chapter 4 - circuit theorems

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Chapter 4

Circuit Theorems

EEE3103 Circuits and Signals

PowerPointSlides

by Alex Chan


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2 I-Station Solutions Sdn BhdLast Updated:

Chapter Outline

4.1 Superposition

4.2 Source Transformation

4.3 Thevenins Theorem

4.4 Nortons Theorem4.5 Maximum Power Transfer

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4.1 Superposition Theorem

Superposition is another approach introduced to determine

the value of a specific variable (voltage or current) if the

circuit has two or more independent sources.

Definition:

Superposition states that the voltage across (or current

through) an element in a linear circuit is the algebraic sum

of the voltage across (or currents through) that element due

to EACH independent source acting alone.

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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 and then adding them up.

Example:

We consider the effects of 8A and 20V one by one, then

add the two effects together

for final v0.

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Steps to apply superposition theorem:

1. Turn off all independent sources except one source.

Find the output (voltage or current) due to that active

source using nodal or mesh analysis.

2. Repeat step 1 for each of the other independent

sources.

3. Find the total contribution by adding algebraically all the

contributions due to the independent sources.

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Two things to keep in mind:

1. When we say turn off all other independent sources:

Independent voltage sources are replaced by 0 V

(short-circuit) and Independent current sources are replaced by 0 A

(open-circuit).

2. Dependent sources are left intact because they are

controlled by circuit variables.

PP 4.3 4.5

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Source transformation is the process of replacing a

voltage source Vs in series with a resistor R by a current

source is in parallel with a resistor R, or vice versa.

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s sv i Rs

s

vi

R




Independent Source Transform

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Dependent Source Transform

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Two things to keep in mind:

1. During transformation, the arrow of current source is

directed toward the positive terminal of voltage source.

2. Not possible when: R = 0 for voltage source.

R = for current source.

PP 4.6 4.7

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In practice the load usually varies, while the source is

fixed eg. Fixed household outlet terminal and different

electrical appliances which constitute variable loads.

Each time the load is changed, the entire circuit has to

be analyzed all over again.

To avoid this problem, Thevenins theorem provides a

technique by which the fixed part of the circuit is

replaced with an equivalent circuit.

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Thevenins theorem states that a linear two-terminal circuit

can be replaced by an equivalent circuit consisting of a

voltage source VTh in series with resistor RTh.

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Definitions:

VTh = open-circuit voltage at the terminals.

RTh = input or equivalent resistance at the terminals when

the independent sources are turned off.

ie.

Voltage sources = 0 V (short circuit) Current sources = 0 A (open circuit)

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How to find VTh:

Find the voltage across point a and b using any methodin previous chapters (by taking out the load from the

circuit).

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How to find RTh:

Case 1: No dependent sources in the circuit

1. Turn off all independent sources.

2. Find RThby finding the equivalent resistance at point a

and b.

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Case 2: Circuit has dependent sources.

1. Turn off all independent sources.

2. Leave dependent sources intact.

3. Apply voltage source vo across a and b then find

=0

0

OR apply current source i0 and find =0

0

.

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Consider a linear circuit terminated by load RL.

Current IL through the load and voltage VL across the load

is given by:

PP 4.8 4.10

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Th

L

ThL

VI

R R

L

L L L Th

ThL

RV R I V

R R



4.4 Nortons Theorem

Nortons theorem states that a linear two-terminal circuit

can be replaced by an equivalent circuit consisting of a

current source IN in parallel with resistor RN.

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4.4 Nortons Theorem

Definitions:

IN = short-circuit current through the terminals.

RN = input or equivalent resistance at the terminals when

the independent sources are turned off.

ie.

Voltage sources = 0 V (short circuit) Current sources = 0 A (open circuit)

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4.4 Nortons Theorem

Relation between Nortons and Thevenins Theorem

The Thevenins and Norton equivalent circuits are related

by a source transformation.

In source transformation, the resistor does not change.

Thus:

=

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4.4 Nortons Theorem

How to find IN:

1. The short-circuit current flowing

from terminal a to b is IN.

Since the resistors, = :

2. Dependent and independent sources are treated the

same way as in Thevenins Theorem.

PP 4.11 4.12

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Th

N

Th

V

I R


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4.5 Maximum Power Transfer

By varying the load resistance RL, the power delivered will

also vary, as per the graph.

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References

Alexander & Sadiku, Fundamentals of Electrical Circuits,

4th Edition, McGraw-Hill Company.

chapter 4 - circuit theorems

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