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Lab-in-a-Box
Experiment 9: Superposition and Thévenin Equivalent
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Procedure
Analysis:
1. Using either mesh current or node voltage analysis, determine vL, iL and PL, for the circuit shown in
Figure 1in each of the following cases:
a) As shown in Figure 1. (You may use the results from Experiment 8 if that experiment
was performed.)
b) With the 9V power supply removed (replaced with a short).
c) With the 5V power supply removed (replaced with a short).
2. Verify that the node voltages and mesh current given in step 1(a) are given by the sums of the
voltages and currents found in steps 1(b) and 1(c).
3. Calculate the Thévenin voltage VTH and Thévenin resistance RTH as viewed across the load resistor
R5 looking into the circuit at XY. Draw the Thévenin equivalent circuit.
X
R1
R2
470
1k
V1
5Vdc
iL
com
R5
V2
0
vL
680
R3
9Vdc
1.2k
R4
270
Y
Figure 1: Circuit for verifying the superposition theorem and Thévenin’s theorem.
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Modeling:
4. Using PSpice, model the circuit shown in Figure 1. Display all of the node voltages and mesh
currents on your circuit diagram. Verify that they agree with the results of step Error! Reference
source not found.(a). Insert a printout of your results in your lab notebook.
5. Repeat step 3 with the 9 V source removed. Verify that the results agree with step 1(b).
6. Repeat step 3 with the 5 V source removed. Verify that the results agree with step 1(c).
7. Following the methodology of Svoboda (p47) or Tront (p29), or other PSpice references, determine
the Thévenan equivalent for the circuit. Verify that the result agrees with step 2. Insert a printout of
your results in your lab notebook.
Measurements (Superposition):
8. Build the circuit shown in Figure 1 with all voltage sources active. Note that both the 5 V and the 9 V
sources are provided by the ANDY board.
9. Using the DMM, measure vL and iL for the circuit as shown in Figure 1 with both sources active.
Calculate the percent deviation from the results computed in step Error! Reference source not
found.(a).
10. Repeat step 9 with the 9 V source removed (replaced with a short). Be sure you disconnect the source
before you make a short circuit connection between R4 and GND. Calculate the percent deviation
from the results computed in step 1(b).
11. Repeat step 9 with the 5 V source removed (replaced with a short). Be sure to replace the 9 V source
before performing this step and be sure you disconnect the source before you make a short circuit
connection between R1 and GND. Calculate the percent deviation from the results computed in step
1(c).
12. Calculate vL1 = vL2 + vL3, where vL2 is the voltage over the load measured in step 9 and vL3 is the
voltage over the load measured in step 10.
13. Calculate the percent deviation of vL1 from vL determined in step 1(a). Verify that your results confirm
the superposition theorem.
14. Calculate iL1 = iL2 + iL3, where iL2 is the current through the load measured in step 9 and iL3 is the
current through the load measured in step 10. Calculate the percent deviation of iL1 from iL
determined in step 1(a). Verify that your results confirm the superposition theorem.
15. Calculate PL1 = PL2 + PL3, where PL2 is the power dissipated by the load in step 9 and PL3 is the power
dissipated by the load in step 10. Calculate the percent deviation of PL1 from PL determined in step
1(a). Verify that your results confirm the superposition theorem.
16. Reconnect both sources in the circuit as per Figure 1.
Measurements (Thévenin Equivalent):
17. Remove the 680 Ω load resistor (R5) from the circuit and measure the open circuit voltage, vOC,
between nodes X and Y. This is the Thévenin equivalent voltage.
18. Disconnect both power supplies from the circuit and replace them with short circuits. Note: if you
measure a powered circuit with your DMM set for resistance, you may damage your meter!
19. With the 680 Ω load resistor removed, measure the resistance ROC between nodes X and Y. This is the
Thévenin equivalent resistance.
20. Reconnect both power supplies as per Figure 1.
21. With the 680 Ω load resistor removed, measure the current iOC between nodes X and Y. Divide the
voltage determined in step 16 by this current. This is also the Thévenin equivalent resistance.
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22. Calculate the percent differences between vOC and ROC determined in steps 16, 18, and 20 with the
analytical results for VTH and RTH calculated in step 2. Verify that your experimental and analytical
estimates of the Thévenin voltages and resistances agree.
23. Draw the Thévenin equivalent circuit for the circuit shown in Figure 1.
Last Revision:
Rev 3.1: 10/28/2006
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