Download 1. Pre-Lab Introduction

EECE 322
Lab 7: Analog Computer Applications using the Operational
Amplifier
Page 1 of 5
Laboratory Goals
This project will focus on the use of the operational amplifier in performing the
mathematical operations of integration and differentiation. The design of a simple circuit
(analog computer) to solve a differential equation will also be included.
Reading
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Student Reference Manual for Electronic Instrumentation Laboratories by Stanley Wolf
and Richard Smith, Copyright 1990.
Oscilloscope User’s Guide (Copies of this reference book are available in the lab, or at
the website)
Tektronics 571 Curve Tracer Manual
BS170 Transistor Data Sheet
Read the pre-lab introduction below
Equipment needed
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Lab notebook, pencil
Oscilloscope (Agilent or Tektronics)
2 oscilloscope probes (already attached to the oscilloscope)
BNC/EZ Hook test leads
Tektronics 571 Curve Tracer
PB-503 Proto-Board
Workstation PC, with PSICE application
Parts needed
741 op-amp
Lab safety concerns
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Make sure before you apply an input signal to a circuit, all connections are
correct, and no shorted wires exist.
Do not short the function generator signal and ground connections together
Do not touch the circuit wiring while power is applied to it
Ensure you connect the correct terminal of the transistor to prevent blowing the
transistor
EECE 322
Lab 7: Analog Computer Applications using the Operational
Amplifier
Page 2 of 5
1. Pre-Lab Introduction
Figures 7-1 and 7-2 illustrate two op-amp based circuits designed to perform
differentiation and integration respectively. The operations are performed "real-time" and
can be helpful in observing both initial transients and steady state response. The analysis
of the circuits is based on the "ideal" op-amp assumptions and performed in the time
domain. The resistor RI shown in the two circuits is included to help with stability and
for general circuit protection. The value for RI is nominally set equal to the feedback
resistor (Figure 7-1) or the input resistor (Figure 7-2). The purpose of the optional resistor
is left for student investigation in conjunction with the summary questions.
The differentiator and integrator circuits may be combined with "standard" inverting and
non-inverting op-amp circuits to provide the building blocks for analog computers. The
resultant analog computer circuits are designed to solve differential and/or
integral/differential equations in a real time environment. The ability to easily include,
and change, initial conditions and forcing functions are additional benefits of the analog
computers. Figure 3-3 illustrates a circuit designed to solve the second order differential
equation KY - Y = 0 with the initial condition Y(0) = - VX and K = R1R2C1C2. The
initial condition is "set" by using the momentary contact switch to force the output to
equal the applied voltage at t = 0 (the time the switch is closed).
While the major advances in digital computers and digital signal processing have reduced
the use of these three circuits, they are still a fast and relatively inexpensive method for
process control and stability/operation analysis for systems that can be represented in
terms of differential equations.
2. Design
1. Derive the expressions relating the input and output signals for the circuits shown in
Figures 7-1 and 7-2.
2. Design an analog computer to solve
with y(0) = 2. Solve the
differential equation when f(t) = 0 and verify your results using PSpice®.
EECE 322
Lab 7: Analog Computer Applications using the Operational
Amplifier
Page 3 of 5
Figure 7 - 1: Differentiator
Figure 7 - 2: Integrator
EECE 322
Lab 7: Analog Computer Applications using the Operational
Amplifier
Page 4 of 5
Figure 7 - 3: Analog Computer (linear, second order, homogenous differential equation)
3. Lab Procedure
1. Construct the circuit shown in Figure 7-1. Use ± 15 V supplies for the op-amp and a
load resistance of 2.4 k-Ohms.
2. Verify the operation of the circuit using a 500 mV peak, 50 Hz sinewave as the input
signal. Be sure to design the "gain" such that the output does not saturate.
3. Repeat step 2 with a sinewave frequency of 500 Hz. Does the circuit still operate
correctly? What changes need to be made to prevent output saturation?
4. Repeat steps 2 and 3 using a triangle wave and then using a square wave with the same
magnitudes and frequencies as used in steps 2 and 3.
5. Construct the circuit shown in Figure 7-2. Again, use ± 15 V supplies for the op-amp
and a load resistance of 2.4 k-Ohms.
6. Repeat steps 2 through 4 for this circuit. Be sure to adjust your "gain" as necessary to
maintain an output signal within the saturation limits of ± 12 V.
7. Construct the circuit designed to solve the differential equation in part 2 of the design
section. Verify the operation of the design using three different input waves (sine,
triangle, and square). Determine the operation for at least three different
frequencies -- 10 Hz, 1 kHz, and 100 kHz. Explain any differences in operation of the
circuit. What affect does the initial condition have on the result?
EECE 322
Lab 7: Analog Computer Applications using the Operational
Amplifier
Page 5 of 5
4. Analysis
1. How could you use the differentiator to obtain an estimate of the slew rate for the opamp?
2. Why should you include a resistor in parallel with the capacitor in the integrator?
3. What is the purpose of the resistor in series with the input capacitor in the
differentiator?
4. Is it possible to design a circuit to perform the differentiation and integration functions
using the non-inverting input? Explain your answer.