This file contains a report for the 4th experiment in the Lab "Instrumentation and Dynamic Systems", take by mechanical engineering students.

1. Jordan University of Science and Technology
Faculty of Engineering
Department of Mechanical Engineering
Instrumentation and Dynamic Systems Lab
Experiment #4
Op-amp: Integrator, Differentiator, and Follower

2. Introduction:
By introducing electrical reactance into the feedback loops of op-amp amplifier circuits,
we can cause the output to respond to changes in the input voltage over time. Drawing
their names from their respective calculus functions, the integrator produces a voltage
output proportional to the product of the input voltage and time; and the differentiator
produces a voltage output proportional to the input voltage’s rate of change.
Capacitors oppose voltage change by creating current in the circuit: that is, they either
charge or discharge in response to a change in applied voltage. So, the more capacitance
a capacitor has, the greater its charge or discharge current will be for any given rate of
voltage change across it.
Follower op-amp is a unity gain system, with no phase reversal, i.e. (Vi = Vo), and the
input resistance is very large, theoretically infinity, and the feedback resistance is very
small, theoretically zero.
Differentiator:
We can build an op-amp circuit which measures change in voltage by measuring current
through a capacitor, and outputs a voltage proportional to that current:
Figure 1: Differentiator Circuit
A steady input voltage won’t cause a current through C, but a changing input voltage
will. The formula for determining voltage output for the differentiator is as follows:
Applications for this, besides representing the derivative calculus function inside of an
analog computer, include rate-of-change indicators for process instrumentation. One
such rate-of-change signal application might be for monitoring (or controlling) the rate

3. of temperature change in a furnace, where too high or too low of a temperature rise
rate could be detrimental. The DC voltage produced by the differentiator circuit could
be used to drive a comparator, which would signal an alarm or activate a control if the
rate of change exceeded a pre-set level.
Integrator:
Integrator op-amp circuit would generate an output voltage proportional to the
magnitude and duration that an input voltage signal has deviated from 0 volts. The
output voltage rate-of-change will be proportional to the value of the input voltage.
Figure 2: Integrator Circuit
Equipments and Apparatus:
1- AC Function Generator.
2- Operational Amplifier.
3- Oscilloscope.
The description of these three devices was give in previous experiments and could be
reviewed if necessary.
Procedure:
Part 1: Integrator circuit amplifier:
1- Assemble the integrator circuit shown in Figure 3:

4. Figure 3: Integrator Circuit set up
2- Use the values of: C = 10 nF , Ri = 10kΩ , Rf = 100 kΩ.
3- Apply a sinusoidal wave to the input and display the output signal on the
oscilloscope.
4- Sketch the input and output signals, and note the phase shift.
5- Repeat steps for triangle and square input signals.
Part 2: Differentiator Circuit Amplifier:
1- Assemble the circuit as shown in Figure 4:
Figure 4: Differentiator Circuit Set up
2- Use the values of: C = 10 nF, Ri = 1kΩ.
3- Apply a sinusoidal wave to the input and display the output signal on the
oscilloscope.
4- Sketch the input and output signals, and note the phase shift.
Part 3: Voltage follower circuit:
1- Connect the circuit in Figure 6.
2- Apply a sinusoidal input and note the output.
Figure 6: Follower Circuit Set up
Part 4: Adder Amplifier:

5. 1- Assemble the circuit in Figure 7.
2- Apply a sinusoidal wave to the input and display the output signal on the
oscilloscope.
3- Sketch the input and output signals, and note the phase shift.
Repeat steps for triangle and square input signals.
Figure 7: Adder Circuit Set up
Theoretical Analysis:
1- Differentiator circuit:
The formula for determining voltage output for the differentiator is as follows:
2- Integrator circuit:
3- Follower circuit:
Vin = Vout

6. Results:
1) Integrator Circuit:
Figure 8: Integrator Amplifier, Square Wave
Figure 9: Integrator Amplifier, Ramp Signal
Figure 10: Integrator Amplifier, Sinusoidal Wave

7. 2) Differentiator Circuit:
Figure 11: Differentiator Amplifier, Ramp Signal
Figure 12: Differentiator Amplifier, Sinusoidal Wave

8. 3) Follower Amplifier:
Figure 13: Follower Amplifier, Square Wave
Figure 14: Follower Amplifier, Ramp Signal
Figure 15: Follower Amplifier, Sinusoidal Wave

9. Discussion:
The three different amplifier circuits configurations were built and the response for
each configuration was recorded. Two characteristics are of a major concern in
response curves: 1) Amplifier gain value, and 2) Change in wave type.
Figures 8-10 show the response for the integrator amplifier circuit, its characterized
by high gain value. Phase shift is noted for the sinusoidal input wave (Figure 10)
The Differentiator circuit response is recorded in Figures 11, and 12 for the ramp
and the sinusoidal input waves. the differentiator gives a poor gain value.
In the Follower Amplifier, the input signals don’t exhibit any change either in
magnitude or signal type. The gain value is equal to unity. Figures 13 and 14 show
the response for this configuration.
Conclusions:
 Operational Amplifiers are widely used and it can be used for several
purposes depending on the object under concern.
 The gain value for the three configuration investigated in the experiment s as
follows (ascending): Differentiator, Follower, and Integrator which gives the
highest gain value.
 The sinusoidal wave experiences a phase shift n both the integrator and
differentiator circuits.
 Capacitors do have a major rule in determining the characteristics of circuits.
References:
1- http://www.allaboutcircuits.com/textbook/semiconductors/chpt-
8/differentiator-integrator-circuits/
2- Instrumentation and Dynamic Systems Lab Manual.