ECE 3183
Problems in ideal Opamps
Version 3.7
OA-1: Assuming ideal opamps, determine the voltage transfer gain T = vO/vS and input resistance Rin for each of the configurations shown. Resistances are in kΩ.
100
200
25
25
vS
vO
vO
vS
40
25
125
25
25
vO
vS
vS
10
vO
40
10
OA-2: (a) Using resistances no larger than 10 MΩ design an amplifier with gain -50 V/V, using the inverting configuration. Assume
ideal opamp. (b) What is the input resistance (c) What is the feedback ratio β?
R2
R1
vS
vO
Answers : (a) 200 kΩ, 10MΩ (b)100 kΩ, (c) 1/51
OA-3: Find (a) transfer function T = vO/vS and (b) input resistance
Rin. Resistances are in kΩ
200
200
50
50
Answers ((a) -24 V/V, (b) 50 kΩ
OA-4:
vS
vO
Find (a) transfer function T = vO/vS and (b) input resistance Rin
200
200
200
200
200
50
vS
200
200
200
100
vO
vS
vO
OA-5:
Find (a) transfer function T = vO/vS and (b) input resistance Rin
200
200
100
200
100
100
200
100
100
200
200
100
vO
vS
vO
vS
Answers: (a) 8 V/V, (b) 16 V/V
OA-6:
Find transfer function T = vO/vS
vO
vS
100
100
100
OA-7: Design a 4-bit digital-analog converter using the R2R ladder as shown such that Vo = 4.0V when the input word
= $C = %1100. Assume input levels of 2.0V and 0.0 V,
respectively.
V0
V1
2R
V2
2R
50
50
50
V3
2R
2R
vO
And assume R1 = R = 10 kΩ
2R
R
R
R
2R
R2
R1
OA-8: A sinusoidal input with phase shift = 0 is fed to a Miller integrator that uses an ideal opamp and an RC pair with R =
50 kΩ and C =.001 µF.
(a) At what frequency are the input and output signals equal in magnitude?
(b) What is the phase of VO relative to Vin?
(c) If the frequency is decreased by a factor of 10 from that of part (a), by how many dB does the output change?
Answers: 3.2kHz, +90o, 20 dB
OA-9: A lossy Miller integrator, as shown, uses an ideal opamp.
A sinusoidal signal is applied to the input.
(a) at what frequency are the input and output signals equal in
magnitude?
(b) What is the phase of vo relative to vin?
(c) If the frequency is decreased by a factor of 10 from that
of part (a), by how many dB does the output change?
.002µF
500
vO
vin
50
OA-10: (a) Show that the transfer function for the configuration
shown is
Cf
R2 ⁄ R1
T = – -----------------------------------------------------( 1 + ω1 ⁄ s ) ( 1 + s ⁄ ω2 )
C1
Rf
vO
vS
where ω1 = 1/R1C1 and ω2 = 1/RfCf
R1
The circuit has the frequency response of a bandpass for which
the low-frequency roll-off is at ω1 and the high-frequency roll-off
is at ω2
(b) By choice of R1, R2, C1, C2, design a circuit such that Rin = 10 kΩ (ω1 << ω < ω2), midband gain = 46 dB, low-frequency rolloff corner = 200Hz and high-frequency rolloff corner is 40 kHz.
OA-11: The circuit shown uses a 250kΩ potentiometer to
implement an adjustable gain amplifier.
vO
vS
(a) Assuming R1 = 20k, derive an expression for the
gain as a function of parameter setting x.
1-x
100kΩ POT
x
(b) What value of R1 is necessary so the gain will range
from T = 1.0 to T = 21 V/V?
OA-12: A photodetector with source voltage 100 mV and
source resistance 100 kΩ is connected to a 1 kΩ load. Find
the voltage that will appear across the load if:
R1
RSOURCE
(a)
vS
RLOAD
(a) it is connected directly to the load.
(b) an ideal unity-gain buffer is inserted between the
source and the load.
RSOURCE
(b)
vS
RLOAD
OA-13: The circuit shown is called a level-shifting buffer.
+10V
25kΩ
(a) Determine the range over which the output level V
can be adjusted.
v
x
(b) Assume that a 20-turn potentiometer is used. Find
the change of V with respect to each turn of the pot.
vO = V + v
1-x
25kΩ
-10V
200kΩ POT
OA-14: Find transfer functions for each of the following circuits
(A)
R
(B)
2C
vO
C
vS
vS
R
R/2
C
R
R
C
vO
R
(C)
R
R
R’ = xR
+
R’
0<x<1
vS
vO
-
R
R
R
OA-15: Find vo as a function of v1 and v2.
Resistances in kΩ
v1
Answer (a) vo = 10 (v2 - v1)
(b) What is the transfer gain if R3 is changed to 100 kΩ?
10
20
25
vO
R3 = 10
25
10
20
v2
OA-16: Design the variable-gain instrumentation amplifier
shown such that it will realize a differential gain that is variable in the range 1 to 50 using a 100 kΩ potentiometer as a
variable resistance. Suggestion: Design the second stage for a
gain of 0.5.
v1
R2
R1
R4
r
vO
Answers (a) R2/R1 = 0.5, r = 0.5kΩ, R4 = 50kΩ.
R
R4
R1
R2
v2
OA-17: Assuming ideal opamps determine the 3dB frequency for the following 4-stage circuit in terms of the time constant
τ = RC. (Hint: Assume each stage loses 3/4 dB)
R
R
R
R
vI
vO
C
C
200
C
C
200
200
100
200
50
200
200
100
100
vO
vS
vS
vO
0.52µm
20nm
1µm
2µm