UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE
Department of Electrical and Computer Engineering
Experiment No. 2 - Operational Amplifiers
Overview: The purpose of this lab is to introduce the operational amplifier (op-amp), and provide
some experience with its applications in electronic circuits.
An Operational Amplifier is a very high-gain, direct-coupled amplifier that uses feedback for
control of its response characteristic. A direct-coupled amplifier is capable of amplifying DC as
well as time varying signals. The standard symbol for an op-amp is shown below.
1
-
2
+
3
Terminals 1 and 2 are the input terminals and terminal 3 is the output terminal. A simple single
stage amplifier can be built with a single transistor; however, the gain of such an amplifier is often
insufficient and cascaded amplifiers are required. Using integrated circuit technology multistage
amplifiers are built on a single “chip.” In addition to the increased packaging density, the integrated
amplifier has numerous other advantages, some of which are: noise immunity, superior frequency
response, stability, low power consumption and low cost. The output voltage of an op-amp is the
difference between the voltages applied to its input terminals multiplied by its open loop gain, A.
The output voltage is positive when the voltage applied to the positive (non-inverting) input exceeds
that applied to the negative (inverting) input. An ideal op-amp would have an infinite open-loop
gain, requiring that the difference between V+ and V- be infinitesimally small in order for the
output voltage to be finite. Thus, for circuit analysis purposes, this voltage difference is assumed to
be zero. Furthermore, the ideal op-amp would have infinite input impedance and zero output
impedance. These are, of course, the ideal characteristics for a buffer amplifier that would make it
possible to drive a low impedance load with a large impedance source. For circuit analysis
purposed, the current at the input terminals is assumed to be zero, while the output voltage when
driving a load is assumed to be the same as the open circuit output voltage. The output voltage of an
op-amp is given by
Vout = A ((V+) - (V-))
In this equation, observe that when A is infinite, the difference between V+ and V- must be zero for
V0 is to be finite.
Operational amplifiers are versatile and useful devices. They can perform many functions, some of
which are: inverting, amplification, attenuation, summing, integrating, differentiating, filtering, and
signal generation (oscillators).
Pre-Lab – Operational Amplifiers
1.
Study the chip layout of Fig. 3. The standard procedure on DIP (dual in-line package)
“chips” is to identify pin 1 with a notch in the end of the chip package. The notch always
separates pin 1 from the last pin on the chip. In the case of the 741, the notch is between
pins 1 and 8. Pin 2 is the inverting input, V-, Pin 3 is the non-inverting input, V+, and
the amplifier output, Vo, is pin 6. These three pins are the three terminals that normally
appear on the op-amp symbol in a circuit diagram. Even though the ±VCC connections
must be completed for the op-amp to work, they usually are omitted from the circuit
schematic to improve clarity. The null-offset pins (1 and 5) provide a way to eliminate
any “offset” in the output voltage of the amplifier. The offset voltage (usually denoted by
Vos) is an artifact of the integrated circuit. It is additive with Vo (pin 6 in this case), is
normally less than 10 mV, and can be either positive or negative. Because the offset
voltage is small, in most cases we can ignore its contribution to Vo , and leave the nulloffset pins open. Pin 8, labeled “NC”, has no connection to the internal circuitry of the
741, and is not used.
2.
Determine the transfer function, Vo/Vi and the function that the operational amplifier is
performing in the figure below for the impedance parameters listed below
Zf
Vi
Zi
-
+
a. Zf : resistor R = 60 KΩ
Vo
Zi : resistor R = 100 KΩ
2
2
b. Zf : resistor R = 100 KΩ
Zi : resistor R = 60 KΩ
c.
Zi : resistor R = 100 KΩ
Zf : capacitor C = 0.002 μF
(INSTRUCTOR’S SIGNATURE_____________________________DATE
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Lab Session – Operational Amplifiers
1. Prepare the power supplies.
The schematic of Figure 1 shows a standard ±VCC configuration for op-amps
(these supplies need to be a constant DC voltage). Adjust the output so the +VCC and –VCC are
equal — but opposite in sign — at 15 V.
2. Configure the signal source.
Connect the ±Vcc to the potentiometer as shown in Fig. 2. This will provide a variable-output
DC signal source ranging from –Vcc to +Vcc , for input to the op-amp circuit. Check this circuit
with a volt meter to ensure that it provides the range of voltages desired. The red voltmeter lead
should be connected to the center terminal of the potentiometer and the common ground between
±Vcc.
The way in which the power supplies are connected to each other, and to the potentiometer
produces four nodes, +Vcc, -Vcc, Vin and (GND) or reference.
3. Turn the power supply off.
4
4
4. Connect the circuit shown in Figure 4.
5. Connect the circuit in figure 5.
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5
Figure 6 is the pseudo-schematic, it shows the physical layout of the circuit and the
connections on the protoboard.
6. The inverting amplifier
Carefully measure the values of the resistors that will be used in the circuit of Fig. 4. Use these
measured values to compute the circuit gain, A. With the power supply off, construct the
inverting op-amp circuit using Figure 6 as a guide. Check the circuit carefully. Turn on the Vin
power supply. Adjust the 10 kΩ potentiometer to achieve a Vin of 1 V. Measure Vin and Vout
and verify that the actual Vout is A*Vin. If Vout is correct, your amplifier circuit is probably
working correctly, and you may proceed. If the measured Vout is different from A Vin, by more
than 10%, you probably have an error in the circuit. Troubleshoot the circuit until it is operating
properly. Remember that the inverting amplifier has a negative gain.
a.
