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Published byStewart Harper Modified over 3 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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Network Theorems (AC). OBJECTIVES Be able to apply the superposition theorem to ac networks with independent and dependent sources. Become proficient.

Network Theorems (AC). OBJECTIVES Be able to apply the superposition theorem to ac networks with independent and dependent sources. Become proficient.

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