Op Amp Supplemental Questions.
Consists of inverting, non-inverting, summing and differencing op amp circuits.
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1
Questions
Question 1
For all practical purposes, how much voltage exists between the inverting and noninverting input
terminals of an op-amp in a functioning negative-feedback circuit?
file 00930
Question 2
Complete the table of voltages for this opamp ”voltage follower” circuit:
+15 V
−
Vin
+
-15 V
Vin
0 volts
+5 volts
+10 volts
+15 volts
+20 volts
-5 volts
-10 volts
-15 volts
-20 volts
Vout
0 volts
file 02289
2
Vout
Question 3
Calculate the overall voltage gain of this amplifier circuit (A V ), both as a ratio and as a figure in units
of decibels (dB). Also, write a general equation for calculating the voltage gain of such an amplifier, given
the resistor values of R 1 and R 2 :
+
Vin
Vout
−
R1
27 kΩ
27 kΩ
R2
file 02457
Question 4
What would have to be altered in this circuit to increase its overall voltage gain?
Vin(+)
+
Vout
−
R1
R2
file 00931
3
Question 5
Calculate all voltage drops and currents in this circuit, complete with arrows for current direction and
polarity markings for voltage polarity. Then, calculate the overall voltage gain of this amplifier circuit (A V ),
both as a ratio and as a figure in units of decibels (dB):
22 kΩ
R2
47 kΩ
R1
−
Vout = ???
+
Vin = +3.2 volts
file 02459
Question 6
Calculate all voltage drops and currents in this circuit, complete with arrows for current direction and
polarity markings for voltage polarity. Then, calculate the overall voltage gain of this amplifier circuit (A V ),
both as a ratio and as a figure in units of decibels (dB):
Vout = ???
Ra
−
+
Vin = -2.35 V
10 kΩ
Rb
file 02460
4
2.7 kΩ
Question 7
Determine both the input and output voltage in this circuit:
+
Vout
−
Vin
5 kΩ
18 kΩ
I = 2 mA
file 02726
Question 8
Calculate the voltage gain for each stage of this amplifier circuit (both as a ratio and in units of decibels),
then calculate the overall voltage gain:
Stage 1
1 kΩ
Stage 2
470 Ω
3.3 kΩ
−
2.7 kΩ
−
Vout
+
Vin
+
file 02727
Question 9
There is something wrong with this amplifier circuit. Note the relative amplitudes of the input and
output signals as measured by an oscilloscope:
12 kΩ
+12 V
7.9 kΩ
−
0V
Vout
+
Vin
-12 V
0.4 V RMS
This circuit used to function perfectly, but then began to malfunction in this manner: producing a
”clipped” output waveform of excessive amplitude. Determine the approximate amplitude that the output
voltage waveform should be for the component values given in this circuit, and then identify possible causes
of the problem and also elements of the circuit that you know cannot be at fault.
file 02465
5
Question 10
The equation for voltage gain (A V ) in a typical inverting, single-ended opamp circuit is as follows:
AV =
R1
R2
Where,
R 1 is the feedback resistor (connecting the output to the inverting input)
R 2 is the other resistor (connecting the inverting input to voltage signal input terminal)
Suppose we wished to change the voltage gain in the following circuit from 3.5 to 4.9, but only had the
freedom to alter the resistance of R 2 :
Vout
−
+
7k7
R1
2k2
R2
Vin
Algebraically manipulate the gain equation to solve for R 2 , then determine the necessary value of R 2 in
this circuit to give it a voltage gain of 4.9.
file 02708
Question 11
Calculate the necessary resistor value (R 1 ) in this circuit to give it a voltage gain of 15:
Vin
R1
−
+
22 kΩ
Vout
file 02729
6
Question 12
Calculate the output voltage of this op-amp circuit (using negative feedback):
+
Vout
−
5 kΩ
27 kΩ
1.5 V
Also, calculate the DC voltage gain of this circuit.
