- The document discusses Norton's Theorem, which states that any Thevenin equivalent circuit is equivalent to a current source in parallel with a resistor, known as a Norton equivalent circuit. - Finding the Norton equivalent circuit involves computing the short circuit current and then the equivalent resistance, similar to finding the Thevenin equivalent circuit. - An example of applying Norton's Theorem to a strain gauge circuit is provided, where the resistance of the strain gauge varies with applied strain and is measured using a Wheatstone bridge circuit.

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

3. Independent Sources ECE201 Lect-14 Circuit with one or more independent sources R Th Norton equivalent circuit I sc

4. No Independent Sources ECE201 Lect-14 Circuit without independent sources R Th Norton equivalent circuit

5. Finding the Norton Equivalent Circuits with independent sources: Find V oc and I sc Compute R Th Circuits without independent sources: Apply a test voltage (current) source Find resulting current (voltage) Compute R Th ECE201 Lect-14

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. ECE201 Lect-14

7. 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 ECE201 Lect-14 Backing Foil

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 120  , 350  , and 1000  . A typical change in resistance is  R = 2•10 -3 •120  = 0.24  ECE201 Lect-14

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  R . ECE201 Lect-14

10. The Bridge Circuit ECE201 Lect-14 R+  R V ex R R R + – V out + –

11. Norton Equivalent for Any  ECE201 Lect-14

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, V OC . Norton : Compute the short circuit current, I SC . For case 3( b ) both V OC =0 and I SC =0 [so skip step 2] ECE201 Lect-14

13. Thevenin/Norton Analysis 3. Compute the Thevenin equivalent resistance, R Th (or impedance, Z Th ). ( 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 R Th (or Z Th ) = V Test / I test ( c ) If there are both independent and dependent sources, then compute R Th (or Z Th ) from V OC / I SC . ECE201 Lect-14

14. Thevenin/Norton Analysis 4. Thevenin : Replace circuit with V OC in series with R Th , Z Th . Norton : Replace circuit with I SC in parallel with R Th , Z Th . Note: for 3( b ) the equivalent network is merely R Th (or Z Th ), that is, no voltage (or current) source. Only steps 2 & 4 differ from Thevenin & Norton! ECE201 Lect-14