ECE Fun II Test 2 Review
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ECE Fun II
Test 2
Topics
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Fourier transform: U&Y, 5-7, 5-8, some of 5-10
o Definition
o Properties
o Basic functions
LTIC systems U&Y, 5-12
o Input/output in time and frequency domains
o Sinusoids, periodic, and transient functions
Impulse Response U&Y,
o Delta function properties
o Convolution
o h(t)
Matlab, Tutorials and U&Y Appendix D
o Basic syntax
o Creating signals
o Using the fft and conv functions
o Plotting
Diodes A&L 16.1 thru 16.3
o Ideal Model
o Constant forward voltage drop model
o CFVD + Internal resistance model
o Exponential model
o Use of diodes with opamps.
MOSFETs A&L 7.1-7.4, 6.7
o Basic operation, terminals and polarities
o Biasing
o Small signal model J&B 13.8,13.10
 Transconductance
 Assumed linear range
o Common source amplifier
Given the following circuit values: R1=R4=1K, R2=R3=3K, V1=12V. Assuming
the Constant Forward Voltage Drop model, (CFVD, VF=0.7V) which of the
following is true?
A. The diode current is approximately 0.5 mA.
B. The diode current is approximately 1.0 mA
C. The diode current is approximately 6.0 mA
D. None of the other choices is correct.
Given the following circuit values: R1=R4=1K, R2=R3=3K, V1=12V. Assuming
the Constant Forward Voltage Drop model, (CFVD, VF=0.7V) which of the
following is true?
A. The diode current is approximately 0.5 mA.
B. The diode current is approximately 1.0 mA
C. The diode current is approximately 6.0 mA
D. None of the other choices is correct.
If R2=R3=1K, R4=R1=1000K, V1=10.7 V, and assuming the CFVD model,
which of the following is true?
A. The diode current is approximately 5 mA.
B. The diode current is approximately 2.5 mA.
C. The diode is not conducting.
D. None of the other choices is correct.
If R2=R3=1K, R4=R1=1000K, V1=10.7 V, and assuming the CFVD model,
which of the following is true?
A. The diode current is approximately 5 mA.
B. The diode current is approximately 2.5 mA.
C. The diode is not conducting.
D. None of the other choices is correct.
Which of the following best describes the display?
A. The system settings for the vertical scale should be increased, i.e.
more volts per division.
B. The system settings for the horizontal scale should be decreased,
i.e. less time per division .
C. Both the vertical and horizontal scales are set incorrectly.
D. None of the other choices is correct.
Which of the following best describes the display?
A. The system settings for the vertical scale should be increased, i.e.
more volts per division.
B. The system settings for the horizontal scale should be decreased,
i.e. less time per division .
C. Both the vertical and horizontal scales are set incorrectly.
D. None of the other choices is correct.
If the setting of the signal generator is 2 VP-P and the
oscilloscope displays a 0.1 V amplitude signal, which of the
following is true.
A. The probe setting is at 10X but the VB setting is at 1X .
B. The signal generator is set at 10X, and the probe is set to 1X.
C. The signal generator is set to 10X and the probe is set to 10X.
D. None of the other choices is correct.
If the setting of the signal generator is 2 VP-P and the
oscilloscope displays a 0.1 V amplitude signal, which of the
following is true.
A. The probe setting is at 10X but the VB setting is at 1X .
B. The signal generator is set at 10X, and the probe is set to 1X.
C. The signal generator is set to 10X and the probe is set to 10X.
D. None of the other choices is correct.
You are given the following circuit in the figure. Assume that the op amp has infinite
gain, unlimited bandwidth, but is bounded in output by VCC and VEE, where VCC is
the most positive voltage in the system and VEE is the most negative voltage in the
system.
A
C
B
D
You are given the following circuit in the figure. Assume that the op amp has infinite
gain, unlimited bandwidth, but is bounded in output by VCC and VEE, where VCC is
the most positive voltage in the system and VEE is the most negative voltage in the
system.
A
C
B
D
Suppose a simple system, such as a channel from a cell tower
to a cell phone, has impulse response as shown in the figure
below.
