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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: