Download Thevenin`s Theorem

Introduction
• Thevenin’s Theorem is a very important
and useful theorem.
• It is a method for the reduction of a portion
of a complex circuit into a simple one.
• It reduces the need for repeated solutions
of the same sets of equations.
Thevenin’s Theorem
V-I Characteristic of Thevenin Equivalent
Thevenin Equivalent Circuit
Any two-terminal linear network, composed of
voltage sources, current sources, and resistors,
can be replaced by an equivalent two-terminal
network consisting of an independent voltage
source in series with a resistor.
Network of
Sources
and
Resistors
.
RTh
i a
+
v
b
.
Arbitrary
Network
i
VTh
RTh
i
.
a
+
.V
v = VTh-RThi
VTh
v
b
.
.
a
+
v
Th
0
.i
i
sc
Arbitrary
Network
v
b
.
1
Finding VTh and RTh
•
RTh
Open circuit across
terminals
Finding VTh and RTh – Cont’d
.
i a
•
+
VTh
i = 0, v = voc = vTh
voc=VTh
.
v = 0, i = isc =
-
b
.
a
Calculate the opencircuit voltage in the
original network, voc
voc
.
-
VTh = voc
b
Thevenin Equivalent - Example
Find the Thevenin equivalent with respect to terminals a,b.
25 V
20 Ω
4Ω
.
a
3A
.
b
RTh =
RTh
.
i a
isc=VTh/RTh
VTh
vTh
RTh
Calculate the shortcircuit current in the
original network, isc
+
Network of
Sources
and
Resistors
5Ω
Short circuit across
terminals
.b
.
a
Network of
Sources
and
Resistors
voc
isc
isc
.
b
Alternative Method of finding RTh
-- for circuits containing only independent sources
1. Set all independent sources to zero
2. Find equivalent resistance Req of the dead
circuit between the terminals
Circuit with
all
independent
sources set
equal to
zero
.
a
Req
.
b
RTh = Req
2
Alternative Method of finding RTh
-- for circuits containing dependent sources
1. Set all independent
sources to zero
2. Apply either a test
voltage source v0 (or
a test current
source i0 ) to the
terminals
3. Calculate i0 (or v0 )
v0
RTh =
i0
Circuit
with all
independe
nt sources
set equal
to zero
Circuit
with all
independe
nt sources
set equal
to zero
.a
.b
Thevenin Equivalent - Example
Find the Thevenin equivalent of the following circuit. If a 10Ω resistor
is connected between the terminals, what current will flow in it?
i0
v0
- +
3Ω
2i1
a
o
i1
10 A
.
4Ω
6Ω
a
+
v0
.
-
i0
o
b
b
3