This impulse response resulted from one signal path with delay t0=0.125
µs. The input to the system is the sinusoid:
x(t)=3sin2πf0t
where f0=1 MHz.
What could the output of the system, i.e., the signal received at the cell
phone, be?
A. A sinusoid with frequency 1/t0 Hz.
B. A sinusoid with frequency 2π/t0 Hz.
C. A sinusoid with frequency 2πf0 Hz.
D. None of the above.
Suppose a simple system, such as a channel from a cell tower
to a cell phone, has impulse response as shown in the figure
below.
This impulse response resulted from one signal path with delay t0=0.125
µs. The input to the system is the sinusoid:
x(t)=3sin2πf0t
where f0=1 MHz.
What could the output of the system, i.e., the signal received at the cell
phone, be?
A. A sinusoid with frequency 1/t0 Hz.
B. A sinusoid with frequency 2π/t0 Hz.
C. A sinusoid with frequency 2πf0 Hz.
D. None of the above.
Suppose a simple system, such as a channel from a cell tower
to a cell phone, has impulse response as shown in the figure
below.
This impulse response resulted from one signal path with delay t0=0.125
µs. The input to the system is the sinusoid:
x(t)=3sin2πf0t
where f0=1 MHz.
What is the phasor form of the output signal?
A. 9𝑒 𝑗𝜋/4
B. 9𝑒 −𝑗𝜋/4
C. 9𝑒 −𝑗3𝜋/4
D. 9𝑒 𝑗3𝜋/4
Suppose a simple system, such as a channel from a cell tower
to a cell phone, has impulse response as shown in the figure
below.
This impulse response resulted from one signal path with delay t0=0.125
µs. The input to the system is the sinusoid:
x(t)=3sin2πf0t
where f0=1 MHz.
What is the phasor form of the output signal?
A. 9𝑒 𝑗𝜋/4
B. 9𝑒 −𝑗𝜋/4
C. 9𝑒 −𝑗3𝜋/4
D. 9𝑒 𝑗3𝜋/4
For the system described below determine if it is linear and time invariant.
Rubric:
A: Yes
B: No
C: Cannot tell
 A system with input x(t) and output y(t)= x(0) + x(t).
Linear?
Time invariant?
For the system described below determine if it is linear and time invariant.
Rubric:
A: Yes
B: No
C: Cannot tell
 A system with input x(t) and output y(t)= x(0) + x(t).
Linear? A
Time invariant?
For the system described below determine if it is linear and time invariant.
Rubric:
A: Yes
B: No
C: Cannot tell
 A system with input x(t) and output y(t)= x(0) + x(t).
Linear? A
Time invariant? B
For the system described below determine if it is linear and time invariant.
Rubric:
A: Yes
B: No
C: Cannot tell
 An ordinary light switch, where the input is the force
with which the switch is pressed, and the output is the
amount of light produced.
Linear?
Time invariant?
For the system described below determine if it is linear and time invariant.
Rubric:
A: Yes
B: No
C: Cannot tell
 An ordinary light switch, where the input is the force
with which the switch is pressed, and the output is the
amount of light produced.
Linear? B
Time invariant?
For the system described below determine if it is linear and time invariant.
Rubric:
A: Yes
B: No
C: Cannot tell
 An ordinary light switch, where the input is the force
with which the switch is pressed, and the output is the
amount of light produced.
Linear? B
Time invariant? A
For the system described below determine if it is linear and time invariant.
Rubric:
A: Yes
B: No
C: Cannot tell
 A second order passive RLC circuit driven by an input
voltage Vin(t) and measuring as output the voltage drop
across the capacitor. Assume the components have zero
energy stored before the input is applied.
Linear?
Time invariant?
For the system described below determine if it is linear and time invariant.
Rubric:
A: Yes
B: No
C: Cannot tell
 A second order passive RLC circuit driven by an input
voltage Vin(t) and measuring as output the voltage drop
across the capacitor. Assume the components have zero
energy stored before the input is applied.
Linear? A
Time invariant?
For the system described below determine if it is linear and time invariant.
