Review for Fun II Test 1
Fun II Topics for Test 1
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Op Amp Abstraction- circuit model
Inverting and non-inverting amplifiers
Sum and Difference amplifiers.
Integrator and Differentiator
Comparator and Schmidt Trigger
Op Amp Limits – voltage, current, frequency
Signal Manipulation
Phasors
Trigonometric and Exponential Fourier Series
Input-output systems
Linearity and Memory
FFT
If VCC and VEE are +/- 10V respectively, and R1 and R2 are each 20K ohms, which
of the following is true?
A. A. If V3 is a sinusoidal source of magnitude 1 volt and 0 degrees phase, Vout is a
sinusoidal waveform of the same amplitude and 180 degrees phase.
B. If V3 is a sinusoidal source of magnitude 1 volt and 0 degrees phase, Vout is a
sinusoidal waveform of the same amplitude and phase.
C. If V3 is a sinusoidal source of magnitude 1 volt and 0 degrees phase, Vout is -1 Volt.
D. If V3 is a sinusoidal source of magnitude 11 volts, the output will be a sinusoidal
waveform of 5.5 Volts
If VCC and VEE are +/- 10V respectively, and R1 and R2 are each 20K ohms, which
of the following is true?
→ A. A. If V3 is a sinusoidal source of magnitude 1 volt and 0 degrees phase, Vout is a
sinusoidal waveform of the same amplitude and 180 degrees phase.
B. If V3 is a sinusoidal source of magnitude 1 volt and 0 degrees phase, Vout is a
sinusoidal waveform of the same amplitude and phase.
C. If V3 is a sinusoidal source of magnitude 1 volt and 0 degrees phase, Vout is -1 Volt.
D. If V3 is a sinusoidal source of magnitude 11 volts, the output will be a sinusoidal
waveform of 5.5 Volts
If VCC and VEE are +/- 10V respectively, and R1 = 1K, R2 = 20K,
which of the following is true?
A. A. The maximum input signal that can be amplified without
distortion is 0.1 volts, with an output of 20 V volts Pk.-Pk.
B. The maximum input signal that can be amplified without distortion
is 0.5 volts magnitude.
C. The maximum undistorted output is 10 volts amplitude and the
phase is the same as the input voltage.
D. A square wave cannot be suitably amplified by this circuit unless the
amplitude is less than 0.1 volts.
If VCC and VEE are +/- 10V respectively, and R1 = 1K, R2 = 20K,
which of the following is true?
→
A. A. The maximum input signal that can be amplified without
distortion is 0.1 volts, with an output of 20 V volts Pk.-Pk.
B. The maximum input signal that can be amplified without distortion
is 0.5 volts magnitude.
C. The maximum undistorted output is 10 volts amplitude and the
phase is the same as the input voltage.
D. A square wave cannot be suitably amplified by this circuit unless the
amplitude is less than 0.1 volts.
Input Signal
If R1 = 1K, R2 = 9K, V3 = 0.25 V, and the
signal voltage is a 1.1V amplitude sinusoid
at 1 KHZ. VCC= VEE = +/- 10V. Which Plot
best depicts the output?
A
C
B
D
Input Signal
If R1 = 1K, R2 = 9K, V3 = 0.25 V, and the
signal voltage is a 1.1V amplitude sinusoid
at 1 KHZ. VCC= VEE = +/- 10V. Which Plot
best depicts the output?
A
→C
B
D
Suppose that the input signal is a sinusoid at 2 KHz.
Which is a reasonable setting for the horizontal scale on the
oscilloscope, assume that you wish to display several cycles
of the output in a readable fashion and that there are 10
horizontal divisions across the display?
A. 200 nS per division
B. 200 µS per division
C. 2 mS per division
D. 200 mS per division
Suppose that the input signal is a sinusoid at 2 KHz.
Which is a reasonable setting for the horizontal scale on the
oscilloscope, assume that you wish to display several cycles
of the output in a readable fashion and that there are 10
horizontal divisions across the display?
A. 200 nS per division
→ B. 200 µS per division
C. 2 mS per division
D. 200 mS per division
Suppose the input voltages and resistors are configured such that the magnitude
of the Fourier series of the output signal is given in the Figure above. Which of the
following is true?
A. The circuit is non-linear and the gain from Signal_Voltage to Vout is 2.
B. The circuit is linear and the gain from Signal_Voltage to Vout is 2.
C. The circuit is nonlinear and the amplitude of the fundamental frequency
component of Vout is 2.
D. The circuit is linear and the amplitude of the fundamental frequency
components of Vout is 2.
Suppose the input voltages and resistors are configured such that the magnitude
of the Fourier series of the output signal is given in the Figure above. Which of the
following is true?
