1. Ch. 4B – Circuit Theorems II
Thevenin’s Theorem
- Any linear circuit can be reduced to
a voltage source in series with a resistor
Norton’s Theorem
- Any linear circuit can be reduced to
a current source in parallel with a resistor

2. Motivation

3. Motivation – Circuit Simplification

4. Ch 4B - Thevenin’s Theorem
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 = Voc = open-circuit voltage at the terminals
RTh = equivalent resistance at the terminals with all the independent sources turned off.

5. Example 5. Find the Thevenin equivalent circuit with respect to terminals a-b. Find the current through RL = 6, 16, and 36 .
Ans: 30V, 4

7. Thevenin Equiv. Circuit: with dependent sources
VTh = Voc = open-circuit voltage at the terminals
RTh = equivalent resistance at the terminals with all the independent sources turned off.
Finding RTh:
Turn off all independent sources.
Apply either:
A test voltage source Vo  Find Io.
A test current source Io  Find Vo.
c) RTh = Vo/Io
Note: Easier to use test voltage or test current of value ONE.

8. Example 6. Find the Thevenin equivalent circuit.

10.  Norton’s Theorem - A corollary of to Thevenin’s Theorem
RN = RTh, and IN = VTh/Rth
Finding Norton Current:

11. Norton Equivalent Circuit
A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source IN in parallel with a resistor RN, where:
IN = Isc = short-circuit current through the terminals
RN = equivalent resistance at the terminals with all the independent sources turned off.

12. Example 7. Find the Norton equivalent circuit.
Answer: 1A, 4 ohms

14. Maximum Power Transfer
Find the value of the load resistor that will receive maximum power from the circuit.