Ch. 4B – Circuit Theorems II

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Presentation transcript:

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

Motivation

Motivation – Circuit Simplification

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.

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

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.

Example 6. Find the Thevenin equivalent circuit.

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

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.

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

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