Adding stripped down 6002x course for testing, along with CMS test for edit pages for same

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Calen Pennington
2012-07-17 10:42:47 -04:00
parent 6bf0e093bc
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<html>
<body>
<center>
Final Exam
</center>
<p>This exam covers weeks 1-13. You may use your calculator, your notes, your book, the internet, or any other auxiliary materials that you think can help you. However, you are not allowed to communicate with any person on any topic associated with this course while you are taking this exam.</p>
<p>
Once you click on the next tab, you will have 24 hours to complete the examination. For each problem you will be allowed exactly three submissions. Your
answers to that problem will be checked after each submission, so you
can fix mistakes you may have made, within the three-submission limit.
Your most recently checked answer is the answer that will contribute to your grade on the exam.
</p>
<p>
Each answer box on the exam contributes equally to your grade on the exam, regardless of how they are grouped as problems.
</p>
</body>
</html>

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Hint
<br/><br/>
Remember that the time evolution of any variable \(x(t)\) governed by
a first-order system with a time-constant \(\tau\) for a time \(t) between an initial
value \(x(t_0)\) and a final value \(x(\infty)\) is the following:
<br/><br/>
\(x(t) = x(\infty) + (x(t_0) - x(\infty)) e^(-(t-t_0)/\tau)\)
<br/><br/>

