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University of Sharjah
Electrical and Electronics Engineering Department
0402203
Circuit Analysis I Laboratory
Experiment # 6
Superposition for DC Circuits
OBJECTIVE:
To understand and verify the principle of superposition by the use of DC circuits.
PRE-LAB:
1. Using the principle of superposition, find VL and IL in the circuit shown in Figure 1. Use PSPICE
instead of hand calculation.
2. Without resolving the circuit again, just using the results of part 1, find the following:
a)
b)
c)
d)
e)
The values of VL and IL when the 6-volts source becomes 12-volts.
The values of VL and IL when the 20-volts source becomes –20-volts
To what value the 20-volts source must be changed so that VL=0
To what value the 1.5-volts source must be changed so that VL=0
To what value the 6-volts source must be changed so that IL=3 mA
THEORY:
For a linear DC network, the Superposition Principle can be stated as
The voltage across (or current through) an element of a linear network, which contains
multiple sources, is the algebraic sum of the voltages (or currents) due to each independent
source acting alone with all other sources replaced by their internal resistances.
Since the internal resistance of an ideal voltage source is zero, and of an ideal current source is infinite;
the non-acting voltage sources are replaced by shorts, and current sources by open-circuits in the
application.
As an example, refer to Figure 1. The circuit contains three voltage sources (V s1, Vs2, Vs3), thus
according to Superposition Principle VL and IL are composed of three components, one component
from each source i.e.
VL = VL20 + VL6 + VL1.5
and
IL = IL20 + IL6 + IL1.5
where VL20 and IL20 are the circuit response due to 20-volts source alone, VL6 and IL6 are the circuit
response due to 6-volts source alone, and VL1.5 and IL1.5 are the circuit response due to 1.5-volts source
alone. Moreover, each component of VL or IL is proportional to its source: if the source is scaled by a
factor, the component will be scaled by the same factor. This means if Vs1 is scaled by α (Vs1=20 α
volts), Vs2 is scaled by β (Vs2=6 β volts) and Vs3 is scaled by γ (Vs3=1.5 γ volts), then
VL = α VL20 + β VL6 + γ VL1.5
Circuit Analysis I Lab Manual
and
IL = α IL20 + β IL6 + γ IL1.5
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PROCEDURE:
1.
2.
3.
4.
Connect the circuit shown in Figure 1.
Measure VL and IL.
Remove the 6-volts and 1.5-volts sources and replace them with a short circuit. Measure VL20 and IL20
Restore the original circuit then remove the 20-volts and 1.5-volts sources and replace them with a
short circuit. Measure VL6 and IL6
5. Restore the original circuit then remove the 20-volts and 6-volts sources and replace them with a short
circuit. Measure VL1.5 and IL1.5
6. Restore the original circuit then change the 6-volts source to 12-volts. Measure VL and IL
7. Restore the original circuit then change the 20-volts source to –20-volts. Measure VL and IL
8. Restore the original circuit then change the 20-volts source until VL becomes zeros. Record the value
of this source.
9. Restore the original circuit then change the 1.5-volts source until VL becomes zeros. Record the value
of this source.
10. Restore the original circuit then change the 6-volts source until IL becomes 3mA. Record the value of
this source.
VL20
VL6
VL1.5
VL20+ VL6+ VL1.5
VL
Percent Error
IL20
IL6
IL1.5
IL20+ IL6+ IL1.5
IL
Percent Error
Circuit Analysis I Lab Manual
Measured
0.444 V
0.594 V
-0.474 V
0.564 V
0.544 V
Calculated
0.442 V
0.593 V
-0.479 V
0.556 V
0.554 V
Percent Error
0.452 %
0.169 %
1.04%
1.44%
1.81%
-----
Measured
0.65 mA
0.87 mA
-0.69 mA
0.83 mA
0.79 mA
Calculated
0.649 mA
0.873 mA
-0.705 mA
0.817 mA
0.81 mA
Percent Error
0.154 %
0.344%
2.128%
1.591%
2.47%
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Measured
2.886 mW
5.168 mW
3.371 mW
11.325 mW
4.298 mW
Calculated
2.868 mW
5.177 mW
3.377 mW
11.422 mW
4.487 mW
Percent Error
PL20
0.628 %
PL6
0.174 %
PL1.5
0.159 %
PL20+ PL6+ PL1.5
0.849 %
PL
4.212 %
Percent Error
----Notice that the value we obtain in adding the power for each resistance is differ from the value we
obtain directly in PL which mean that the power does not follow superposition (Not linear)
Measured
Calculated
Percent Error
VL
1.147 V
1.149 V
0.174 %
Vs2=12 Volts
IL
1.67 mA
1.69 mA
1.18 %
VL
-0.337 V
-0.327
3.06 %
Vs1= -20 Volts
IL
-0.50 mA
-0.482 mA
3.73 %
When VL=0,
Vs1=
4.7 V
4.7 V
0%
When VL=0,
Vs3=
3.1 V
3.1 V
0%
When IL=3 mA, Vs2=
20.3 V
20.3 V
0%
Results:
1. Fill all the Tables; show all the hand or PSPICE calculations.
2. Is the principle of superposition verified based on the measured and calculated values of VL and IL?
Yes it is based on the measured and calculated values because to obtain the values of VL and IL
We added the values we found in each source according to the linearity principle .
3. Is the principle of superposition verified based on the measured and calculated values of the power? and
why?
No it is not , Because power is not linear and does not obey the superposition principle which
can be shown in our calculated values when we add the result we found it is differ from the
value we obtains in PL (PL= I^2 R or V^2 \R )
Circuit Analysis I Lab Manual
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