Operational Amplifiers
Classroom Practice Problems
1. Design a current source using BJT transistors for an output current Io 2mA. The reference current is to be
derived from a +15V and ground power supply using a resistor. Find the output resistance of the source if
the transistors have an early voltage of 100V .
2. Use the configuration shown below to design a current source that will provide and output current IO = 5µA
as shown. Assume β = ∞ for all transistors and use RM = 5kΩ.
12V
Q1
R
IO=5µΑ
Q2
Q3
RM
-12V
3. The operational amplifier in the following circuit is ideal.
50kΩ
vi
+
vo
−
100kΩ
100kΩ
Find the circuit’s gain Av =
900Ω
100Ω
vo
vi .
4. The amplifier shown in the following sketch has a voltage gain Av = −100 and input resistance Rin = 10kΩ.
R2
vi
R1
−
vo
+
(a) Determine R1 and R2 assuming an ideal operational amplifier.
(b) Find the circuit’s bandwidth if the operational amplifier has unity gain bandwidth ωτ = 106 Hz, but is
otherwise ideal.
5. The amplifier shown in the following sketch has a voltage gain Av = +100 and input resistance Rin = 10kΩ.
R2
R1
−
vi
vo
+
R1
R2
(a) Determine R1 and R2 assuming an ideal operational amplifier.
(b) Find the circuit’s bandwidth if the operational amplifier has unity gain bandwidth ωτ = 106 Hz, but is
otherwise ideal.
(c) Find the circuit’s gain if the operational amplifier has an opel-loop gain of 105 .
6. For the circuit shown in the following sketch, R = 1kΩ and C = 1µF . The opamp is ideal.
R
1V
C
vi
−
vo
vi
0V
+
0ms
0.5ms
1ms
Draw the output waveform when the input voltage is the one shown on the right hand side of the figure.
7. For the circuit shown in the following sketch, R = 1kΩ and C = 1µF .
C
vi
vi
1V
R
−
vo
1ms
0V
+
-1V
0ms
0.5ms
Draw the output waveform when the input voltage is the one shown on the right hand side of the figure.
8. For the following circuit
+
vi
vo
−
R
C
(a) Derive an expression for vo in terms of vi and the component values. Notice that vi does not need to be
sinusoidal.
(b) Find an expression for vo in terms of the Laplace operator s, valid when vi is sinusoidal.
9. Determine the input impedance Zin =
vi
ii
for the following circuit. Assume an ideal opamp.
ii
vi
i R2
R2
iC
+
C
vO
−
R1
10. Find vO in terms of vIN for the following circuit.
+
vIN
vO
−
10kΩ
10kΩ
10kΩ
10kΩ
+
5V
11. Find
vO1
vIN
and
vO2
vIN
for the following circuit.
10R
10R
R
−
vIN
v01
+
+
vO2
−
R
R
12. For the following circuit, express the output voltage vO as a differential equation of vin in terms of the component values.
R2
L
R1
vin
−
C
vO
+
13. Assuming ideal operation of the amplifiers (Av = ∞), find the expression for IL in terms of the differential
voltage v2 − v1 and the resistors Rx , R1 , and R2 .
v1
R1
R2
−
Rx
+
R1
R2
−
v2
+
ZL
iL