l4 thevinin norton superposition
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Introduction to electronics IIT KanpurLecturesTRANSCRIPT
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L4: Basic Circuit Analysis
S Sundar Kumar Iyer
Dept. of Electrical Engineering
IIT Kanpur
Acknowledgements to Baquer Mazhari, A.R. Harish, Adrish Banerjee
07.01.2013
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Recap L3
• Equivalent Circuit – Resistance; series, parallel, …
• Node and Mesh Analysis
Take home message
• Basic results of resistance combination
• Series-parallel analysis not enough
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v1 v2
v3
Node 1 and node 2 are merged together into a super node. KCL is applied to the super node
Sum of currents leaving a super node is zero
1 3 2 31 2
2 1 3 4
0v v v vv v
R R R R
− −+ + + =
Super Node
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Mesh-3
Super mesh
Super Mesh
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Today Let Us Look at …
• Thévenin Equivalent
• Norton Equivalent
• Superposition
The above a useful tools for circuit analysis
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Any circuitAny circuit
Thévenin Equivalent Circuits
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We can apply Thevenin’s theorem to any part of the circuit
Vt1
Rt1
Vt2
Rt2
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Thévenin Equivalent Circuits
What is Vt ?
t o cV v=
Any circuit
Any circuit
+
Voc
-
+
Voc
-
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Thévenin Equivalent Circuits
What is Rt ?
scisc
i
Any circuitAny circuit
t oct
sc sc
V vR
i i= =
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Summary
t o cV v=
+
Voc
-
o ct
sc
vR
i=
sci
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Examples
t o cV v=
+
Voc
-
2
2 1
1 5 5t
RV
R R= × =
+
1
0 .1 5ssc
vi A
R= =
3 3 .3o ct
sc
vR
i= = Ω
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Currents and voltages in the circuit are only due to Independent Sources
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Finding the Thévenin Resistance Directly
Suppose we make all independent sources zero in the circuit
Circuit with no Independent sources
tR
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1.Turn off independent sources in the original network:
-A voltage source becomes a short circuit
-A current source becomes an open circuit
2. Compute the resistance between the terminals
Finding the Thévenin Resistance Directly
Circuit with no Independent sources
tR
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0 V
0 A
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5 2 04
5 2 0eq
R×
= = Ω+
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Find Thévenin resistance for each of the circuits shown below
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Circuit with dependent Sources
?t
R =
VZ
IZ
Zt
Z
VR
I=
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Norton’s equivalent
sci
sci
n scI i=
Any circuit Any circuit
How do we find IN ?
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Norton’s equivalent
+
Voc
-
+
Voc
-
o c n tv I R= ×o c
t
sc
vR
i=
Any circuit Any circuit
How do we find RN ?
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Norton’s equivalent: Summary
n scI i=o c
t
sc
vR
i=
sci
+
Voc
-
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Examples
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tn
t
VI
R=
t n tV I R= ×
Source Transformation
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Example
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Use source transformation to solve for the indicated currents
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Linearity and Superposition
IRV =
kVkIR =
Increasing the current by a constant k
RIV 11 =
Response to two excitations:
RIV 22 =
( )212121 VVRIRIRIIV +=+=+=
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The superposition principle states that the total response is the sum of the responses to each of the independent sources acting individually.
Superposition Principle
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Example
Circuit with only voltage source active. Current source is open circuited.
Circuit with only current source active. Voltage source is open circuited.
1 2Ti i i= +1 2Tv v v= +
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Example
1 2Ti i i= +1 2Tv v v= +
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10V is discarded by short circuit
Example
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Maximum Power Transfer for dc circuits
RL
R
VS
What value of RL will give rise to maximum load power ?
S
L
VI
R R=
+
2 2
2( )
LL L S
L
RP I R V
R R= = ×
+
0L
L
P
R
∂=
∂
LR R=2
m ax4
SL
L
VP
R=
I
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RL5V
1KΩ 1 6 .2 5L LR K P m W= ⇒ =
1 0 2L LR K P m W= ⇒ =
0 .2 3 .4 7L LR K P m W= ⇒ =
Maximum power is delivered to the load when RL = R
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General Case
RL
Resistors and Sources RLVt
Rt
Maximum power is delivered to the load when RL = Rt
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Using Thevenin’s theorem, find the equivalent circuit to the left of the terminals in the circuit shown below. Hence find i.
6o cv V= 3tR = Ω
1 .5i A=