1. 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
Circuit A
(Linear)
Circuit B A B +
VAB -
IAB
Fall 2001
ENGR-201 Thevenin's Theorem

2. ENGR-201 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.
Circuit A
(Linear)
Circuit B A B +
VAB -
IAB
Circuit B A B +
VAB -
IAB
VTH
RTH
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

3. ENGR-201 Thevenin's Theorem
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.
Circuit A
(Linear)
Circuit B A B +
VAB -
IAB
Circuit B A B +
VAB -
IAB IN RN
The trick is to find the values of VTH and RTH (IN and RN).
Fall 2001
ENGR-201 Thevenin's Theorem

4. ENGR-201 Thevenin's Theorem
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.
Circuit A
(Linear) A B +
VAB = VOC -
IAB = 0 A A B +
VAB = VTH -
IAB = 0 A
VTH
RTH
If the two circuits are equivalent, then VTH = Voc.
Fall 2001
ENGR-201 Thevenin's Theorem

5. ENGR-201 Thevenin's Theorem
Finding VTH and RTH
Consider the other extreme load condition: short circuit where
VAB = 0 A.
Circuit A
(Linear) A B +
VAB = 0 V -
IAB = ISC A B +
VAB = 0 -
VTH
RTH
ISC
If the two circuits are equivalent, then ISC = VTH/RTH 
RTH = VTH/ ISC
Fall 2001
ENGR-201 Thevenin's Theorem

6. Summary: Finding VTH and RTH
In summary, VTH and RTH can be found by performing two tests on a linear circuit:
Circuit A
(Linear) A B +
VAB -
IAB A B +
VAB -
VTH
RTH
IAB =
Open Circuit Test: VTH = VOC
Short Circuit Test: RTH = VTH/ ISC
Circuit A
(Linear) A B +
VAB = VOC -
IAB = 0 A
Circuit A
(Linear) A B +
VAB = 0 V -
IAB = ISC
Q: How practical are these two tests?
Fall 2001
ENGR-201 Thevenin's Theorem

7. 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
Circuit A
(Linear)
Circuit B A B +
VAB -
IAB
Circuit B A B +
VAB -
IAB IN RN
Fall 2001
ENGR-201 Thevenin's Theorem