Circuit Theorems
4.1 Superposition Theorem
4.2 Source Transformation,
Thevenin’s and Norton’s
Theorem
4.3 Maximum Power Transfer
1
Learning Outcomes
1. Discuss the Superposition
p p
Principles
p
2. Solve circuit problems using Superposition
theorem
3. Apply the Source Transformation in the
circuits
4. Carry out the Thevenin's and Norton's
Theorem in the circuits
5. Describe Maximum Power Transfer
2
SUPERPOSITION THEOREM
3
Superposition Theorem
Superposition : the voltage across (or
current through) an element in a linear
circuits is the algebraic sum of the voltage
across (or current through) that element
due to each independent source acting
alone.
Current Source Æ open circuit(0 A)
Voltage Source Æ short circuit (0 V)
4
Superposition Theorem
Step to apply:
1. Turn off all independent sources except
one source. Find the output
p ((voltage
g or
current) due to that active source.
2. Repeat
p
step
p 1 for each other
independent sources.
3. Find the total contribution by adding
algebraically all the contribution due to
the independent source.
5
SOURCE TRANSFORMATION
6
Source Transformation
Source transformation :
replacing a voltage source vs in
series with a impedance Z by a
currentt source is in
i parallel
ll l with
ith a
impedance Z, or vice versa.
7
Source Transformation
8
THEVENIN’S
’ THEOREM
9
Thevenin’s Theorem
Thevenin’s theorem : a linear two
terminal circuit can be replaced by an
equivalent circuit consisting of a
voltage VTh in series with an impedance
ZTh , where VTh is the open circuit
voltage at the terminals and ZTh is the
input or equivalent impedance at the
terminals when the independent source
are turned off.
10
Thevenin’s Theorem
11
Thevenin’s Theorem
Finding VTh and ZTh
12
Thevenin’s Theorem
Z
Finding ZTh when circuit has dependent sources
13
Thevenin’s Theorem
Circuit with load
VTh
IL =
RTh + RL
RL
VL = RL I L =
VTh
RTh + RL
14
NORTON’S
’ THEOREM
15
Norton’s Theorem
Norton’s Theorem : a linear twoterminal circuit can be replaced by an
equivalent circuit consisting of a current
source IN in parallel with an impendence
ZN, where IN is the short circuit current
through the terminals and ZN is the input
or equivalent impedance at the terminals
when the independent source are turned
off.
16
Norton’s Theorem
RN = RTh
17
Norton’s Theorem
Fi di N
Finding
Norton current IN.
I N = isc
VTh
IN =
RTh
18
Thevenin and Norton Equivalent
VTh = voc
I N = isc
voc VTh
RTh =
=
= RN
isc
IN
19
MAXIMUM POWER
TRANSFER
20
Maximum Power Transfer
Maximum power : transferred to
the load when the load resistance
equals the Thevenin resistance as
seen from the load (RL = RTh)
21
Maximum Power Transfer
R L = R Th
p max
V Th2
=
4 R Th
22