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<script type="text/javascript">
$(document).ready(function() {
$("#r1_slider").slider({
value: 1, min: 1, max: 10, step: 1, slide: schematic.component_slider,
schematic: "ctrls", component: "R1", property: "r", analysis: "dc",
})
$("#r2_slider").slider({
value: 1, min: 1, max: 10, step: 1, slide: schematic.component_slider,
schematic: "ctrls", component: "R2", property: "r", analysis: "dc",
})
$("#r3_slider").slider({
value: 1, min: 1, max: 10, step: 1, slide: schematic.component_slider,
schematic: "ctrls", component: "R3", property: "r", analysis: "dc",
})
$("#r4_slider").slider({
value: 1, min: 1, max: 10, step: 1, slide: schematic.component_slider,
schematic: "ctrls", component: "R4", property: "r", analysis: "dc",
})
$("#slider").slider(); });
</script>
<b>Lab 2A: Superposition Experiment</b>
<br><br><i>Note: This part of the lab is just to develop your intuition about
superposition. There are no responses that need to be checked.</i>
<br/><br/>Circuits with multiple sources can be hard to analyze as-is. For example, what is the voltage
between the two terminals on the right of Figure 1?
<center>
<input width="425" type="hidden" height="150" id="schematic1" parts="" analyses="" class="schematic ctrls" name="test2" value="[[&quot;w&quot;,[160,64,184,64]],[&quot;w&quot;,[160,16,184,16]],[&quot;w&quot;,[64,16,112,16]],[&quot;w&quot;,[112,64,88,64]],[&quot;w&quot;,[64,64,88,64]],[&quot;g&quot;,[88,64,0],{},[&quot;0&quot;]],[&quot;w&quot;,[112,64,160,64]],[&quot;w&quot;,[16,64,64,64]],[&quot;r&quot;,[160,16,0],{&quot;name&quot;:&quot;R4&quot;,&quot;r&quot;:&quot;1&quot;},[&quot;1&quot;,&quot;0&quot;]],[&quot;r&quot;,[160,16,1],{&quot;name&quot;:&quot;R3&quot;,&quot;r&quot;:&quot;1&quot;},[&quot;1&quot;,&quot;2&quot;]],[&quot;i&quot;,[112,64,6],{&quot;name&quot;:&quot;&quot;,&quot;value&quot;:&quot;6A&quot;},[&quot;0&quot;,&quot;2&quot;]],[&quot;r&quot;,[64,16,0],{&quot;name&quot;:&quot;R2&quot;,&quot;r&quot;:&quot;1&quot;},[&quot;2&quot;,&quot;0&quot;]],[&quot;r&quot;,[64,16,1],{&quot;name&quot;:&quot;R1&quot;,&quot;r&quot;:&quot;1&quot;},[&quot;2&quot;,&quot;3&quot;]],[&quot;v&quot;,[16,16,0],{&quot;name&quot;:&quot;&quot;,&quot;value&quot;:&quot;8V&quot;},[&quot;3&quot;,&quot;0&quot;]],[&quot;view&quot;,-24,0,2]]"/>
Figure 1. Example multi-source circuit
</center>
<br/><br/>We can use superposition to make the analysis much easier.
The circuit in Figure 1 can be decomposed into two separate
subcircuits: one involving only the voltage source and one involving only the
current source. We'll analyze each circuit separately and combine the
results using superposition. Recall that to decompose a circuit for
analysis, we'll pick each source in turn and set all the other sources
to zero (i.e., voltage sources become short circuits and current
sources become open circuits). The circuit above has two sources, so
the decomposition produces two subcircuits, as shown in Figure 2.
<center>
<table><tr><td>
<input style="display:inline;" width="425" type="hidden" height="150" id="schematic2" parts="" analyses="" class="schematic ctrls" name="test2" value="[[&quot;w&quot;,[160,64,184,64]],[&quot;w&quot;,[160,16,184,16]],[&quot;w&quot;,[64,16,112,16]],[&quot;w&quot;,[112,64,88,64]],[&quot;w&quot;,[64,64,88,64]],[&quot;g&quot;,[88,64,0],{},[&quot;0&quot;]],[&quot;w&quot;,[112,64,160,64]],[&quot;w&quot;,[16,64,64,64]],[&quot;r&quot;,[160,16,0],{&quot;name&quot;:&quot;R4&quot;,&quot;r&quot;:&quot;1&quot;},[&quot;1&quot;,&quot;0&quot;]],[&quot;r&quot;,[160,16,1],{&quot;name&quot;:&quot;R3&quot;,&quot;r&quot;:&quot;1&quot;},[&quot;1&quot;,&quot;2&quot;]],[&quot;r&quot;,[64,16,0],{&quot;name&quot;:&quot;R2&quot;,&quot;r&quot;:&quot;1&quot;},[&quot;2&quot;,&quot;0&quot;]],[&quot;r&quot;,[64,16,1],{&quot;name&quot;:&quot;R1&quot;,&quot;r&quot;:&quot;1&quot;},[&quot;2&quot;,&quot;3&quot;]],[&quot;v&quot;,[16,16,0],{&quot;name&quot;:&quot;&quot;,&quot;value&quot;:&quot;8V&quot;},[&quot;3&quot;,&quot;0&quot;]],[&quot;view&quot;,-24,0,2]]"/>
