Lecture 6, Slide 1EECS40, Fall 2004 Prof. White

Slides from Lecture 6 with clearer markups 16 Sept. 2004

Lecture 6, Slide 2EECS40, Fall 2004 Prof. White

SuperpositionA linear circuit is one constructed only of linear

elements (linear resistors, and linear capacitors and

inductors, linear dependent sources) and independent sources. Linear means I-V charcteristic of elements/sources are straight lines when plotted.

Principle of Superposition:• In any linear circuit containing multiple

independent sources, the current or voltage at any point in the network may be calculated as the algebraic sum of the individual contributions of each source acting alone.

Lecture 6, Slide 3EECS40, Fall 2004 Prof. White

Superposition

Procedure:1. Determine contribution due to one independent source

• Set all other sources to 0: Replace independent voltagesource by short circuit, independent current source by opencircuit

2. Repeat for each independent source3. Sum individual contributions to obtain desired voltage

or current

Lecture 6, Slide 4EECS40, Fall 2004 Prof. White

Superposition Example

• Find Vo

–+

24 V

2

4 4 A

4 V

+ –+

Vo

–

Lecture 6, Slide 5EECS40, Fall 2004 Prof. White

Lecture 6, Slide 6EECS40, Fall 2004 Prof. White

Calculating a Thévenin Equivalent

1. Calculate the open-circuit voltage, voc

2. Calculate the short-circuit current, isc

• Note that isc is in the direction of the open-circuit voltage drop across the terminals a,b !

networkof

sourcesand

resistors

a

b

+

voc

–

networkof

sourcesand

resistors

a

b

isc

sc

ocTh

ocTh

i

vR

vV

Lecture 6, Slide 7EECS40, Fall 2004 Prof. White

Thévenin Equivalent Example

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

Lecture 6, Slide 8EECS40, Fall 2004 Prof. White

Lecture 6, Slide 9EECS40, Fall 2004 Prof. White

Lecture 6, Slide 10EECS40, Fall 2004 Prof. White

Thévenin Equivalent Example

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

Lecture 6, Slide 11EECS40, Fall 2004 Prof. White

Lecture 6, Slide 12EECS40, Fall 2004 Prof. White

Alternative Method of Calculating RTh

For a network containing only independent sources and linear resistors:

1. Set all independent sources to zerovoltage source short circuitcurrent source open circuit

2. Find equivalent resistance Req between the terminals by inspection

Or, set all independent sources to zero1. Apply a test voltage source VTEST

2. Calculate ITEST

eqRR Th

TEST

TESTTh I

VR

network ofindependentsources and

resistors, witheach sourceset to zero

Req

network ofindependentsources and

resistors, witheach sourceset to zero

ITEST

–+

VTEST

Lecture 6, Slide 13EECS40, Fall 2004 Prof. White

RTh Calculation Example #1

Set all independent sources to 0: