Analog Electronics Homework Problems
Fall 2011
Physics 338
Dr. Adam T. Whitten
4k
1. Find the current in each resistor in the circuit to the right. Note
that the unit “k” indicates “kΩ” and that it is common practice
to leave off the Ω. Find the voltage across each resistor and make
sure Kirchhoff’s loop rule is obeyed.
+9V
2. Find the Thévenin equivalent resistance between the two terminals
in the middle of the bridge in the circuit to the right. What current
would flow through a 6.8 kΩ resistor connected between the two
terminals? Draw the Thévenin and Norton equivalent circuits.
2k
1k
10k
+3.3V
3k
1.0k
1.5k
2.2k
3.3k
+12V
3. An ac voltage source follows the equation: v(t) = A sin(ωt + ϕ) + B
where A = 15 V, B = 12V, ω = 9400 rad/s, and ϕ = −π/4 rad. Calculate values for each of
the following:
(a) average voltage
(f) period
(b) voltage amplitude
(g) peak voltage
(c) angular frequency
(h) peak-to-peak voltage
(d) phase angle
(i) rms voltage
(e) frequency
(j) voltage at t = 0
4. What is the smallest value of inductance, L, that can be connected directly to a 120 VAC,
60 Hz wall outlet without blowing a 15 A fuse? What is the largest value of capacitance, C,
that can be connected directly to a 120 VAC, 60 Hz wall outlet without blowing a 15 A fuse?
How much power is being used in each case and where does it “go”?
5. For the circuit to the right, ε = 8.5 Vrms at f = 1 kHz, R = 1 kΩ, C =
0.1 µF, and L = 200 mH. Find the voltage drop across each component and
the phase shift between that voltage and the current.
6. Find the complex impedance of the RLC circuit shown to the right when
it is driven by an angular frequency ω = 105 s−1 . What voltage would
an ac voltmeter placed between the terminals measure? What current
would an ac ammeter measure between the two terminals?
R
C
L
ε
75Ω
10mH
.01µF
5Vrms
7. In the circuit below, R = 10 kΩ, C = 0.01 µF, and L = 10 mH. Plot V as a function
of frequency for Vin with a peak amplitude of 10 V. Plot the phase difference between V
and Vin as a function of frequency. Make sure to use a range of frequencies for which both
XC ≪ XL and XC ≫ XL . Note: if z = Aejϕ for A, ϕ ∈ ℜ, then in Mathematica A=Abs[z]
and ϕ=Arg[z].
R
C
V in
L
V
8. Rework problem 7 assuming that the inductor has a resistance of 100 Ω (i.e., treat it as a
real inductor: a series combination of a resistor and an ideal inductor of the same inductance).
1
9. Consider the high pass filter pictured below. If Vin = 10 V @ f = 1 kHz, C = 0.01 µF, and
R = 10 kΩ, what is f−3dB for this filter? Also determine:
(a) the current through R
(b) the voltage across R
(c) the voltage across C
(d) the phase angle between V and Vin
R
C
V in
R
V
V in
High Pass Filter
V
C
Low Pass Filter
10. Consider the low pass filter pictured above. If Vin = 1.0 V @ f = 1 kHz, C = 6.8 µF, and
R = 50 Ω, what is f−3dB for this filter? Also determine:
(a) the current through R
(b) the voltage across R
(c) the voltage across C
11. The circuit to the right is driven by a 12 V rms sinusoidal waveform
at a frequency of 1000 Hz.
12V@1.0kHz
(d) the phase angle between V and Vin
1.0kΩ
1.0kΩ
A
(a) Calculate the equivalent ac Thévenin voltage and express it in
complex rectangular form. Hint: find the effective impedances
0.082µF
of the left and right sides of the bridge and substitute known
values in right away.
(b) Calculate the ac Thévenin current and express it in complex rectangular form.
B
79mH
(c) Calculate the ac Thévenin impedance, ZTH , and express it in complex rectangular form.
(d) Draw a Thévenin equivalent circuit with a series combination of resistor and capacitor
in series with a voltage source. Express the voltage source in polar coordinate form and
calculate the values of R and C. Draw a Thévenin equivalent circuit with a parallel
combination of resistor and capacitor in series with a voltage source. Calculate the
values of R and C.
(e) Show why you can not make a Thévenin equivalent circuit with a resistor and inductor
(either in series or parallel).
(f) Extra Credit: Draw the Norton equivalent circuits for parts (d).
2
12. The circuit below on the left shows a half-wave rectifier used to make a dc supply. If the dc
droop is specified to be 0.5 V for a current of 1.0 A, what value of capacitance, C, should be
used? What is the ripple at I = 0.250 A?
C
12 V
120 VAC
Vout
+
12 V
+
120 VAC
Vout
C
13. The circuit above on the right shows a half-wave rectifier used to make a dc supply. What is
the value of Vout ? If C = 4.7 µF, what are the ripple and dc droop at I = 25.0 mA?
14. The circuit below on the left shows a full-wave bridge rectifier. If the transformer is 36 V,
what is the value of Vout ? If C = 4700 µF, what are the ripple and dc droop at I = 1.0 A?
120 VAC
Vout
C
Bridge Rectifier
+
+
120 VAC
Vout
Center-tapped Rectifier
15. If the same transformer from problem 14 is used in center-tapped mode (see circuit above
right), what is the value of Vout ? If the dc droop is specified to be 0.5 V for a current of 1.0
A, what value of capacitance, C, should be used? What is the ripple at I = 0.250 A?
16. Design an emitter follower with ±15 V supplies to operate over the audio range (20 Hz –
20kHz). Use 2.5 mA quiescent current and capacitive input coupling. Note: this problem is
virtually identical to H&H exercise 2.5 (see H&H p. 71-72 for design procedure). Specify all
values of R and C used and calculate the current gain.
+15V
vin
Q1
C1
vout
RB
RE
C2
−15V
Emitter Follower
3
17. Design a tuned common-emitter amplifier for a 1.0 MHz input signal using a +15 V supply.
Assume L1 = 0.01 mH and that the Q spoiling resistor, RQ = 680 Ω, gives a 10% bandpass
(see H&H section 1.22). Set the quiescent current at 1.0 mA. Specify all remaining component
values and calculate the voltage gain. It may be helpful to proceed in this order:
(a) Set the output characteristics by specifying VC , VE , RE , RC , and CE .
(b) Set the biasing by specifying VB , R1 , R2 , and C2 .
(c) Set the input filtering by specifying C1
Remember that the bandpass filter allows for ±10%.
+15V
RC
vout
vin
C2
R in
R1
Q1
R2
L1
C1
RQ
RE
CE
Tuned Common-Emitter Amplifier
R2
+15V
18. The figure to the right shows a generic inverting op-amp.
R1
−
Vin
+
(a) Choose reasonable values of R1 and R2 to give this circuit a gain of −50.
V out
−15V
(b) What value should you then choose for R3 ?
R3
+15V
19. The figure to the right shows a generic non-inverting op-amp.
You would like the circuit to have a low frequency 3dB point Vin
of 10 Hz.
C1
−
R3
−15V
(a) Choose reasonable values of R1 and R2 to give this circuit a gain of 100.
(b) If C1 = 0.1 µF, what value should you choose for R3 ?
(c) Given your choice for R1 , what value should you choose
for C2 ?
V out
+
R2
R1
C2
20. Design a differential amplifier with a gain of 10. Draw your circuit and specify values for all
components.
4
21. Design a summing amplifier to add four binary digits whose input voltages are either 0 or +5
V. Assume your op-amp is using ±15 V supplies and that the output should range from 0 to
−12 V. Draw your circuit and specify values for all components.
22. The figure to the right shows a generic op-amp integrator.
Let R1 = 100 kΩ and C = 0.01 µF.
R2
(a) To compensate for offset and input bias current, choose
a value of R2 that will roll off the integrating action for
f < 1.0 Hz.
C
+15V
(b) How could you replace this large value of R2 with a
Vin
resistive T network? Draw the circuit.
R1
−
+
(c) The circuit as shown has no resistor at the V+ input
to compensate for bias current. What value of resistor
would you use for part (a)? For part (b)?
V out
−15V
C2
23. The figure to the right shows a generic op-amp differentiator.
Let R2 = 100 kΩ and C = 0.01 µF.
(a) At what frequency does the differentiator’s internal
phase shift begin to appear?
(b) Choose R1 and C2 to roll off the differentiating action
at f > 1.0 MHz.
R2
+15V
Vin
R1
C1
−
+
V out
−15V
24. The last page of this assignment has characteristic curves for an n-channel JFET. Directly on
the curves, label the ohmic region, the sub-threshold region (a.k.a “cut-off” region), and the
saturation region (a.k.a. “active” region). Remember that “saturated” for a FET is different
from “saturated” for a bipolar transistor. Draw a schematic diagram for a p-channel JFET
and label each lead with its proper name.