Create a table with four columns labeled Vin, A Vin (the theoretical output voltage), Vout
(the actual output), and percent error. Leave enough room to record 21 rows of data.
Turn on the power supply, adjust Vin to -10 V, and carefully measure Vin and Vout.
Increase Vin from -10 V to +10 V in 1V increments, measuring Vin and Vout for each step.
For each line of data, compute and record AVin and the error between AVin and Vout.
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b.
At Vin = 2 volts, accurately measure and record Vin, +VCC, -VCC, V+ and V-. If measured
using a sensitive voltage scale, a very small difference in V+ and V- may be detected.
If possible measure and record the voltage difference ∆V+.
c.
Turn off the power supply. Without removing the op-amp, disassemble the circuit of
Figure 6.
7. The non-inverting amplifier
a.
Calculate and record the expected gain for the circuit of Figure 7.
b.
You will use the source circuit of Figure 2 to provide Vin for the non-inverting amplifier
of Figure 7. Draw a circuit diagram similar to Figure 5 for the schematic of Figure 7.
You may also want to draw a pseudo-schematic similar to Figure 6 for this circuit.
c.
Connect the circuit of Figure 7, using your pseudo-schematic as a guide. Test the circuit
by verifying that Vout is equal to AVin. If not, troubleshoot the circuit until it is operating
properly.
d. Create a table for recording the Vin, A*Vin, Vout and % error. Starting at a Vin of –10 V,
make 21 measurements of Vin and Vout, incrementing Vin by 1 V after each measurement.
Fill in the remaining two columns of the table with the needed calculated values.
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8. The integrator amplifier
By placing a capacitor in the feedback path (in figure 4.) and a resistor at the input we
obtain a circuit that performs the mathematical operation of integration.
a. Measurement of DC integrator output voltage.
1. Construct the circuit in Figure 8.
2. Open the switch at t=0, and observe Vout(t). Measure the time it takes for the
output voltage to fall from 0V to -4V. Calculate Ic.
C1
10uF
R1
-
1M
Vin
Vout
LM741
10V
+
Figure 8.
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b. Figure 9 shows the circuit diagram of a simple low pass filter with a high frequency
cutoff of fh = 1/2πRfCf. As a rule of thumb this circuit will also function as an
integrator for time varying signals of frequency greater than 5fh . We will use this circuit
to integrate a square wave, sine wave, and triangle wave.
1. Construct the circuit in figure 9.
2. Let Vin be a square wave with a 4Vp-p amplitude and 200 Hz frequency.
Record and save the waveforms of Vin and Vout to your compact flash card.
3. Repeat 2 with Vin changed to a 4Vp-p sine wave at 200 Hz, and
then for a frequency to 400 Hz. Save the results.
4. Repeat 2 with Vin changed to a triangle wave (4Vp-p, 200 Hz).
Save the results.
5. Again using the 4Vp-p square wave, reduce the frequency until the circuit
ceases to integrate the input signal. Record this frequency.
Figure 9.
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9. The differentiator amplifier of Figure 10 is also known as a high pass filter and has a lower
cutoff frequency fl , given by 1/2π CR1. As a rule of thumb this circuit will differentiate input
signals of frequency less than fl /5. To justify this rule of thumb, look at the transfer function
and observe what must be true about the frequency for this transfer function to approximate a
positive imaginary quantity. Note that the impedance of the capacitor becomes very small at
high frequencies. Thus, the magnitude of gain increases to a value of Rf /R1 for frequencies
significantly above fl . Because of its frequency response the differentiator circuit is very
susceptible to high frequency noise and is generally avoided in practice.
1. Construct the circuit of Figure 10, using a 0.1µF capacitor , a 1kΩ resistor for
R1, and a 4.3kΩ resistor for Rf .
2. With Vin a sine wave of 2Vp-p at 200 Hz , record the input and output waveforms.
Save them to the compact flash card as in the previous section. Repeat for triangle and
square waves of the same amplitude and frequency.
3. Which input waveform gives the best results and which the worst?
4. With the square wave input, increase the frequency until the circuit ceases to
differentiate the input signal. Record this frequency.
5. Measure and record the circuit gain for a frequency much greater than fl .
Rf
Vi
R1
C
Vo
+
Figure 10.
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Lab Session – Operational Amplifiers (Data Sheet)
INSTRUCTOR'S INITIALS
DATE:
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Post Lab – Operational Amplifiers
1. For the inverting amplifier, include in your report, plots of Vout, AVin, and the error vs.
Vin (i.e., three plots superimposed onto the same graph).
2. Repeat 1 for the non-inverting amplifier circuit.
3. Using the numerical values in the differentiator circuit, calculate Vout in terms of Vin, f,
R1, RF and C. Compare the measured and calculated values of Vout , for a frequency much
greater than fl.
4. Simulate the integrator and differentiator circuits using the same setup as in the
experiment, using schematics or netlist in PSpice. Compare the results with those
obtained in the experiment. Run a transient simulation with the same inputs used in parts
b2, b3, and b4 for the integrator and with the same inputs used in part 2 for the
differentiator.
5. The integrator circuit should cease to integrate the input for f < 5fh, where fh is the high
frequency cutoff. Likewise, the differentiator should cease to differentiate the input for
f > (1/5)fl , where fl is the low frequency cutoff. Calculate these frequencies and compare
them with the results from the experiment.
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