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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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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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