PHYSC 3322
Experiment 1.4
12 February, 2016
Analog Devices (Operational Amplifiers)
Purpose
This experiment will introduce you to the operational amplifier, or op amp, an
important building block used in many electronic circuits. Using the op amp, you will
construct two useful circuits, a non-inverting amplifier and a sine-wave oscillator.
Background
The op amp is a differential amplifier having very high voltage gain (on the order of
10 4  10 7 ). There are two inputs: a non-inverting input, denoted by (+), and an
inverting input, denoted by (–). The output voltage is equal to the gain multiplied by
the difference between the two inputs:
vo  A v  v  ,
(1)
where v  and v  are the voltages at the non-inverting and inverting inputs,
respectively, A is the voltage gain, and v o is the output voltage. For this experiment,
you will consider the op amp to be a “black box”—you will not need to know what
goes on inside the op amp, and will only be concerned with the fact that the input and
output voltages obey the above equation.
Procedure
You will use the LT1013 integrated circuit in this experiment. The LT1013 contains two
complete op amps in one package, as shown in Figure 1. Pin 1 of the integrated circuit
is marked with a dot on the package. Pins 4 and 8, labeled with +V and -V in the figure,
are the power supply connections. In the following circuits, pin 4 should be connected
to the 12V terminal of the power supply, pin 8 should be connected to the 12V
terminal of the power supply, and the points marked with the ground symbol should
be connected to the 0 V terminal of the power supply.
Non-inverting amplifier: Using the LT1013 integrated circuit and two 1.0 k resistors,
construct the non-inverting amplifier circuit shown in Figure 2.
Figure 1. LT1013 integrated circuit.
Figure 2. Non-inverting amplifier.
Connect a function generator to the input of the amplifier. Using an oscilloscope, adjust
the function generator so that its output is a 1 kHz sine wave, having an amplitude of
approximately 1 V peak-to-peak. With the oscilloscope, measure the output of the
amplifier. You should find that the output amplitude is twice the input amplitude.
Verify that this relationship holds true as you vary the input voltage and frequency.
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PHYSC 3322
Experiment 1.4
12 February, 2016
The overall gain of the non-inverting amplifier is controlled by the two resistors, a
result which can easily be derived from Eq. 1 in the previous section. In addition to that
equation, we need one other equation, which relates the voltages across the two
resistors. To a very good approximation, the current flow into the input terminals of an
op amp is zero. Thus, the current through R 1 is equal to the current through R 2 , and
so we have a simple voltage divider:
v / R1   vo  v  / R2 .
(2)
Rearranging the terms give us
 R1 
v  vo 
.
 R1  R 2 
(3)
Combining this with Eq. 1 gives

 R1  
v o 1  A
   Av  .
 R1  R2  

(4)
Finally, noting that v   v i , and using the fact that A  1 to simplify, we obtain
 R  R2 
vo  v i  1
.
 R1 
(5)
Wien bridge oscillator: The Wien bridge is a convenient means of generating highquality (i.e., low distortion) sine waves at audio frequencies. Without disturbing the
non-inverting amplifier, construct the Wien bridge oscillator shown in Figure 3. Note
that R 4 is a potentiometer, not a resistor. The combination of R 3 and R 4 provide
negative feedback, as in the amplifier circuit. The two RC networks provide positive
feedback at a frequency determined by the RC time constants. When the positive and
negative feedback are precisely in balance, the circuit will oscillate. After assembling
and checking the circuit, connect the oscilloscope to the output of the oscillator (pin 1 of
the op amp) and apply power.
Figure 3. Wien bridge oscillator.
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PHYSC 3322
Experiment 1.4
12 February, 2016
On the first try, the signal will probably be either a square wave or zero. Adjust the
negative feedback loop by varying the setting of the potentiometer R 4 until you obtain
a sine wave output. At this time, the output will be unstable and the adjustment will be
very sensitive.
You can stabilize the output by replacing R 3 with a small incandescent lamp. The lamp
acts as a nonlinear resistance: If the amplitude of oscillation increases, the voltage
across the lamp increases, causing it to get hotter; this causes its resistance to increase as
well, thus increasing the negative feedback and reducing the gain of the amplifier.
Conversely, if the amplitude of oscillation decreases, the voltage across the lamp
decreases, its resistance decreases, and the gain of the amplifier is increased.
Next, connect the output of the oscillator to the input of your non-inverting amplifier.
Use the oscilloscope to measure the output of the amplifier. Describe and sketch the
output waveform.
Finally, replace R 2 in the non-inverting amplifier with a 10 k resistor (what is the
gain now?). Again, describe and sketch the output waveform.
Questions
In a Wien bridge oscillator, when the two RC networks have the same time constant,
the output voltage is three times the voltage at the non-inverting input of the op amp.
Verify that this is the case.
The frequency of oscillation of the Wien bridge oscillator is given by
f 
1
.
2RC
(6)
Verify that this is the case in your circuit, and discuss any discrepancies between the
calculated and measured frequencies.
Explain the shape of the waveforms you measured at the output of the amplifier +
oscillator combination.
The nonlinear resistance of an incandescent lamp depends on the filament temperature,
which changes relatively slowly. Would a nonlinear resistor having a faster response
improve the regulations of the circuit, or make it worse?
When you build an amplifier having a gain of 2, using an op amp with a gain of ~ 10 6 ,
it seems like you're "throwing away" most of the gain. Can you speculate on why this is
often a good idea?
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