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INC 341 PT & BP
INC 112 Basic Circuit Analysis
Lecture 4
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Special Techniques
Superposition Theorem
Source Transformation
Thevenins Theorem
Nortons Theorem
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Linear elements vs. linear circuits
Linear element: passive element that has a
linear voltage-current relationship, i.e.
v(t)=R*i(t)
Linear dependent source: source whose output
is proportional only to the first power, i.e.,
v1 = 0.6i1-14v2
Linear circuit: composed of independentsources, linear dependent sources, and linear
elements
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INC 341 PT & BP
Superposition Theorem
One of the properties of linearity
Definition:
voltage across or current thru anyresistor or source may be calculated by
adding all the individual voltage or currents
caused by the separate independent
source acting alone
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INC 341 PT & BP
Implementation
Other independent
voltage sources give
zero voltage, then act
like short circuits. Other independent
current sources give
zero current, then actlike open circuits.
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Example
I1 = 1A
I2 = 2A
I total = 1+2 = 3A
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Example
I1 = 1A
I2 = 0A
I total = 1+0 = 1A
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Example
Find voltage Vx
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V
VxV
333.9
42)7/12(6
)7/12(42
)4||3(6
)4||3()42(
!
v
!v
!
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INC 341 PT & BP
V
VxV
333.3
1042
210
4)3||6(
)3||6()10(
!
v
!v
!
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INC 341 PT & BP
V
VxVxVxVV
6333.3333.9
)10()42(
!!
!
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Example 5.1
use superposition to find ix
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Example 5.1 (cont.)
= 0.2A'
xi = 0.8A
''
xi
= 1.0Axi
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Superposition and dependent source
one cannot use superposition to
dependent source!!!
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INC 341 PT & BP
Example 5.3
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INC 341 PT & BP
KVL:
2
021210
'
'''
!
!
x
xxx
i
iii
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INC 341 PT & BP
Supermesh:
6.0
02)3(12
''
''''''
!
!
x
xxx
i
iii
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A
iiixxx
4.1)6.0(2
'''
!
!
!
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INC 341 PT & BP
Special Techniques
Superposition Theorem
Source Transformation
Thevenins Theorem
Nortons Theorem
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INC 341 PT & BP
Practical voltage source
LssLiRvv !
s
sLsc
soc
R
vi
vv
!
!
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INC 341 PT & BP
Practical current source
p
L
sLR
vii !
sLsc
spLoc
ii
iRv
!
!
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INC 341 PT & BP
Equivalent practical sources
THNTH
NTH
RIV
RR
v!
!
Head of current = +
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Equivalent practical sources (cont.)
The two practical sources are equivalent
only with respect to what transpires at the
load terminals; they are not equivalent
internally!
Note: goal is to have either all current sources or all
voltage sources in the circuitmaking nodal/mesh
analysis easier
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Example
Usesource transformation to findIx
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INC 341 PT & BP
AIX 3
1
6
2
321
2!!
!
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Special Techniques
Superposition Theorem
Source Transformation
Thevenins Theorem
Nortons Theorem
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Thevenins Theorem
Equivalent circuit
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Thevenins Equivalent Circuit
Composed of VTH and
RTHconnected in series
VTH = Voc (open-circuit voltage)
RTH= equivalent R (total R) in the circuit
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A statement of Thevenins Theorem
Disconnect a load network from the circuit
by substituting an open circuit, and find
Voc across the load, which is equivalent to
VTH.
Open load and evaluate RTH by zeroing
out every independent source (open
current source, short voltage source).
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Example
Find Thevenins equivalent circuit
and the current passing thruRL
given RL = 1
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0V
10V
0V 0V
6V 6V
VVTH 61032
3!v
!
Find VTH
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Short voltage source
RTH
;!
v!
!
2.13
232
3210
23||210THR
Find RTH
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Thevenins equivalent circuit
The current thru RL = 1is A423.012.13
6 !
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Example
Find Thevenins equivalent circuit
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Find VTH
0V
5V
0V 0V
3V 3V
VVTH 331
!v!
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Open circuit
current source
RTH
;!
!
15
2310THR
Find RTH
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Thevenins equivalent circuit
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Example: Bridge circuit
Find Thevenins equivalent circuit
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Find VTH
0V
10V
8V 2V
VTH = 8-2 = 6V
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Find RTH
RTH
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KKK
KKKKRTH
4.28.06.1
1||48||2
!!
!
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Thevenins equivalent circuit
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HW#3
Read Superposition and source
transformation
Ex
ercise 5.13, 5.24