.",
|
||||
"This is a standard pickle into which we are",
|
||||
"pumping 110 volts AC.",
|
||||
"[LAUGHTER]",
|
||||
"ANANT AGARWAL: I promise you, this is a standard pickle.",
|
||||
"So as you can tell, it has a fixed resistance, but your",
|
||||
"lumped abstraction cannot predict the nice light and",
|
||||
"sound effect.",
|
||||
"[LAUGHTER]"
|
||||
]
|
||||
}
|
||||
@@ -1,1997 +0,0 @@
|
||||
{
|
||||
"start": [
|
||||
0,
|
||||
4400,
|
||||
8922,
|
||||
15033,
|
||||
22366,
|
||||
28111,
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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."
|
||||
]
|
||||
}
|
||||
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
||||
"text": []
|
||||
}
|
||||
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
||||
"text": []
|
||||
}
|
||||
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
||||
"text": []
|
||||
}
|
||||
@@ -1,29 +0,0 @@
|
||||
{
|
||||
"start": [
|
||||
250,
|
||||
3300,
|
||||
7990,
|
||||
13470,
|
||||
17840,
|
||||
18740,
|
||||
21970
|
||||
],
|
||||
"end": [
|
||||
3300,
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||||
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||||
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||||
17840,
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||||
18740,
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||||
21970,
|
||||
23220
|
||||
],
|
||||
"text": [
|
||||
"SPEAKER 1: OK, so this is case the V-I relationship is V",
|
||||
"equals capital V. In this is it's a constant and so the",
|
||||
"relationship is given by this where V is a constant at",
|
||||
"capital V volts in respect to the current that is flowing",
|
||||
"through the element.",
|
||||
"So here are examples of a couple of elements and their",
|
||||
"I-V relation."
|
||||
]
|
||||
}
|
||||
@@ -1,1916 +0,0 @@
|
||||
{
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||||
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||||
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||||
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||||
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||||
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||||
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],
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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."
|
||||
]
|
||||
}
|
||||
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
||||
"text": []
|
||||
}
|
||||
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
||||
"text": []
|
||||
}
|
||||
@@ -1,287 +0,0 @@
|
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"text": [
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||||
"PROFESSOR: In the previous segment, we looked at the",
|
||||
"Thevenin method, which applied to linear circuits.",
|
||||
"And in that method, I could take an arbitrary network, n,",
|
||||
"containing a whole bunch of sources and resistors where",
|
||||
"the current sources are voltage sources.",
|
||||
"And I could replace that with its Thevenin equivalent, where",
|
||||
"the Thevenin equivalent pattern was given by a voltage",
|
||||
"source VTH.",
|
||||
"in series with the resistance RTH.",
|
||||
"Now one of the things that I want you to think about in",
|
||||
"circuits is that whenever you have circuits containing",
|
||||
"voltages and properties involving voltages, you can",
|
||||
"immediately think of complimentary properties",
|
||||
"involving current sources.",
|
||||
"So much as I was able to replace an arbitrary network n",
|
||||
"with its Thevenin equivalent, you can think about replacing",
|
||||
"the arbitrary network n with some pattern involving a",
|
||||
"current source.",
|
||||
"And indeed, that method where you replace an arbitrary",
|
||||
"network with a pattern involving a current source is",
|
||||
"called the Norton method.",
|
||||
"So in the Norton method, what we do is we are able to",
|
||||
"replace an arbitrary network n with its Norton equivalent,",
|
||||
"where the Norton equivalent contains the current source IN",
|
||||
"in parallel with the resistance RTH.",
|
||||
"The current source in parallel with RTH is a Norton pattern,",
|
||||
"and you should contrast it with the corresponding",
|
||||
"Thevenin pattern.",
|
||||
"So a voltage source in series with a resistor is a Thevenin",
|
||||
"pattern, and a current source in parallel with the",
|
||||
"resistance is the Norton pattern.",
|
||||
"So in the case of the Norton pattern, which contains the",
|
||||
"current source IN and the Norton resistance RN, in the",
|
||||
"same manner that you defined the Thevenin equivalent, we",
|
||||
"can derive the Norton equivalent.",
|
||||
"So to obtain the current IN, what you do is you obtain the",
|
||||
"short circuit current seen at the port.",
|
||||
"So recall for the Thevenin method, I open-circuited the",
|
||||
"port here, and measured the voltage, and that was my VTH.",
|
||||
"So the Norton method, what I do is I short circuit this",
|
||||
"port and measure the current I. That current is IN, or the",
|
||||
"Norton current.",
|
||||
"And then I can get a Norton resistance RN--",
|
||||
"oh, I should say RN here-- the Norton resistance RN, which,",
|
||||
"incidentally, is identical to the Thevenin resistance RTH.",
|
||||
"I can get that in the same manner as I got RTH, which is",
|
||||
"I shut off all the independent voltage sources and current",
|
||||
"sources and simply take the resistance measure at the",
|
||||
"port, of course, without the short.",
|
||||
"I go ahead and measure the resistance seen at the port",
|
||||
"with all the voltages and currents turned off.",
|
||||
"OK?",
|
||||
"That would be my Norton resistance, RN.",
|
||||
"So again, we stated this pattern, a current source IN",
|
||||
"parallel to a Norton resistance RN, where this",
|
||||
"corresponds to the Thevenin equivalent, where I have VTH",
|
||||
"and RTH in series.",
|
||||
"So the Norton is the dual of the Thevenin.",
|
||||
"OK?",
|
||||
"Where the Thevenin is the voltage in series with the",
|
||||
"resistance, and its dual is the Norton equivalent, which",
|
||||
"is the current source in parallel with resistance.",
|
||||
"An immediate question that comes to mind is how are the",
|
||||
"Thevenin and Norton equivalents",
|
||||
"related to each other?",
|
||||
"After all, they are the duals of one another.",
|
||||
"And so notice the Thevenin equivalent on the left-hand",
|
||||
"side and the Norton equivalent on the right-hand side.",
|
||||
"The resistances RTH and the Norton",
|
||||
"resistance RN are equal.",
|
||||
"And then we can also relate the Norton current IN and the",
|
||||
"Thevenin voltage as follows.",
|
||||
"IN is VTH divided by RTH.",
|
||||
"And so if you take the Thevenin voltage and divide",
|
||||
"that by the Thevenin resistance, you get the Norton",
|
||||
"current, IN.",
|
||||
"So this very quickly shows you how you can go from the Norton",
|
||||
"to the Thevenin.",
|
||||
"One question I am often asked is when do I use the Thevenin",
|
||||
"method and when do I use the Norton method?",
|
||||
"Well, you know, that comes from experience.",
|
||||
"Like you look at circuits in one of our earlier examples",
|
||||
"where the external network contained a voltage source in",
|
||||
"series with a resistance, it made sense to take the rest of",
|
||||
"the network and turn that into Thevenin equivalent.",
|
||||
"However, if I have a basic circuit containing a current",
|
||||
"source and a resistance in parallel, then it might be",
|
||||
"easier to take my external network and convert that into",
|
||||
"a Norton equivalent.",
|
||||
"So, really, when you want to get things in",
|
||||
"parallel, think Norton.",
|
||||
"When you want to get things in series to simplify analysis,",
|
||||
"think Thevenin."
|
||||
]
|
||||
}
|
||||
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
||||
"text": []
|
||||
}
|
||||
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
||||
"text": []
|
||||
}
|
||||
@@ -1,5 +0,0 @@
|
||||
{
|
||||
"start": [],
|
||||
"end": [],
|
||||
"text": []
|
||||
}
|
||||
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user