In this circuit, the element values are R1  4 kΩ , R2  2 kΩ , R3  6 kΩ , R4  5 kΩ
and C1  50 nF , C2  1μF . The op amp is ideal.
Determine the voltage transfer function H(j) and rearrange it into pole/zero form.
Spring 2015, Exam #4, Problem #1
Answer:
4
j
1
5000
1
In this circuit, the element values are R1  200 Ω , R2  5 kΩ , C1  4 μF , C2  20 nF .
The value of k is 250 mA/V .
Determine the frequencies of the poles and zeros in the voltage transfer function.
Spring 2015, Exam #4, Problem #2
Answers: pole at 1250 rad/s, pole at 104 rad/s
2
Sketch a Bode amplitude plot corresponding to this network function:
H  j  
80
20  12 j   2
Use a logarithmic scale for both |H| and  . Label tick marks along your axes appropriately.
Spring 2015, Exam #4, Problem #3
Answer: 12 dB + { 20 dB/decade } – { 20 dB/decade at  = 2 } – { 20 dB/decade at  = 10 }
3
Sketch a Bode phase plot corresponding to this network function:
H  j  
j  j  300  1012
3  j  105  j  108 
Use a logarithmic scale for  . Label tick marks along your axes appropriately.
Spring 2015, Exam #4, Problem #4
Answer: 90 offset, zero at 300 rad/s, pole at 105 rad/s, pole at 108 rad/s
4
In this circuit, the element values are L  5 mH , R1  2 Ω , R2  100 Ω , C  800 μF .
Determine the resonant frequency of this circuit
with respect to the impedance measured at terminals a–b .
Spring 2015, Exam #4, Problem #5
Answer: 300 rad/s
5
Parts (a) and (b) refer to the RC circuit depicted. Neglect transients.
(a) Determine vout(t) for vin(t) = 10cos(0.8t + 30) V .
(b) Determine vout(t) for vin(t) = 10cos(80t + 60) V .
Spring 2014, Exam #3, Problem #3
Answers: (a) 1cos  0.8t  114 V , (b) 10cos 80t  66 V
6
Parts (a) and (b) refer to the op-amp circuit depicted.
Assume that the op-amp is ideal.
(a) Determine the voltage transfer function of this circuit: H(j) = Vout(j)/Vin(j) .
(b) Sketch the transfer function amplitude |H(j)| vs. for 1 rad/s <  < 106 rad/s .
You may use linear or logarithmic scales.
Label clearly your axes and the frequencies of transition, maxima, minima, etc.
Spring 2014, Exam #3, Problem #4
Answers: (a) 5
j
, (b) 20 dB/decade + { pole at 104 rad/s }
4
j  10
7
Determine the magnitude of the steady-state voltage transfer function of this circuit for
R1  1 k , R2  10 k , C1  0 , C2  100 nF at an operating frequency of 1000 rad/s.
Spring 2015, Final exam, Problem #9
Answer: 7.1
8
For this circuit, compute the frequencies of all zeros and poles
of the steady-state voltage transfer function.
Spring 2015, Final exam, Problem #10
Answer: poles at   2,5 rad s
9
Sketch an amplitude Bode plot for the voltage transfer function of this circuit.
Label your axes appropriately.
Spring 2015, Final exam, Problem #11
starts with a 20 dB dec slope ,
Answer: single pole at   500 rad s ,
levels off at 34 dB
10
Parts (a) and (b) refer to the following transfer function: H  j  
1010  j106 
.
105  j104 
(a) Rewrite H(j) so that its poles and zeros are clearly visible.
(b) Draw a Bode plot of |H(j)| .
(c) Draw a Bode plot of phase{H(j)} .
Spring 2014, Take-home exam, Problem #4
j
4
Answers: (a) 105 10 , (b,c) pole at  = 10 rad/s, zero at  = 104 rad/s
j
1
10
1
11
Parts (a) and (b) refer to this transfer function: H  j  
10
104 102  j 
3
 j 104  j 
.
(a) Rewrite H(j) so that its poles and zeros are clearly visible.
(b) Draw a Bode plot of |H(j)| .
(c) Draw a Bode plot of phase{H(j)} .
Spring 2014, Take-home exam, Problem #5
j
102
Answers: (a)
, (b,c) zero at  = 100 rad/s, poles at  = 103, 104 rad/s
j 
j 