(a) Subcircuit for analyzing contribution of voltage source
</td><td>
<input width="425" type="hidden" height="150" id="schematic3" parts="" analyses="" class="schematic ctrls" name="test2" value="[[&quot;w&quot;,[16,16,16,64]],[&quot;w&quot;,[160,64,184,64]],[&quot;w&quot;,[160,16,184,16]],[&quot;w&quot;,[64,16,112,16]],[&quot;w&quot;,[112,64,88,64]],[&quot;w&quot;,[64,64,88,64]],[&quot;g&quot;,[88,64,0],{},[&quot;0&quot;]],[&quot;w&quot;,[112,64,160,64]],[&quot;w&quot;,[16,64,64,64]],[&quot;r&quot;,[160,16,0],{&quot;name&quot;:&quot;R4&quot;,&quot;r&quot;:&quot;1&quot;},[&quot;1&quot;,&quot;0&quot;]],[&quot;r&quot;,[160,16,1],{&quot;name&quot;:&quot;R3&quot;,&quot;r&quot;:&quot;1&quot;},[&quot;1&quot;,&quot;2&quot;]],[&quot;i&quot;,[112,64,6],{&quot;name&quot;:&quot;&quot;,&quot;value&quot;:&quot;6A&quot;},[&quot;0&quot;,&quot;2&quot;]],[&quot;r&quot;,[64,16,0],{&quot;name&quot;:&quot;R2&quot;,&quot;r&quot;:&quot;1&quot;},[&quot;2&quot;,&quot;0&quot;]],[&quot;r&quot;,[64,16,1],{&quot;name&quot;:&quot;R1&quot;,&quot;r&quot;:&quot;1&quot;},[&quot;2&quot;,&quot;3&quot;]],[&quot;view&quot;,-24,0,2]]"/>
(b) Subcircuit for analyzing contribution of current source
</td></tr></table>
<br>Figure 2. Decomposition of Figure 1 into subcircuits
</center>
<br/>Let's use the DC analysis capability of the schematic tool to see superposition
in action. The sliders below control the resistances of R1, R2, R3 and R4 in all
the diagrams. As you move the sliders, the schematic tool will adjust the appropriate
resistance, perform a DC analysis and display the node voltages on the diagrams. Here's
what you want to observe as you play with the sliders:
<ul style="margin-left:2em;margin-top:1em;margin-right:2em;margin-bottom:1em;">
<i>The voltage for a node in Figure 1 is the sum of the voltages for
that node in Figures 2(a) and 2(b), just as predicted by
superposition. (Note that due to round-off in the display of the
voltages, the sum of the displayed voltages in Figure 2 may only be within
.01 of the voltages displayed in Figure 1.)</i>
</ul>
<br>
<center>
<table><tr valign="top">
<td>
<table>
<tr valign="top">
<td>R1</td>
<td>
<div id="r1_slider" style="width:200px; height:10px; margin-left:15px"></div>
</td>
</tr>
<tr valign="top">
<td>R2</td>
<td>
<div id="r2_slider" style="width:200px; height:10px; margin-left:15px; margin-top:10px;"></div>
</td>
</tr>
<tr valign="top">
<td>R3</td>
<td>
<div id="r3_slider" style="width:200px; height:10px; margin-left:15px; margin-top:10px;"></div>
</td>
</tr>
<tr valign="top">
<td>R4</td>
<td>
<div id="r4_slider" style="width:200px; height:10px; margin-left:15px; margin-top:10px;"></div>
</td>
</tr>
</table>
</td></tr></table>
</center>

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<center>
Midterm Exam
</center>
<p>
This is a twenty four hour examination. You can start the exam when it is
convenient for you, but you must complete this examination by 12:00pm (noon)
GMT on April 30th. Please look up what time this is in your local time zone.
</p>
<p>
When you open the next page, you will have started the examination.
You do not need to start now: you will not be timed until you open the
next page. Once you have opened the next page page you must complete
the exam and make your final submission within twenty four hours of starting
the exam.
</p>
<p>
You may use any notes, computational, or auxiliary materials that you
think can help you. However, you may not communicate with any person
about this examination while working on it. Furthermore, you may not
communicate about the exam until the exam has been closed for everyone.
</p>
<p>
For each problem you will be allowed exactly three submissions. Your
answers to that problem will be checked after each submission, so you
can fix mistakes you may have made, within the three-submission limit.
</p>
<p>
If you want to go back and study some more before starting this
exam you can do so. Good Luck!
</p>