A. The circuit is non-linear and the gain from Signal_Voltage to Vout is 2.
B. The circuit is linear and the gain from Signal_Voltage to Vout is 2.
→ C. The circuit is nonlinear and the amplitude of the fundamental frequency
component of Vout is 2.
D. The circuit is linear and the amplitude of the fundamental frequency
components of Vout is 2.
Suppose you need to generate a simple square wave using a single opamp driven
with a noise-free sinusoidal input.
Which of the following will always work, regardless of the input amplitude?
A. A single opamp with one input biased at 0 volts and the sinusoid applied to
the other input and no feedback.
B. A single opamp with negative feedback, and the sine wave applied to the noninverting input.
C. A single opamp with positive feedback as long as the magnitude of the trip
points are greater than the magnitude of input sinusoid.
D. None of the other answers is correct.
Suppose you need to generate a simple square wave using a single opamp driven
with a noise-free sinusoidal input.
Which of the following will always work, regardless of the input amplitude?
→ A. A single opamp with one input biased at 0 volts and the sinusoid applied to
the other input and no feedback.
B. A single opamp with negative feedback, and the sine wave applied to the noninverting input.
C. A single opamp with positive feedback as long as the magnitude of the trip
points are greater than the magnitude of input sinusoid.
D. None of the other answers is correct.
Suppose you need to generate a simple square wave using a single opamp
driven with a noise-free sinusoidal input.
Which of the following is true about the system?
A. The system is linear and memoryless.
B. The system is nonlinear and memoryless.
C. The system is linear and has memory.
D. The system is nonlinear and has memory.
Suppose you need to generate a simple square wave using a single opamp
driven with a noise-free sinusoidal input.
Which of the following is true about the system?
A. The system is linear and memoryless.
→ B. The system is nonlinear and memoryless.
C. The system is linear and has memory.
D. The system is nonlinear and has memory.
Suppose you need to generate a simple square wave using a single opamp
driven with a noise-free sinusoidal input.
Let the input be precisely Vin(t)=sin(π 1000 t). Consider the
trigonometric FS of the output signal. Which statement is true?
A. bn = 0 for all n
B. an = 0 for all n
C. Both bn = 0 and an = 0 for all n.
D. None of the other answers is correct.
Suppose you need to generate a simple square wave using a single opamp
driven with a noise-free sinusoidal input.
Let the input be precisely Vin(t)=sin(π 1000 t). Consider the
trigonometric FS of the output signal. Which statement is true?
A. bn = 0 for all n
→ B. an = 0 for all n
C. Both bn = 0 and an = 0 for all n.
D. None of the other answers is correct.
Suppose you need to generate a simple square wave using a single opamp driven
with a noise-free sinusoidal input.
Let the input be precisely Vin(t)=sin(π 1000 t). Consider the
trigonometric FS of the output signal.
For the FS in the question above, the fundamental frequency is:
A. 500 HZ
B. 1000 HZ
C. 2000 HZ
D. None of the other answers is correct.
Suppose you need to generate a simple square wave using a single opamp driven
with a noise-free sinusoidal input.
Let the input be precisely Vin(t)=sin(π 1000 t). Consider the
trigonometric FS of the output signal.
For the FS in the question above, the fundamental frequency is:
→ A. 500 HZ
B. 1000 HZ
C. 2000 HZ
D. None of the other answers is correct.
R1 is 10 Ω and carries a current of 1 ampere. R2 is 5 Ω.
What current is supplied by I1, the DC current source?
A. 3 amps
B. 5 amps
C. 2 amps
D. None of the other responses is correct.
R1 is 10 Ω and carries a current of 1 ampere. R2 is 5 Ω.
What current is supplied by I1, the DC current source?
→ A. 3 amps
B. 5 amps
C. 2 amps
D. None of the other responses is correct.
A system is known to only cause a delay of 𝑡0 =
0.125 µs and a gain of -3. The input to the system is
the sinusoid:
𝑥 𝑡 = 3 sin 2𝜋𝑓0 𝑡
where 𝑓0 = 1 MHz.
What could the output of the system be?
A. A sinusoid with frequency 2π/t0 Hz.
B. A sinusoid with frequency 1/t0 Hz.
C. A sinusoid with frequency 2πf0 Hz.
D. None of the above.
A system is know to only cause a delay of 𝑡0 =
0.125 µs and a gain of -3. The input to the system is
the sinusoid:
𝑥 𝑡 = 3 sin 2𝜋𝑓0 𝑡
where 𝑓0 = 1 MHz.
What could the output of the system be?