Rubric:
A: Yes
B: No
C: Cannot tell
 A second order passive RLC circuit driven by an input
voltage Vin(t) and measuring as output the voltage drop
across the capacitor. Assume the components have zero
energy stored before the input is applied.
Linear? A
Time invariant? A
Let the input x(t) and impulse response h(t) to a linear time invariant system be:
Determine whether each of the following statements about the
output of the system y(t) is true (A) or false (B):
•y(t) is even symmetric
•y(t) = 0 for all t < 0
•The maximum value for y(t) is 9
•y(t) is piecewise linear
•The duration of the non-zero portion of y(t) is 6 s.
Let the input x(t) and impulse response h(t) to a linear time invariant system be:
Determine whether each of the following statements about the
output of the system y(t) is true (A) or false (B):
•y(t) is even symmetric F
•y(t) = 0 for all t < 0
•The maximum value for y(t) is 9
•y(t) is piecewise linear
•The duration of the non-zero portion of y(t) is 6 s.
Let the input x(t) and impulse response h(t) to a linear time invariant system be:
Determine whether each of the following statements about the
output of the system y(t) is true (A) or false (B):
•y(t) is even symmetric F
•y(t) = 0 for all t < 0 F
•The maximum value for y(t) is 9
•y(t) is piecewise linear
•The duration of the non-zero portion of y(t) is 6 s.
Let the input x(t) and impulse response h(t) to a linear time invariant system be:
Determine whether each of the following statements about the
output of the system y(t) is true (A) or false (B):
•y(t) is even symmetric F
•y(t) = 0 for all t < 0 F
•The maximum value for y(t) is 9 T
•y(t) is piecewise linear
•The duration of the non-zero portion of y(t) is 6 s.
Let the input x(t) and impulse response h(t) to a linear time invariant system be:
Determine whether each of the following statements about the
output of the system y(t) is true (A) or false (B):
•y(t) is even symmetric F
•
•y(t) = 0 for all t < 0 F
•The maximum value for y(t) is 9 T
•y(t) is piecewise linear F
•The duration of the non-zero portion of y(t) is 6 s.
Let the input x(t) and impulse response h(t) to a linear time invariant system be:
Determine whether each of the following statements about the
output of the system y(t) is true (A) or false (B):
•y(t) is even symmetric F
•
•y(t) = 0 for all t < 0 F
•The maximum value for y(t) is 9 T
•y(t) is piecewise linear F
•The duration of the non-zero portion of y(t) is 6 s. T
Which of the following is true?
A. By displaying a large number of cycles, the FFT math function will give a good
approximation of the Fourier series for the displayed signal.
B. In order to get a good approximation of the Fourier series, it will be necessary to decrease
the horizontal scale until no more than 3 cycles of the signal are displayed.
C. In order to get a good approximation of the Fourier series for the displayed signal, it will
be necessary to decrease the vertical scale, i.e. fewer volts per division such that the
peaks of the signal extend beyond the screen limits in order to minimize the effects of
amplitude variations.
D. None of the other choices is correct.
Which of the following is true?
A. By displaying a large number of cycles, the FFT math function will give a good
approximation of the Fourier series for the displayed signal.
B. In order to get a good approximation of the Fourier series, it will be necessary to decrease
the horizontal scale until no more than 3 cycles of the signal are displayed.
C. In order to get a good approximation of the Fourier series for the displayed signal, it will
be necessary to decrease the vertical scale, i.e. fewer volts per division such that the
peaks of the signal extend beyond the screen limits in order to minimize the effects of
amplitude variations.
