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Thévenin and Norton
Equivalent Circuits
ELEC 308
Elements 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 twoterminal 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
Vt

Rt

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Circuit Parameters
 The Thévenin resistance is given by
Vt v oc
Rt  
isc isc
 Thus, we can determine a Thévenin
equivalent circuit simply by measuring the
OPEN-CIRCUIT VOLTAGE and SHORTCIRCUIT CURRENT

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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
PL max
Vt2

4Rt
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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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