1. ECE201 Lect-141 Norton's Theorem (5.3, 8.8) Dr. Holbert March 20, 2006

2. ECE201 Lect-142 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. ECE201 Lect-143 Independent Sources Circuit with one or more independent sources R Th Norton equivalent circuit I sc

4. ECE201 Lect-144 No Independent Sources Circuit without independent sources R Th Norton equivalent circuit

5. ECE201 Lect-145 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

6. ECE201 Lect-146 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. ECE201 Lect-147 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

8. ECE201 Lect-148 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 = 210 -3 120  = 0.24 

9. ECE201 Lect-149 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.

10. ECE201 Lect-1410 The Bridge Circuit R+  R V ex R R R +– V out +–+–

11. ECE201 Lect-1411 Norton Equivalent for Any 

12. ECE201 Lect-1412 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]

13. ECE201 Lect-1413 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.

14. ECE201 Lect-1414 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!

15. ECE201 Lect-1415 Class Examples Learning Extension E5.4 Learning Extension E8.15(c)