Th é venin and Norton Equivalent Circuits

Thévenin and Norton Equivalent Circuits

ELEC 308Elements of Electrical Engineering

Dr. Ron Hayne

Images Courtesy of Allan Hambley and Prentice-Hall

Equivalent Circuits

Two-terminal circuit Circuit that has any complex interconnection of

resistances and sources Has ONLY two points that can be connected to

other circuits We will learn how to represent complex two-

terminal circuits by simple equivalent circuits

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Thévenin Equivalent Circuits

Consists of voltage source in series with a resistance

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Circuit Parameters

The Thévenin source voltage is equal to the open-circuit voltage of the original network, or Vt = voc

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Circuit Parameters

The Thévenin short-circuit current is given by

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Vt

Rt

Circuit Parameters

The Thévenin resistance is given by

Thus, we can determine a Thévenin equivalent circuit simply by measuring the OPEN-CIRCUIT VOLTAGE and SHORT-CIRCUIT CURRENT

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Rt Vt

isc

voc

isc

Example 2.16

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Exercise

Find the Thévenin equivalent circuit

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Norton Equivalent Circuits

Consist of independent CURRENT source in PARALLEL with a resistance

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Circuit Parameters

The Norton source current is equal to the short-circuit current of the original network, or In = isc

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Circuit Analysis Algorithm Complete two of the following:

Determine the open-circuit voltage (Vt = voc). Determine the short-circuit current (In = isc). Zero the sources and find the Thévenin resistance Rt

looking back into the terminals. Use Ohm’s Law (Vt=InRt) to compute the remaining

parameter. Draw one of the following:

Thévenin equivalent circuit with independent VOLTAGE source Vt in SERIES with Rt

Norton equivalent circuit with independent CURRENT source In in PARALLEL with Rt

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Exercise 2.29

Find the Norton equivalent circuit

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Maximum Power Transfer

Consider the two-terminal circuit and load resistance below. What value of RL would deliver maximum to the load resistance RL?

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Maximum Power Transfer

The load resistance RL that absorbs the maximum power from a two-terminal circuit is equal to the Thévenin resistance, or RL=Rt

The maximum power transferred to the load resistance is given by

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PL max Vt

2

4Rt

Example 2.21

Find the load resistance for max power transfer Find the max power

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Principle of Superposition

Suppose we have a circuit with MULTIPLE independent sources

We wish to determine a specific response (current or voltage) in the circuit

We can EASILY determine the response due to a SINGLE independent source (by zeroing out the other independent sources)

The SUPERPOSITION principle states that the total response is the SUM of the responses to each of the independent sources acting INDIVIDUALLY

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Superposition Illustration

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Strain Measurements

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Wheatstone Bridge

Circuit used to measure UNKNOWN resistances

Used by ME’s and CE’s to measure the resistances of strain gauges in experimental stress studies of machines and buildings

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Wheatstone Bridge

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Summary

Thevenin Equivalent Circuit Norton Equivalent Circuit Maximum Power Transfer Superposition Wheatstone Bridge

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