1. Lecture 371 Norton Equivalent Circuits

2. Lecture 372 Introduction Any Thevenin equivalent circuit is in turn equivalent to a current source in parallel with a resistor. 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. Lecture 373 Independent Sources Circuit with one or more independent sources R Th Norton equivalent circuit I sc

4. Lecture 374 No Independent Sources Circuit without independent sources R Th Norton equivalent circuit

5. Lecture 375 Finding the Norton Equivalent Circuits with independent sources: –Find V oc and I sc –Compute R Th Circuits w/o independent sources: –Apply a test voltage (current) source –Find resulting current (voltage) –Compute R Th

6. Lecture 376 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. Lecture 377 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. Lecture 378 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 

9. Lecture 379 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 exitation source voltage source and produces a voltage that depends on  R.

10. Lecture 3710 The Bridge Circuit R+  R V ex + - R R R + - V out

11. Lecture 3711 Find the Norton Equivalent 10V + - 120  + - 120.24  120 

12. Lecture 3712 Find V oc 10V + - 120  + - 120.24  120  V oc

13. Lecture 3713 10V + - 120  + - 120.24  120  V oc V1V1 V2V2

14. Lecture 3714 Compute V oc

15. Lecture 3715 Find I sc 10V + - 120  120.24  120  I sc

16. Lecture 3716 10V + - 120  120.24  120  I sc VxVx

17. Lecture 3717 Compute R Th

18. Lecture 3718 The Norton Equivalent 41.6  A 120.18 

19. Lecture 3719 Norton Equivalent for Any 

20. Lecture 3720