# Operational Amplifiers: Part II solution

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## Description

Objectives
• Measurement of non-ideal op amp characteristics such as DC open-loop gain, slew rate, full- power bandwidth,
and input offset voltage.
Parts and Equipment Required
Components and Materials Needed:
• 741 Operational amplifier (1).
• 100Ω resistor (1).
• 10kΩ resistor (2).
• 100kΩ resistor (1).
• Data sheet for the uA741 Operational amplifier.
Equipment to be Used:
• Banana cable sets (5).
• Oscilloscope probes (2).
• BNC-to-BNC cable (1)
• BNC-to-alligator cable (1)
Utah State University Spring 2015 1
ECE 3410– Microelectronics I Lab 3: Operational Amplifiers: Part II
vIN
R1
R3
R4

+
+
VOFS −
R2
vOUT
vx
vy
i1 i2
i3
Figure 1: Circuit used for measuring the op amp’s open-loop gain with resistor values R1 = 10kΩ, R2 = 10kΩ,
R3 = 100kΩ, and R4 = 100Ω.

vIN +
vOUT
Figure 2: A unity-gain voltage follower configuration.
1 Pre-Lab Exercises
In this lab, you will measure several non-ideal characteristics of the 741 op amp. In practice, these characteristics are
very challenging to measure. The exercises below introduce some practical measurement techniques that can be used
in our laboratory.
Exercise 1. The circuit shown in Fig. 1 is configured to allow measuring the op amp’s offset voltage and open-loop
gain. In this exercise, you will analyze the circuit’s response to the offset voltage when vIN = 0. Assume
that the op amp has infinite open-loop gain and zero input bias current. Then there should be a perfect
virtual short so that VX ≈ VOFS (note that we are using the all-capital notation to indicate a DC offset).
Examine the circuit and verify that the following equations are correct:
I2 = I1 +I3
I1 =
VY
R1
I2 =
VOUT −VY
R2
I3 =
VOFS
r4
From these equations, solve for VOUT and show that it is equal to
VOUT = VOFS 1+
R3
R4
1+
R2
R1

+
R2
R4

. (1)
Utah State University Spring 2015 2
ECE 3410– Microelectronics I Lab 3: Operational Amplifiers: Part II
Using the resistor values stated in Fig. 1, evaluate the expression in parenthesis and state the numerical
value for the offset gain Go = VOUT/VOFS.
Exercise 2. The circuit shown in Fig. 1 can also be used to estimate the op amp’s open-loop gain A. To do this, we
apply a sinusoidal input at vin and measure the gain as the ratio of amplitudes vout/vin (here we are using
the all-lowercase notation to indicate AC signal amplitudes). To analyze the AC behavior, we assume
finite open-loop gain but we still assume zero input bias current (this assumption is acceptable for the
uA741 since Ibias is extremely small, around 10 nA).
By analyzing the currents in this circuit, it can be shown that
vy ≈ vin 
R2 (R3 +R4)
(R1 +R2) (R3 +R4) +R1R2 +AR1R4

(2)
≈ vin 
R2 (R3 +R4)
AR1R4

, (3)
where the approximation is made because the op amp’s open-loop gain A is expected to be very large.
(You are encouraged, but not required, to try and derive this result as an exercise). By using this approximation,
the op amp’s open-loop gain can be estimated:
A ≈

vin
vy
R2 (R3 +R4)
R1R4

(4)
To abbreviate this result, we define a constant
Ga =

R2 (R3 +R4)
R1R4

,
so that the open-loop gain can be quickly computed as
A ≈
vin
vy
Ga.
Suppose that vin = 1V and vy is measured to be 0.01V. Based on Equation 4, calculate the op amp’s
open-loop gain A. Once you have obtained an estimate for A, substitute it into both (2) and (3), and
compare the differences in these results. Based on your comparison, how accurate is the approximation
used to obtain Equation 3?
Exercise 3. Suppose the op amp has a slew rate SR = 0.5V/µs and the rail voltages are ±15V. Calculate the Full
Power Bandwidth (FPBW):
FPBW =
SR
2π |VR|
. (5)
Now suppose the op amp is configured as a voltage follower as shown in Fig. 2, and the input is a
sinusoid with zero offset:
vIN = (2V)sin(2π ft). (6)
What is the maximum operating frequency frmmax for which slewing is avoided?
Utah State University Spring 2015 3
ECE 3410– Microelectronics I Lab 3: Operational Amplifiers: Part II
2 Physical Experiments
In your hardware session, you will attempt to measure the op amp’s input offset voltage, open-loop gain and slew rate.
When you complete each of your measurements, write your result in a table on the white board so that you can
compare your measurements with those obtained by other students. This will give us a picture of how much variation
occurs in these parameters.
Procedure 1. Connect your op amp in the configuration shown in Fig. 1. Use the DMM to precisely measure all
resistor values in your circuit. Using the measured values, evaluate the expressions in Equation 1 and 4.
Procedure 2. Connect the input vIN to ground. Measure VOUT and infer the value of VOFS based on Equation 1.
Procedure 3. Now measure the DC open-loop gain of the op amp. To do this, use the function generator to supply an
input signal at vin with a frequency below 1 Hz. To observe such low frequencies on the oscilloscope,
you will need to adjust the time setting to about SEC/DIV and use the RUN/STOP button to capture
a snapshot of the waveforms. Adjust the amplitude and offset of vin to ensure that vout is not saturated
or distorted, and is large enough to obtain a precise amplitude measurement. Use the oscilloscope to
measure the peak-to-peak amplitudes at vin and vy, then estimate A using Equation 4.
Procedure 4. Wire your op amp in a unity-gain voltage follower configuration. Using the function generator, provide
an input signal vin with a peak-to-peak amplitude of about 4 V and a frequency of 50 kHz. On the
oscilloscope, observe the waveform at vout and estimate the slew rate by using the cursors to obtain ∆vout
and ∆t in the linear segments. AC coupling is recommended for this measurement.
Procedure 5. Reduce the signal frequency to about 40 kHz and observe the waveform at vout. Can you perceive any
distortion in the output waveform? Switch the oscilloscope to the FFT display. Can you see evidence of
distortion in the FFT display? Repeat these observations at 30 kHz.
3 Post-Lab
In your lab book, write a summary of your findings, and write a brief report describing your objectives, methods and
major findings. Submit this report to the TA or Instructor along with your Lab Book.