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Published byStewart Harper Modified over 10 years ago
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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
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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
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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?
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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!
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“Derivation” – continued
Kill independent sources in circuit A Get equivalent resistance seen at terminals a-b Resulting voltage across terminals: v1=RTH·i
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“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
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“Derivation” – continued
3. Superimpose v1 and v2 Get expression for voltage at terminals of circuit A Represent as a conceptual “circuit”
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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
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Thévenin’s Theorem – example 1
Replace everything except the load resistor R with its Thévenin equivalent
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Example 1 – Get RTH
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Example 1 – Get Voc
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Example 1 – Thévenin circuit
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Norton’s Theorem Norton’s Theorem: any linear circuit can be modeled as a current source in parallel with a resistor
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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!
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“Derivation” – continued
Kill independent sources in circuit A Get equivalent resistance seen at terminals a-b Resulting voltage across terminals:
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“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
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“Derivation” – continued
3. Superimpose i1 and i2 Get expression for voltage at terminals of circuit A Represent as a conceptual “circuit”
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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
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Norton’s Theorem – example 1
Replace everything except the load resistor R with its Norton equivalent
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Example 1 – Get RTH
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Example 1 – Get isc
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Example 1 – Norton circuit
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Source Transformations
The Thévenin and Norton equivalent circuits both represent the same circuit They have the same voltage-current characteristics
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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:
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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
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Source Transformation – example
Use source transformations to determine the voltage v
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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
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Maximum Power Transfer – example
Choose R so that maximum power is delivered to the load Previously found the loaded Thévenin equivalent circuit:
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