# Operational Amplifiers: Part I solution

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## Description

Objectives
• To demonstrate the principle of superposition by examining the characteristics of a weighted summer op amp
configuration.
• To observe the effects of non-ideal amplifier characteristics, including finite input resistance, finite open-loop
gain, and systematic offset voltages.
• To demonstrate methods of offset cancellation via capacitive coupling.
Parts and Equipment Required
Components and Materials Needed:
• 741 Operational amplifiers (2).
• 10nF capacitor (1).
• 10kΩ resistors (5).
• 10kΩ potentiometer (1).
Equipment to be Used:
• Banana cable sets (4).
• Oscilloscope probes (2).
Utah State University Sping 2015 1
ECE 3410– Microelectronics I Lab 2: Operational Amplifiers: Part I
• BNC-to-BNC cable (1)
• BNC-to-alligator cable (1)
1 Pre-Lab Exercises
Exercise 1. Consider the inverting weighted summer circuit shown in Fig. 1. Using only parallel combinations of
10kΩ resistors, design the amplifier stage to implement the function vout = −v1 − 2v2. (You will use a
total four 10 kΩ resistors). Predict the input resistances seen at terminals v1 and v2.
5V
v1
10kΩ
R1

+
R2 v2
RF
vout
Figure 1: Circuit for Exercise 1.
Exercise 2. Consider the revised weighted summer circuit shown in Fig. 2. In this circuit, an AC coupling capacitor,
C = 10nF, is inserted in the signal path of v2. This creates a high-pass filter which rejects the DC offset
of v2, allowing only the AC part to be summed with v1. What is the cutoff frequency (i.e. the lowest
frequency that will be passed) for this high-pass configuration?
Exercise 3. Consider another circuit, shown in Fig. 3, which is similar to the circuit from Exercise 2. In this circuit,
a unity-gain follower is used to isolate the high-pass offset-reject filter from the input resistance in the
second stage. Note that a 10MΩ resistor is inserted with the coupling capacitor in order to pass the op
amp’s non-ideal bias current. Predict the high-pass cutoff frequency for this two-stage configuration.
Utah State University Sping 2015 2
ECE 3410– Microelectronics I Lab 2: Operational Amplifiers: Part I
5V
v1
10kΩ
R1

+
R2 v2
C
RF
vout
Figure 2: Circuit for Exercise 2.
5V
v1
10kΩ
R1

+

+
R2
10 kΩ
10nF
v2
RF
vout
Figure 3: Circuit for Exercise 3.
Utah State University Sping 2015 3
ECE 3410– Microelectronics I Lab 2: Operational Amplifiers: Part I
2 Physical Experiments
Procedure 1. Using a breadboard, construct the circuit described in Fig. 1. Use +15V and −15V for the 741’s power
supplies. Perform the following experiments:
Step A. Adjust the potentiometer so that v1 = 1V. Connect v2 to the 5V supply. Measure the precise
value of v2 using the DMM, since it won’t be exactly 5 V. Predict the amplifier’s output for
these input values. Measure the actual input and output values using the digital multimeter. How
closely do the values match? Offer explanations for any discrepancy.
Step B. Connect v2 to ground (zero potential). By adjusting the potentiometer, vary v1 from 1V to 2V
in steps of 0.25V. Record a table that includes precise measurements of both v1 and vout. In your
table, also record the expected value of vout for each measured v1, and record the error (i.e. the
difference between the expected and measured vout).
Step C. Record two plots in your lab note book. In both plots, let the horizontal (x) axis be the input
voltage v1. In the first plot, draw graphs showing the measured and expected values of vout for
each measured v1. In the second plot, draw a graph of the error. Answer the following questions,
i Does the circuit’s gain differ from the designed value?
ii Does the op amp exhibit a systematic offset voltage?
Procedure 2. Construct the circuit described in Fig. 2. Using a BNC-to-alligator cable, connect the function generator’s
output to the circuit’s input at v2. Perform the following experiments.
Step A. Offset Cancellation:
i Set the function generator to provide a sinusoidal waveform with 1V peak-to-peak amplitude
and 50kHz frequency. Use the 0–2 V range setting on the function generator.
ii Using an oscilloscope probe, record a precise measurement of the peak-to-peak amplitude
and offset voltage at v2 and at vout. You will need to use AC coupling in the Channel
settings to get an accurate amplitude measurement, and DC coupling to get an accurate
offset measurement.
iii What is the gain at this frequency? Is it the same as the DC gain measured in Proc. 1?
iv Vary the function generator’s DC offset and describe how v2 and vout respond. Note: you
may need to pull out the offset adjustment knob in order to change the setting. Make sure
both Channel settings are configured for DC coupling.
v While keeping the function generator’s offset voltage fixed, vary v1 by adjusting the potenUtah
State University Sping 2015 4
ECE 3410– Microelectronics I Lab 2: Operational Amplifiers: Part I
tiometer. For three separate values of v1, record measured values for v1, and predict the
effect that the value will have on vout. Using the oscilloscope, measure and record the offset
voltage of vout at each value. Do the measured values agree with your predictions? Offer
explanations for any discrepancies.
Step B. Frequency Response:
i Using the FFT procedure that you practiced in Lab 1, measure the 3 dB cutoff frequencies
of the circuit. Due to the capacitor C, there will be two cutoff frequencies, one at a low
frequency (flow) and another at a high frequency (fhigh). The transfer function is maximized
for frequencies between flow and fhigh. You may need to use different sampling rate settings
to measure the high and low frequencies.
Procedure 3. Construct the circuit shown in Fig. 3. Repeat the frequency-sweep measurement described in Proc. 2 B.
After completing the measurement, explain any observed differences between the measured frequency
responses, the cutoff frequencies, and the bandwidth of these two circuits.
3 Post-Lab
In your lab book, write a brief summary of your findings. Prepare a formal report describing the objectives, methods
and major findings of this lab experience. Your report should compare results from pre-lab analyses, SPICE simulations
and physical experiments. Submit this report online in Canvas, and have the TA examine and grade your lab
book.