D. None of the other choices is correct.
For the time function 𝑥 𝑡 (not periodic) on the
left, choose a plot on the right that corresponds
to the magnitude Fourier transform of x 𝑡 :
A
B
C
D
For the time function 𝑥 𝑡 (not periodic) on the
left, choose a plot on the right that corresponds
to the magnitude Fourier transform of x 𝑡 :
A
B
C
D
For the time function 𝑥 𝑡 (not periodic) on the
left, choose a plot on the right that corresponds
to the magnitude Fourier transform of x 𝑡 :
A
B
C
D
For the time function 𝑥 𝑡 (not periodic) on the
left, choose a plot on the right that corresponds
to the magnitude Fourier transform of x 𝑡 :
A
B
C
D
For the time function 𝑥 𝑡 (not periodic) on the
left, choose a plot on the right that corresponds
to the magnitude Fourier transform of x 𝑡 :
A
B
C
D
For the time function 𝑥 𝑡 (not periodic) on the
left, choose a plot on the right that corresponds
to the magnitude Fourier transform of x 𝑡 :
A
B
C
D
For the time function 𝑥 𝑡 (not periodic) on the
left, choose a plot on the right that corresponds
to the magnitude Fourier transform of x 𝑡 :
A
B
C
D
For the time function 𝑥 𝑡 (not periodic) on the
left, choose a plot on the right that corresponds
to the magnitude Fourier transform of x 𝑡 :
A
B
C
D
Assume that the circuit is operating in the saturated region for Q1.
Which of the following is true?
A. If the value of RD is reduced by a factor of 2, the voltage gain
will go down, approximately by 2 but the operating region will
not change.
B. If the value of RD is increased by a factor of 2 the voltage gain
will increase by 2 and the operating region will not change.
C. If R1 is decreased the operating region will not change.
D. None of the other choices is true.
Assume that the circuit is operating in the saturated region for Q1.
Which of the following is true?
A. If the value of RD is reduced by a factor of 2, the voltage gain
will go down, approximately by 2 but the operating region will
not change.
B. If the value of RD is increased by a factor of 2 the voltage gain
will increase by 2 and the operating region will not change.
C. If R1 is decreased the operating region will not change.
D. None of the other choices is true.
Assume that RD is 2K, RL is 100K and the overall voltage gain is 3 with a gm of
0.05S. The frequency of V2 is 100KHZ and the circuit is operating in mid-band and
the small signal model applies. Which of the following is true?
A. The voltage gain will be relatively stable over significant changes in the
values of the circuit parameters for Q1.
B. RS affects the value of the low-pass breakpoint associated with C2.
C. If R1 is decreased, the value of the gain will decrease, but the breakpoint
frequencies for the overall circuit will not be affected.
D. None of the other answers is correct.
Assume that RD is 2K, RL is 100K and the overall voltage gain is 3 with a gm of
0.05S. The frequency of V2 is 100KHZ and the circuit is operating in mid-band and
the small signal model applies. Which of the following is true?
A. The voltage gain will be relatively stable over significant changes in the
values of the circuit parameters for Q1.
B. RS affects the value of the low-pass breakpoint associated with C2.
C. If R1 is decreased, the value of the gain will decrease, but the breakpoint
frequencies for the overall circuit will not be affected.
D. None of the other answers is correct.
Using the values from the previous question, assume that a 10000 µF capacitor is
placed in parallel with RS. Which of the following is true?
A. The voltage gain would increase to approximately 100, but the input signal
would have to be reduced to stay in the range of operation for which the
small signal model would apply.
B. The voltage gain would decrease dramatically as this capacitor would short
the signal to ground.
C. The voltage gain would be unaffected, but the Q point would shift towards
the triode region.
D. None of the other choices is correct.
Using the values from the previous question, assume that a 10000 µF capacitor is
placed in parallel with RS. Which of the following is true?
A. The voltage gain would increase to approximately 100, but the input signal
would have to be reduced to stay in the range of operation for which the
small signal model would apply.
B. The voltage gain would decrease dramatically as this capacitor would short
the signal to ground.
C. The voltage gain would be unaffected, but the Q point would shift towards
the triode region.
D. None of the other choices is correct.
Consider a LTIC system. Let the frequency response be given by
𝐻 𝜔 = 3𝜋𝑗(𝑟𝑒𝑐𝑡 𝜔 − 10 − 𝑟𝑒𝑐𝑡 𝜔 + 10 ).
What is a correct expression for the impulse response?
A. ℎ 𝑡 = −3 sinc(10𝑡)
B. ℎ 𝑡 = −3 𝑗 cos 10𝑡 sinc(𝑡/2)
C. ℎ 𝑡 = −3 cos 10𝑡 sinc(𝑡/2)
D. ℎ 𝑡 = −3 sin 10𝑡 sinc(𝑡/2)
Consider a LTIC system. Let the frequency response be given by
𝐻 𝜔 = 3𝜋𝑗(𝑟𝑒𝑐𝑡 𝜔 − 10 − 𝑟𝑒𝑐𝑡 𝜔 + 10 ).
What is a correct expression for the impulse response?
A. ℎ 𝑡 = −3 sinc(10𝑡)
B. ℎ 𝑡 = −3 𝑗 cos 10𝑡 sinc(𝑡/2)
C. ℎ 𝑡 = −3 cos 10𝑡 sinc(𝑡/2)
D. ℎ 𝑡 = −3 sin 10𝑡 sinc(𝑡/2)
Consider a LTIC system. Let the frequency response be given by
𝐻 𝜔 = 3𝜋𝑗(𝑟𝑒𝑐𝑡 𝜔 − 10 − 𝑟𝑒𝑐𝑡 𝜔 + 10 ).
Let the Fourier transform of an input to the system be given by 𝑋(𝜔). What is the
Fourier transform of the output of the system?
A. 𝑌 𝜔 = 𝑋 𝜔 ∗ 𝐻 𝜔
B. 𝑌 𝜔 = sin(10𝑡)𝑋 𝜔
C. 𝑌 𝜔 = 𝑋 𝜔 𝐻 𝜔
D. 𝑌 𝜔 = 𝑋 𝜔
Consider a LTIC system. Let the frequency response be given by
𝐻 𝜔 = 3𝜋𝑗(𝑟𝑒𝑐𝑡 𝜔 − 10 − 𝑟𝑒𝑐𝑡 𝜔 + 10 ).
Let the Fourier transform of an input to the system be given by 𝑋(𝜔). What is the
Fourier transform of the output of the system?
A. 𝑌 𝜔 = 𝑋 𝜔 ∗ 𝐻 𝜔
B. 𝑌 𝜔 = sin(10𝑡)𝑋 𝜔
C. 𝑌 𝜔 = 𝑋 𝜔 𝐻 𝜔
D. 𝑌 𝜔 = 𝑋 𝜔
Consider a LTIC system. Let the frequency response be given by
𝐻 𝜔 = 3𝜋𝑗(𝑟𝑒𝑐𝑡 𝜔 − 10 − 𝑟𝑒𝑐𝑡 𝜔 + 10 ).
Let the input to the system be given by 𝑥 𝑡 = −cos(10𝑡 + 0.1). What is the
output of the system?
𝜋
A. 𝑥 𝑡 = cos(10𝑡 + 0.1 + 2 )
𝜋
B. 𝑥 𝑡 = 3cos(10𝑡 + 0.1 + 2 )
C. 𝑥 𝑡 = −3𝜋𝑗cos(10𝑡 + 0.1)
𝜋
D. 𝑥 𝑡 = 3𝜋cos(10𝑡 + 0.1 − 2 )
Consider a LTIC system. Let the frequency response be given by
𝐻 𝜔 = 3𝜋𝑗(𝑟𝑒𝑐𝑡 𝜔 − 10 − 𝑟𝑒𝑐𝑡 𝜔 + 10 ).
Let the input to the system be given by 𝑥 𝑡 = −cos(10𝑡 + 0.1). What is the
output of the system?