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<html>
<body>
<center>
Midterm Exam
</center>
<p>
This is a twenty four hour examination. You can start the exam when it is
convenient for you, but you must complete this examination by 12:00pm (noon)
GMT on April 30th. Please look up what time this is in your local time zone.
</p>
<p>
When you open the next page, you will have started the examination.
You do not need to start now: you will not be timed until you open the
next page. Once you have opened the next page page you must complete
the exam and make your final submission within twenty four hours of starting
the exam.
</p>
<p>
You may use any notes, computational, or auxiliary materials that you
think can help you. However, you may not communicate with any person
about this examination while working on it. Furthermore, you may not
communicate about the exam until the exam has been closed for everyone.
</p>
<p>
For each problem you will be allowed exactly three submissions. Your
answers to that problem will be checked after each submission, so you
can fix mistakes you may have made, within the three-submission limit.
</p>
<p>
If you want to go back and study some more before starting this
exam you can do so. Good Luck!
</p>
</body>
</html>

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<html>
<body>
<center>
Midterm Exam
</center>
<p>
This is a twenty four hour examination. You can start the exam when it is
convenient for you, but you must complete this examination by 12:00pm (noon)
GMT on April 30th. Please look up what time this is in your local time zone.
</p>
<p>
When you open the next page, you will have started the examination.
You do not need to start now: you will not be timed until you open the
next page. Once you have opened the next page page you must complete
the exam and make your final submission within twenty four hours of starting
the exam.
</p>
<p>
You may use any notes, computational, or auxiliary materials that you
think can help you. However, you may not communicate with any person
about this examination while working on it. Furthermore, you may not
communicate about the exam until the exam has been closed for everyone.
</p>
<p>
For each problem you will be allowed exactly three submissions. Your
answers to that problem will be checked after each submission, so you
can fix mistakes you may have made, within the three-submission limit.
</p>
<p>
If you want to go back and study some more before starting this
exam you can do so. Good Luck!
</p>
</body>
</html>

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<html>
<body>
<h1>Week 13 Tutorials</h1>
<section class="tutorials">
<h2> Basic Tutorials </h2>
<ul>
<li><a href="/section/wk13_solder">Soldering</a> -- Steve
Finberg, one of the pioneers in from Draper Lab, talks about
soldering. </li>
</ul>
<h2> Bonus Tutorials </h2>
<ul>
<li><a href="/section/wk13_FreqResp">Frequency Response
Curves</a> -- We explain several techniques for understanding
and approximating Bode plots. </li>
</ul>
</section>
</body>
</html>

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<html>
<body>
<h1>Week 1 Tutorials</h1>
<section class="tutorials">
<h2> Introduction </h2>
<ul>
<li><a href="/section/intro"> Welcome! </a> - We introduce
ourselves and explain the tutorial format. </li>
</ul>
<h2>Basic Tutorials </h2>
<ul>
<li><a href="/section/circuit_abstraction">The Circuit
Abstraction</a> - We look at a lightbulb, and see that abstracting
away the circuit from the geometry of the wiring has no visible
effect. </li>
<li><a href="/section/a_real_circuit/">Lightbulb Circuit</a> - We
look at the voltage across a lightbulb with a multimeter, and
confirm the device is symmetric. In the process, we see reference
directions for currents, voltages, and polarity for powers. </li>
<li><a href="/section/parallel_resistors">Parallel Resistors</a> -
An explanation of equivalent circuits in the context of parallel
resistors.</li>
<li><a href="/section/series_and_parallel">Combination of Series
and Parallel</a> - Slightly more complex networks of resistors
simplified with equivalent networks.</li>
<li><a href="/section/3r_nodal">Nodal Analysis</a> - A simple
example of nodal analysis.</li>
<li><a href="/section/floating_voltage_3r">Floating Voltage</a> -
Nodal analysis with a floating source.</li>
<li><a href="/section/combination_rules">Combination Rules</a> -
We show how to apply combination rules to solving simple
circuits.</li>
</ul>
<h2>Worked Problems </h2>
<p> For the first week, we work through <a href="http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/assignments/hw1.pdf"> the first problem set from 2007</a></p>
<ul>
<li><a href="/section/exercise_1_1">OCW Exercise 1-1</a>: Find voltages in a simple series and parallel circuit, and show power is conserved</li>
<li><a href="/section/ex_1_2">OCW Exercise 1-2</a> - Synthesize a network of 3/5k and 5/3k from at most four 1k resistors</li>
<li><a href="/section/problem_1-1">OCW Problem 1-1/Textbook 2.7</a> - Find the current through a resistor in a network of resistors</li>
<li><a href="/section/problem_1-2_part1">OCW Problem 1-2</a> - Analyze long chains of resistors (similar to transmission lines or R1R2 ladders) </li>
<li><a href="/section/problem_1_3">OCW Problem 1-3 </a> - Reverse engineer a black-box resistor network</li>
</ul>
<hr/>
<p> Since the course has students from a diverse set of backgrounds, the first week's tutorials includes several extra segments, worked out with greater detail, to help bring everyone up to speed. </p>
</section>
</body>
</html>

