Operational Amplifier
Elankumaran Nagarajan
21st march 2012
Summary
Operational amplifiers are important building blocks for a wide range of
electronic circuits. The aim of this experiment was to provide practical
experience of the use of operational amplifiers. The voltage gain of two basic
amplifiers: the inverting and the non-inverting amplifier were measured. To
achieve those measurements a small voltage, 0.1 volts, was applied to the
amplifier input and the amplifier output was measured using a multimeter. The
small voltage was obtained from a 3.3 volt source using a potential divider. The
theoretical voltage gain and the output voltages of both the amplifiers were also
calculated using the provided theoretical formulas. The theoretical predictions
were proved by the experimental results. There were differences between the
theoretical and experimental values of the amplifier gain and the output voltage.
This was due to the instrumental errors associated with the experiment. It was
also found that the higher the ratio of the feedback resistance to the input
impedance, the higher would be the amplifier gain.
1
Index
page no
 List of symbols
2
 Introduction
3
 Theory
3
 Experimental method
4
 Results
6
 Discussions
10
 Conclusion
12
 References
12
List of symbols
1. Vout – input voltage
2. Vin – output voltage
3. Rf – feedback resistance
2
4. R1 – input impedance (resistance)
Introduction
An operational amplifier ("op-amp") is a DC-coupled high-gain electronic
voltage amplifier with a differential input and, usually, a single-ended output. An
op-amp produces an output voltage that is typically hundreds of thousands times
larger than the voltage difference between its input terminals. Op-amps are
among the most widely used electronic devices today, being used in a vast array
of consumer, industrial, and scientific devices. Many standard IC op-amps cost
only a few cents in moderate production volume; however some integrated or
hybrid operational amplifiers with special performance specifications may cost
over $100 US in small quantities. Op-amps may be packaged as components, or
used as elements of more complex integrated circuits. (ref A)
The aim of this experiment was to provide practical experience of the use of
operational amplifiers. The voltage gain of two basic amplifiers: the inverting
and the non-inverting amplifier were measured.
Theory
The voltage gain of the inverting amplifier, whose circuit diagram shown in fig 2,
is provided in equation (1).
Vout/Vin = -(Rf/R1) …………………………(1) (ref C)
The voltage gain of the non-inverting amplifier, whose circuit diagram shown in
fig 3, is provided in equation (2).
Vout/Vin = (1+ (Rf/R1)) ……………...........(2) (ref C)
3
Experimental method
The two-position switch on the motherboard was set on the input voltage source
(a circuit diagram of the input voltage source was shown in fig 1) to apply 3.3
volts across the 10 K potentiometer (potential divider). Then the op-amp was
connected in the inverting amplifier configuration. The circuit diagram for the
inverting amplifier connection was shown in fig 2. The op-amp was ensured to
be connected in the + 15 volt power supply. A 508  resistor was used for the
input resistor R1.
10 different resistors were selected to act as feedback resistors that resulted in
10 different amplifier voltage gains. The output voltage of the amplifier was
measured using each of those resistors by connecting the 0.1 volts input voltage
to the amplifier input and measuring the amplifier output voltage using the
digital multimeter. The digital multimeter was used to measure the resistance of
each of those feedback resistors.
4
fig 1. Circuit diagram for the input voltage source.
Then the op-amp was connected in the non-inverting amplifier configuration and
the measurements of the amplifier output voltage were measured for each of
those 10 feedback resistors. The circuit diagram of the non-inverting amplifier
configuration was shown in fig 3.
fig 2. Circuit diagram for the inverting amplifier configuration.
fig 3. Circuit diagram for the non-inverting amplifier configuration.
5
Finally the input voltage source from the op-amp circuit was disconnected and
the two-position switch was turned to apply a short circuit across the
potentiometer. This enabled a direct measurement to be made of the Thevenin
source impedance of the potentiometer set to provide the required 0.1 volt input
voltage. The multimeter was connected between the wiper terminal of the
potentiometer and 0v to measure the source impedance.
Results
The data obtained from the inverting amplifier experimental setup was shown in
table 1. The theoretical output voltages were calculated using equation (1) and
also were shown in table 1.
Feedback resistance
Experimental output
Theoretical output
()
voltage (v)
voltage (v)
509
0.12
0.10
678
0.15
0.13
979
0.18
0.19
1492
0.24
0.29
4720
0.62
0.93
9930
1.26
1.95
22000
2.60
4.30
66400
6.98
13.07
100000
9.25
19.69
177800
11.52
35
Table 1. Results of the inverting amplifier experimental setup
A graph form of table 1 was shown in fig 4.
6
40
35
30
25
20
experimental output
voltage (volts)
15
theoretical output
voltage (volts)
10
5
0
0
50000
100000
150000
200000
fig 4. Theoretical and experimental output voltage versus feedback resistance
for inverting amplifier experimental setup.
40
35
30
25
20
experimental output
voltage (volts)
15
theoretical output
voltage (volts)
10
5
0
0
50000
100000
150000
200000
fig 5. Theoretical and experimental output voltage versus feedback resistance
for non-inverting amplifier experimental setup.
7
The data obtained from the non-inverting amplifier experimental setup was
shown in table 2. The theoretical output voltages were calculated using equation
(2) and also were shown in table 2. A graph form of table 2 was shown in fig 5.
Feedback resistance
Experimental output
Theoretical output
()
voltage (v)
voltage (v)
509
0.20
0.20
678
0.23
0.23
979
0.29
0.29
1492
0.39
0.39
4720
1.01
1.03
9930
2.01
2.05
22000
4.36
4.40
66400
13.20
13.17
100000
14.36
19.79
177800
14.37
35.10
Table 2. Results of the non-inverting amplifier experimental setup.
400
350
300
250
experimental voltage
gain
200
theoretical voltage gain
150
100
50
0
0
50000
100000
150000
200000
fig 6. Theoretical and experimental voltage gain versus feedback resistance
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for inverting amplifier experimental setup.
The theoretical and experimental voltage gain of the inverting amplifier were
calculated and shown in table 3. A graph form of table 3 was shown in fig 6.
Feedback resistance
Experimental voltage
Theoretical voltage
()
gain
gain
509
1.20
1
678
1.50
1.30
979
1.80
1.90
1492
2.40
2.90
4720
6.20
9.30
9930
12.60
19.50
22000
26
43
66400
69.80
130.70
100000
92.50
196.90
177800
115.20
350
Table 3. Theoretical and experimental voltage gain for the inverting amplifier
Experimental setup.
400
350
300
250
experimental voltage
gain
200
theoretical voltage gain
150
100
50
0
0
50000
100000
150000
200000
9
fig 7. Theoretical and experimental voltage gain versus feedback resistance
for non-inverting amplifier experimental setup.
The theoretical and experimental voltage gain of the non-inverting amplifier
were calculated and shown in table 4. A graph form of table 4 was shown in fig 7.
Feedback resistance
Experimental voltage
Theoretical voltage
()
gain
gain
509
2
2
678
2.30
2.30
979
2.90
2.90
1492
3.90
3.90
4720
10.10
10.30
9930
20.10
20.50
22000
43.60
44
66400
132
131.70
100000
143.60
197.90
177800
143.70
351
Table 4. Theoretical and experimental voltage gain for the non-inverting
amplifier Experimental setup.
After the input source was disconnected and a short circuit across the
potentiometer was applied, the Thevenin source impedance of the potentiometer
set to provide the required 0.1 volt input voltage was measured using a
multimeter and was found to be 439.
Discussions
It is evident from the above results that the experimental results agree with the
theoretical predictions shown in equation (1) And equation (2), although there
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were differences in the experimental and theoretical values of the output voltage
and the amplifier gain.
The graphs in fig 4 and fig 5 shows that the output voltage of the inverting and
the non-inverting amplifier increases with the increase in the feedback
resistance, which is what the theoretical predictions are. But the experimental
and theoretical values of output voltages were not the same. These differences
were due to the instrumental errors associated with the experiment.
The instruments such as the multimeter used during the experiment were not
calibrated for their validity before the experiment was carried on. Any small
error associated with the instrument would be good enough to cause a difference
in the readings, which could possibly be the reason for the differences in the
experimental and theoretical values of the output voltages in both the inverting
and non-inverting amplifiers.
From the graphs in fig 4 and fig 5 and also from table 1 and table 2, one could see
that the experimental and theoretical output voltages were almost the same for
most of the feedback resistors except the one with high resistances. The answer
for this lies in itself that if there were some error associated with the experiment,
then with increase in the feedback resistance values the percentage of that error
would also increase. This once again proves that the experimental results agree
with the theoretical predictions.
Looking at fig 6 and fig 7 one can understand that the voltage gain of both the
inverting and non-inverting amplifiers were directly proportional to the
feedback resistances i.e. with the increase in the resistance of the feedback
resistors the voltage gain of the amplifier increased which again demonstrates
the theoretical predictions. The differences in the theoretical and experimental
voltage gain values were justified by the instrumental errors associated with the
experiment as said above.
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From above discussions one could understand that with increase in the ratio of
the feedback resistance to the input resistance the gain of both the inverting and
non-inverting amplifier will increase.
Conclusion
The analysis of the results show that the experimental results agree with the
theoretical predictions. The differences in the theoretical and experimental
values of the output voltages and the amplifier gain were due to the instrumental
error associated with experiment. The maximum gain was obtained by both the
inverting and non-inverting amplifiers when using the 177800 resistor (the
resistor with the highest resistance value among the resistors used during the
experiment) as the feedback resistor. The Thevenin source impedance of the
potentiometer set to provide the required 0.1 volt input voltage was 439.
References
A. Operational amplifier (online). Available from:
http://www.analog.com/library/analogDialogue/archives/3905/Web_ChH_final.pdf
B. Wikipedia (online). Available from:
http://en.wikipedia.org/wiki/Operational_amplifier
C. Lab sheet
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