Nortans Theorem

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Nortans Theorem

  1. 1. Norton's Theorem (5.3, 8.8) Dr. Holbert March 20, 2006 ECE201 Lect-14
  2. 2. Introduction <ul><li>Any Thevenin equivalent circuit is in turn equivalent to a current source in parallel with a resistor [source transformation]. </li></ul><ul><li>A current source in parallel with a resistor is called a Norton equivalent circuit. </li></ul><ul><li>Finding a Norton equivalent circuit requires essentially the same process as finding a Thevenin equivalent circuit. </li></ul>ECE201 Lect-14
  3. 3. Independent Sources ECE201 Lect-14 Circuit with one or more independent sources R Th Norton equivalent circuit I sc
  4. 4. No Independent Sources ECE201 Lect-14 Circuit without independent sources R Th Norton equivalent circuit
  5. 5. Finding the Norton Equivalent <ul><li>Circuits with independent sources: </li></ul><ul><ul><li>Find V oc and I sc </li></ul></ul><ul><ul><li>Compute R Th </li></ul></ul><ul><li>Circuits without independent sources: </li></ul><ul><ul><li>Apply a test voltage (current) source </li></ul></ul><ul><ul><li>Find resulting current (voltage) </li></ul></ul><ul><ul><li>Compute R Th </li></ul></ul>ECE201 Lect-14
  6. 6. Example: Strain Gauge <ul><li>Strain is the amount of deformation of a body due to an applied force-it is defined as the fractional change in length. </li></ul><ul><li>Strain can be positive (tensile) or negative (compressive). </li></ul><ul><li>One type of strain gauge is made of a foil grid on a thin backing. </li></ul>ECE201 Lect-14
  7. 7. A Strain Gauge <ul><li>The strain gauge’s resistance varies as a function of the strain: </li></ul><ul><li> R = GF  R </li></ul><ul><li> is the strain, R is the nominal resistance, GF is the Gauge Factor </li></ul>ECE201 Lect-14 Backing Foil
  8. 8. Typical values <ul><li>Measured strain values are typically fairly small-usually less than 10 -3 . </li></ul><ul><li>GF is usually close to 2. </li></ul><ul><li>Typical values for R are 120  , 350  , and 1000  . </li></ul><ul><li>A typical change in resistance is </li></ul><ul><li> R = 2•10 -3 •120  = 0.24  </li></ul>ECE201 Lect-14
  9. 9. Measuring Small Changes in R <ul><li>To measure such small changes in resistance, the strain gauge is placed in a Wheatstone bridge circuit. </li></ul><ul><li>The bridge circuit uses an excitation voltage source and produces a voltage that depends on  R . </li></ul>ECE201 Lect-14
  10. 10. The Bridge Circuit ECE201 Lect-14 R+  R V ex R R R + – V out + –
  11. 11. Norton Equivalent for Any  ECE201 Lect-14
  12. 12. Thevenin/Norton Analysis <ul><li>1. Pick a good breaking point in the circuit (cannot split a dependent source and its control variable). </li></ul><ul><li>2. Thevenin : Compute the open circuit voltage, V OC . </li></ul><ul><li>Norton : Compute the short circuit current, I SC . </li></ul><ul><li>For case 3( b ) both V OC =0 and I SC =0 [so skip step 2] </li></ul>ECE201 Lect-14
  13. 13. Thevenin/Norton Analysis <ul><li>3. Compute the Thevenin equivalent resistance, R Th (or impedance, Z Th ). </li></ul><ul><li>( a ) If there are only independent sources, then short circuit all the voltage sources and open circuit the current sources (just like superposition). </li></ul><ul><li>( b ) If there are only dependent sources, then must use a test voltage or current source in order to calculate </li></ul><ul><li>R Th (or Z Th ) = V Test / I test </li></ul><ul><li>( c ) If there are both independent and dependent sources, then compute R Th (or Z Th ) from V OC / I SC . </li></ul>ECE201 Lect-14
  14. 14. Thevenin/Norton Analysis <ul><li>4. Thevenin : Replace circuit with V OC in series with R Th , Z Th . </li></ul><ul><li>Norton : Replace circuit with I SC in parallel with R Th , Z Th . </li></ul><ul><li>Note: for 3( b ) the equivalent network is merely R Th (or Z Th ), that is, no voltage (or current) source. </li></ul><ul><li>Only steps 2 & 4 differ from Thevenin & Norton! </li></ul>ECE201 Lect-14

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