The George Washington University
School of Engineering and Applied Science
Department of Electrical and Computer Engineering
ECE 2110 - LAB
Experiment # 6
DC Circuits: Thévenin's Circuits, Mesh Current, Node Voltage Analysis
Equipment:
Lab Equipment
Equipment Description
(1 Set) Digital Multimeter (DMM)
Keithley Model 175 Digital Multimeter (DMM)
(3 Pairs) Test Leads
Banana to mini-grabber test leads
(1 Set) Bread Board
Prototype Bread Board
(1) DC Power Supply
Agilent E3631A Triple Output DC Power Supply
Table A – Equipment List
Components:
Kit Part #
Spice Part
Name
Resistors
R
Part Description
750Ω, 1 kΩ, 1.5 kΩ, 3 kΩ, 4 kΩ, 10 kΩ, 12 kΩ,
Table B – Components List
Objectives:




To understand Thévenin‟s theorem of equivalent circuits.
To analyze and reduce three DC circuits to their Thévenin equivalent circuits by hand
To analyze and reduce three DC circuits to their Thévenin equivalent circuits with SPICE
To analyze and reduce three DC circuits to their Thévenin equivalent circuits in lab
Introduction:
In this lab you will find the Thevenin and Norton equivalents for 3 circuits. You will first perform
the analysis by hand using techniques you‟ve learned in lecture and in your homework. Then you
will build the circuits using the SPICE circuit simulator and use it to find the Thevenin and Norton
equivalents. Finally you will build the 3 circuits in lab and measure them to find the Thevenin and
Norton equivalents. In your laboratory write-up you will compare and analyze the results from
each technique.
GWU SEAS ECE Department ©2012
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ECE 2110 – Experiment: DC Circuits: Thévenin's Circuits, Mesh Current, Node Voltage Analysis
I Prelab:
This prelab consists of three circuits to be reduced by using Thévenin's Theorem. You are
required to complete both hand calculations and PSpice simulations for problems 1, 2, and 3
before coming to lab. Problem #1 serves as an example for how to complete problems 2 and 3.
This lab requires more analysis than previous labs; please allocate the proper amount of
time to complete it early on.
Problem #1
Figure 1A – Circuit #1
In figure 1A, the voltage source, V1 = 6 V, and the current source, I1 = 10 mA.
Resistors: R1 = 4 kΩ, R2 = 12 kΩ, R3 = 10 kΩ.
1. From the perspective of terminals A and B, calculate the following for figure 1A:
a. Thévenin voltage (Vth).
b. The Norton current, also called the short circuit current (Isc).
c. Thévenin resistance (Rth).
2. Use the values you found in step 1 to complete figure 1B below:
Figure 1B - Thévenin & Norton Equivalents of Circuit #1
GWU SEAS ECE Department ©2012
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ECE 2110 – Experiment: DC Circuits: Thévenin's Circuits, Mesh Current, Node Voltage Analysis
3. For the circuit in figure 1A, a 1 kΩ load resistor, RL, has been attached across terminals
A & B. The resulting circuit is shown in figure 1C.
a. Calculate the voltage across & current through RL for the circuit in figure 1C.
Figure 1C - Circuit #1 with Load Resistor Attached
4. For the circuits in figure 1B, a 1 kΩ load resistor, RL, has been attached across terminals
A & B. The resulting circuits are shown in figure 1D.
a. Calculate the voltage across & current through RL for the circuits in figure 1D.
Figure 1D – Equivalent Circuits #1 with Load Resistor Attached
5. SPICE Simulation:
a. Use the tutorial on the lab website (PSPICE Tutorial #2: Using PSPICE to find
VTH, IN, RTH) to learn how to find VTH, ISC, and RTH for a circuit in SPICE.
b. Build the circuit in figure 1A in SPICE, and then find its VTH, ISC, and RTH.
c.
Build the equivalent circuits in figure 1B in SPICE.
d. In SPICE, attach a 1 kΩ load resistor (RL) to the circuit in figure 1A, as you did in
step 3a. Measure & record the simulated voltage across and current through RL.
e. In SPICE, attach a 1 kΩ load resistor (RL) to the circuit in figure 1B, as you did in
