LAB EXERCISE #3
BASIC LM741 OPERATIONAL AMPLIFIER CIRCUITS,
LIMITATIONS, AND APPLICATIONS
ACCOMPANYING COURSE: EE 230
DEPARTMENT OF ELECTRICAL ENGINEERING
IOWA STATE UNIVERSITY
Working toward a sustainable future
Author: Alexander Sics (Section 16)
Last Updated: 5 May 2009
Contents
Overview of Lab Exercise ................................................................................................ 3
Equations ........................................................................................................................ 5
Part 1: Non-Inverting Amplifier Circuit ............................................................................. 6
Part 2: Inverting Amplifier Circuit ..................................................................................... 7
Part 3: The Integrating Amplifier Circuit........................................................................... 8
Part 4: The Differentiating Amplifier Circuit ..................................................................... 9
Part 5: Observing the Non-Idealities of the LM741 Op Amp .......................................... 12
Part 6: Comparing the Bandwidths of Two Inverting Amplifiers ..................................... 13
Part 7: Designing an Integrating Amplifier Circuit .......................................................... 15
Part 8: Designing an Audio Mixer .................................................................................. 16
LM741 Operational Amplifier Data Sheet 1 ................................................................... 18
LM741 Operational Amplifier Data Sheet 2 ................................................................... 19
Internal Circuitry of a LM741 Operational Amplifier ....................................................... 20
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Overview of Lab Exercise
This lab exercise relies heavily on the usage of the Agilent E33120A waveform
generator, Agilent E3630A power supply, Agilent 34401A multi-meter, Tektronix DPO
3012 oscilloscope, and Signal Express program (on all computers in the lab room).
Refer to lab exercise #1 (“Getting Familiar with Lab Equipment”) if a reminder on how to
operate the machines found in the laboratory is needed.
The LM741 Op Amp is the focal point of this lab exercise; the goals of this lab are:

Get familiar with building inverting, non-inverting, differentiating and integrating
amplifier circuits

Gain a basic understanding of how Op Amp circuits are used to modify signals

Explore some common applications of the Op Amp

Observe some of the fundamental limitations of the device
The operational amplifier is one of the most useful and widespread circuit devices. After
completing this lab exercise, a whole world of circuit design and functions relying on
operation amplifiers will be available to you.
Image 1: Assortment of Op Amps
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How this relates to material from class
In lecture, the mathematical analysis of Op Amps in circuits has been thoroughly
covered. In this lab exercise, the analysis techniques studied in class are used to
describe real circuits. This shows that the material being learned in class is worthwhile
and has real world applications.
Why this is an important lab exercise to complete
Operational amplifiers are found in virtually every electronic circuit in modern
technology. Knowing how the devices work, their function in circuits, and their limitations
is essential for any electrical engineer that works in the industry.
Setup
All of the parts for this lab exercise are found in the supplied lab kit. A LM741 Op Amp,
an assortment of resistors, a potentiometer, and a breadboard (the plastic circuit board)
will be needed. Also, eight cables (found hanging on the labeled racks on the wall) will
be needed to connect the amplifier circuits to the waveform generator, multi-meter, and
oscilloscope.
For quick wiring reference, the terminals of the LM741 Op Amp are shown below.
Figure 1: LM741 Op Amp Terminals
Note: for this lab, the rail voltages (Vcc+ and Vcc-) are to be set at +/- 12V.
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Equations
 Gain:
 Vout 
Av  

 Vin 
 Non-inverting Amplifier:
 Rf 
Vout = Vin 1+ 
 Ri 
 Inverting Amplifier:
 Rf 
Vout = Vin  
 Ri 
 Integrating Amplifier:
 1  t
Vout(t )   
 t (0)  vi dt  v 0  t 0 
R
s
C
f


