1. Circuit Theorems 1

2.  Introduction  Linearity property  Superposition  Source transformations  Thevenin’s theorem  Norton’s theorem  Maximum power transfer Circuit Theorems2

3. Introduction 3 A large complex circuits A large complex circuits Simplify circuit analysis Simplify circuit analysis Circuit Theorems ‧ Thevenin’s theorem ‧ Norton theorem ‧ Circuit linearity ‧ Superposition ‧ source transformation ‧ max. power transfer ‧ Thevenin’s theorem ‧ Norton theorem ‧ Circuit linearity ‧ Superposition ‧ source transformation ‧ max. power transfer

4. Linearity Property Circuit Theorems4 Homogeneity property (Scaling) Additivity property

5.  A linear circuit is one whose output is linearly related (or directly proportional) to its input  Fig. 4.1 Circuit Theorems5 v V0V0 I0I0 i

6.  Linear circuit consist of ●linear elements ●linear dependent sources ●independent sources  Nonlinear: ●Exponential, square, logarithmic ●Example Circuit Theorems6

7. Example 1  For the circuit shown find I 0 when v s =12V and v s =24V. Circuit Theorems7

8. Example 1  KVL Eqs(4.1.1) and (4.1.3) we get Circuit Theorems8 (1.1) (1.2) (1.3)

9. Example 1 Eq(1.1), we get When Showing that when the source value is doubled, I 0 doubles. Circuit Theorems9

10. Example 2  Assume I 0 = 1 A and use linearity to find the actual value of I 0 in the circuit shown. Circuit Theorems10

11. Example 4.2 Circuit Theorems11

12. Superposition Superposition  The superposition principle states that the voltage across (or current through) an element in a linear circuit is the algebraic sum of the voltages across (or currents through) that element due to each independent source acting alone.  Turn off, killed, inactive source: ●independent voltage source: 0 V (short circuit) ●independent current source: 0 A (open circuit)  Dependent sources are left intact. Circuit Theorems12

13.  Steps to apply superposition principle: 1.Turn off all independent sources except one source. Find the output (voltage or current) due to that active source using nodal or mesh analysis. 2.Repeat step 1 for each of the other independent sources. 3.Find the total contribution by adding algebraically all the contributions due to the independent sources. Circuit Theorems13

14. How to turn off independent sources  Turn off voltages sources = short voltage sources; make it equal to zero voltage  Turn off current sources = open current sources; make it equal to zero current Circuit Theorems14

15.  Superposition involves more work but simpler circuits.  Superposition is not applicable to the effect on power. Circuit Theorems15

16. Example 3  Use the superposition theorem to find v in the circuit shown. Circuit Theorems16

17. Example 3 Since there are two sources, let Voltage division to get Current division, to get Hence And we find Circuit Theorems17

18. Example 4  Find I 0 in the circuit shown using superposition. Circuit Theorems18

19. Example 4 Circuit Theorems19 Fig. 4.10

20. Example 4 Circuit Theorems20

21. Source Transformation  A source transformation is the process of replacing a voltage source v s in series with a resistor R by a current source i s in parallel with a resistor R, or vice versa Circuit Theorems21

22. Circuit Theorems22

23. Equivalent Circuits Circuit Theorems23 i i ++ - - vv v i vsvs -i s

24.  Arrow of the current source positive terminal of voltage source  Impossible source Transformation ●ideal voltage source (R = 0) ●ideal current source (R=  ) Circuit Theorems24

25. Example 6  Use source transformation to find v o in the circuit shown. Circuit Theorems25

26. Example 6 Circuit Theorems26

27. Example 6 we use current division in Fig. (c) to get and Circuit Theorems27

28. Example 7  Find v x in the next figure using source transformation Circuit Theorems28

29. Example 7 Applying KVL around the loop in Fig (b) gives (7.1) Appling KVL to the loop containing only the 3V voltage source, the resistor, and v x yields (7.2) Circuit Theorems29

30. Example 7 Substituting this into Eq.(7.1), we obtain Alternatively thus Circuit Theorems30

31. Summary Circuit Theorems31