Lab 10
Application of Superposition theorem in Sinusoidal Steady State
INTRODUCTION:
Any voltage or current in a multi-source linear network may be determined by summing the
contributions caused by each source acting alone, with all other source replaced by their internal
impedance. The basic idea is to determine the contribution of each source by itself, and then
combine the results to get the final answer. The contributions are either all voltages or all currents,
depending on need
OBJECTIVES:
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To analysis of multi-source AC circuits using the superposition theorem.
To use the function generator, oscilloscope and DMM to analyze the circuit parameters.
To solve the circuit by using the superposition theorem for AC networks.
EQUIPMENT NEEDED:
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Breadboard
AC function generators
Oscilloscope
Digital multi-meter (DMM)
BACKGROUND
The superposition theorem can be used to analyze multi-source AC linear networks. Each source
is considered in turn, with the remaining sources replaced by their internal impedance, and
appropriate series-parallel analysis techniques employed. The resulting signals are then summed
to produce the combined output signal. To see this process more clearly, the exercise will utilize
two sources operating at different frequencies. Note that as each source has a different frequency,
the inductor and capacitor appear as different reactance’s to the two sources.
PREPARATION
1. Built the circuit shown in Figure 1 on the breadboard.
2. To test the superposition theorem, sources E1 and E2 will be examined separately and then
together.
SOURCE ONE ONLY
3. Consider the circuit of Figure 1, with C=100 nF, L=10 mH, R=1 k , using only source
E1=2 V p-p at 1 kHz and with source E2 replaced by its internal impedance of 50 . Using
standard series-parallel techniques, calculate the voltages across E1, R, and E2. Remember
to include the 50 internal impedances in the calculations. Record the results in Table 1.
4. Now, build the circuit of Fig. 1 using C=100 nF, L=10 mH, and R=1 k . Replace E2 with
a 50 resistor to represent its internal impedance. Set E1 to 2 V p-p at 1 kHz, unloaded.
Place probe one across E1 and probe two across R. Measure the voltages across E1 and R,
and record in Table 1. Record a copy of the scope image. Move probe
two across E2 (the 50 ), measure and record this voltage in Table 1.
Fig 1: Circuit for AC superposition Analysis
SOURCE TWO ONLY
1. Consider the circuit of Fig. 1 using only source E2=2 V p-p at 10 kHz and with source
E1 replaced by its internal impedance of 50 . Using standard series-parallel techniques,
calculate the voltages across E1, R, and E2. Remember to include the 50 internal
impedances in the calculations. Record the results in Table 2.
2. Replace the 50 with source E2 and set it to 2 V p-p at 10 kHz, unloaded. Replace E1
with a 50 resistor to represent its internal impedance. Place probe one across E2 and
probe two across R. Measure the voltages across E2 and R, and record in Table1.
Record a copy of the scope image. Move probe two across E1 (the 50 ), measure and
record this voltage in Table 2.
SOURCES ONE AND TWO
1 Consider the circuit of Fig. 1 using both sources, E1=2 V p-p at 1 kHz and E2=2 V pp at
10 kHz. Add the calculated voltages across E1, R, and E2 from Tables 1 and 2. Record
the results in Table 3. Make a note of the expected maxima and minima of these waves
and sketch how the combination should appear on the scope.
2 Replace the 50 with source E1 and set it to 2 V p-p at 1 kHz, unloaded. Both sources
should now be active. Place probe one across E1 and probe two across R. Measure the
voltages across E1 and R, and record in Table 3. Record a copy of the scope image. Move
probe two across E2, measure and record this voltage in Table 3.
RESULT’S SUMMARY SOURCE ONE ONLY
Table 1
Theory
Experimental
%Error
E1
E2
VR
SOURCE TWO ONLY
Table 2
Theory
Experimental
%Error
E1
E2
VR
SOURCES ONE AND TWO
Table 3
Write your mathematical calculations here along with the steps to follow superposition Principle:
Conclusion: