CHAPTER III

CIRCUIT ANALYSIS TECHNIQUES

• Circuit Reduction & Source Transformation

• Node-Voltage method

• Mesh- Current method.

• Superposition method.

• Thevenin’s and Norton’s circuits.

• Maximum Power Transfer theorem

THE SUPERPOSITION

METHOD

OBJECTIVES

• To apply the superposition principle to solve linear circuits.

• To introduce the concept of equivalent circuits.

• To determine “Thevenin” and “Norton” Equivalent circuits.

THE SUPERPOSITION PRINCIPLE

“In any linear circuit containing multiple

independent sources, the current or voltage at any

point in the circuit may be calculated as the

algebraic sum of the individual contributions of

each source acting alone.”

HOW TO APPLY SUPERPOSITION

• To find the contribution due to an individual independent

source, zero out the other independent sources in the circuit.

• Voltage source short circuit.

• Current source open circuit.

• Solve the resulting circuit using your favorite technique(s).

THE SUPERPOSITION PRINCIPLE

• The idea is that we can isolate the effect of 2 or more

independent power sources.

10V +

- 5W

5W 5W

i?

10A 10V +

- 5W

5W 5W

i’

5W

5W 5W

i”

10A i = i’ + i” = 1A + 5A = 6A

SUPERPOSITION PROCEDURE

For each independent source (repeat the following):

• Replace the other independent voltage sources with a short

circuit (i.e., V = 0).

• Replace the other independent current sources with an open

circuit (i.e., I = 0).

Note: Dependent sources are not changed!

• Calculate the contribution of this particular voltage or current

source to the desired output parameter.

• Algebraically sum the individual contributions (current and/or

voltage) from each independent source.

Example

Solution

Example

Use the superposition method to find Vo

THÉVENIN EQUIVALENT CIRCUIT

• Any linear 2-terminal (1-port) and active network can be

replaced by an equivalent circuit consisting of an

independent voltage source in series with a resistor.

network

of

sources

and

resistors

≡

– +

VTh

RTh

RL

iL +

vL

–

a

b

RL

iL +

vL

–

a

b

Thévenin equivalent circuit Actual circuit

NORTON EQUIVALENT CIRCUIT

• Any linear 2-terminal (1-port) network of independent voltage

sources, independent current sources, and linear resistors can

be replaced by an equivalent circuit consisting of an

independent current source in parallel with a resistor without

affecting the operation of the rest of the circuit.

Norton equivalent circuit

network

of

sources

and

resistors

≡ RL

iL +

vL

–

a

b

a

RL

iL +

vL

–

iN

b

RN

DETERMINATION OF THÉVENIN/NORTON EQUIVALENT

Calculate the open-circuit voltage, voc

Calculate the short-circuit current, isc

Note that isc is in the direction of the open-circuit voltage drop

across the terminals a,b !

sc

oc

Th

ocTh

i

vR

vV

network

of

sources

and

resistors

a

b

+

voc

–

network

of

sources

and

resistors

a

b

isc

ALTERNATIVE METHOD OF CALCULATING RTH

For a network containing only independent sources

and linear resistors:

1. Set all independent sources to zero

voltage source short circuit

current source open circuit

2. Find equivalent resistance Req between the terminals by

inspection

Or, set all independent sources to zero

1. Apply a test voltage source VTEST

2. Calculate ITEST

TEST

TEST

ThI

VR

network of

independent

sources and

resistors, with

each source

set to zero

Req

network of

independent

sources and

resistors, with

each source

set to zero

ITEST

– +

VTEST

FINDING IN

IN ≡ isc = VTh/RTh

Analogous to calculation of Thevenin Equivalent Circuit:

• Find open-circuit voltage and short-circuit current

• Or, find short-circuit current and Norton (Thevenin) resistance

FINDING IN AND RN

• We can derive the Norton equivalent circuit from a Thévenin equivalent

circuit simply by making a source transformation:

RL RN

iL

iN

+

vL

–

a

b

– +

RL

iL +

vL

–

vTh

RTh

sc

Th

Th

N

sc

oc

ThN ; i

R

vi

i

vRR

a

b

EXAMPLE

Find the Thevenin equivalent with respect to the terminals a,b: