Md.
Abdul Malek
Assistant Professor, Dept. of Electrical & Electronic Engineering (EEE)
Rajshahi University of Engineering & Technology (RUET)
Superposition Theorem
The superposition principle states that the voltage across (or current
through) an element in a linear circuit is the algebraic sum of the
voltages across (or currents through) that element due to each
independent source acting alone.
Superposition Theorem
The principle of superposition helps us to analyze a linear circuit
with more than one independent source by calculating the
contribution of each independent source separately.
we must keep two things in mind:
1. We consider one independent source at a time while all other
independent sources are turned off. This implies that we replace
every voltage source by 0 V (or a short circuit), and every current
source by 0 A (or an open circuit). This way we obtain a simpler and
more manageable circuit.
2. Dependent sources are left intact because they are controlled by
circuit variables.
Superposition Theorem
Steps to Apply Superposition Principle:
1. Turn off all independent sources except one source.
2. Find the frequency domain circuit for frequency of the active
independent source.
3. Find the output (voltage or current) due to that active source using
mesh analysis or nodal analysis
4. Repeat step 1 to step 3 for each of the other independent sources.
5. Find the total contribution by adding all the contributions due to
each the independent sources in time domain.
Superposition Theorem
Problem: Find vo of the following circuit using the superposition
theorem.
Superposition Theorem
Solution: Since the circuit operates at three different frequencies (ω=0
for the dc voltage source), one way to obtain a solution is to use
superposition, which breaks the problem into single-frequency
problems.
Let,
vo v1 v 2 v3 ........(i )
Where, v1 is due to the 5V dc voltage source, v2 is due to the 10 cos 2t
V voltage source, and v3 is due to the 2 sin 5t A current source
Superposition Theorem
To find v1, we set to zero all sources except the 5V dc source.
In steady state, a capacitor
is an open circuit to dc
while an inductor is a short
circuit to dc (ω=0).
We find v1 by voltage divider principle.
1 v1 1V
v1 * 5 1
1 4
Superposition Theorem
To find v2, we set to zero all sources except the 10 cos2t V source.
Transform the circuit time to
frequency domain (ω=2rad/s).
4Ω and –j5Ω are
connected in parallel.
Equivalent impedance is
Superposition Theorem
We find v2 by voltage
divider principle.
In time domain,
Superposition Theorem
To find v3, we set to zero all sources except the 2 sin5t A source.
Transform the circuit time to
frequency domain (ω=5rad/s).
4Ω and –j2Ω are
connected in parallel.
Equivalent impedance is
Superposition Theorem
By current division
Voltage v3 is
In the time domain, v3 is
Superposition Theorem
Voltage vo is found by adding the v1,v2 , and v3 in time domain
Thank You
