Lecture 11 Thévenin’s Theorem Norton’s Theorem and examples

Presentation on theme: "Lecture 11 Thévenin’s Theorem Norton’s Theorem and examples"— Presentation transcript:

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

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

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?

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!

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

“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

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

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

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

Example 1 – Get RTH

Example 1 – Get Voc

Example 1 – Thévenin circuit

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

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!

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

“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

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

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

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

Example 1 – Get RTH

Example 1 – Get isc

Example 1 – Norton circuit

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

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:

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

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

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

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