th é venin and norton equivalent circuits
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Th é venin 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 - PowerPoint PPT PresentationTRANSCRIPT
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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