→
A. A sinusoid with frequency 2π/t0 Hz.
B. A sinusoid with frequency 1/t0 Hz.
C. A sinusoid with frequency 2πf0 Hz.
D. None of the above.
A system is know to only cause a delay of 𝑡0 =
0.125 µs and a gain of -3. The input to the system is
the sinusoid:
𝑥 𝑡 = 3 sin 2𝜋𝑓0 𝑡
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
A system is know to only cause a delay of 𝑡0 =
0.125 µs and a gain of -3. The input to the system is
the sinusoid:
𝑥 𝑡 = 3 sin 2𝜋𝑓0 𝑡
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 each of the three systems described below determine if it is linear and if it
has memory:
Rubric:
A: Yes
B: No
C: Cannot tell
A system with input x(t) and output y(t)= x(0) + x(t).
Linear
Memory
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
Memory
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
Memory
For each of the three systems described below determine if it is linear and if it
has memory:
Rubric:
A: Yes
B: No
C: Cannot tell
A system with input x(t) and output y(t)= 3 + x(t).
A. Linear
B. Memory
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.
B. Linear
B. Memory
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.
A. Linear
A. Memory
Suppose you measure the output y(t) of a system to
input x(t) = cos(ω0t).
(a) If y(t) = cos(2ω0t + π/2), what does that tell you about
the linearity of the
system? If the system is linear, what can you tell me
about H(s)?
(b) If y(t) = 2 cos(ω0t + π/2), what does that tell you
about the linearity of the
system? If the system is linear, what can you tell me
about H(s)?
Suppose you measure the output y(t) of a system to
input x(t) = cos(ω0t).
(a) If y(t) = cos(2ω0t + π/2), what does that tell you about
the linearity of the
system? Nonlinear
If the system is linear, what can you tell me about H(s)?
Nothing
(b) If y(t) = 2 cos(ω0t + π/2), what does that tell you
about the linearity of the
system? Could be linear
If the system is linear, what can you tell me about H(s)?
Know 𝐻(𝑠) 𝑠=𝑗𝜔0 = 2𝑒 𝜋/2
A periodic signal x(t) has period T = π
and complex exponential Fourier
series given by
D1 = D−2 = j, D−1 = D2 = −j
with all other Fourier series
coefficients equal to zero.
Find x(t).
A periodic signal x(t) has period T = π
and complex exponential Fourier
series given by
D1 = D−2 = j, D−1 = D2 = −j
with all other Fourier series
coefficients equal to zero.
Find x(t):
𝑥 𝑡 = −2 sin 2𝑡 + 2sin(4𝑡)
𝜋𝑡
2
Let a signal 𝑥 𝑡 = −4 cos
− 5sin(𝜋𝑡/7 + 𝜋 /4) .
Which statement is true?
A. The magnitude of the fundamental frequency is
42 + 52
B. The fundamental frequency is π/2 and the magnitude
of the 7th harmonic is 5.
C. The fundamental frequency is π/14 and the magnitude
of the 7th harmonic is 4.
D. The fundamental frequency is π and the magnitude of
the 1/7th harmonic is 5.
E. None of the other answers is correct.
𝜋𝑡
2
→
𝜋𝑡
− 5sin(
7
𝜋
)
4
Let a signal 𝑥 𝑡 = −4 cos
+
. Which
statement is true?
A. The magnitude of the fundamental frequency is
42 + 52
B. The fundamental frequency is π/2 and the magnitude
of the 7th harmonic is 5.
C. The fundamental frequency is π/14 and the magnitude
of the 7th harmonic is 4.
D. The fundamental frequency is π and the magnitude of
the 1/7th harmonic is 5.
E. None of the other answers is correct.
A periodic signal x(t) is uniformly sampled at a constant rate
such that 64 samples are collected and placed in a vector. The
FFT of this vector is a vector we call FFT_x. Which of the
following is true:
A. The first element of FFT_x approximates the DC value of
x(t) and the second approximates the positive
fundamental frequency component of the FS.
B. The first element of FFT_x is exactly the DC value of x(t)
and the second is exactly the positive fundamental
frequency component of the FS.
C. The first element of FFT_x/64 approximates the DC value
of x(t) and the second approximates the positive
fundamental frequency component of the FS.
→
A periodic signal x(t) is uniformly sampled at a constant rate
such that 64 samples are collected and placed in a vector. The
FFT of this vector is a vector we call FFT_x. Which of the
following is true:
A. The first element of FFT_x approximates the DC value of
x(t) and the second approximates the positive
fundamental frequency component of the FS.
B. The first element of FFT_x is exactly the DC value of x(t)
and the second is exactly the positive fundamental
frequency component of the FS.
C. The first element of FFT_x/64 approximates the DC value
of x(t) and the second approximates the positive
fundamental frequency component of the FS.
Let 𝑥(𝑡) = 𝑡𝑢(𝑡)
Sketch 𝑦(𝑡) = 𝑥((5 − 𝑡)/2).
Let 𝑥(𝑡) = 𝑡𝑢(𝑡)
Sketch 𝑦(𝑡) = 𝑥((5 − 𝑡)/2).