5
25. The circuit shown below on the right is a variable (voltage-controlled) gain amplifier which
makes use of a JFET operating in the ohmic region. The characteristic curves for this
n-channel JFET for small VDS are shown below on the left. Each characteristic curve is
labeled with the corresponding gate voltage VG . Hint: use the FET’s characteristic curves to
determine RDS for the gate voltages in question.
(a) If R1 = 10 kΩ and VG = 0 V, what is the gain of this circuit?
(b) If R1 = 10 kΩ and VG = −1.5 V, what is the gain of this circuit?
(c) If R1 = 100 kΩ and VG = 0 V, what is the gain of this circuit?
0.0014
7
0.0V
0.0012
6
−0.5V
0.0010
5
−1.0V
I D (mA)
Characteristic Curve for n-channel JFET − Small V DS
−1.5V
+15V
V in
V out
+
−
0.0008
4
−15V
0.0006
3
VG
−2.5V
0.0002
1
0
0.0000
0.0
R1
−2.0V
0.0004
2
0.1
0.2
0.3
0.4
0.5
0.6
V DS (V)
+20V
2kΩ
26. The figure to the right shows a common source FET amplifier.
(a) Someone claims the ammeter reads 20 mA. Explain why
this is impossible and report what the ammeter should
read if the circuit is properly designed. (Assume this
current in answering the remaining questions.)
(b) What is the gate bias voltage?
A
V out
1µF
6
100µF
(e) What is the output impedance?
+
(d) What is the input impedance?
100Ω
(c) If the transconductance is 10 mS, what is the gain?
100kΩ
V in
V DD
27. A common source amplifier (pictured to the right) is to
be built using an n-channel JFET with the characteristic
curves shown below. Assume VDD = 12 V and choose
your quiescent point to lie on one of the curves. For each
component of this amplifier, report a value and how that
value was determined (graphically, by formula, or other
considerations). Be specific and explain fully. Report
your gate bias voltage, transconductance at that voltage,
amplifier gain, input impedance, and output impedance
along with all specified component values.
RD
V out
C out
V in
RG
+
RS
CS
Characteristic Curve for n-channel JFET
0.0035
0.0V
0.0030
6
0.0025
5
−0.1V
I D (mA)
0.0020
4
−0.2V
0.0015
3
−0.3V
2
0.0010
−0.4V
0.0005
1
−0.5V
0
0.0000
0
2
4
6
8
10
12
V DS (V)
28. The last page of this assignment has characteristic curves for an n-channel JFET. What is
IDSS ? Calculate g for VGS = −1.5 V. Estimate the threshold gate voltage. Assuming a
supply voltage of 12 V, draw directly on the plot the load line for a 2 kΩ drain resistor. Label
the operating point Q obtained with VGS = −1.5 V. What is the quiescent drain current?
How much power is dissipated in the transistor in this quiescent state? Design a common
source amplifier (see problem 27) using this FET. Your schematic diagram of the circuit
should show all component values as well as input and output locations.. As usual, you will
bias the gate (here to VGS = −1.5 V) using a source resistor bypassed with a capacitor CS
so the ac signal doesn’t see it. What value of CS should you use if the amplifier is to amplify
signals with frequencies between 100 Hz and 10 kHz? Report the expected voltage gain, the
input impedance, and the output impedance.
7
29. Design a 4-pole voltage-controlled voltage-source (VCVS) low pass filter with maximal flatness
in the passband. Set the –3dB cutoff frequency fc = 1.0 kHz. Draw your circuit and specify
all values of R and C. Show how you calculated these values of R and C. What is the gain
at 2fc ?
30. Design a 4-pole voltage-controlled voltage-source (VCVS) high pass filter with maximal rolloff
steepness between the passband and stopband. Set the –3dB cutoff frequency fc = 1.0 kHz
and limit the ripple in the passband to 0.5dB. Draw your circuit and specify all values of R
and C. Show how you calculated these values of R and C. What is the gain at 0.5fc ?
8
Graph for Problem 24.
Characteristic Curve for n-channel JFET
0.0035
0.0V
0.0030
6
0.0025
5
−0.5V
I D (mA)
0.0020
4
−1.0V
0.0015
3
−1.5V
0.0010
2
−2.0V
0.0005
1
−2.5V
−3.0V
0
0.0000
0
5
10
15
V DS (V)
Graph for Problem 28.
Characteristic Curve for n-channel JFET
0.0035
0.0V
0.0030
6
0.0025
5
−0.5V
I D (mA)
0.0020
4
−1.0V
0.0015
3
−1.5V
0.0010
2
−2.0V
0.0005
1
−2.5V
−3.0V
0
0.0000
0
5
10
V DS (V)
9
15