10 1  3 1  4 
 10  10 
1
12
Given this Bode amplitude plot, determine the corresponding transfer function.
Spring 2014, Take-home exam, Problem #6
Answer:
j
j 
j 

10 1  2 1  4 
 10  10 
2
13
For the circuit shown, (a) draw a Bode plot of the voltage amplitude response,
and (b) draw a Bode plot of the voltage phase response.
Spring 2014, Take-home exam, Problem #7
Answers:
j
j 

103 1 

 100 
14
For the network below, derive an expression for the steady-state input impedance and determine
the (radian) frequency at which it has maximum amplitude.
Spring 2014, Homework #7, Problem #3
Answer: 707.1 rad/s
15
For the circuit below, (a) derive an expression for the transfer function H(s) = Vout/Vin ,
and (b) sketch the corresponding Bode magnitude and phase plots for H(j) .
Spring 2014, Homework #7, Problem #4
Answers: (a)
s 2
, (b) single pole at  = 50 rad/s
s
1
50
16
The input to the circuit shown below is the voltage source vi(t) . The output is the voltage vo(t)
across the 6- resistor. Determine the network function H() = Vo() / Vi() .
Spring 2015, Homework #5, Problem #1
Answer:
0.6
1  0.8 j
17
The input to the circuit below is vs  50  30cos  500t  115  20cos  2500t  30 mV .
Find the steady-state output voltage vo for (a) C = 0.1 F , and (b) C = 0.01 F .
Assume an ideal op amp.
Spring 2015, Homework #5, Problem #2
Answers: (a) 49.8cos  500t  70  14.8cos  2500t  146 mV ,
(b) 55.7cos  500t  46  38.7cos  2500t  190 mV
18
The input to the circuit shown below is the source voltage vin(t) , and the response is the voltage
across R3 , vout(t) . The component values are R1 = 5 k , R2 = 10 k , C1 = 0.1 F , and C2 =
0.1 F . Sketch the asymptotic magnitude Bode plot for the network function.
Spring 2015, Homework #5, Problem #3
Answer: starts at 20 dB/dec, levels off at  = 1000 rad/s, decays at 20 dB/dec at  = 2000 rad/s
19
The network function of a circuit is H   
2  2 j  5
.
 4  3 j  j  2 
Sketch the asymptotic magnitude Bode plot corresponding to H .
Spring 2015, Homework #5, Problem #4
Answer: starts leveled, decays at 20 dB/dec at 4/3,
decays at 40 dB/dec at 2, decays at 20 dB/dec at 5/2
20
The input to the circuit shown below is the source voltage vs . The output of the circuit is the
capacitor voltage vo . Determine the values of the resistances R1 , R2 , R3 , and R4 required to
cause the network function of the circuit to correspond to the asymptotic Bode plot given.
Spring 2015, Homework #5, Problem #5
Answers: R1 = 250 k , R2 = 10 k , R3 = 390 k , R4 = 6.25 k
21
The circuit shown below represents a capacitor, coil, and resistor in parallel.
Calculate the resonant frequency of the circuit.
Spring 2015, Homework #5, Problem #6
Answer: 12.9 Mrad/s
22
In the circuit below, determine the gain |Vo/Vi| as a function of frequency.
Spring 2016, Homework #5, Problem #1
Answer:
1
5  20 j
23
In the circuit below, determine the phase of Vo/Vi in degrees as a function of frequency.
Spring 2016, Homework #5, Problem #2
Answer: 180  tan 1  10   tan 1  25
24
The figure shows the measured oscilloscope traces vs and vc . The circuit is the series
combination of a voltage source vs , a 1-k resistor, and an unknown capacitance C . The
voltage across the capacitor is vc . Determine the value of the capacitance.
Spring 2016, Homework #5, Problem #3
Answer: 300 nF
25
The network function of the circuit below is
Vo
Ho
. Determine the value of p .

Vs 1  j  p 
Spring 2016, Homework #5, Problem #4
Answer: 5 rad/s
26
When the input to the circuit below is vs  t   8cos  40t  V , the output is
vo  t   2.5cos  40t  14 V . Determine the value of the unknown resistance R .
Spring 2016, Homework #5, Problem #5
Answer: 14.8 
27
Sketch the magnitude Bode plot of the network function H   
Spring 2016, Homework #6, Problem #1
Answer:
28
4  5  j 
.
1  j  50 
Determine H(j) from the magnitude Bode plot given in the figure.
Spring 2016, Homework #6, Problem #2
Answer:
3 2 1  j 10 
1  j
0.7  1  j 100 1  j 600 
2
29
2
Sketch the magnitude Bode plot of the network function for the circuit below.
Spring 2016, Homework #6, Problem #3
Answer:
30
Sketch the magnitude Bode plot of H   
4  20  j   20 103  j 
 200  j  2000  j 
Spring 2016, Homework #6, Problem #4
Answer:
31
.
In the circuit, specify the values of the resistors required to cause the network function of the
circuit to correspond to the asymptotic Bode plot shown in the figure.
Spring 2016, Homework #6, Problem #5
Answers: R1 = 20 k , R2 = 320 k
32
Determine the resonant frequency of the network below.
Spring 2016, Homework #6, Problem #6
Answer: 707 rad/s
33
Write the transfer function Vo/Vi in pole-zero form, and from this transfer function identify the
poles (if there are any) and zeros (if there are any) as frequencies in Hz. Let R1 = 6 k , R2 = 2
k, and C = 5 F .
Spring 2016, Exam #3, Problem #1
Answer: one pole at 4 Hz
34
Write the transfer function H(j) in pole-zero form,
and using this transfer function, determine the gain
of this circuit in decibels at a frequency of 0 Hz.
Let Ri = 5 k , Rf = 20 k ,
C = 25 nF , and RL = 7 k .
Spring 2016, Exam #3, Problem #2
Answers:
4
, 12 dB
1  j 2000
35
Sketch the magnitude Bode plot of the given transfer function.
Remember to label your axes appropriately.
H  j  
1.78 103  j 
10  j 
Spring 2016, Exam #3, Problem #3
rad 


3 rad 
Answer: 45 dB  20 dB/dec starting at 10
 + 20 dB/dec starting at 10

s 
s 


36
Design a circuit that filters out voltages with frequencies well above 10 kHz
and amplifies voltages by 12 dB at frequencies well below 10 kHz.
Spring 2014, Take-home exam, Problem #8
Answer: inverting op amp, Rf = 1.6 k , Cf = 10 nF , R1 = 400 
37
The amplitude of the voltage across a parallel RLC circuit vs. frequency is given in the plot.
The horizontal and vertical scales are both linear. Estimate quality factor from this data.
Spring 2014, Final exam, Problem #12
Answer: 2.5
38
For the circuit shown, calculate
(a) the resonant frequency (rad/s),
(b) the half-power frequencies (rad/s),
(c) the quality factor,
(d) the bandwidth, and
(e) the amplitude of the current i(t) at the half-power frequencies.
Spring 2014, Take-home exam, Problem #1
Answers: (a) 50 krad/s , (b) 49, 51 krad/s , (c) 25 , (d) 2 krad/s , (e) 7.1 A
39
Design a series RLC resonant circuit with a center frequency of 1 kHz
and a quality factor of 100, given an inductance of L = 25 mH .
Spring 2014, Take-home exam, Problem #2(a)
Answers: R = 1.6  , C = 1 F
40
Design a parallel RLC resonant circuit with a center frequency of 2.25 kHz
and a quality factor of 14, given a resistance of R = 4 k .
Spring 2014, Take-home exam, Problem #3(a)
Answers: L = 20 mH , C = 248 nF
41