MORGAN STATE UNIVERSITY
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
EEGR 203: INTRODUCTION TO ELECTRICAL LABORATORY
Instructor: Dr. Gregory M. Wilkins
Lab 4: Superposition Principle and Thevenin’s Theorem
You will see this reminder in all of your labs.
Please take notes and commit all you learn in each lab to memory
You will need every bit of this information to complete your project !!!
The following is a statement of the principle of superposition:
The value of any variable may be found as the sum of the values of that variable produced
by each of the values of that variable produced by each of the excitation sources acting
Let’s try another:
In any Linear circuit containing more than one independent source, any voltage (or current)
in the circuit may be calculated as the algebraic sum of the individual voltages (or currents)
caused by each independent source acting alone; i.e., with all other independent sources set
Note that a voltage source is set to zero if it is replaced by a short circuit. (There is no voltage
across a short regardless of the amount of current flowing, so the short continues to meet the
definition of a voltage source, of a magnitude of 0.0 volts).
A current source is set to zero if it is replaced by an open circuit. Recall that the definition of a
current source is that it provides the same current regardless of the voltage across it. An open circuit
provides zero current regardless of the voltage across it.
The linearity aspect is important. In a previous lab we looked at a diode. There was a certain voltage
across the diode when 10 mA was flowing through it. However, twice the voltage was not required to
force 20 mA. The diode is a non-linear element, so superposition cannot be applied to a circuit
containing a diode.
A statement of Thevenin’s Theorem is offered:
Any network consisting of (only) linear resistance and independent sources may be replaced
at a given pair of nodes by an equivalent circuit consisting of a single voltage source and
series resistor as illustrated in Figure 1.
The value of the resistor is the input resistance seen at the pair of nodes when all the independent
sources are set to zero. The value of the voltage source is that seen at the open circuit terminals.
Figure 1 - Thevenin Equivalent
Figure 2 – Circuit for Principle of Superposition
Lab Procedure (Superposition):
Construct the circuit illustrated in Figure 2. Measure the value of resistors R1, (nominally 1.8
k), R2 (220 ) and R3 (220 ) and record in Table 1.
Mount the resistors on your breadboards. The supply on the left of the Figure (10 V) is the
large 6038 supply you used in previous labs. The supply on the right is either the same model
or a 6236B Triple Supply. Note that the 6038 has the current limiting feature which you
should use. The 6236 does not have this capability.
To use the triple supply, adjust the +6 V Output to 4.5 V using the +6 V adjust control. Note
that the meter switch must be in the +6 position. The voltage is available at terminals +6 and
COM. Supply voltages should be set prior to connection to the circuit.
Measure and record the data as required in Table 1. Note that quantities V1, V2 and VR1, VR2
and VR3 are measured using the multimeter, Currents IR1, IR2 and IR3 are to be calculated using
Repeat this for each of the following conditions:
Both sources on.
With the 10 V (V1) source replaced with a short circuit and 4.5 V on.
With the 10 V source on and the 4.5 V (V2) source replaced with a short
Using the values measured for R1, R2, R3, V1, and V2 calculate the theoretical values of VR1
VR2 VR3, IR1, IR2 and IR3- (This may be done outside the lab).
Using Table 1, briefly illustrate that the principle of superposition appears to be valid.
Lab Procedure (Thevenin Equivalent):
Using your breadboard, set up the circuit illustrated in Figure 3. Note that the load resistor is
variable; use the Heath decade boxes. Vary the value of the load resistor (Rload) from 0 to
infinity, and record the voltage and current readings as indicated in Table 2. Note that one can
easily take voltage and current measurements with a single multimeter. Figure 4 shows the
same circuit except that the physical location of the ammeter has been relocated. Note that
voltage is measured between the top and middle terminals, and current flowing in the bottom
and out the middle. In the second representation the meter is configured as in a previous lab.
By depressing the DC voltage, the voltage may be read and by depressing the DC current,
current may be read, all without reconfiguring.
Plot the I-V characteristics of the circuit illustrated in Figure 3. Use the x-axis for current and
the y-axis for voltage. Using the plot determine the Rthev and Vthev for the circuit of Figure 3.
