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Thevenin’s Theorem
Norton’s Theorem
Maximum Power Transfer
Thevenin’s Theorem

Thevenin’s Theorem says that a linear
two-terminal circuit can be replaced by an
equivalent circuit consisting of a voltage
source VTh in series with a resistor RTh,
where VTh is the open circuit voltage at
the terminals and RTh is the input or
equivalent resistance at the terminals
when the independent sources are turned
off.
V Th  V oc
R Th  R In
Thevenin’s Theorem
Thevenin’s Theorem is important because
it replaces a large circuit with a single
independent voltage source and a single
resistor.
 Case 1: If the network has no dependent
sources, turn off all independent sources.
RTh is the input resistance of the network
looking between terminals a and b.

Thevenin’s Theorem
Case 2: If the network has dependent sources,
turn off all independent sources. Do not turn
off dependent sources because they are
controlled by circuit variables.
 Apply a voltage source vo and determine the
resulting current, or apply a current source io
and determine the resulting voltage.
 Then R TH  v o . You may assume any value of
io
vo and io.

Examples

Find the Thevenin equivalent of the circuit
shown to the left of the terminals a-b.
Then find the current through RL = 6, 16,
and 36 Ω.
Examples

We find RTH by turning off all independent
sources. This is the resulting circuit.
Examples

To find VTH, consider the circuit below.
Examples

The Thevenin equivalent circuit:
Examples

Find the Thevenin equivalent of the circuit
at terminals a-b.
Examples

Since the circuit has a dependent source, to find RTH we set the
independent source equal to zero but leave the dependent source
alone. However, we have to apply a voltage source vo and
determine the resulting current io.
Examples

To get VTH, we find voc in the circuit.
Examples
 VTH
= voc = 6i2 = 20 V
Norton’s Theorem

Norton’s Theorem says that a linear twoterminal circuit can be replaced by an
equivalent circuit consisting of a current
source IN in parallel with a resistor RN,
where IN is the short-circuit current
through the terminals and RN is the input
or equivalent resistance at the terminals
when the independent sources are turned
off.
Norton’s Theorem

We find RN in the same way we find RTh.
In fact, from what we know about source
transformation,
R N  R Th
IN 
V Th
R Th
Examples

Find the Norton equivalent circuit at
terminals a-b.
Examples

We find RN in the same way we find RTh.

To find IN, we short-circuit terminals a and b. Ignore the
5 Ω resistor because it has been short-circuited.
Examples

Alternatively, we may determine IN from
VTh/RTh.
Examples
 I2 = 1A = iSC = IN
 This is the Norton
equivalent circuit.
Maximum Power Transfer

Maximum power is transferred to the load when the
load resistance equals the Thevenin resistance as seen
from the load.
R L  R Th
p max 
V
2
Th
4R Th
, for R L  R Th
2






v


2
Th


p  i RL  

R L , for R L  R Th






R

R
 

Th
L




Examples

Find the value of RL for maximum power
transfer in the circuit.
Examples

We need to find VTh and RTh. To get RTh,
we use the circuit.
Examples

To get VTh, use the circuit below.
 VTh
= 22 V; for maximum power transfer,
RL = RTh = 9 Ω
 Max Power is: