Norton's Theorem (4.3)

1
Norton's Theorem (4.3)

• Prof. Phillips
• February 26, 2003

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.

3
Independent Sources
Isc
RTh
Circuit with one or more independent sources
Norton equivalent circuit
4
No Independent Sources
RTh
Circuit without independent sources
Norton equivalent circuit
5
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

6
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.

7
A Strain Gauge

• The strain gauges resistance varies as a
  function of the strain
• DR GF e R
• e is the strain, R is the nominal resistance, GF
  is the Gauge Factor

8
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 120W, 350W, and 1000W.
• A typical change in resistance is
• DR 210-3120W 0.24W

9
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 DR.

10
The Bridge Circuit
R
RDR



Vex
Vout
R
R
11
Norton Equivalent for Any e
12
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 VOC0 and ISC0 so skip step
  2

13
Thevenin/Norton Analysis

• 3. Compute the Thevenin equivalent resistance,
  RTh.
• (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 VTest/Itest
• (c) If there are both independent and
  dependent sources, then compute RTh from VOC/ISC.

14
Thevenin/Norton Analysis

• 4. Thevenin Replace circuit with VOC in series
  with RTh.
• Norton Replace circuit with ISC in parallel
  with RTh.
• Note for 3(b) the equivalent network is merely
  RTh, that is, no voltage (or current) source.
• Only steps 2 4 differ from Thevenin Norton!

15
Class Examples