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7/8/20
Special Techniques
Superposition Theorem
Source Transformation
Thevenins Theorem
Nortons Theorem
1
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 outputis proportional only to the first power, i.e.,
v1 = 0.6i1-14v2 Linear circuit: composed of independent
sources, linear dependent sources, and linearelements
2
Superposition Theorem
One of the properties of linearity
Definition:
voltage across or current thru anyresistor or source may be calculated byadding all the individual voltage or currents
caused by the separate independentsource acting alone
3
Implementation
Other independentvoltage sources givezero voltage, then actlike short circuits.
Other independentcurrent sources givezero current, then actlike open circuits.
4
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Example
I1 = 1A
I2 = 2A
I total = 1+2 = 3A
5
Example
I1 = 1A
I2 = 0A
I total = 1+0 = 1A
6
Example
Find voltage Vx
7
V
VxV
333.9
42)7/12(6
)7/12(42
)4||3(6
)4||3()42(
=
+
=+
=
8
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V
Vx V
333.3
1042
210
4)3||6(
)3||6()10(
=
+
=+
=
9
V
VxVxVx VV
6333.3333.9
)10()42(
==
+=
10
Example 1
use superposition to find ix
11
Example 1 (cont.)
= 0.2 A'xi
= 0.8 A''xi
= 1.0 Axi
12
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Special Techniques
Superposition Theorem
Source Transformation
Thevenins Theorem
Nortons Theorem
13
Practical voltage source
LssL iRvv =
s
sLsc
soc
R
vi
vv
=
=
14
Practical current source
p
LsL
R
vii =
sLsc
spLoc
ii
iRv
=
=
15
Equivalent practical sources
THNTH
NTH
RIV
RR
=
=
Head of current = +
16
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Equivalent practical sources (cont.)
The two practical sources are equivalent
only with respect to what transpires at theload terminals; they are not equivalentinternally!
Note: goal is to have either all current sources or all
voltage sources in the circuitmaking nodal/meshanalysis easier
17
Special Techniques
Superposition Theorem
Source Transformation
Thevenins Theorem
Nortons Theorem
18
Thevenins Theorem
Equivalent circuit
19
Thevenins Equivalent Circuit
Composed of VTH andRTHconnected 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 findVoc across the load, which is equivalent toVTH.
Open load and evaluate RTH by zeroingout every independent source (opencurrent source, short voltage source).
21
Example
Find Thevenins equivalent circuit and thecurrent passing thruRL given RL = 1
22
0V
10V
0V 0V
6V 6V
VVTH 61032
3=
+=
Find VTH
23
Short voltage source
RTH
=
++
+=
++=
2.13
232
3210
23||210TH
R
Find RTH
24
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Thevenins equivalent circuit
The current thru RL = 1is A423.012.13
6=
+
25
Example
Find Thevenins equivalent circuit
26
Find VTH
0V
5V
0V 0V
3V 3V
VVTH
331 ==
27
Open circuitcurrent source
RTH
=
++=
15
2310THR
Find RTH
28
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Thevenins equivalent circuit
29
Example: Bridge circuit
Find Thevenins equivalent circuit
30
Find VTH
0V
10V
8V 2V
VTH = 8-2 = 6V
31
Find RTH
RTH
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KKK
KKKKRTH
4.28.06.1
1||48||2
=+=
+=
33
Thevenins equivalent circuit
34
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