1. Lecture 11 Thévenin’s Theorem Norton’s Theorem and examples
Background and justification
Examples
Norton’s Theorem and examples
Source Transformations
Maximum Power Transfer
Related educational materials:
Chapter 4.5, 4.6

2. Thévenin’s Theorem
We want to replace a complicated circuit with a simple one without affecting the load
We can do this by taking advantage of superposition

3. Thévenin’s Theorem
Lecture 10: Any linear circuit can be represented by an ideal voltage source in series with a resistance, without affecting any “load” connected to the circuit
Why?

4. Thévenin’s Theorem – “Derivation”
Represent circuit “B” (load) as a current source, providing some voltage
Note that we haven’t changed the i-v characteristics at terminals!

5. “Derivation” – continued
Kill independent sources in circuit A
Get equivalent resistance seen at terminals a-b
Resulting voltage across terminals: v1=RTH·i

6. “Derivation” – continued
2. Replace sources in circuit A and kill current source representing circuit B
Get voltage seen at terminals a-b
Resulting voltage across terminals: v2 = voc

7. “Derivation” – continued
3. Superimpose v1 and v2
Get expression for voltage at terminals of circuit A
Represent as a conceptual “circuit”

8. Creating the Thévenin equivalent circuit
Identify the circuit for which the Thévenin equivalent circuit is desired
Kill sources and determine RTH of the circuit
Re-activate the sources and determine VOC
Place the Thévenin equivalent circuit into the original overall circuit and perform the desired analysis
Note: a slightly different process is necessary if the circuit contains dependent sources

9. Thévenin’s Theorem – example 1
Replace everything except the load resistor R with its Thévenin equivalent

10. Example 1 – Get RTH

11. Example 1 – Get Voc

12. Example 1 – Thévenin circuit

13. Norton’s Theorem
Norton’s Theorem: any linear circuit can be modeled as a current source in parallel with a resistor

14. Norton’s Theorem – “Derivation”
Represent circuit “B” (load) as a voltage source, providing some current
Note that we still haven’t changed the i-v characteristics at terminals!

15. “Derivation” – continued
Kill independent sources in circuit A
Get equivalent resistance seen at terminals a-b
Resulting voltage across terminals:

16. “Derivation” – continued
2. Replace sources in circuit A and kill voltage source representing circuit B
Get current seen at terminals a-b
Resulting current: i2 = -isc

17. “Derivation” – continued
3. Superimpose i1 and i2
Get expression for voltage at terminals of circuit A
Represent as a conceptual “circuit”

18. Creating the Norton equivalent circuit
Identify the circuit for which the Norton equivalent circuit is desired
Kill sources and determine RTH of the circuit
Re-activate the sources, short the output terminals, and determine isc
Place the Norton equivalent circuit into the original overall circuit and perform the desired analysis
Note: a slightly different process is necessary if the circuit contains dependent sources

19. Norton’s Theorem – example 1
Replace everything except the load resistor R with its Norton equivalent

20. Example 1 – Get RTH

21. Example 1 – Get isc

22. Example 1 – Norton circuit

23. Source Transformations
The Thévenin and Norton equivalent circuits both represent the same circuit
They have the same voltage-current characteristics

24. Source Transformations – continued
We can equate the two representations
Solving for i from the Thévenin equivalent
Equating this current with the Norton Equivalent circuit:
So that:

25. Using Source Transformations in Circuit Analysis
Any voltage source in series with a resistance can be modeled as a current source in parallel with the same resistance and vice-versa

26. Source Transformation – example
Use source transformations to determine the voltage v

27. Maximum Power Transfer
We can use Thevenin’s Theorem to show how to transfer the maximum amount of power to a load
Problem: choose RL so that RL receives the maximum power
For maximum power transfer, choose RL = RTH

28. Maximum Power Transfer – example
Choose R so that maximum power is delivered to the load
Previously found the loaded Thévenin equivalent circuit: