EE 442 Laboratory Experiment 3
Introduction to Thevenin’s Theorem and Maximum Power Transfer
EE 442
Lab Experiment No. 3
1/22/2007
Introduction to Thevenin’s Theorem and
Maximum Power Transfer
1
EE 442 Laboratory Experiment 3
Introduction to Thevenin’s Theorem and Maximum Power Transfer
I.
INTRODUCTION
The purpose of this experiment is to study the principle of Thevenin’s
Theorem. Thevenin’s Theorem will be explored by numerically analyzing a
particular circuit in the preliminary part of this experiment. This same
circuit will then be experimentally examined in the laboratory.
Corresponding calculated and measured circuit response values will be
compared. A secondary purpose of this experiment is to use the Thevenin
equivalent circuit to study the principle of maximum power transfer.
We will demonstrate the validity of Thevenin’s Theorem in the laboratory
by applying it to the circuit shown in Figure 1.
A
33k
4.7k
+
+
V1
20 Vdc
15k
vL
10k
iL
RL
10k
-
-
B
Figure 1 Circuit used to study Thevenin’s Theorem
II.
PRELAB EXERCISES
1.
Use either the node voltage or the mesh current methods to find the
value of the load current, iL, through the 10 kΩ resistor, RL, as
shown in Figure 1. Also find the value of the load voltage, vL.
Record your results below.
iL = __________
vL = __________
2.
Find the Thevenin equivalent circuit of the network to the left of
terminals A-B in Figure 1. Record the open circuit voltage and the
Thevenin resistance below.
vOC = __________
Rt = __________
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EE 442 Laboratory Experiment 3
Introduction to Thevenin’s Theorem and Maximum Power Transfer
III.
LABORATORY EXPERIMENTS
A
33k
DC Power Supply
4.7k
+
+
V1
20 Vdc
15k
vL
10k
iL
RL
10k
-
-
B
Figure 2 Laboratory version of the circuit in Figure 1
1.
With the DC supply turned off, construct the circuit shown in
Figure 2 to the left of terminals A-B.
2.
Energize the DC supply and set it at 30 Volts.
3.
Measure the open circuit voltage between terminals A-B and
record below. Compare this value with the open circuit voltage
determined analytically in step 2 of the preliminary exercise.
vOC = __________
4.
The short circuit current between terminals A-B can be measured
by connecting an ammeter across terminals A-B. It is assumed that
the internal resistance of the ammeter is low enough that it appears
as a short circuit to the circuit between terminals A-B. Record the
measured value of the short circuit current below.
iSC = __________
5.
On the basis of the data recorded in steps 3 and 4, the Thevenin
equivalent circuit can be derived. Calculate the Thevenin
equivalent resistance, Rt, and record below. Compare this
experimentally derived equivalent circuit with the one obtained by
circuit analysis in step 2 of the preliminary part of this experiment.
Rt = __________
6.
Before performing step 7, do the following. Turn off the 30 VDC
supply. Disconnect the two leads connected to the DC supply
terminals. Connect these two leads together, creating a short
circuit. This procedure replaces the 30 V source with its ideal
internal resistance of zero ohms. The 30 V source is now
“suppressed.” An open circuit should exist between terminals A-B.
Use an ohmmeter to measure the Thevenin equivalent resistance,
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EE 442 Laboratory Experiment 3
Introduction to Thevenin’s Theorem and Maximum Power Transfer
Rt, at terminals A-B. Compare this value with the results of step 5.
Remember, an ohmmeter should never be used to
measure resistance of an energized circuit.
7.
The next step is to measure the load current, iL, and the load
voltage, vL, of the circuit in Figure 2. To perform the first of these
tasks, connect the 10 kΩ load resistor in series with an ammeter
and measure iL. Measure the voltage drop across RL. Record the
values of iL and vL below and compare them with step 1 of the
preliminary exercise.
iL = __________
vL = __________
8.
Turn off the DC voltage source and dismantle the circuit. Now
construct the circuit shown in Figure 3. Adjust the DC supply to the
value of vOC found in step 2 of the preliminary exercise. Use the
resistor value found in step 2 of the preliminary exercise for the
value of Rt.
Rt
A
DC Power Supply
+
+
V1
vL
VOC
iL
RL
10k
-
-
B
Figure 3 Thevenin Equivalent of the circuit in Figure 2
9.
Using the DMM, measure the open circuit voltage of this circuit at
terminals A-B. Record this value below and compare with the
results of step 3 of the experimental exercise. This measurement
verifies the equivalence of the two circuits (Figures 2 and 3) under
open circuit loading conditions. Note that RL is infinitely large and
iL is zero in this case.
vOC = __________
10.
Using an ammeter, measure the short circuit current of this circuit
between terminals A-B. Record below and compare with the results
of step 4 of this experiment. This measurement verifies the
equivalence of the two circuits (Figures 2 and 3) under short circuit
loading conditions. Note that vL = 0 in this case.
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EE 442 Laboratory Experiment 3
Introduction to Thevenin’s Theorem and Maximum Power Transfer
iSC = __________
11.
Next connect the 10 kΩ load resistor between the terminals of the
circuit in Figure 3. Measure iL and record below. Also measure vL
with the DMM and record below. Compare these values with the
results of step 6 of this experiment. These measurements verify the
equivalence of the two circuits under “in-between” loading
conditions.
iL = __________
vL = __________
12.
This concludes the study of Thevenin’s Theorem. The next part of
this experiment will use the Thevenin equivalent circuit to
experimentally study the concept of maximum power transfer.
Rt
Ammeter
DC Power Supply
+
+
V1
vL
VOC
iL
RL
Voltmeter
-
-
Figure 4 Circuit to study maximum power transfer
13.
The circuit of Figure 4 is the same as that in Figure 3, except that in
Figure 4, RL is a variable resistance. The Thevenin equivalent
portion of this circuit can be interpreted as representing the
terminal equivalent of a more complicated circuit such as a DC
power supply or a generator.
Consider a hypothetical problem which requires solving for the
current iL through a given value of RL. The direct solution of the
original circuit could involve a lot of work to obtain iL. An
alternative solution would be to find the Thevenin equivalent of the
original circuit, then solve for iL using the resultant simple series
circuit. This technique would also certainly take a lot of work,
perhaps more work than just solving the circuit outright. However,
if the value of iL for a range of RL values is desired, a lot of work will
be required to find the Thevenin equivalent, but finding iL for
subsequent values of RL would require solving only the simple
Thevenin equivalent circuits.
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EE 442 Laboratory Experiment 3
Introduction to Thevenin’s Theorem and Maximum Power Transfer
14.
For the last part of this experiment, we want to examine the power
delivered from the supply to the load and determine what load
resistor value will dissipate the most power. What value of Rt
should result in maximum power dissipation in RL?
RL = __________
15.
Calculate the maximum power dissipated in RL.
PL = __________
16.
RL (kΩ)
Assemble the circuit of Figure 4. The values of vOC and Rt are the
same as those used for the circuit of Figure 3. Use the decade
resistance box for RL since RL will take on a range of values. For
each value of RL given in the table below, measure iL and vL and
record in the spaces provided. Calculate the corresponding value of
power, PL, dissipated in RL, and record. Make a note of which value
of RL gives rise to maximum power dissipation. Plot PL vs. RL on
the attached grid (Page 7).
iL (mA)
(measured)
vL (Volts)
(measured)
0
1
2
3
4
5
6
7
8
9
10
11
12
6
PL (mW)
(calculated)
EE 442 Laboratory Experiment 3
Introduction to Thevenin’s Theorem and Maximum Power Transfer
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