Nortans Theorem

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ECE201 Lect-14 1 Norton's Theorem (5.3, 8.8) Dr. Holbert March 20, 2006

Transcript of Nortans Theorem

Page 1: Nortans Theorem

ECE201 Lect-14 1

Norton's Theorem (5.3, 8.8)

Dr. Holbert

March 20, 2006

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ECE201 Lect-14 2

Introduction

• Any Thevenin equivalent circuit is in turn equivalent to a current source in parallel with a resistor [source transformation].

• A current source in parallel with a resistor is called a Norton equivalent circuit.

• Finding a Norton equivalent circuit requires essentially the same process as finding a Thevenin equivalent circuit.

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Independent Sources

Circuit with one or more independent

sources

RTh

Norton equivalent circuit

Isc

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No Independent Sources

Circuit without independent sources

RTh

Norton equivalent circuit

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Finding the Norton Equivalent

• Circuits with independent sources:

– Find Voc and Isc

– Compute RTh

• Circuits without independent sources:

– Apply a test voltage (current) source

– Find resulting current (voltage)

– Compute RTh

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Example: Strain Gauge

• Strain is the amount of deformation of a body due to an applied force-it is defined as the fractional change in length.

• Strain can be positive (tensile) or negative (compressive).

• One type of strain gauge is made of a foil grid on a thin backing.

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A Strain Gauge

• The strain gauge’s resistance varies as a function of the strain:

R = GF R

• is the strain, R is the nominal resistance, GF is the Gauge Factor

Backing

Foil

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Typical values

• Measured strain values are typically fairly small-usually less than 10-3.

• GF is usually close to 2.

• Typical values for R are 120, 350, and 1000.

• A typical change in resistance is

R = 2•10-3•120 = 0.24

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Measuring Small Changes in R

• To measure such small changes in resistance, the strain gauge is placed in a Wheatstone bridge circuit.

• The bridge circuit uses an excitation voltage source and produces a voltage that depends on R.

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The Bridge Circuit

R+R

Vex

R

R

R

+– Vout+–

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Norton Equivalent for Any

64

2

R

VI ex

sc

21

64

4

R

RTh

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Thevenin/Norton Analysis

1. Pick a good breaking point in the circuit (cannot split a dependent source and its control variable).

2. Thevenin: Compute the open circuit voltage, VOC.

Norton: Compute the short circuit current, ISC.

For case 3(b) both VOC=0 and ISC=0 [so skip step 2]

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Thevenin/Norton Analysis

3. Compute the Thevenin equivalent resistance, RTh (or impedance, ZTh).

(a) If there are only independent sources, then short circuit all the voltage sources and open circuit the current sources (just like superposition).

(b) If there are only dependent sources, then must use a test voltage or current source in order to calculate

RTh (or ZTh) = VTest/Itest

(c) If there are both independent and dependent sources, then compute RTh (or ZTh) from VOC/ISC.

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Thevenin/Norton Analysis

4. Thevenin: Replace circuit with VOC in series with RTh, ZTh.

Norton: Replace circuit with ISC in parallel with RTh, ZTh.

Note: for 3(b) the equivalent network is merely RTh (or ZTh), that is, no voltage (or current) source.

Only steps 2 & 4 differ from Thevenin & Norton!


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