 Differentiating Amplifier:
Vout(t ) = -  RfCs 
dvi
dt
Equivalent Circuit Representation
Show below is the equivalent circuit of an operational amplifier. Recall from lecture that
this model is used when analyzing circuits containing the devices in order to accurately
determine the capability limits of the circuit’s operation.
Image 2: Equivalent Circuit Model of Op Amp
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First Half of Lab Exercise: Basic Amplifier Circuits
Part 1: Non-Inverting Amplifier Circuit
For the first exercise of this lab, the non-inverting amplifier shown below will be
analyzed.
Figure 2: Non-Inverting Amplifier
Procedure for Part 1
1. Calculate value of output voltage of the non-inverting amplifier using the
appropriate equation. Rf = 22kΩ, Ri = 1.5kΩ, and Vi = 200mV.
2. Build the circuit shown in figure 2 on the breadboard using the same resistor and
input voltage values as in step one.
3. Measure the output voltage with the Agilent 34401A multi-meter and compare
this to the calculated output voltage.
Questions to Answer from Part 1
1. How close was the measured gain to the calculated gain?
2. What caused the different (if any)?
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Part 2: Inverting Amplifier Circuit
For the second exercise of this lab, the inverting amplifier shown below will be analyzed.
Figure 3: Inverting Amplifier
Procedure for Part 2
1. Build the inverting amplifier show in figure 3. Using the equation for the output
voltage of an inverting amplifier, choose values for Ri (keep between 1kΩ and
10kΩ) and Rf so that the gain of the circuit is approximately -4.7.
2. Using Vi = 100mV, measure the output voltage and find out the actual gain of the
amplifier.
3. Next, put a 1kΩ resistor in for Ri (if not already there) and replace Rf with a 4.7kΩ
resistor. Measure the gain of this circuit.
4. Lastly, make a plot of the output voltage vs. the input voltage. Use Signal
Express to sweep the input voltage in 0.5V increments from -4V to 4V; export the
data to Excel and create the plot.
Questions to Answer from Part 2
1. How much did the actual gain differ from the calculated gain in step 2?
2. What was the actual gain of the circuit in step 3?
3. Find the slope of the linear region in the plot created in step 4. How close is this
to the actual gain of the circuit?
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Part 3: The Integrating Amplifier Circuit
Now that the basics of Op Amp circuits have been covered, it is time to look at more
complicated configurations that modify both the amplitude and waveform of an input
signal. Shown below is an integrating amplifier circuit. As the name implies, the output
signal is the integral of the input signal.
Figure 4: Integrating Amplifier
Procedure for Part 3
1. Build the integrating amplifier circuit shown in figure 4. Use the same values for
the resistors and capacitor as labeled. Make sure to use a non-electrolytic
capacitor.
2. Use the Agilent E33120A waveform generator to supply a 2V (peak-to-peak)
square wave at 1 kHz as the input to the amplifier.
3. View the input and output waveform with the Tektronix DPO 3012 oscilloscope
(make sure to match the output impedance of the waveform generator to the
input impedance of the oscilloscope). Notice the non-linear relationship between
the input and output waveforms.
4. Set the seconds/division of the oscilloscope window to 500µs/div. Print a
screenshot of the waveforms to include in your lab report.
5. Next, decrease the frequency of the input to 50 Hz. Note the change in the
amplitude of the output. Print a screenshot of the waveforms for your lab report.
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6. Lastly, set the frequency back to 1 kHz but change the waveform to a ramp wave.
Notice the similarities and differences to the square wave input. Print a
screenshot.
Questions to Answer from Part 3
1. Is the input/output relationship observed in step 3 accurately described by the
equation for an integrating amplifier circuit? Mathematically prove this in your lab
report using the 500µs screenshot as the data source.
2. How did the amplitude of the output waveform in step 3 (1 kHz square wave)
differ from that in step 5 (50 Hz square wave)?
3. How did the output signal in step 3 (1 kHz square wave input) differ from the
output signal in step 6 (1 kHz ramp wave input)?
Part 4: The Differentiating Amplifier Circuit
The differentiating amplifier circuit shown below modifies both the amplitude and
waveform of an input signal in a similar fashion as the integrating amplifier; however, the
relationship between input and output signal is the exact opposite of the integrator’s, as
will soon be seen.
Figure 5: Differentiator Amplifier
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Procedure for Part 4
1. Build the differentiating amplifier circuit shown in figure 5. Use the same values of
resistors and capacitor as labeled.
2. Use the Agilent E33120A waveform generator to supply a 2V (peak-to-peak)
triangle wave (ramp with 50% symmetry) at 1 kHz as the input to the amplifier.
3. View the input and output waveform with the Tektronix DPO 3012 oscilloscope
(make sure to match the output impedance of the waveform generator to the
input impedance of the oscilloscope). Notice how the input and output’s
relationship differs from that of the integrator’s.
4. Set the seconds/divisions of the oscilloscope window to 200µs/div. Print a
screenshot of the waveforms to include in your lab report.
5. Next, decrease the frequency of the input to 50 Hz. Take note of the change in