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Clarification of the term "Linear"
<p>
The term "linear" is very clear when applied to a
mathematical function. A function F is linear if and only
if it obeys homogeneity and superposition:
</p><p>
Homogeneity: F(cx) = cF(x)
<br/>
Superposition: F(x+y) = F(x) + F(y)
</p><p>
In the context of what we have seen so far, the only
elements that are linear as mathematical functions are
resistors. An independent voltage source or an independent
current source is not a linear element. (There are also
linear dependent sources, linear capacitors and linear
inductors, but we have not yet introduced them in our class.
You will see them later.)
</p><p>
Formally, a circuit composed of only linear elements is a
linear circuit. When we add independent sources to a linear
circuit as inputs, we get a circuit that is not linear
because it has an offset: its v-i characteristic at a pair
of exposed terminals may not pass through the origin.
However, we can make a Thevenin or Norton equivalent model
of such a circuit: the Thevenin resistance summarizes the
effect of the linear elements and the Thevenin voltage
summarizes the effect of the independent sources.
</p><p>
However the term "linear," when applied to an electrical
circuit often takes on an informal meaning. We often say
that a circuit containing only linear elements and
independent sources is a "linear circuit." So, in the
informal sense, a linear circuit is one where we can apply
the Thevenin or Norton theorems to summarize the behavior at
a pair of exposed terminals.
</p><p>
Sorry for the confusion of words -- natural language is like
that!
</p>

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Clarification of the term "Linear"
<p>
The term "linear" is very clear when applied to a
mathematical function. A function F is linear if and only
if it obeys homogeneity and superposition:
</p><p>
Homogeneity: F(cx) = cF(x)
<br/>
Superposition: F(x+y) = F(x) + F(y)
</p><p>
In the context of what we have seen so far, the only
elements that are linear as mathematical functions are
resistors. An independent voltage source or an independent
current source is not a linear element. (There are also
linear dependent sources, linear
inductors, and other linear elements, but we have not yet introduced them in our class.
You will see them later.)
</p><p>
Formally, a circuit composed of only linear elements is a
linear circuit. When we add independent sources to a linear
circuit as inputs, we get a circuit that is not linear
because it has an offset: its v-i characteristic at a pair
of exposed terminals may not pass through the origin.
However, we can make a Thevenin or Norton equivalent model
of such a circuit: the Thevenin resistance summarizes the
effect of the linear elements and the Thevenin voltage
summarizes the effect of the independent sources.
</p><p>
However the term "linear," when applied to an electrical
circuit often takes on an informal meaning. We often say
that a circuit containing only linear elements and
independent sources is a "linear circuit." So, in the
informal sense, a linear circuit is one where we can apply
the Thevenin or Norton theorems to summarize the behavior at
a pair of exposed terminals.
</p><p>
Sorry for the confusion of words -- natural language is like
that!
</p>

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<p/><b>Usage Summary:</b>
<table style="border-spacing:2em; border-collapse: separate;">
<tr>
<td style="width:10em;">Add a component</td>
<td>Click on the component in the parts bin (the columns of part icons to
the right of the diagram area) and drag it onto the diagram. Release
the mouse when the component is in the correct position.
</td>
</tr>
<tr>
<td>Move a component</td>
<td>Click to select a component in the diagram (it will turn green)
and then drag it to its new location. You can use shift-click to add
a component to the current selection. Or you can click somewhere in
the diagram that is not on top of a component and drag out a selection
rectangle -- components intersecting the rectangle will be added to
the current selection.
</td>
</tr>
<tr>
<td>Rotate a component</td>
<td>Click to select a component in the diagram (it will turn green)
and then type the letter "r" on the keyboard. The component will
be rotated 90 degrees. Additional rotations will move the component
through its eight possible orientations (4 compass points and their
reflections).
</td>
</tr>
<tr>
<td>Delete a component</td>
<td>Click to select the component in the diagram (shift-click to
select multiple components) then type DEL or BACKSPACE on your
keyboard.
</td>
</tr>
<tr>
<td>Change a component's properties</td>
<td>Double click on the component. This will bring up an Edit Properties
window that has input fields for each of the component's properties.
Click OK to change the values. Click CANCEL or the window's close
button to abort the changes. Numeric values can be entered using
engineeering notation:
<center><table style="border-collapse:separate; border-spacing:1em;">
<tr><th>suffix</th><th>multiplier</th> <th style="width:3em"></th> <th>suffix</th><th>multiplier</th></tr>
<tr><td>T</td><td>\(10^{12}\)</td> <td></td> <td>u</td><td>\(10^{-6}\)</td></tr>
<tr><td>G</td><td>\(10^{9}\)</td> <td></td> <td>n</td><td>\(10^{-9}\)</td></tr>
<tr><td>M</td><td>\(10^{6}\)</td> <td></td> <td>p</td><td>\(10^{-12}\)</td></tr>
<tr><td>k</td><td>\(10^{3}\)</td> <td></td> <td>f</td><td>\(10^{-15}\)</td></tr>
<tr><td>m</td><td>\(10^{-3}\)</td></tr>
</table></center>
</td>
</tr>
<tr>
<td>Add a wire</td>
<td>Wires start at connection points, the open circles that
appear at the terminals of components or the ends of wires.
Click on a connection point to start a wire -- a green wire
will appear with one end anchored at the starting point.
Drag the mouse and release the mouse button when the other
end of the wire is positioned as you wish. Once a wire has
been added to the diagram it can be manipulated like any other
component.
</td>
</tr>
</table>