𝜋
A. 𝑥 𝑡 = cos(10𝑡 + 0.1 + 2 )
𝜋
B. 𝑥 𝑡 = 3cos(10𝑡 + 0.1 + 2 )
C. 𝑥 𝑡 = −3𝜋𝑗cos(10𝑡 + 0.1)
𝜋
D. 𝑥 𝑡 = 3𝜋cos(10𝑡 + 0.1 − 2 )
Find a compact expression for the Fourier transform of
𝑥 𝑡 = 𝑠𝑛𝑔 𝑡 cos 2000𝜋𝑡 ,
where
s𝑛𝑔 𝑡 =
1 𝑡>0
−1 𝑡 < 0
Find a compact expression for the Fourier transform of
𝑥 𝑡 = 𝑠𝑛𝑔 𝑡 cos 2000𝜋𝑡 ,
where
s𝑛𝑔 𝑡 =
1 𝑡>0
−1 𝑡 < 0
−𝑗2𝜔
(𝜔 2 − 2000𝜋)2
Find a compact expression for the inverse Fourier transform of a
frequency response 𝐻(𝜔) with magnitude and phase
𝐻 𝜔
=
1
0
𝜔 < 2000𝜋
otherwise
∡𝐻 𝜔 = −30𝜔
Find a compact expression for the inverse Fourier transform of a
frequency response 𝐻(𝜔) with magnitude and phase
𝐻 𝜔
=
1
0
𝜔 < 2000𝜋
otherwise
∡𝐻 𝜔 = −30𝜔
2000𝑠𝑖𝑛𝑐(2000𝜋 𝑡 − 30 )
The first four lines of a Matlab script are as follows:
dt=0.01;
t=0:dt:3;
x=sin(2*pi*t);
X=fft(x);
What command to follow produces the
following output:
A. plot(X)
B. plot(phase(X))
C. plot(abs(X))
D. plot(abs(x))
The first four lines of a Matlab script are as follows:
dt=0.01;
t=0:dt:3;
x=sin(2*pi*t);
X=fft(x);
What command to follow produces the
following output:
A. plot(X)
B. plot(phase(X))
C. plot(abs(X))
D. plot(abs(x))
The first four lines of a Matlab script are as follows:
dt=0.01;
t=0:dt:3;
x=sin(2*pi*t);
X=fft(x);
What command creates a vector of samples of
(sin 2𝜋𝑡)[𝑢 𝑡 − 𝑢 𝑡 − 3 ] ∗ 𝑒 −10𝑡 𝑢 𝑡 ,
where ‘∗’ represents convolution?
A. x*e^(-10t);
B. conv(x,e^(-10t))*dt;
C. conv(x,exp(-10*t));
D. conv(x,exp(-10*t))*dt;
The first four lines of a Matlab script are as follows:
dt=0.01;
t=0:dt:3;
x=sin(2*pi*t);
X=fft(x);
What command creates a vector of samples of
(sin 2𝜋𝑡)[𝑢 𝑡 − 𝑢 𝑡 − 3 ] ∗ 𝑒 −10𝑡 𝑢 𝑡 ,
where ‘∗’ represents convolution?
A. x*e^(-10t);
B. conv(x,e^(-10t))*dt;
C. conv(x,exp(-10*t));
D. conv(x,exp(-10*t))*dt;
The first four lines of a Matlab script are as follows:
dt=0.01;
t=0:dt:3;
x=sin(2*pi*t);
X=fft(x);
What is the best description for the contents of vector X?
A. X is the Fourier transform of the signal (sin 2𝜋𝑡)[𝑢 𝑡 − 𝑢 𝑡 − 3 ].
B. X is the Fourier series of the signal (sin 2𝜋𝑡)[𝑢 𝑡 − 𝑢 𝑡 − 3 ].
C. X contains scaled values of the Fourier series of signal (sin 2𝜋𝑡)[𝑢 𝑡 − 𝑢 𝑡 − 3 ].
D. X is the Fourier transform of the vector x.
The first four lines of a Matlab script are as follows:
dt=0.01;
t=0:dt:3;
x=sin(2*pi*t);
X=fft(x);
What is the best description for the contents of vector X?
A. X is the Fourier transform of the signal (sin 2𝜋𝑡)[𝑢 𝑡 − 𝑢 𝑡 − 3 ].
B. X is the Fourier series of the signal (sin 2𝜋𝑡)[𝑢 𝑡 − 𝑢 𝑡 − 3 ].
C. X contains scaled values of the Fourier series of signal (sin 2𝜋𝑡)[𝑢 𝑡 − 𝑢 𝑡 − 3 ].
D. X is the Fourier transform of the vector x.