the amplitude of the output. Print a screenshot of the waveforms for your lab
report.
6. Now, gradually increase the frequency of the input until the Op Amp begins to
operate in saturation mode and record the frequency. Remember from lecture
that the saturation of an Op Amp occurs when the output of the amplifier reaches
its maximum value. When this happens, the waveform seen on the oscilloscope
will “clip” (i.e., the top of the output waveform will become flat).
Image 3: A clipped waveform
7. Lastly, set the frequency of the input back to 1 kHz and change the waveform
shape to a ramp. Print a screenshot of what is seen on the oscilloscope. Take
note of how the output waveform differs from that in step 3 (1 kHz triangle wave).
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Questions to Answer from Part 4
1. Is the input/output relationship observed in step 3 accurately described by the
equation for a differentiating amplifier circuit? Mathematically prove this in your
lab report using the 200µs screenshot as the data source.
2. How did the amplitude of the output waveform in step 3 (1 kHz triangle wave)
differ from that in step 5 (50 Hz triangle wave)?
3. At what frequency did the Op Amp reach saturation? What was the maximum
value of the output?
4. How did the output signal in step 7 (1 kHz ramp wave input) differ from the output
signal in step 3 (1 kHz triangle wave input)?
Second Half of Lab Exercise: Op Amp Limitations and
Applications
The first half of this lab exercise was aimed at providing you with a good understanding
of the basic concepts of the Op Amp. Now that the foundation has been laid, it’s time to
progress onward and observe a few fundamental limitations of these devices and look at
some of their common applications.
In the second part of this lab exercise, two aspects of the LM741 will be explored—ideal
operation and non-ideal operation. In the following experiments, you will be expected to
identify the conditions that cause non-ideal operation and how the resulting operation
affects circuit performance. You will not be expected to identify the source of the
non-idealities until lab exercise #4 (“Measurement and Management of Operational
Amplifier Parameters”).
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Part 5: Observing the Non-Idealities of the LM741 Op Amp
In this part of the lab, an inverting amplifier with a potentiometer as the load will be used
to observe some non-idealities of the Op Amp.
Rf
4
-Vcc
2
V-
Ri
-
3
Vi
+
OUT
V2
6
V+
uA741
Potentiometer
7
Vout
+Vcc
Figure 6: Inverting Amplifier with Variable Load Resistance
Procedure for Part 5
1. Design and build an inverting amplifier as shown in figure 6 that has a voltage
gain of -10. Unwanted behavior of the Op Amp will be observed with this circuit.
2. Apply a 1 kHz sine wave and keep the output voltage around 20V (peak-to-peak).
Decrease the load resistance until the circuit no longer behaves as desired (e.g.,
clipping, distortion, etc.).
3. Next, make the load resistance large (e.g., 2kΩ) and reduce the output voltage to
about 1V (peak-to-peak). Increase the frequency of the input sine wave until the
circuit no longer behaves as desired.
4. Now, keep the load resistance the same as in step 3 but increase the output
voltage level to around 20V (peak-to-peak). Increase the frequency of the input
sine wave until the circuit no longer behaves as desired.
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5. Finally, keep the load resistance large as in the previous step and set the input
frequency of the sine wave to 1 kHz. Increase the input amplitude (peak-to-peak
voltage) until non-ideal behavior occurs.
Questions to Answer from Part 5
1. In step 2, at what resistance value did the amplifier circuit exhibit undesired
behavior? What non-ideal behaviors took place?
2. In step 3, how, and at what frequency, did the amplifier circuit start behaving
undesirably?
3. Again, in step 4, at what frequency did the amplifier circuit start behaving
undesirably? Compare with the results from step 3. How does the output voltage
level affect the frequency handling limits?
4. In step 5, what was the input amplitude at which non-ideal behavior occurred?
Describe what the output did when too large of an input was applied.
Part 6: Comparing the Bandwidths of Two Inverting Amplifiers
In part 6 of this lab exercise, the effects of gain on amplifier bandwidth will be looked at.
Recall from lecture that the bandwidth of an amplifier is the range of frequencies where
the output signal’s Fourier transform is non-zero above a certain amplitude limit
(commonly 3 dB).
Figure 7: Depiction of 3 dB bandwidth
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Procedure for Part 6
1. Build two inverting amplifiers, one with a gain of -10 and the other with a gain of
-50.
2. Use Signal Express to measure the 3 dB bandwidth of both amplifier setups.
Refer to lab exercise #1 (“Getting Familiar with Lab Equipment”) if a reminder on
how to make the measurement is needed. Be sure to print off the resulting plots
for later analysis.
Questions to Answer from Part 6
1. How did the bandwidth change with gain in step 1? Does a higher gain
correspond to a larger bandwidth?
2. Use the plots printed in step 2 to graphically find the pole locations of both
amplifiers.
Note on Finding Pole Location
The pole location of an amplifier is the zero-solution of the transfer function of the circuit.
The equation shown below is the general form of a single pole first-order transfer
function in the s (complex frequency) domain.
a sa 
H( s)  

