Physics 201 Laboratory:
Analog and Digital Electronics
II-2. The Operational Amplifier
The operational amplifier (“op amp”) is the basic building block for many analog devices. Its
symbol in circuit diagrams is shown in Figure 1. (Usually, we do not indicate the connections
V± explicitly, but instead draw the circuit element as in Figure 2.)
V+
inverting input
−
non-inverting input
+
output
V−
Figure 1: Op Amp Circuit Symbol.
inverting input
−
non-inverting input
+
output
Figure 2: Op Amp, V± suppressed.
In this experiment, we will examine some basic characteristics of the op amp, particularly
the effects of feedback. We will investigate the gain and phase shift as a function of frequency
for three different circuits that can be built using an op amp: an inverting amplifier circuit,
a non-inverting amplifier circuit, and a voltage follower.
Inverting Amplifier
Construct the circuit shown in Figure 3 using a 741 operational amplifier in an 8-pin DIP
configuration (see Figure 4). The minus input is the inverting input (pin 2) and the plus
input is the non-inverting input. The 10 kΩ resistor between pins 1 and 5 is for adjusting
the balance on the inputs (we will return to this later). Pin 7 should be connected to the
+12 V supply and pin 4 to the −12 V supply.
Rf
Vin
Rin = 1 kΩ
Vs
−
+
Vout
5
1
10 kΩ
Figure 3: Inverting Amplifier.
II-2. The Operational Amplifier
p. 2
offset null
1
“−” input
2
741
top view
8
no connection
7
V+ = +15 V
−
+
“+” input
3
6
output
V− = −15 V
4
5
offset null
Figure 4: 741 Op Amp 8-Pin DIP.
1. For Rf = 100 kΩ, apply a 100 mV sine wave input (200 mV peak-to-peak) with zero
DC offset and measure, using the scope, the voltage gain and phase shift as a function of
frequency. Make sure the output signal is not distorted. Make sure you go to the highest
frequencies available and take more data where there is a rapid frequency (or phase) variation.
If the output becomes distorted at high frequency, decrease the input amplitude. Plot voltage
gain as a function of frequency on a log-log graph. Pay particular attention to the phase
study. Plot phase verses frequency on a linear(phase)-log(frequency) graph.
2. The dominant characteristic of an operational amplifier is that the voltage levels at the
two inputs are the same. (If a situation arises that this is not so, then negative feedback will
make it so.) Thus in Figure 3, Vs = 0 because the other input is grounded. This means that
there is only one current to consider and Vin − IRin = Vs = 0, Vs − IRf = 0 − IRf = Vout .
So, the gain is g = Vout /Vin = −Rf /Rin .
How does the measured gain in the “flat” part of the frequency spectrum (low frequency
region) compare with this theoretical gain?
3. For Rf = 1 kΩ and 10 kΩ measure the voltage gain as a function of frequency for the
same frequencies as in step 1. (You need not measure the phase shift.) Choose the input
voltage swing to be small enough so that the output signal is not distorted. Plot all of the
gain versus frequency curves on the same graph (log-log plot). This should give you a clear
idea of the trade off between gain and bandwidth. (Bandwidth is defined as the range in
frequency for which the gain is no less than 3 dB below the gain of the “flat” part of the
spectrum. Gain in dB (decibels) is dB = 10 log10 (Vout /Vin ).
II-2. The Operational Amplifier
p. 3
Non-Inverting Amplifier
Construct the circuit shown in Figure 5. Don’t forget the 10 kΩ offset nulling resistor
which will not normally be shown in the circuit diagrams. The 1 kΩ resistor to ground
at the input is required to provide a route for the very small input current. On the scope
look at Vin (which should be in the 100–200 mV range), not the function generator output.
Measure and plot the voltage gain and phase shift as a function of frequency. Note that
Vs = (Rin /(Rin + Rf )) Vout and Vs = Vin , so that g = (Rf + Rin )/Rin . Start with Rf = 10 kΩ
and Rin = 1 kΩ. Make sure you go to the highest frequencies available. How do these
characteristics differ from those found above?
Rin = 1 kΩ
Vs
1 kΩ
Vin
Rf
−
Vout
+
1 kΩ
Figure 5: Non-Inverting Amplifier.
Unity Gain Voltage Follower
Construct the circuit shown in Figure 6. Note that the input signal is now being applied
to the non-inverting input. Again, don’t forget the 10 kΩ offset nulling resistor. Apply a
sinusoidal signal at about f = 1 kHz to the input and measure the voltage gain of the circuit.
(This is the op amp equivalent of a single transistor emitter follower and is useful for the
same reason: very high input impedance). You are replacing Rf in Figure 5 by a short circuit
(Rf → 0) and Rin by an open circuit (Rin → ∞). What gain do you expect?
1 kΩ
−
Vin
+
1 kΩ
Figure 6: Voltage Follower.
Vout