Figure 3 – Original Network
Determine the Thevenin equivalent of the circuit illustrated in Figure 3. Build up such an
equivalent circuit and repeat step 6. Note that the precise value of Rthev probably will not be a
standard value. Try to come within 10 by connecting resistors in series.
Figure 4 – Thevenin Equivalent Network
Summary of Written Assignment:
The written assignment is to include Table 1, Items 3 and 4, Table 2 and Items 6 and 7 (plus the extra
credit). Please use this as your checklist to assure your write-up is complete. The report should also
include difficulties which were encountered and a general discussion of the results.
In part 3, you are asked to calculate some theoretical values based on measured values. Calculate
those values based on theoretical values.
Actual Measured Values:
R1 = __________
R2 = __________
R3 = __________
Thevenin Equivalent Data
Thevenin Equivalent Circuit
EEGR 203: Introduction to Electrical Laboratory
Report Requirements for Lab 4
Superposition Principle and Thevenin’s Theorem
Be sure to include ALL of the following information in your lab report.
1. Discuss the purpose of the lab, i.e. explain both principles listed in the title of this lab, namely
the Superposition Principle and Thevenin’s Theorem
2. For the Superposition Principle, show all work which led to the theoretical values for each
part, namely Part A (both sources V1 and V2 on), Part B (V1 off, V2 on), and Part C (V1 on,
V2 off). Be sure to show that Superposition is upheld, making sure to adhere to the polarities
and current directions indicated in class. Compare and discuss the theoretical values with the
values obtained through measurement.
3. For Thevenin’s Theorem, plot the results from both the original circuit and the Thevenin
equivalent circuit. Show the calculations which led to VTHEV and RTHEV. Indicate on the graphs
the location and value where the graph crosses the horizontal axis, corresponding to VLOAD =
0 V (short circuit, RLOAD = 0 , and where the graph crosses the vertical axis, corresponding
to ILOAD = 0 A (open circuit, RLOAD = ∞ . For the open circuit, the graph will need to be
extrapolated to cross the vertical axis since the largest value of load resistance used is RLOAD =
5 kIndicate the equations of the lines plotted, which may be obtained directly by
performing Kirchoff’s Voltage Law (KVL) on the Thevenin equivalent circuit.
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Morgan State University
School of Engineering
Department of Electrical and Computer Engineering
Introduction to Electrical Laboratory
Dr. Gregory M. Wilkins
Lab (Number): Lab Title
Name 1: Student 1
Name 2: Student 2
Name 3: Student 3
A brief outline of the overall purpose of the experiment including techniques being used and goals.
Techniques used may be optional depending on the lab being performed.
This section should include information needed in order to derive the theoretical features of the
experiment. All sources of information from which expressions and definitions are obtained are to be
included here. If equations are used, be sure that they are numbered sequentially, beginning with
List the model and make of equipment being used in the experiment, including the components used,
such as resistors, capacitors, diodes, etc.
If the experiment is one of a design nature (i.e., the experiment is developed by you), then this section
should show the development of your circuit. The actual calculations used by you to determine the
values used in your circuit must be shown.
This describes all measurement techniques, the procedural steps and the test equipment used. The
manufacturer’s name and the model number of each piece of test equipment should be given. This
section should also include a schematic showing the circuit and how the test equipment is connected to
the circuit. List ALL schematic diagrams for the circuits analyzed. Be sure to label the values of the
components used and indicate the nodes at which measurements may have been made. Label
schematics sequentially, beginning with the Figure 1 as listed in YOUR report. Be sure to provide a
caption for the figure. For example,
Figure 1: Series Resistive Network
This section would include all theoretical and experimental data obtained by you. These can be shown
in tabular form or in graph form. In either case it is necessary to clearly identify the various data
obtained by you. If graphs are used the axis must be labeled showing the type of information (current,
voltage, etc) as well as the units (milli amps, volts etc). If more than one plot is shown on a graph then
each plot should be individually identified with captions. For example,
Figure 1: Series Resistive Network
Table 1: Voltages Measure at Node A
Discuss your results in relation to how well it matched the theoretical results and any errors that may be
determined by you.
Summarize your report. Briefly state what you set out to do, what you did and any conclusions that can
be drawn from your results.
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