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Salt Lake Community College
Electrical Engineering Department
EE2210
Thevenin Equivalent and Superposition Lab
Original Adapted from University of Utah’s “Thevenin & Superposition” by A. Stolp
Revisions by S. Farida, L. Brinton, J. Quebbeman, H. Wilson for Salt Lake Community College
Latest revision 9/18/2015 by Harvey Wilson.
Introduction
A Thevenin Equivalent circuit may sometimes be easier to understand
than the original circuit. Also, superposition may enable easier analysis of a
circuit with many independent sources. This lab applies both analysis methods.
Objectives
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Learn about Thevenin equivalent circuits.
Find the Thevenin equivalent of the servo’s “Input” potentiometer.
Learn about Superposition.
Learn to simulate circuits.
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Pre Lab
Calculate the Thevenin equivalent voltage, VTH, and resistance, RTH,
between Points A and B of Figure 1:
Equipment
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Resistors: 1.0kΩ, 2.2kΩ, 3.0kΩ, 4.7kΩ, 6.8kΩ, 10kΩ and 10kΩ variable
resistor (trim pot).
Servo or equivalent setup.
Adjustable power supply with 5V and 12V outputs, DMM and wires.
Experiment
Thevenin Equivalent
1. I vs. V Plot of original circuit & Measure Vth.
Set the power supply to 10V and construct the circuit shown in Figure 2,
including a voltmeter or ammeter as needed. Record the meter readings with
each of the following loads; RLOAD=∞ (open circuit), RLOAD=3.0kΩ,
RLOAD=1.0kΩ, and finally, RLOAD=0 (short circuit). The first voltage
measurement (with RL completely removed) is called the open-circuit voltage
and will be your Thevenin voltage (Vth) (should be ~6V). The last current
measurement (with RLOAD=0) is called the short-circuit current (should be ~4.5
mA). Draw an “I vs. V” plot in your notebook. (Plot your four sets of
measurements, I on vertical axis, V on horizontal.)
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2. Zero the source
Disconnect the power supply and replace it with
a wire (a short). This is the best way to zero the
voltage source. You could turn the output down to
0V, but that method is not as good and not as
easy. Don’t short the supply; place the short in the
circuit where the supply used to be. See Figure 3.
3. Measure Rth
Use an ohmmeter to measure the resistance between the load terminals
[~1.5kΩ] (Place the ohmmeter across the open terminals where RLOAD would
be connected.) This is the Thevenin source resistance (Rth).
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4. Build Thevenin circuit
Build the circuit as shown in Figure 4 with Vth, Rth,
Ammeter, RL and Voltmeter. Adjust the power supply
to the Vth value. Adjust the 10kΩ Trim Potentiometer
(pot) to the Rth value with the aid of an Ohmmeter.
(It’s best to put the pot in the proto board, connect the
Ohmmeter to the center and one of the other
terminals, adjust the pot to the right value, and then
build the rest of the circuit around it without touching it
again). Warning! Don’t apply power to this circuit
until you have the right Rth value on your
potentiometer, it is about to be the only thing stopping a short circuit!
Confirm that this new circuit behaves just
like the one it supposedly replaces, that is,
take another set of readings with each of the
preceding loads. Graph these on your “I vs.
V” plot and comment on circuit equivalence.
5. Compare
Document in your notebook your
observations of the comparison between the
experiment and the pre-lab.
6. Simulate both Circuits
Use a circuit simulator as demonstrated
to verify your calculated and measured
values (if instructor requests this).
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Thevenin Equivalent of Servo Input Control
In the last lab you saw how the “Input” potentiometer
translates desired shaft position into a voltage. Sensors are
often modeled as variable sources with a source resistance,
just like a Thevenin equivalent. In this case that’s not a
perfect model, since the Thevenin resistance (Rth) also
changes a little as you turn the pot. In this lab we will find a
Thevenin equivalent for the “Input” pot.
1. Calculate Vth and Rth of Servo Input Position Control
Assume that the “Input” position pot in Figure 5 is in the
most-positive-voltage position. Calculate the expected
Thevenin equivalent voltage, Vth, and resistance, Rth,
between the pot wiper (output) and ground.
2. Measure Vth and VL of Servo Input Position Control
Assemble the circuit of Figure 5. Connect the red lead of the voltmeter to the
center lead of the “Input” pot. Connect the negative lead of the volt meter to
power and servo ground. Rotate the pot control as needed to the most-positivevoltage position. Measure and record this voltage as Vth.
Attach a 10kΩ resistor, RL, between the servo pot center lead (where the
DMM red lead connects) and ground (where the DMM black lead connects). The
measured voltage will decrease to about +1.2 Volts. Record this as the loaded
voltage, VL. Calculate the expected Thevenin equivalent voltage, Vth, and
resistance, Rth, between the pot wiper (output) and ground.
3. Calculate Rth of Assembled and Powered Servo Input Position Control
Draw the Thevenin circuit (something like Figure 6)
including the load and show the values that you know
(Vth, VL, and RL).
Calculate the value of Thevenin resistance, Rth, by
solving this formula:
VL = Vth * RL / (RL + Rth)
4. Measure Rth of Not-Powered Servo Input Position Control
Turn servo power to off. Short the servo power connections to fully
deactivate ServoVth. Remove the resistor ServoRload. Set the DMM to the
20kΩ range. Measure and record this ServoRth resistance as Rth. Last, remove
the power supply shorts.
Was your Rth powered value close to your non-powered value? It should be.
Adding a load and observing the change in the voltage is the most common
way to find the output resistance, and is the method you should try to remember.
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Superposition
1. Measure Vo(both)
The B&K power supply includes a fixed 12V output and a fixed 5V output DC
power source. Use these sources and resistors to make the circuit shown in
Figure 7. With both power supplies connected and turned on, the voltmeter
(shown as XMM1) should read about -1.4V. Record this voltmeter reading as Vo.
(J1, Key = A, J2, Key = B are not assembled, but are part of the simulation.)
2. Measure Vo(1)
“Zero” power supply V2. (Pull out the wire leading up to the +5V terminal
and replace it with a jumper wire connected to ground. This effectively
disconnects the second power supply and replaces it with a short.) Record
the new voltmeter reading as Vo(1) [≈-3.7V], the voltage due to source V1.
3. Measure Vo(2)
Reconnect power supplyV2. Now “Zero” power supply V1. Record the
new voltmeter reading as Vo(2) [≈+2.3V], the voltage due to source V2.
4. Compare Vo(both) with Vo(1) added to Vo(2)
“Compare Vo(1) + Vo(2) to the Vo that you originally measured with both
power supplies connected. This is superposition. The effects of several
sources can be considered separately and added later. Isn’t linearity nice?
Conclusion
As always, get your lab instructor to check you off. Write a conclusion in
your notebook that touches on each of the subjects in your objectives. Say
something about the usefulness of Thevenin and Superposition. Discuss the
agreement of measurements and calculations. Mention any problems that you
encountered in this lab and how you overcame them.
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