MAE 2055: Mechetronics I
Mechanical and Aerospace Engineering
Lab Exercise #4
Name
Partner 1
Partner 2
Partner 3
Objectives – Analytically determine the Thévenin equivalent for an electrical circuit, then
experimentally verify your analysis in the lab. Devise and implement a practical method for
determining the Thévenin resistance of real-world circuits.
Pre-lab – complete prior to coming to lab
R1
R3
R5
1KΩ
3KΩ
330Ω
R4
10 V
R2
3KΩ
RL
3KΩ
V2
+
+
V1
+
5V
-
Rth
Figure 1. Circuit you will be analyzing, then building in the lab.
Thévenin equivalent circuits
As we have seen in class, any complex network of resistors and sources can be represented by a
Thévenin equivalent circuit. That is, it can be represented by the circuit shown in Figure 2, which
comprises an open-circuit voltage source, Voc, and a Thévenin resistance, Rth. Once we know the
Thévenin equivalent for a complex network, such as the circuit of Figure 1, we can easily determine how
the circuit will behave when a given load is connected across the terminals of that circuit. The load
resistor in Figure 1, , represents such a load. (The load is connected across the terminals of the circuit,
but is not part of the circuit itself.)
Rth
+
Voc
Figure 2. A Thévenin equivalent circuit.
The open-circuit voltage is the voltage seen at the output terminals of the circuit when no load is
attached (open-circuit condition at the terminals). The Thévenin resistance is the resistance seen looking
MAE2055 Mechetronics I
Lab Exercise #4
into the terminals with all sources set to zero (i.e. voltage sources short-circuited, and current sources
open-circuited).
You will now determine the Thévenin equivalent circuit for the circuit shown in Figure 1 (everything to
the left of the terminals, not including the load resistor, RL).
1) What is the open-circuit voltage,
, for the circuit of Figure 1? Show your calculations below.
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Lab Exercise #4
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2) What is the Thévenin resistance,
below.
Lab Exercise #4
, for the circuit of Figure 1? Again, show all of your calculations
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Lab Exercise #4
3) Using your answers to questions 1 and 2, draw the Thévenin equivalent of the circuit from Figure 1.
4) Calculate the power dissipated in a 100Ω load resistor connected to the Figure 1 circuit.
When you come to the lab, you will be verifying your answers to questions 1-4.
------------------------------------------ End of the pre-lab ------------------------------------------
Have your instructor initial here to verify completion of the pre-lab.
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Lab Exercise #4
---------------------------------- To be completed in the lab ----------------------------------
5) Build the circuit shown in Figure 1 on your breadboard.
6) Measure the open-circuit voltage of your circuit. Verify that your measurement agrees reasonably
well with the open-circuit voltage you calculated in question 1.
7) Measure the Thévenin equivalent resistance of the circuit. You can do this by setting each of the
voltage sources in your circuit to zero (set them to zero or replace them with shorts) and measuring
the resistance between the terminals of the circuit. Verify that your measurement agrees
reasonably well with the Thévenin resistance you calculated in question 2.
8) Next, connect a 100Ω resistive load across the circuit terminals and measure the power dissipated in
that load. Verify that your measurement agrees reasonably well with the power dissipation you
calculated in question 4.
You have just experimentally verified the analysis you performed in the pre-lab. However, the method
you used to experimentally determine the Thévenin equivalent circuit is not very useful when dealing
with real circuits in practice. The reason for this is that when you measured the Thévenin resistance of
your circuit, you were required to set each of the voltage sources in the circuit to zero. In general, when
dealing with real circuits, you will neither have access to nor control over the sources in the circuit – you
will only have access to the terminals across which you can connect a load. For example, imagine the
circuit for which you want to generate a Thévenin equivalent is an audio amplifier. You may only have
access to the terminals where the speaker cables connect to the amplifier. You wouldn’t be able to set
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MAE2055 Mechetronics I
Lab Exercise #4
the sources inside the amplifier to zero in order to measure the Thévenin resistance, so you would
therefore need a different method for determining
. You will now come up with such a method.
9) Devise a method that will allow you to determine the Thévenin resistance of any practical circuit for
which you don’t have the ability to set the sources to zero. Clearly explain your method below
including appropriate equations and circuit diagrams. Describe any precautions that may be
necessary in order to prevent damage to the circuit or possibly to prevent physical harm to the
person taking the measurement.
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Lab Exercise #4
10) Using the method you just devised, measure the Thévenin resistance of your circuit. Your answer
should agree reasonably well with your measurement from part 7, as well as your calculation from
part 2 of the pre-lab.
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