s

w


1
0
0
Equation 1: First-Order Transfer Function
The quantity ω0, called the pole frequency, is equal to the inverse of the time constant of
the single-time-constant (STC) network; the constants a1 and a0 determine the type of
network. Review chapter 8 of the book accompanying this course (Microelectronic
Circuits, Sedra/Smith, 5e) and the lecture notes covering Laplace Transforms for
additional information on the procedure of finding poles and zeros of transfer functions.
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Part 7: Designing an Integrating Amplifier Circuit
In part 7 of this lab exercise the effect of the feedback resistor in an integrator will be
observed. Also, recall that the unity gain frequency of an amplifier is when the closedloop voltage gain is equal to one; this represents the highest useable frequency of the
circuit.
Figure 8: Integrating Amplifier Circuit
Procedure for Part 7
1. Design and build an integrating amplifier with an integrator unity gain frequency
of approximately 2 kHz. Make sure to use a non-electrolytic capacitor.
2. Test the output of your circuit with both square and sinusoidal input waveforms
with the Tektronix DPO 3012 oscilloscope. Check to see if output behaves as
expected (i.e., the relationship between input and output is as observed in Part 3:
The Integrating Amplifier Circuit).
3. Now, modify the feedback of integrator by replacing R1 with a resistor that is at
approximately 100 times larger. Take a screenshot of the input and output
waveforms and include in your report.
4. Remove R1 and notice what happens to the output.
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Questions to Answer from Part 7
1. How did the output of the circuit change when R1 was replaced in step 3?
2. What happened to the output in step 4?
Part 8: Designing an Audio Mixer
In the last part of this lab exercise an amplifier circuit that handles more than one input
signal at once will be worked with; this circuit is called a “summing amplifier”. Below is
the diagram of a summing amplifier:
Figure 9: Summing Amplifier Circuit
The output gain for each input can be calculated by analyzing each signal input and
resistor pair individually. The equation for the gain of an inverting amplifier is still used:
 Rf 
Vout = Vin  
 Ri 
Equation 2: Inverting Amplifier Gain
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Procedure for Part 8
1. Design an audio mixer that can add two signals—one a 400 Hz sine wave and
the other a 900 Hz square wave. Follow the design shown in figure 9.
2. Build the mixer so that the gain from the sine wave input is -5 and the gain from
the square wave input is -2.
3. Use the Agilent E33120A waveform generator to feed the circuit the two signals
mentioned in step 1.
4. Observe the input and output waveforms with the Tektronix DPO 3012
oscilloscope. Print out a screenshot to include with your report.
Questions to Answer from Part 8
1. Describe the shape of the output seen in step 4. How does this compare to the
output of an integrating amplifier that only has one input signal?
2. Is it easy to verify that the signal mixing is correctly occurring? Why or why not?
Hint: imagine how each input would pass through the system individually if it were
not being mixed.
Conclusion
This lab exercise has provided you with a basic understanding of operational amplifier
circuits, their limitations, and applications. Combining the conceptual aspects learned in
lecture with their physical manifestations is very important in order to see the “big
picture” of how the many hours spent studying books has real world merit.
After completing this lab exercise, create a report answering the questions asked at the
end of each experiment and thoroughly describing your procedure and calculations. Be
sure to provide figures, graphs, and screenshots as support for your data.
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LM741 Operational Amplifier Data Sheet 1
Obtained from National Semiconductor
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LM741 Operational Amplifier Data Sheet 2
Obtained from National Semiconductor
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Internal Circuitry of a LM741 Operational Amplifier
Below is a schematic of the LM741 Op Amp.
Obtained from National Semiconductor
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