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<script type="text/javascript" src="/static/courses/6002/js/sound_labs/sound.js"></script>
<script type="text/javascript" src="/static/courses/6002/js/sound_labs/plotter.js"></script>
<script type="text/javascript" src="/static/courses/6002/js/sound_labs/circuit.js"></script>
<script type="text/javascript" src="/static/courses/6002/js/sound_labs/mosfet_amplifier.js"></script>
<h2>LAB 5B: MOSFET AMPLIFIER EXPERIMENT</h2>
<section class="problem">
<startouttext />
<p>Note: This part of the lab is just to develop your intuition about
amplifiers and biasing, and to have fun with music! There are no responses
that need to be checked.</p>
<p>The graph plots the selected voltages from the amplifier circuit below. You
can also listen to various signals by selecting from the radio buttons to
the right of the graph. This way you can both see and hear various signals.
You can use the sliders to the right of the amplifier circuit to control
various parameters of the MOSFET and the amplifier. The parameter \(V_{MAX}\)
sets the maximum range on the plots. You can also select an input voltage
type (e.g., sine wave, square wave, various types of music) using the drop
down menu to the right of the graph. When describing AC signals, the
voltages on the sliders refer to peak-to-peak values.</p>
<p>1. To begin your first experiment, go ahead and use the pull down menu to
select a sine wave input. Then, adjust the sliders to an approximate
baseline setting shown below.</p>
<p>Baseline setting of sliders:
<br />
\(V_{S}=1.6V\), \(v_{IN}=3V\), \(Frequency=1000Hz\), \(V_{BIAS}=2.5V\), \(R=10K\Omega\), \(k=1mA/V^{2}\), \(V_{T}=1V\), \(V_{MAX}=2V\).</p>
<p>You will observe in the plot that the baseline setting of the sliders for
the various amplifiers parameters produces a distorted sine wave signal for
\(v_{OUT}\). Next, go ahead and select one of the music signals as the input and
listen to each of \(v_{IN}\) and \(v_{OUT}\), and confirm for yourself that the
output sounds distorted for the chosen slider settings. You will notice
that the graph now plots the music signal waveforms. Think about all the
reasons why the amplifier is producing a distorted output.</p>
<p>2. For the second experiment, we will study the amplifier's small signal
behavior. Select a sine wave as the input signal. To study the small
signal behavior, reduce the value of \(v_{IN}\) to 0.1V (peak-to-peak) by
using the \(v_{IN}\) slider. Keeping the rest of the parameters at their
baseline settings, derive an appropriate value of \(V_{BIAS}\) that will ensure
saturation region operation for the MOSFET for the 0.1V peak-to-peak swing
for \(v_{IN}\). Make sure to think about both positive and negative excursions
of the signals.</p>
</p>Next, use the \(V_{BIAS}\) slider to choose your computed value for \(V_{BIAS}\) and
see if the observed plot of \(v_{OUT}\) is more or less distortion free. If
your calculation was right, then the output will indeed be distortion free.</p>
<p>Next, select one of the music signals as the input and listen to each of
\(v_{IN}\) and \(v_{OUT}\), and confirm for yourself that the output sounds much
better than in Step 1. Also, based on sound volume, confirm that \(v_{OUT}\) is
an amplified version of \(v_{IN}\).</p>
<p>3. Now go ahead and experiment with various other settings while listening
to the music signal at \(v_{OUT}\). Observe the plots and listen to \(v_{OUT}\) as
you change, for example, the bias voltage \(V_{BIAS}\). You will notice that
the amplifier distorts the input signal when \(V_{BIAS}\) becomes too small, or
when it becomes too large. You can also experiment with various values of
\(v_{IN}\), \(R_{L}\), etc., and see how they affect the amplification and distortion.</p>
<endouttext />
</section>
<section class="tool-wrapper">
<div id="controlls-container">
<div class="graph-controls">
<div class="music-wrapper">
<select id="musicTypeSelect" size="1">
<option value = "0">Zero Input</option>
<option value = "1">Unit Impulse</option>
<option value = "2">Unit Step</option>
<option selected="selected" value = "3">Sine Wave</option>
<option value = "4">Square Wave</option>
<option value = "5">Classical Music</option>
<option value = "6">Folk Music</option>
<option value = "7">Jazz Music</option>
<option value = "8">Reggae Music</option>
</select>
<input id="playButton" type="button" value="Play" />
</div>
<div class="inputs-wrapper">
<div id="graph-output">
<p>Graph:</p>
<ul>
<li><label for="vinCheckbox"><input id="vinCheckbox" type="checkbox" checked="yes"/>v<sub>IN</sub></label></li>
<li><label for="voutCheckbox"><input id="voutCheckbox" type="checkbox" checked="yes"/>v<sub>OUT</sub></label> </li>
<li><label for="vrCheckbox"><input id="vrCheckbox" type="checkbox"/>v<sub>R</sub></label></li>
</ul>
</div>
<div id="graph-listen">
<p>Listen to:</p>
<ul>
<li><label for="vinRadioButton"><input id="vinRadioButton" type="radio" checked="yes" name="listenToWhat"/>v<sub>IN</sub></label></li>
<li><label for="voutRadioButton"><input id="voutRadioButton" type="radio" name="listenToWhat"/>v<sub>OUT</sub></label></li>
<li><label for="vrRadioButton"><input id="vrRadioButton" type="radio" name="listenToWhat"/>v<sub>R</sub></label></li>
</ul>
</div>
</div>
</div>
<div class="schematic-sliders">
<div class="slider-label" id="vs"></div>
<div class="slider" id="vsSlider"></div>
<div class="slider-label" id="vin"></div>
<div class="slider" id="vinSlider"></div>
<div class="slider-label" id="freq"></div>
<div class="slider" id="freqSlider"></div>
<div class="slider-label" id="vbias"></div>
<div class="slider" id="vbiasSlider"></div>
<div class="slider-label" id="r"></div>
<div class="slider" id="rSlider"></div>
<div class="slider-label" id="k"></div>
<div class="slider" id="kSlider"></div>
<div class="slider-label" id="vt"></div>
<div class="slider" id="vtSlider"></div>
<div class="slider-label" id="vmax"></div>
<div class="slider" id="vmaxSlider"></div>
</div>
</div>
<div id="graph-container">
<canvas id="graph" width="500" height="500">Your browser must support the Canvas element and have JavaScript enabled to view this tool.</canvas>
<canvas id="diag1" width="500" height="500">Your browser must support the Canvas element and have JavaScript enabled to view this tool.</canvas>
</div>
</section>