file 00932
Question 13
Calculate the voltage gain for each stage of this amplifier circuit (both as a ratio and in units of decibels),
then calculate the overall voltage gain:
Stage 1
10 kΩ
Vin
15 kΩ
Stage 2
3.3 kΩ
−
5.1 kΩ
−
Vout
+
+
file 02470
7
Question 14
Operational amplifier circuits employing negative feedback are sometimes referred to as ”electronic
levers,” because their voltage gains may be understood through the mechanical analogy of a lever. Explain
this analogy in your own words, identifying how the lengths and fulcrum location of a lever relate to the
component values of an op-amp circuit:
Lever
Fulcrum
Vin
−
Vout
+
Lever
Fulcrum
−
Vin
Vout
+
file 00933
Question 15
Calculate the voltage gain for each stage of this amplifier circuit (both as a ratio and in units of decibels),
then calculate the overall voltage gain:
Stage 1
10 kΩ
Vin
15 kΩ
Stage 2
3.3 kΩ
−
5.1 kΩ
−
Vout
+
+
file 02470
8
Question 16
Operational amplifier circuits employing negative feedback are sometimes referred to as ”electronic
levers,” because their voltage gains may be understood through the mechanical analogy of a lever. Explain
this analogy in your own words, identifying how the lengths and fulcrum location of a lever relate to the
component values of an op-amp circuit:
Lever
Fulcrum
Vin
−
Vout
+
Lever
Fulcrum
−
Vin
+
Vout
file 00933
Question 17
Compare and contrast inverting versus noninverting amplifier circuits constructed using operational
amplifiers:
Inverting amplifier circuit
Vin
Noninverting amplifier circuit
−
−
Vout
Vout
+
Vin
+
How do these two general forms of opamp circuit compare, especially in regard to input impedance and
the range of voltage gain adjustment?
file 02469
9
Question 18
Determine the amount of current from point A to point B in this circuit:
1 kΩ
1 kΩ
2V
A
I = ???
1 kΩ
3.5 V
B
1V
file 02516
Question 19
Determine all current magnitudes and directions, as well as voltage drops, in this circuit:
8.33 kΩ
25 kΩ
−
+
5 kΩ
10 V
5 kΩ
5 kΩ
5 kΩ
3V
5V
11 V
file 02515
10
Vout
Question 20
Determine the amount of current from point A to point B in this circuit, and also the output voltage
of the operational amplifier:
1 kΩ
1 kΩ
2V
3.5 V
A
1 kΩ
B
I = ???
1 kΩ
−
+
1V
Vout
file 02517
Question 21
Complete the table of values for this opamp circuit, calculating the output voltage for each combination
of input voltages shown:
10 kΩ
10 kΩ
V1
−
Vout
+
V2
10 kΩ
V1
0V
+1 V
0V
+2 V
+3.4 V
-2 V
+5 V
-3 V
10 kΩ
V2
0V
0V
+1 V
+1.5 V
+1.2 V
+4 V
+5 V
-3 V
Vout
What pattern do you notice in the data? What mathematical relationship is there between the two
input voltages and the output voltage?
file 02518
11
Question 22
How does the operation of this difference amplifier circuit compare with the resistor values given (2R =
twice the resistance of R ), versus its operation with all resistor values equal?
R
2R
−
+
R
2R
Describe what approach or technique you used to derive your answer, and also explain how your
conclusion for this circuit might be generalized for all difference amplifier circuits.
file 02525
12
Answers
Answer 1
Zero volts
Answer 2
Vin
0 volts
+5 volts
+10 volts
+15 volts
+20 volts
-5 volts
-10 volts
-15 volts
-20 volts
Vout
0 volts
+5 volts
+10 volts
+15 volts
+15 volts
-5 volts
-10 volts
-15 volts
-15 volts
Follow-up question: the output voltage values given in this table are ideal. A real opamp would probably
not be able to achieve even what is shown here, due to idiosyncrasies of these amplifier circuits. Explain
what would probably be different in a real opamp circuit from what is shown here.
Answer 3
A V = 2 = 6:02 dB
AV =
R1
+1
R2
(expressed as a ratio, not dB)
Follow-up question: explain how you could modify this particular circuit to have a voltage gain (ratio)
of 3 instead of 2.
Answer 4
The voltage divider would have to altered so as to send a smaller proportion of the output voltage to
the inverting input.
