Thevenin and Norton Equivalent Circuits
Read: pages 120 – 133
Problems: 4.53 and 4.68
(Due 10/29/01)
Consider any circuit divided into separate circuits, where the two parts
are connected at two points A and B as shown.
Any Circuit
IAB
Circuit A
(Linear)
Fall 2001
A
+
VAB
B
Circuit B
ENGR-201 Thevenin's Theorem
1
Thevenin’s Theorem
Everything inside the linear circuit (A) can be replaced by an equivalent
circuit that consists of two components, an ideal voltage source in
series with a resistor.
IAB
A
+
Circuit A
Circuit B
VAB
(Linear)
B
IAB
RTH
A
+
+
VTH
Circuit B
VAB
B
Two circuits are equivalent if they produce the same load voltage and
current (VAB and IAB) for every possible load condition.
Fall 2001
ENGR-201 Thevenin's Theorem
2
Norton’s Theorem
Everything inside the linear circuit (A) can be replaced by an equivalent
circuit that consists of two components, an ideal current source in
parallel with a resistor.
IAB
A
+
Circuit A
Circuit B
VAB
(Linear)
B
IAB
IN
RN
A
+
VAB
B
Circuit B
The trick is to find the values of VTH and RTH (IN and RN).
Fall 2001
ENGR-201 Thevenin's Theorem
3
Finding VTH and RTH
Two circuits are equivalent if they produce the same load voltage and
current (VAB and IAB) for every possible load condition. Consider one
extreme load condition: open circuit where IAB = 0 A.
A
IAB = 0 A
+
Circuit A
VAB = VOC
(Linear)
B
RTH
VTH
Fall 2001
+
-
IAB = 0 A
A
+
VAB = VTH
B
If the two circuits are
equivalent, then VTH = Voc.
ENGR-201 Thevenin's Theorem
4
Finding VTH and RTH
Consider the other extreme load condition: short circuit where
VAB = 0 A.
IAB = ISC A
+
VAB = 0 V
-
Circuit A
(Linear)
B
RTH
VTH
+
-
ISC
A
+
VAB = 0
B
If the two circuits are equivalent,
then ISC = VTH/RTH 
RTH = VTH/ ISC
Fall 2001
ENGR-201 Thevenin's Theorem
5
Summary: Finding VTH and RTH
In summary, VTH and RTH can be found by performing two tests on a linear
circuit:
IAB
RTH
IAB
A
A
+
+
Circuit A
+
VAB = VTH
VAB
(Linear)
B
B
Open Circuit Test: VTH = VOC
IAB = 0 A
Circuit A
(Linear)
Short Circuit Test: RTH = VTH/ ISC
IAB = ISC A
A
+
VAB = VOC
B
+
VAB = 0 V
-
Circuit A
(Linear)
B
Q: How practical are these two tests?
Fall 2001
ENGR-201 Thevenin's Theorem
6
Norton’s Theorem: Finding IN and RN
Using arguments similar to the ones for finding RTH an VTH, it can be
shown that :
IN = ISC
and
RN = RTH = VOC/ISC
IAB
Circuit A
(Linear)
IAB
IN
Fall 2001
RN
A
+
VAB
B
A
+
VAB
B
Circuit B
Circuit B
ENGR-201 Thevenin's Theorem
7