Ústav fyzikální elekotroniky
Přírodovědecká fakulta, Masarykova univerzita, Brno
Physics laboratory 3
Task 7. Operational ampliﬁer
Introduction
An operational ampliﬁer (OA) is an electrical circuit widely used in almost all areas of analogue
electronics. OA can be described as a high gain diﬀerential voltage ampliﬁer. In other words, OA
provides an output voltage that is many times higher than the diﬀerence of the potentials between
the two OA inputs. An ideal OA has an inﬁnite ampliﬁcation, inﬁnite input resistance (thus there
are no current losses at the OA inputs), zero output resistance and an inﬁnite bandwidth (i.e. OA
ampliﬁes all the frequencies equally). A real OA electrical circuit delivers varying ampliﬁcations —
sometimes less than 1 000 and sometimes more than 106. The input resistance is usually at least a
MΩ and the output resistance is usually around 50 Ω. The bandwidth of a real OA is in the range
of few kHz to hundreds of MHz, however, for higher frequencies the ampliﬁcation decreases and a
phase diﬀerence between the input and the output arises as well. A wide bandwidth is necessary
not only for high-frequency systems but also for feedback circuits, where a lag between the output
signal and the input signal can lead to system instability.
The electronic schematic of an OA is shown in Fig. 1. This electrical component typically has
two inputs (an inverting one and a non-inverting one) and one output. If the non-inverting input
potential is higher than the inverting input potential, the output voltage is positive and vice versa.
Besides the input and output pins, an OA has also power-in pins for positive as well as negative
voltage.
Figure 1: An electronic schematic of an operational ampliﬁer.
In this laboratory you will work with some typical applications of an OA. A circuit board with
an OA and all the necessary components (resistors, capacitors, diodes, leads) for easy connection
to the circuit board are available. The OA has its own dedicated 15 V power supply. Moreover, two
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direct current (DC) and one alternating current (AC) power supplies are available. The frequency
of the AC power supply is tunable from 10 Hz to several MHz. Several multimeters are used
for the measurement of the DC voltage; an oscilloscope is used to measure the AC voltage. Avoid
saturating the output voltage in all measurements (except for the comparator measurement no. 5).
Choose the correct input voltage to achieve the output voltage not higher than 10 V.
1 2 3 4 5 6 7
Figure 2: Operational ampliﬁer setup: 1. Multimeters. 2. AC power supply. 3. Diﬀerent electrical
components. 4. DC power supplies. 5. Circuit board with the operational ampliﬁer. 6. Power
supply. 7. Oscilloscope.
Comparator
To understand the principle of an OA it is good to try its simple application in comparing two
voltages. Because the OA multiplies the diﬀerence of the input voltages by a large number, it
can compare two input signals with a high sensitivity (i.e. distinguish, which one is higher). An
example of this type of comparator is shown in Fig. 3. This type of a circuit well demonstrates
the function of an OA, however, it needs to be said that much faster components in are nowadays
used in practice.
Task
Try how this type of a circuit behaves and how does the OA output voltage react to the diﬀerence
between the input voltages.
Inverting input ampliﬁer connection
An electrical circuit diagram of an inverting ampliﬁer is shown in Fig. 4. The input voltage
is connected to the inverting input via resistor R1, the second input is grounded. The input
voltage is ampliﬁed and a voltage of opposite polarity appears at the output. The output voltage
is back-connected the input voltage via a feedback resistor and this output voltage of opposite
polarity decreases the voltage in point A. Because of the high OA ampliﬁcation, the circuit is
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Figure 3: Comparator.
stabilized at the point, where the voltage between the inputs is near zero. The non-inverting input
is grounded, therefore the inverting input potential (in the point A) is also zero. As the OA input
resistance is high, the current through the resistor R1 must be identical with the current through
the feedback resistor R2. Therefore U1/R1 = −UO/R2 and this OA circuit system ampliﬁes the
voltage according to
UO = −
R2
R1
U1 (1)
Figure 4: Electrical circuit of OA with inverting input.
Make the two following measurements for the abovementioned electrical circuit:
• Connect such resistors, so that the whole circuit ampliﬁes 2 times. Verify that the circuit
connection of the inverting ampliﬁer works according to eq. (1) for several diﬀerent input
DC voltages. Fit the measured data with a line that should cross the zero point and its slope
should give the theoretical ampliﬁcation.
• Measure the bandwidth of the OA with inverting ampliﬁer. The bandwidth is the maximal
frequency, where the operational ampliﬁer works well at a given electrical circuit. This
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limit is usually taken as the frequency at which the ampliﬁcation decreases by 3 dB over
the ampliﬁcation of low-frequency signals Au,max theoretically described by eq. (1). The
decrease of 3 dB corresponds to the decrease of the ampliﬁcation to the value of Au,max/
√
2.
Because you will measure a wide range of frequencies, it is better to plot the graph of the
ampliﬁcation dependent on the frequency logarithm.
Low-pass ﬁlter
By a simple change in the electrical circuit with inverting ampliﬁer (Fig. 4) you can get a circuit
that allows only low frequencies from input signal (see Fig. 5) to pass through. The added capacitor
reduces the impedance of the feedback line for high frequencies, which leads to the ampliﬁcation
(gain) of
Au = −
RF
RA
1
1 + iωCF RF
(2)
Figure 5: Low-pass ﬁlter.
Task
Measure the gain dependence on the frequency and determine the bandwidth from the graph. Plot
the theoretical dependence of the gain on the frequency in the graph as well. Besides the gain,
provide also a commentary for the behaviour of the phase diﬀerence between the input and the
output signal.
Non-inverting input ampliﬁer connection
Look at the electrical circuit with the non-inverting ampliﬁer diagram in Fig. 6. The input voltage
is applied to the non-inverting input. The inverting input is grounded via resistor R1 and the
feedback branch is connected to the same input via resistor R2. Think about what this circuit
will do before the laboratory. The relation between the input and the output voltage can be easily
deduced using the same line of thought as to the one leading to equation (1).
Task
Verify the validity of your equation during the laboratory.
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Figure 6: Electrical circuit with non-inverting ampliﬁer.
Diﬀerential ampliﬁer
A diﬀerential ampliﬁer can be connected by a combination of the inverting and the non-inverting
ampliﬁer as is shown in Fig. 7. The following equation is valid for its output voltage:
UO = U2 ·
R4(R1 + R2)
R1(R3 + R4)
− U1 ·
R2
R1
. (3)
When we choose resistors R1 = R3 = 10 kΩ and R2 = R4 = 20 kΩ, we can simplify this equation
to:
UO = 2 (U2 − U1) (4)
Figure 7: Diﬀerential ampliﬁer.
Task
Connect the diﬀerential ampliﬁer and verify equation (4).
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Diﬀerentiator ampliﬁer
Task
There are 4 diﬀerent OA circuit diagrams in Fig. 8. Consider which one works as a diﬀerentiator
before the laboratory. A diﬀerentiator is a circuit that is designed in such a way that the output of
the circuit is directly proportional to the rate of change (the time derivative) of the input. Verify
the correctness of the circuit function during the laboratory.
You will need to solder one component to make the diﬀerentiator circuit.
+
−
+
−
−
+
−
+
Figure 8: Circuit diagrams of an operational ampliﬁer.
Puzzle lovers can also ﬁgure out what the other circuit diagrams in Fig. 8 do. Can you ﬁnd
out how to build a summing ampliﬁer or a device behaving as a negative resistance using an
operational ampliﬁer? However, this is above the basic scope of this laboratory.