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Q1
(15 points possible)The circuit below shows a single-stage amplifier designed around a"QUADFET", a hypothetical transistor similar to a MOSFET, except that
For the purposes of this problem, assume that the QUADFET gainparameter is and that its threshold voltage is
.
Figure 1-1
In the circuit above, , , , , . The saturation-region models for the QUADFET are shownbelow, where (a) is the large-signal (bias) model, and (b) is the small-signal(incremental) model. Note that in both transistor models.
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Math Review
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Practice Exam(Not Graded)
Final Exam
FinalFinal due May 12, 2016at 15:00 UTC
MITx: 6.002.3x Circuits and Electronics 3: Applications
Figure 1-2
For an input signal of the form , the complexamplitude of the output signal will be of theform:
(a) Calculate the numerical value of the high-frequency gain . Expressyour answer to two decimal places.
(b) Calculate the numerical value of the time constant , in milli-seconds (
).
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Q2
(15 points possible)Consider the circuit shown in Figure 2-1, with , ,
radians/second, , and .
Figure 2-1
NOTE: Since the values for , , , and are all provided in the problemstatement, none of these variables should appear in your expressions forparts (a) to (d). Your expressions should only contain functions, numbers,and the variable .
(a) Derive the expression for in terms of , in (milli-amps).
(b) Derive the expression for in terms of , in (volts).
(c) Derive the expression for in terms of , in (milli-amps).
(d) Derive the expression for in terms of , in (volts).
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Q3
(15 points possible)Consider the circuit shown in Figure 3-1. Assume that the op-amp is ideal,and .
Figure 3-1
We model the two diodes with the following I-V characteristics:
where is the current through the diode, is the reverse biassaturation current, is the voltage across the diode, and
is the thermal voltage.
(a) Given , calculate the numerical value for , in milli-Volts (). Express your answer to two decimal places.
(b) Given , calculate the numerical value for , in milli-Volts ( ).
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Q4
(15 points possible)
Assume that the MOSFET in the following circuit behaves according to and
when operating in its saturation region, . Furtherassume that the op-amp in the circuit is ideal.
Figure 4-1
(a) Under these assumptions (and that the MOSFET is operating in itssaturation region), derive the expression of as a function of , interms of one or more of the variables , , , , and .
Enter "VS" for , "VT" for , and "vIN" for .
Note carefully the polarity of the two voltage sources; one is drawn upside downrelative to the other.
(b) Derive the expression of the maximum value of , in terms of one ormore of the variables , , , , and , such that the MOSFEToperates in its saturation region.
Enter "VS" for , "VT" for , and "vIN" for .
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Q5
(10 points possible)For the circuit shown below, find an expression for the value of that willbalance out the bridge to make , for an input voltage
. Express your answer in terms of one or more of thecircuit parameters , , , and . To specify , enter "w".
Figure 5-1
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Q6
(15 points possible)Consider the following circuit. Assume the op-amps are ideal.
Voltage source
Figure 6-1
(a) Derive an expression for the voltage difference in terms of oneor more of the circuit parameters , , and . To specify , enter "RA".
(b) Derive an expression for in terms of one or more of the circuitparameters , , and . To specify , enter "RA".
(c) The output terminals A-A', loaded by the resistor , implements a(n):
Amplifier
Current source
Comparator
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Q7
(15 points possible)Consider each of the following circuits and match the indicated variable tothe form of its response for by selecting the appropriate lettercorresponding to the waveforms in Figure 7-1. The waveforms mayrepresent current or voltage as a function of time for . The arrowsrepresent the slope of the curve at . Assume the parameters , ,
, , and are all positive. For your convenience, a smaller copy ofFigure 7-1 is repeated within each sub-question.
Figure 7-1
(a) Given , where is the unit step function, ,
, and in the circuit shown in Figure 7-2, the form
of :
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Figure 7-2
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(b) Given , where is the Dirac delta function,
, , and in the circuit shown in Figure
7-3, the form of :
Figure 7-3
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(c) Given , , and in the circuit
shown in Figure 7-4, the form of :
Figure 7-4
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(d) Given and in the circuit shown in Figure 7-5, the form of :
Figure 7-5
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