step 3b. Measure & record the simulated voltage across and current through RL.
GWU SEAS ECE Department ©2012
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ECE 2110 – Experiment: DC Circuits: Thévenin's Circuits, Mesh Current, Node Voltage Analysis
Problem #2
Figure 2A – Circuit #2
With respect to terminals A and B of the circuit in Figure 2A, where R1 = R2 = R4 = R5 = 750Ω,
R3 = 1.5 kΩ, R6 = 3.0 kΩ and the voltage sources V1 = 3Vdc, V2 = 6Vdc, V3 = -6Vdc:
1. From the perspective of terminals A and B, hand calculate the following for figure 2A:
a. Thévenin voltage (Vth).
b. The Norton current, also called the short circuit current (Isc).
c. Thévenin resistance (Rth).
2. As you did in problem #1, use the values you found in step 1 to draw the Thevenin and
Norton equivalent circuits. Label this figure 2B.
3. For the circuit in figure 2A, attach a 1 kΩ load resistor, RL, across terminals A & B.
a. Calculate the voltage across & current through RL
b. Calculate the voltage across & current through RL
4. For the circuits in figure 2B, attach a 1 kΩ load resistor, RL, across terminals A & B.
a. Calculate the voltage across & current through RL
b. Calculate the voltage across & current through RL
5. SPICE Simulation:
a. Use the tutorial on the lab website (PSPICE Tutorial #2: Using PSPICE to find
VTH, IN, RTH) to learn how to find VTH, ISC, and RTH for a circuit in SPICE.
b. Build the circuit in figure 2A in SPICE, and then find its VTH, ISC, and RTH.
c.
Build the equivalent circuits in figure 2B in SPICE.
d. In SPICE, attach a 1 kΩ load resistor (RL) to the circuit in figure 1A, as you did in
step 3a. Measure & record the simulated voltage across and current through RL.
e. In SPICE, attach a 1 kΩ load resistor (RL) to the circuit in figure 1B, as you did in
step 3b. Measure & record the simulated voltage across and current through RL.
GWU SEAS ECE Department ©2012
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ECE 2110 – Experiment: DC Circuits: Thévenin's Circuits, Mesh Current, Node Voltage Analysis
Problem #3
Figure 3A – Circuit #3
With respect to terminals A and B of the circuit in Figure 3A, where R1 = R2 = R4 = R5 = 750Ω,
R3 = 1.5 kΩ, R6 = 3.0 kΩ and the voltage sources V1 = 3Vdc, V2 = 6Vdc, V3 = 9Vdc:
1. From the perspective of terminals A and B, hand calculate the following for figure 3A:
a. Thévenin voltage (Vth).
b. The Norton current, also called the short circuit current (Isc).
c. Thévenin resistance (Rth).
2. As you did in problem #1, use the values you found in step 1 to draw the Thevenin and
Norton equivalent circuits. Label this figure 3B.
3. For the circuit in figure 3A, attach a 1 kΩ load resistor, RL, across terminals A & B.
a. Calculate the voltage across & current through RL
b. Calculate the voltage across & current through RL
4. For the circuits in figure 3B, attach a 1 kΩ load resistor, RL, across terminals A & B.
a. Calculate the voltage across & current through RL
b. Calculate the voltage across & current through RL
5. SPICE Simulation:
a. Use the tutorial on the lab website (PSPICE Tutorial #2: Using PSPICE to find
VTH, IN, RTH) to learn how to find VTH, ISC, and RTH for a circuit in SPICE.
b. Build the circuit in figure 3A in SPICE, and then find its VTH, ISC, and RTH.
c.
Build the equivalent circuits in figure 3B in SPICE.
d. In SPICE, attach a 1 kΩ load resistor (RL) to the circuit in figure 1A, as you did in
step 3a. Measure & record the simulated voltage across and current through RL.
e. In SPICE, attach a 1 kΩ load resistor (RL) to the circuit in figure 1B, as you did in
step 3b. Measure & record the simulated voltage across and current through RL.
GWU SEAS ECE Department ©2012
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ECE 2110 – Experiment: DC Circuits: Thévenin's Circuits, Mesh Current, Node Voltage Analysis
What to turn in with your prelab:
1. From Problem 1:

Your completed figure 1B

The hand calculations you used to complete figure 1B

Your completed calculations for steps 3a and 3b

Your completed calculations for steps 4a and 4b

Screenshots of your work from step 5 demonstrating:
i. Figure 1A built in SPICE showing the voltages and currents necessary to
find its VTH, ISC, and RTH
ii. Thévenin and Norton equivalent circuits (Figure 1B) built in SPICE
iii. Figure 1A and its Thévenin and Norton equivalent circuits with load
resistors across their respective sets of A and B terminals
iv. Simulated voltages and currents through R L for the figures in the
previous requirement (iii)
2. From Problem 2:

Your completed figure 2B

The hand calculations you used to complete figure 2B

Your completed calculations for steps 3a and 3b

Your completed calculations for steps 4a and 4b

Screenshots of your work from step 5 demonstrating:
i. Figure 2A built in SPICE showing the voltages and currents necessary to
find its VTH, ISC, and RTH
ii. Thévenin and Norton equivalent circuits (Figure 2B) built in SPICE
iii. Figure 2A and its Thévenin and Norton equivalent circuits with load
resistors across their respective sets of A and B terminals
iv. Simulated voltages and currents through R L for the figures in the
previous requirement (iii)
3. From Problem 3:

Your completed figure 3B

The hand calculations you used to complete figure 3B

Your completed calculations for steps 3a and 3b

Your completed calculations for steps 4a and 4b

Screenshots of your work from step 5 demonstrating:
i. Figure 3A built in SPICE showing the voltages and currents necessary to
find its VTH, ISC, and RTH
ii. Thévenin and Norton equivalent circuits (Figure 3B) built in SPICE
iii. Figure 3A and its Thévenin and Norton equivalent circuits with load
resistors across their respective sets of A and B terminals
iv. Simulated voltages and currents through R L for the figures in the
previous requirement (iii)
GWU SEAS ECE Department ©2012
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ECE 2110 – Experiment: DC Circuits: Thévenin's Circuits, Mesh Current, Node Voltage Analysis
II Lab:
Part 1 - Circuit #2
1. Read through the lab requirement of Part 1, clarify your tasks and design a data table(s)
to record all your measurements. Label your table(s). For example:
VTH
ISC
RTH
VRL
IRL
VRTH
IRTH
Circuit 2
Thévenin Equivalent
Table 1 – Measured Results (Circuit #2)
Don’t forget to record units for each value
2. Construct the circuit in Figure 2A from the prelab.
a. Because this circuit requires three voltage sources, you will need to set and use
the 6V, 25V, and -25V rails present on the lab power supplies. Because the
positive and negative sources are independent, a common ground (as shown
below) is necessary to ensure that there are no “floating” reference points in the
circuit.
3. Measure the circuit:



Vth Measurement:
o Do not place the load resistor across terminals A and B.
o Use the DMM to measure the voltage drop across terminal A and B.
Isc Measurement:
o Short the terminal A and B using a wire.
o Measure the current through terminals A and B using the DMM.
Rth Measurement:
o Remove the wire you were using to short the terminals A and B in Isc
measurement.
o Remove the power supply.
o Use a wire to connect where the power supply was connected in your original
circuit of Figure 2A.
 Although we „short‟ voltage sources when we calculate RTH on paper,
you do not „short‟ the power supply in real life. This would cause an
overload of the power supply. The power supply HAS TO BE
REMOVED to measure RTH.
o Measure the resistance between terminals A and B using the DMM.
GWU SEAS ECE Department ©2012
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ECE 2110 – Experiment: DC Circuits: Thévenin's Circuits, Mesh Current, Node Voltage Analysis
4. Remove the wire you connected for Rth measurement and reconnect the power supply
back to the circuit (keep the circuit same as in Figure 2A).
5. Connect the load RL=1 kΩ between terminals A and B. Measure the voltage drop across
RL and the current through RL.
6. Connect a resistor between terminals A and B that is equal to the Thevenin resistance
you found in the prelab. Measure the voltage drop across (V RTH) and the current through
the resistor (IRTH).
7. Construct the Thévenin Equivalent circuit in Figure 2B.

Set the power supply to Vth.

Connect the load RL between terminal A and B

Measure the voltage drop across RL and the current through RL.
8. Finish the data table(s) you designed and compare/analyze/interpret the results.
Part 2 - Circuit #3

Repeat all the steps in part 1, but for circuit 3A and 3B from the prelab.
GWU SEAS ECE Department ©2012
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ECE 2110 – Experiment: DC Circuits: Thévenin's Circuits, Mesh Current, Node Voltage Analysis
III Lab Writeup:
In the Analysis section of your lab report:
1. Perform the hand analysis for the circuit in figure 3A, finding VTH, ISC, and RTH:
a. Attach a 1 kΩ load resistor RL across terminals A and B in Figure 3A. Calculate
the voltage across and current through RL.
b. Attach a 1 kΩ load resistor RL across terminals A and B in Figure 3B. Calculate
the voltage across and current through RL.
2. Compare your hand calculation results and PSPICE simulation results for circuits #1, #2,
and #3. What are the percent errors for each? As an example:
Example Circuit
VTH
ISC
RTH
VRL
IRL
SPICE Results
3.99 V
1.00 mA
1500 Ω
3.00 V
0.50 mA
Hand Calculations
4.00 V
1.50 mA
1450 Ω
2.75 V
0.70 mA
Percent Error
0.25 %
50.00 %
3.33 %
8.33 V
40.00 %
Table 2 – PSPICE / Hand Calculation Comparison
Note: These values are present only to illustrate percent error calculations.
3. Compare your hand calculation results and lab measurement results for circuits #1, #2,
and #3. What are the percent errors for each?
Critical thinking questions to answer in the discussion portion of the lab writeup:
1. For any circuit in the lab, why is a very large resistor required to determine the Thevenin
voltage in PSPICE? How much current flows through the large resistor?
2. For any circuit in the lab, why is a very small resistor required to determine the short
circuit or Norton current in PSPICE? How much voltage is across this very small
resistor?
3. When you attach the load resistor (RL) to any of the circuits in the lab, is the voltage
across RL equal to VTH? Is the current through RL equal to ISC?
4. Is there any load resistor (RL) that you could attach to the circuit to achieve both VTH
and ISC at the same time? Why or why not?
5. When you attach the Thevenin equivalent resistance (RTH) to any of the circuits in the
lab, is there a relationship between VTH and VRTH? And ISC and IRTH?
In the Conclusion section of your lab report:
1. Discuss how Thévenin Equivalent Theorem helps you simplify the circuit analysis. For
example, consider this idea when writing your conclusion: is it easier to use the Thevenin
equivalent circuit to determine the voltage across and current through the load resistor
(RL) or is it easier to use the original circuit?
2. What is the purpose of the Thévenin Equivalent circuit?
GWU SEAS ECE Department ©2012
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ECE 2110 – Experiment: DC Circuits: Thévenin's Circuits, Mesh Current, Node Voltage Analysis