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Dr. Kasra EtemadiJanuary 27, 2006
1- Summary
2- Thevenin and Norton Equivalent Circuits
3-Maximum Power Transfer
4- Superposition Principal
5- Wheatson Bridge
1.combining resistances in series and Parallel2.The node-voltage technique3.The mesh-current technique
voltage across an element
current passing through an element
Power consumed by an element.
Three techniques to solve circuits:
+-5V 2A 50
+-
50
5V
30
+-5V
2A
50
2A
50=
30
+-
5V=
+-5V 50=
RTh
VTh
+
-
Thevenin equivalent CircuitThevenin
Norton equivalent circuit
RThIsc
Norton
pp. 82-83
Circuit with Resistances and sources
(Controlling variables for any sources must
appear inside)
Two terminal Circuit
VTh
RTh
+
-
Circuit with Resistances and sources
(Controlling variables for any sources must
appear inside)
Two terminal Circuit
VOC =
+-
+-
VThISC ISC
+-
+-VTh
VOC VOC
RTh
RTh
+-
+-
VThVx Vx
RTh
Rx Rx
+-
+-VTh
=
RTh
Two Ways to determine VTh and RTh
VTh & RTh
pp. 82-86
+-
+-
Isc
+-
sc
octh I
VR =
First:
+-
Vth=Voc
Vth
+-
+-
Vth=Voc
+-
Vth
thR
Rth
no dependent source
Second:
Rth
+-
20V 2A
5
20
KCL
AII
II
PSSC
PSPS
62
40520
=+===×+
20V2A
5
20+-
IPS
+-
Ω=
+=
4
201
511
th
Th
R
R
4
24
02205
20
=
=−+−
OC
OCOC
V
VV
24
Example:
Ω== 4624
thR
Example 2.16: Thevenin Equivalent of a Circuit with a Dependent Source
+-
+-
10V2Ix
5
10
Ix
AII
AV
I
xsc
x
63
2510
==
=Ω
=
43.1==SC
OCTh I
VR
8.75VThevenin
Equivalent
+-
10V2Ix
10Ix
5 ISC
VVOC 75.8=
510
102
OCx
OCxx
VI
VII
−=
=+
pp. 86-88
Circuit with Resistances and sources
(Controlling variables for any sources must
appear inside)
Two terminal Circuit
+-
VOC
RThIth
pp. 88-91
+-
+-
+-
Rx,Vx
VOC
ISC
RThIth
RThIth
RThIth
ISC
+-
+-
Isc
+-
Vth=Voc
IThSC
OCTh I
VR =
+-
Rth
no dependent source
+-
Isc
RThITh
+-
20V2A
5
20
Rth
+-
20V 2A
5
20
24
02205
20
=
=−+−
OC
OCOC
V
VVKCL
AII
II
PSSC
PSPS
62
40520
=+===×+
IPS
Ω=
+=
4
201
511
th
Th
R
R 46A
Example:
+-
20V 2A
5
20
46A
+-
4
24
Norton equivalent circuit
Thevenin equivalent Circuit
Sour
ce T
rans
form
atio
n
Using Source Transformation
+-
40V 1A
5
10
I1
I2
+-
40V 10V
5 10
I1+
-
8A 5 10 1AI3 I2
Norton
Thevenin
pp. 91-92
Maximum Power Transfer
Two Terminal Circuit
RL
How much is the maximum power transfer from the Two Terminal Circuit to the Load RL?
RL
RTh
VTh
+
-
Thevenin
Equivalent
( )( ) ( )
( ) 02
4
222
2
2
2
=+
+−+=
+=
+=←=
LTh
LThLThLThTh
L
L
LTh
LThL
LTh
ThLLLL
RRRRRVRRV
dRdP
RRRV
P
RRV
iRIP
Th
ThLThL R
VPRR
4max ==pp. 92-93
Superposition Principle
+-
15V 2A
10
5
IT
+-
VT
VV 5)15(105
51 =
+=
VRIV
R
eqs
eq
66.633.32
33.35/110/1
1
2 =×=×=
Ω=+
=
Voltage divider
VVVVT 66.1166.6521 =+=+=
VT=?
+-
15V
10
5
I1
2A
10
5
V1V2+
-
+-
I2
pp. 95-98
(dependent sources are linear)
+
-Vs
R1
R3Rx Unknown Resistor
R2I1I2
I3
I4
Iga b
Wheatstone Bridge
Adjustable
resistor
Detector
It is used to accurately measure unknown resistances.
pp. 98-100
+
-
Vs
R1
R3Rx
R2I1I2
I3
I4
Iga b
Detector
42
31
II
II
==
433
2211
IRVIR
IRVIR
xab
ab
=+=+
KCL
KVL
433
2211
IRIR
IRIR
x==
21
3
RR
RR x=
Wheatstone Bridge
0=abV
+-
R1
vs1
R2Kix
is2
ix
vT
221
1sx
TsT iKiRv
Rvv =++− 2R
vi T
x =
2121
211
121
2ssT i
KRRRRR
vKRRR
Rv
+++
++=
1121
21 sv
KRRRR
v++
=
2121
212 siKRRR
RRv
++=
21 vvvT +=
