1. Circuit Theorems Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C.

2. Contents Introduction Linearity Property Superposition Source Transformation Thevenin’s Theorem Norton’s Theorem Maximum Power Transfer Summary

3. Introduction To develop analysis techniques applicable to linear circuits To simplify circuit analysis and help handling the complexity

4. Linearity Property Homogeneity (Scaling) + Additivity Homogeneity property: Additivity property: A linear circuit follows the relationship below

5. Superposition Based on linearity property Statement –The voltage across (current through) an element is the algebraic sum of the voltage across (current through) that element due to each independent source acting alone.

6. Example 1 + =

7. Example 2 +=

8. Example 3

9. Source Transformation i1i1 i2i2

10. Applicable to Dependent Sources i1i1 i2i2

11. Example 1

12. Example 2

13. Thevenin’s Theorem A variable element Thevenin equivalent circuit

14. Continued A simple voltage divider =

15. Proof of Thevenin’s Theorem + = = All indep. sources on All indep. sources off +_+_ + _

16. Finding V Th and R Th If no dependent sources included

17. Continued If dependent sources included, two methods can be applied to determine R Th –External voltage source method –External current source method

18. Example 1 = R Th V Th

19. Example 2 = R Th v oc

20. Norton’s Theorem Norton equivalent circuit

21. Proof of Norton’s Theorem + = = All indep. sources on All indep. sources off

22. Example = RNRN ININ

23. Maximum Power Transfer A linear circuit

24. Applications: Source Modeling Voltage source Current source