Answer 5
IR2 = IR1 = 68.09 µA
VR2 = 1.498 V
VR1 = 3.2 V
22 kΩ
47 kΩ
−
Vout = +4.698 V
+
Current arrows drawn in
the direction of conventional
flow notation.
A V = 1.468 = 3.335 dB
13
Vin = +3.2 volts
Answer 6
Current arrows drawn in the
direction of conventional flow
Vout = -11.054 V
VRa = 8.704 V
10 kΩ
−
+
IRa = IRb = 870.4 µA
2.7 kΩ
VRb = 2.35 V
Vin = -2.35 V
A V = 4.704 = 13.449 dB
Follow-up question: how much input impedance does the -2.35 volt source ”see” as it drives this amplifier
circuit?
Answer 7
Vin = 10 V
Vout = 46 V
Answer 8
Stage 1:
A V = 4.3 = 12.669 dB
Stage 2:
A V = 6.745 = 16.579 dB
Overall:
A V = 29.002 = 29.249 dB
Answer 9
Vout (ideal) = 1.01 volts RMS
I’ll let you determine possible faults in the circuit! From what we see here, we know the power supply
is functioning (both +V and -V rails) and that there is good signal getting to the noninverting input of the
opamp.
Answer 10
R2 =
R1
AV
For the circuit shown, R 2 would have to be set equal to 1.571 kΩ.
14
Answer 11
R 1 = 1.467 kΩ
Answer 12
Vout = -8.1 volts
A V = 5.4
Follow-up question: the midpoint of the voltage divider (connecting to the inverting input of the op-amp)
is often called a virtual ground in a circuit like this. Explain why.
Answer 13
Stage 1:
A V = 1.5 = 3.522 dB
Stage 2:
A V = 1.545 = 3.781 dB
Overall:
A V = 2.318 = 7.303 dB
Answer 14
The analogy of a lever works well to explain how the output voltage of an op-amp circuit relates to the
input voltage, in terms of both magnitude and polarity. Resistor values correspond to moment arm lengths,
while direction of lever motion (up versus down) corresponds to polarity. The position of the fulcrum
represents the location of ground potential in the feedback network.
Answer 15
Stage 1:
A V = 1.5 = 3.522 dB
Stage 2:
A V = 1.545 = 3.781 dB
Overall:
A V = 2.318 = 7.303 dB
Answer 16
The analogy of a lever works well to explain how the output voltage of an op-amp circuit relates to the
input voltage, in terms of both magnitude and polarity. Resistor values correspond to moment arm lengths,
while direction of lever motion (up versus down) corresponds to polarity. The position of the fulcrum
represents the location of ground potential in the feedback network.
Answer 17
The noninverting configuration exhibits a far greater input impedance than the inverting amplifier, but
has a more limited range of voltage gain: always greater than or equal to unity.
Answer 18
I = 6.5 mA
15
Answer 19
7.25 V
8.33 kΩ
870 µA
(no current)
21.76 V
25 kΩ
−
+
870 µA
Vout
+29.01 V
+7.25 V
5 kΩ
5 kΩ
550 µA
10 V
3V
5 kΩ
850 µA
5V
5 kΩ
450 µA
750 µA
11 V
Conventional flow notation
used for all current arrows
Follow-up question: what would be required to get this circuit to output the exact sum of the four input
voltages?
Answer 20
I = 6.5 mA
Vout = -6.5 V
Answer 21
V1
0V
+1 V
0V
+2 V
+3.4 V
-2 V
+5 V
-3 V
V2
0V
0V
+1 V
+1.5 V
+1.2 V
+4 V
+5 V
-3 V
16
Vout
0V
-1 V
+1 V
-0.5 V
-2.2 V
+6 V
0V
0V
Answer 22
It is very important that you develop the skill of ”exploring” a circuit configuration to see what it will
do, rather than having to be told what it does (either by your instructor or by a book). All you need to
have is a solid knowledge of basic electrical principles (Ohm’s Law, Kirchhoff’s Voltage and Current Laws)
and know how opamps behave when configured for negative feedback.
As for a generalized conclusion:
R
mR
−
AV(differential) = m
+
R
mR
17