EE 42/100 Discussion sections
Section Day/Time
Room
GSI
Dis
101 M 3-4pm
241 Cory
Liu, Vincent
Dis
102 W 4-5pm
241 Cory
Li, Li
Dis
103 F 9-10am
3108 Etcheverry Liu, Vincent
Dis
104 F 10-11am 71 Evans
Dis
Dis
?105 Th 4-5pm
3107 Etcheverry Li, Li
106 Th 12-1pm 45 Evans
EE 42/100, Spring 2006
Liu, Vincent
Lecture 3a, Prof. White
Li, Li
1
Lecture Week 3a
OUTLINE
• Superposition: Analysis method for
circuits with sources and linear elements
• Thévenin and Norton equivalent circuits
• Maximum Power Transfer
EE 42/100, Spring 2006
Lecture 3a, Prof. White
2
Superposition
A linear circuit is constructed only of linear elements (linear
resistors, linear dependent sources*) and independent
sources.
* We’ll discuss dependent sources a bit later
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.
Procedure:
1. Determine contribution due to an independent source
•
Set all other independent sources to 0
2. Repeat for each independent source
3. Sum individual contributions to obtain desired
voltage or current
EE 42/100, Spring 2006
Lecture 3a, Prof. White
3
Superposition Example
• Find Vo
–
+
24 V
2W
4V
+–
4A
+
4 W Vo
–
EE 42/100, Spring 2006
Lecture 3a, Prof. White
4
Equivalent Circuit Concept
• A network of voltage sources, current sources,
and resistors can be replaced by an
equivalent circuit which has identical terminal
properties (I-V characteristics) without
affecting the operation of the rest of the circuit.
iA
network A
of
sources
and
resistors
iB
+
vA
_
≡
network B
of
sources
and
resistors
+
vB
_
iA(vA) = iB(vB)
EE 42/100, Spring 2006
Lecture 3a, Prof. White
5
Source Combinations
• Voltage sources in series can be replaced by an
equivalent voltage source:
≡
v1+v2
–
+
–
+
v2
–
+
v1
• Current sources in parallel can be replaced by
an equivalent current source:
i1
EE 42/100, Spring 2006
i2
≡
i1+i2
Lecture 3a, Prof. White
6
Thévenin 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 voltage source in series
with a resistor without affecting the operation of the rest
of the circuit.
Thévenin equivalent circuit
Actual circuit
RTh
a
+
iL
vL
RL
≡
VTh
–
–
+
network
of
sources
and
resistors
a
b
+
iL
vL
RL
–
b
“load” resistor
EE 42/100, Spring 2006
Lecture 3a, Prof. White
7
Why use such equivalent circuits?
They may be much easier to use than the actual
circuits when doing circuit analysis
Example: We can reduce the entire telephone
network or the entire power system that delivers
energy to an AC outlet to a Thevenin equivalent
containing just one voltage source (Vth) and one
resistor (Rth) [or one impedance Zth, which we’ll
see a little later]
EE 42/100, Spring 2006
Lecture 3a, Prof. White
8
Calculating a Thévenin Equivalent
1. Calculate the open-circuit voltage, voc
a
network
of
sources
and
resistors
+
voc
–
b
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 !
a
network
of
sources
and
resistors
isc
VTh  voc
RTh
b
EE 42/100, Spring 2006
Lecture 3a, Prof. White
9
voc

isc
Thévenin Equivalent Example
Find the Thevenin equivalent with respect to the terminals a,b:
EE 42/100, Spring 2006
Lecture 3a, Prof. White
10
Alternative Method of Calculating RTh
For a network containing only independent sources
network of
and linear resistors:
independent
sources and
resistors, with
each source
set to zero
1. Set all independent sources to zero
voltage source  short circuit
current source  open circuit
Req
2. Find equivalent resistance Req between the terminals
by inspection
RTh  Req
Or, set all independent sources to zero
RTh
EE 42/100, Spring 2006
VTEST

I TEST
Lecture 3a, Prof. White
network of
independent
sources and
resistors, with
each source
set to zero
VTEST
11
–
+
1. Apply a test voltage source VTEST
2. Calculate ITEST
ITEST
RTh Calculation Example #1
Set all independent sources to 0:
EE 42/100, Spring 2006
Lecture 3a, Prof. White
12
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
a
network
of
sources
and
resistors
+
iL
vL
RL
≡
iN
RN
–
+
iL
vL
RL
–
b
EE 42/100, Spring 2006
a
b
Lecture 3a, Prof. White
13
Finding IN and RN = RTh
Analogous to calculation of Thevenin Eq. Ckt:
1) Find open-circuit voltage and short-circuit current
IN ≡ isc = VTh/RTh
2) Or, find short-circuit current and Norton (Thevenin)
resistance
EE 42/100, Spring 2006
Lecture 3a, Prof. White
14
Finding IN and RN
• We can derive the Norton equivalent circuit from
a Thévenin equivalent circuit simply by making a
source transformation:
RTh
–
+
vTh
a
a
+
iL
vL
RL
iN
RN
–
+
iL
vL
RL
–
b
b
voc
vTh
RN  RTh 
; iN 
 isc
isc
RTh
EE 42/100, Spring 2006
Lecture 3a, Prof. White
15
Maximum Power Transfer Theorem
Thévenin equivalent circuit
Power absorbed by load resistor:
RTh
2
–
+
VTh
+
iL
vL
RL
 VTh 
 RL
p  i RL  
 RTh  RL 
2
L
–
dp
To find the value of RL for which p is maximum, set
to 0:
dRL
2


dp
2 RTh  RL   RL  2RTh  RL 
 VTh 
0
4
dRL
RTh  RL 


2


 RTh  RL  RL  2RTh  RL   0
 RTh  RL
EE 42/100, Spring 2006
A resistive load receives maximum power from a circuit if the
load resistance equals the Thévenin resistance of the circuit.
Example: Maximizing power to speakers from music system
Lecture 3a, Prof. White
16
EE 42/100, Spring 2006
Lecture 3a, Prof. White
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