dc circuit anays is
TRANSCRIPT
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TECHNIQUES OF DC CIRCUIT ANALYSIS:
Superposition Principle
Thevenins Theorem
Nortons Theorem
Source Transformation
Maximum Power Transfer
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Applies only for LINEARCIRCUIT
Circuit containing linear
elements, linear dependent and
independent sources
A LINEARrelationship
between voltage and
current
What do we mean by a linear relationship?
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What do we mean by a linear relationship?
When the relationship fulfilled 2 properties:
Homogeneity (scaling)
Additivity
f(x) = y f(kx) = ky = kf(x)
f(x) = y f(x1+ x2) = f(x1) + f(x2) = y1+ y2
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Superposition Principle: The voltage across an element ( or thecurrent through an element) of a linear circuit containing more than
one independent source, is the algebraic sum the voltage acrossthat element (or the current through that element) due to each
independent source acting alone.
All other independent sources are KILLED
voltage sources are shorted
current sources are opened
Dependent sources CANNOT be killed !
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Superposition Principle: The voltage across an element ( or thecurrent through an element) of a linear circuit containing more than
one independent source, is the algebraic sum the voltage acrossthat element (or the current through that element) due to each
independent source acting alone.
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Superposition Principle: The voltage across an element ( or thecurrent through an element) of a linear circuit containing more than
one independent source, is the algebraic sum the voltage acrossthat element (or the current through that element) due to each
independent source acting alone.
may involve MORE work
cannot be applied to power calculation find ior v
first (using superposition) before calculating power !
most suitably used when involved with sources of different
properties or types, e.g. different frequencies, mixture ofDC and AC, etc.
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Thevenins Theorem: A linear two-terminal circuit can bereplaced by an equivalent circuit consisting of a voltage source in
series with a resistor
Linear two-
terminal
circuit
Load
+
V
+
V LoadVTh
RTh VTh= ?
RTh= ?
In 1883, M.L. Thevenin proposed a theorem .
I
I
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Thevenins Theorem: A linear two-terminal circuit can bereplaced by an equivalent circuit consisting of a voltage source in
series with a resistor
To determine VTh
Linear two-
terminal
circuit Load
VTh
RTh
Load
=
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Thevenins Theorem: A linear two-terminal circuit can bereplaced by an equivalent circuit consisting of a voltage source in
series with a resistor
To determine VTh
Linear two-terminal
circuit Load
VTh
RTh
open circuit voltage = Voc
+
= VTh
Load
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Thevenins Theorem: A linear two-terminal circuit can bereplaced by an equivalent circuit consisting of a voltage source in
series with a resistor
To determine VTh
Linear two-terminal
circuit
VTh
RTh
open circuit voltage = Voc
+
= VTh
open circuit voltage = Voc
+
Load
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Thevenins Theorem: A linear two-terminal circuit can bereplaced by an equivalent circuit consisting of a voltage source in
series with a resistor
To determine VTh
Linear two-terminal
circuit
VTh
RTh
open circuit voltage = Voc
+
= VTh
open circuit voltage = Voc
+
VTh= Voc= Open circuit voltage
= VTh (Since the circuit is equivalent)
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Thevenins Theorem: A linear two-terminal circuit can bereplaced by an equivalent circuit consisting of a voltage source in
series with a resistor
To determine RTh
Case 1 Network with NO dependent sources
Kill all the independent sources
Find the equivalent R looking between the terminals
Linear
circuit
independent
sources
killed
Rin = RTh
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Thevenins Theorem: A linear two-terminal circuit can bereplaced by an equivalent circuit consisting of a voltage source in
series with a resistor
To determine RTh
Case 2 Network with dependent sources
Kill all the independent sources - dependent sources
stay as they are
Introduce a voltage (or current) source.
Linear
Circuit
ONLY
dependent
sources
killed
+
-vo
io
RThis calculated as:
o
o
Th
i
v
R
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Nortons Theorem: A linear two-terminal circuit can be replacedby an equivalent circuit consisting of a current source in parallel with
a resistor
43 years later, E.L. Norton proposed a similar theorem. .
IN= ?
RN= ?
Linear two-
terminal
circuit
Load
+
V
I
+
V
I
LoadIN RN
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Nortons Theorem: A linear two-terminal circuit can be replacedby an equivalent circuit consisting of a current source in parallel with
a resistor
To determine IN
Linear
circuit
ININ
RN
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Nortons Theorem: A linear two-terminal circuit can be replacedby an equivalent circuit consisting of a current source in parallel with
a resistor
IN= Short circuit current
To determine IN
INRN
Linear
circuitShort circuit current = IN
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Nortons Theorem: A linear two-terminal circuit can be replacedby an equivalent circuit consisting of a current source in parallel with
a resistor
To determine IN
IN= Short circuit currentIN
RN
Linear
circuitShort circuit current = IN
IN= Isc= Short circuit current
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Nortons Theorem: A linear two-terminal circuit can be replacedby an equivalent circuit consisting of a current source in parallel with
a resistor
To determine RN
SIMILAR METHOD AS HOW TO OBTAIN RTh
RN= RTh
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Relationship between Nortons and Thevenins equivalents
INRN
b
a
VThRTh
b
a
Since both circuits are equivalent, vocmust
be the sameTh
Thh
V
R s
o
v
NNoc RIv +
Thoc Vv +
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Source Transformation:A tool used to simplify circuit; a process ofreplacing a voltage source in series with a resistor by a current source
in parallel with a resistor or vice versa
vs
R
a
b
is R
a
b
If the circuit is equivalent at terminala-b
, their open-circuit andshort-circuit characteristics are similar
voc= vs
isc= vs/R
voc= isR
isc= is
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Source Transformation:A tool used to simplify circuit; a process ofreplacing a voltage source in series with a resistor by a current source
in parallel with a resistor or vice versa
vs
R
a
b
is R
a
b
voc= vs
isc= vs/R
voc= isR
isc= is
RivorR
vi ss
ss
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Maximum Power Transfer
Linear circuitRL What would be the value of RLfor
power delivered to it become
MAXIMUM?
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Maximum Power Transfer
Linear circuitRL What would be the value of RLfor
power delivered to it become
MAXIMUM?
VTh
RTh
L
2
LTh
L
Th
LR
RR
RV
P L
2
LTh
Th RRR
V
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0 10 20 30 40 50 600.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
RL
p
Maximum Power Transfer
L
2
LTh
L
Th
LR
RR
RV
P L
2
LTh
Th RRR
V
Rl=linspace(1,60,500);
Vth=10;
Rth=12;
p=((Vth./(Rl+Rth)).^2).*Rl;
plot(Rl,p,'r');
grid;
Maximum power
RL= 12
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Maximum Power Transfer
L
2
LTh
L
Th
LR
RR
R
VP L
2
LTh
Th RRR
V
Mathematically, we evaluate RLwhen 0dRdP
L
L
0)RR(
VR
)RR(
V2
dR
dP2
LTh
2Th
L3LTh
2Th
L
L
0
)RR(
RRR2V
dR
dP3
LTh
LThL
2
Th
L
L
ThL RR
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Using PSpice to verify Nortons and Thevenins Theorems
Find Thevenin equivalent at terminals a-b
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Using PSpice to verify Nortons and Thevenins Theorems
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Using PSpice to verify Nortons and Thevenins Theorems
0
R9
2
-+
+-
E2
E
R8
2
R7
6
R6
4
I3
1Aac
TRAN =
0
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Using PSpice to verify Nortons and Thevenins Theorems
0
R9
2
-+
+-
E2
E
R8
2
R7
6
R6
4
I3
1Aac
TRAN =
0
I4
1Aac
TRAN =
1
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Using PSpice to verify Nortons and Thevenins Theorems
R8
2
6.000V
1.333V
R6
4
4.000V
R7
6
I3
1Aac
TRAN =
0
0
R9
2
-+
+-
E2
E
I4
1Aac
TRAN =
1
RTh= 6/1 = 6
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Using PSpice to verify Nortons and Thevenins Theorems
I4
1Aac
TRAN =
0
R8
2
R7
6
20.00V
R6
4
6.667V
0
-+
+-
E2
E
20.00V
I3
1Aac
TRAN =
5
R9
2
VTh= 20V