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<script type="text/javascript" src="/static/courses/6002/js/sound_labs/sound.js"></script>
<script type="text/javascript" src="/static/courses/6002/js/sound_labs/plotter.js"></script>
<script type="text/javascript" src="/static/courses/6002/js/sound_labs/circuit.js"></script>
<script type="text/javascript" src="/static/courses/6002/js/sound_labs/rc_filters.js"></script>
<h2>LAB 10B: RC FILTERS WITH FREQUENCY RESPONSE EXPERIMENT</h2>
<section class="problem">
<startouttext />
<p>Note: Use this part of the lab to build your intuition about filters and frequency response, and to have fun with music! There are no responses that need to be checked.</p>
<p>Recall from the audio lab in Week 5 that the graph plots the selected voltages from the circuit shown below. This week the circuit is an RC filter. You can also listen to various signals by selecting from the radio buttons to the right of the graph. This way you can both see and hear various signals. You can use the sliders to the right of the circuit to control various circuit and input signal parameters. (Note that you can get finer control of some of the slider values by clicking on the slider and using the arrow keys). Recall that the parameter \(V_{MAX}\) sets the maximum range on the graph. You can also select an input voltage type (e.g., sine wave, square wave, various types of music) using the drop down menu to the right of the graph. When describing AC signals, the voltages on the sliders refer to peak-to-peak values.</p>
<p>1. To begin your first experiment, use the pull down menu to select a sine wave input. Then, adjust the sliders to these approximate baseline settings:
<br />
\(v_{IN} = 3V\), \(Frequency = 1000 Hz\), \(V_{BIAS} = 0V\), \(R = 1K\Omega\), \(v_C(0) = 0V\), \(C = 110nF\), \(V_{MAX} = 2V\).
<br />
Observe the waveforms for \(v_{IN}\) and \(v_C\) in the graph. You can also listen to \(v_{IN}\) and \(v_C\). You will observe that the amplitude of \(v_C\) is slightly smaller than the amplitude of \(v_{IN}\).
<br />
Compute the break frequency of the filter circuit for the given circuit parameters. (Note that the break frequency is also called the cutoff frequency or the corner frequency).
<br />
Change the frequency of the sinusoid so that it is approximately 3 times the break frequency.
<br />
Observe the waveforms for \(v_{IN}\) and \(v_C\) in the graph. Also listen to \(v_{IN}\) and \(v_C\). Think about why the sinusoid at \(v_C\) is significantly more attenuated than the original 1KHz sinusoid.
<br />
Keeping the input signal unchanged, observe the waveforms for \(v_{IN}\) and \(v_R\) in the graph. Also listen to \(v_{IN}\) and \(v_R\). Think about why the sinusoid at \(v_R\) is significantly louder than the sinusoid at \(v_C\).</p>
<p>2. Next, use the pull down menu to select a music signal of your choice. Adjust the sliders to the approximate baseline settings:
<br />
\(v_{IN} = 3V\), \(V_{BIAS} = 0V\), \(R = 1K\Omega\), \(v_C(0) = 0V\), \(C = 110nF\), \(V_{MAX} = 2V\).
<br />
Listen to the signals at \(v_{IN}\) and \(v_C\). Notice any difference between the signals?
<br />
Next, increase the capacitance value and observe the difference in the sound of \(v_{IN}\) and \(v_C\) as the capacitance increases. You should notice that the higher frequency components of \(v_C\) are attenuated as the capacitance is increased.
Convince yourself that when the signal is taken at \(v_C\), the circuit behaves like a low-pass filter.</p>
<p>3. Re-adjust the sliders to the approximate baseline settings:
<br />
\(v_{IN} = 3V\), \(V_{BIAS} = 0V\), \(R = 1K\Omega\), \(v_C(0) = 0V\), \(C = 110nF\), \(V_{MAX} = 2V\).
<br />
Try to create a high-pass filter from the same circuit by taking the signal output across a different element and possibly changing some of the element values.
</p>
<endouttext />
</section>
<section class="tool-wrapper">
<div id="controlls-container">
<div class="graph-controls">
<div class="music-wrapper">
<select id="musicTypeSelect" size="1">
<option value = "0">Zero Input</option>
<option value = "1">Unit Impulse</option>
<option value = "2">Unit Step</option>
<option selected="selected" value = "3">Sine Wave</option>
<option value = "4">Square Wave</option>
<option value = "5">Classical Music</option>
<option value = "6">Folk Music</option>
<option value = "7">Jazz Music</option>
<option value = "8">Reggae Music</option>
</select>
<input id="playButton" type="button" value="Play" />
</div>
<div class="inputs-wrapper">
<div id="graph-output">
<p>Graph:</p>
<ul>
<li><label for="vinCheckbox"><input id="vinCheckbox" type="checkbox" checked="yes"/>v<sub>IN</sub></label></li>
<li><label for="vcCheckbox"><input id="vcCheckbox" type="checkbox" checked="yes"/>v<sub>C</sub></label> </li>
<li><label for="vrCheckbox"><input id="vrCheckbox" type="checkbox"/>v<sub>R</sub></label></li>
</ul>
</div>
<div id="graph-listen">
<p>Listen to:</p>
<ul>
<li><label for="vinRadioButton"><input id="vinRadioButton" type="radio" checked="yes" name="listenToWhat"/>v<sub>IN</sub></label></li>
<li><label for="vcRadioButton"><input id="vcRadioButton" type="radio" name="listenToWhat"/>v<sub>C</sub></label></li>
<li><label for="vrRadioButton"><input id="vrRadioButton" type="radio" name="listenToWhat"/>v<sub>R</sub></label></li>
</ul>
</div>
</div>
</div>
<div class="schematic-sliders">
<div class="slider-label" id="fc">f<sub>C</sub> = </div>
<div class="slider-label" id="vin"></div>
<div class="slider" id="vinSlider"></div>
<div class="slider-label" id="freq"></div>
<div class="slider" id="freqSlider"></div>
<div class="slider-label" id="vbias"></div>
<div class="slider" id="vbiasSlider"></div>
<div class="slider-label" id="r"></div>
<div class="slider" id="rSlider"></div>
<div class="slider-label" id="vc0"></div>
<div class="slider" id="vc0Slider"></div>
<div class="slider-label" id="c"></div>
<div class="slider" id="cSlider"></div>
<div class="slider-label" id="vmax"></div>
<div class="slider" id="vmaxSlider"></div>
</div>
</div>
<div id="graph-container">
<div id="graphTabs">
<ul>
<li><a href="#time">Time</a></li>
<li><a href="#magnitude">Magnitude</a></li>
<li><a href="#phase">Phase</a></li>
</ul>
<canvas id="time" width="500" height="500">Your browser must support the Canvas element and have JavaScript enabled to view this tool.</canvas>
<canvas id="magnitude" width="500" height="500">Your browser must support the Canvas element and have JavaScript enabled to view this tool.</canvas>
<canvas id="phase" width="500" height="500">Your browser must support the Canvas element and have JavaScript enabled to view this tool.</canvas>
</div>
<canvas id="diag2" width="500" height="500">Your browser must support the Canvas element and have JavaScript enabled to view this tool.</canvas>
</div>
</section>

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<script type="text/javascript" src="/static/courses/6002/js/sound_labs/sound.js"></script>
<script type="text/javascript" src="/static/courses/6002/js/sound_labs/plotter.js"></script>
<script type="text/javascript" src="/static/courses/6002/js/sound_labs/circuit.js"></script>
<script type="text/javascript" src="/static/courses/6002/js/sound_labs/series_rlc.js"></script>
<h2>SERIES RLC CIRCUIT WITH FREQUENCY RESPONSE EXPERIMENT</h2>
<section class="problem">
<startouttext />
<p>\(I(s) = \frac{1}{R + Ls + 1/Cs}V_{in}(s) = \frac{s/L}{s^2 + sR/L + 1/LC}V_{in}(s)\)</p>
<p>\(I(s) = \frac{s/L}{s^2 + 2\alpha s + \omega_0^2}V_{in}(s)\)</p>
<p>\(\omega_0 = \frac{1}{\sqrt{LC}} , \alpha = \frac{R}{2L}\)</p>
<p>Band-Pass Filter:</p>
<p>\(V_r(s) = RI(s) = \frac{sR/L}{s^2 + 2\alpha s + \omega_0^2}V_{in}(s) = \frac{2\alpha s}{s^2 + 2\alpha s + \omega_0^2}V_{in}(s) = \frac{2\alpha s}{(s-s_1)(s-s_2)}V_{in}(s)\)</p>
<p>Gain magnitude: \(G_R = \frac{2\alpha w}{|j\omega - s_1||j\omega - s_2|}\)</p>
<p>Phase: \(\Phi_R = \pi/2-\Phi(j\omega - s_1) -\Phi(j\omega - s_2)\)</p>
<p>Low-Pass Filter:</p>
<p>\(V_c(s) = I(s)/sC = \frac{1/LC}{s^2 + 2\alpha s + \omega_0^2}V_{in}(s) = \frac{\omega_0^2}{s^2 + 2\alpha s + \omega_0^2}V_{in}(s) = \frac{\omega_0^2}{(s-s_1)(s-s_2)}V_{in}(s)\)</p>
<p>Gain magnitude: \(G_C = \frac{\omega_0^2}{|j\omega - s_1||j\omega - s_2|}\)</p>
<p>Phase: \(\Phi_C = -\Phi(j\omega - s_1) -\Phi(j\omega - s_2)\)</p>
<p>High-Pass Filter:</p>
<p>\(V_l(s) = sLI(s) = \frac{s^2}{s^2 + 2\alpha s + \omega_0^2}V_{in}(s) = \frac{s^2}{(s-s_1)(s-s_2)}V_{in}(s)\)</p>
<p>Gain magnitude: \(G_L = \frac{\omega^2}{|j\omega - s_1||j\omega - s_2|}\)</p>
<p>Phase: \(\Phi_L = -\Phi(j\omega - s_1) -\Phi(j\omega - s_2)\)</p>
<br />
<p>Under-Damped: \(\alpha < \omega_0\)</p>
<p>Complex roots: \(s_{1,2} = -\alpha \pm j\sqrt{\omega_0^2 - \alpha^2}\)</p>
<p>Critically-Damped: \(\alpha = \omega_0\)</p>
<p>Double real root: \(s_{1,2} = -\alpha\)</p>
<p>Over-Damped: \(\alpha > \omega_0\)</p>
<p>Real roots: \(s_{1,2} = -\alpha \pm\sqrt{\alpha^2 - \omega_0^2}\)</p>
<endouttext />
</section>
<section class="tool-wrapper">
<div id="controlls-container">
<div class="graph-controls">
<div class="music-wrapper">
<select id="musicTypeSelect" size="1">
<option value = "0">Zero Input</option>
<option value = "1">Unit Impulse</option>
<option value = "2">Unit Step</option>
<option selected="selected" value = "3">Sine Wave</option>
<option value = "4">Square Wave</option>
<option value = "5">Classical Music</option>
<option value = "6">Folk Music</option>
<option value = "7">Jazz Music</option>
<option value = "8">Reggae Music</option>
</select>
<input id="playButton" type="button" value="Play" />
</div>
<div class="inputs-wrapper">
<div id="graph-output">
<p>Graph:</p>
<ul>
<li><label for="vinCheckbox"><input id="vinCheckbox" type="checkbox" checked="yes"/>v<sub>IN</sub></label></li>
<li><label for="vrCheckbox"><input id="vrCheckbox" type="checkbox"/>v<sub>R</sub></label></li>
<li><label for="vlCheckbox"><input id="vlCheckbox" type="checkbox"/>v<sub>L</sub></label></li>
<li><label for="vcCheckbox"><input id="vcCheckbox" type="checkbox" checked="yes"/>v<sub>C</sub></label> </li>
</ul>
</div>
<div id="graph-listen">
<p>Listen to:</p>
<ul>
<li><label for="vinRadioButton"><input id="vinRadioButton" type="radio" checked="yes" name="listenToWhat"/>v<sub>IN</sub></label></li>
<li><label for="vrRadioButton"><input id="vrRadioButton" type="radio" name="listenToWhat"/>v<sub>R</sub></label></li>
<li><label for="vlRadioButton"><input id="vlRadioButton" type="radio" name="listenToWhat"/>v<sub>L</sub></label></li>
<li><label for="vcRadioButton"><input id="vcRadioButton" type="radio" name="listenToWhat"/>v<sub>C</sub></label></li>
</ul>
</div>
</div>
</div>
<div class="schematic-sliders">
<div class="slider-label" id="vin"></div>
<div class="slider" id="vinSlider"></div>
<div class="slider-label" id="freq"></div>
<div class="slider" id="freqSlider"></div>
<div class="slider-label" id="vbias"></div>
<div class="slider" id="vbiasSlider"></div>
<div class="slider-label" id="r"></div>
<div class="slider" id="rSlider"></div>
<div class="slider-label" id="l"></div>
<div class="slider" id="lSlider"></div>
<div class="slider-label" id="c"></div>
<div class="slider" id="cSlider"></div>
<div class="slider-label" id="vc0"></div>
<div class="slider" id="vc0Slider"></div>
<div class="slider-label" id="i0"></div>
<div class="slider" id="i0Slider"></div>
<div class="slider-label" id="vmax"></div>
<div class="slider" id="vmaxSlider"></div>
</div>
</div>
<div id="graph-container">
<div id="graphTabs">
<ul>
<li><a href="#time">Time</a></li>
<li><a href="#magnitude">Magnitude</a></li>
<li><a href="#phase">Phase</a></li>
</ul>
<canvas id="time" width="500" height="500">Your browser must support the Canvas element and have JavaScript enabled to view this tool.</canvas>
<canvas id="magnitude" width="500" height="500">Your browser must support the Canvas element and have JavaScript enabled to view this tool.</canvas>
<canvas id="phase" width="500" height="500">Your browser must support the Canvas element and have JavaScript enabled to view this tool.</canvas>
</div>
<canvas id="diag3" width="500" height="500">Your browser must support the Canvas element and have JavaScript enabled to view this tool.</canvas>
</div>
</section>

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Test file for HTML in data

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Hint
<br/><br/>
Be careful of units here. Make sure you notice multipliers such
as u, k, m, M.