Impedance parameters

Impedance parameters in Two Port Network...

1. Input Port Output Port + _ _ + V 1 V 2 I 1 I 2 Z P A R A M E T E R S I M P E D A N C E Copyright © 2012 Ahmad Nauman. All Rights Reserved

2. Linear Network V 1 V 2 I 1 I 2 Introduction A two-port network may be voltage-driven as or current-driven as Linear Network I 1 I 2 + _ V 1 _ + V 2 Copyright © 2012 Ahmad Nauman. All Rights Reserved

3. From previous Figures Only two of the four variables ( V 1 , V 2 , I 1 and I 2 ) are independent/known . The other two can be found using equation (a) (a) And in matrix form as Copyright © 2012 Ahmad Nauman. All Rights Reserved

4. or Where z terms are called impedance parameters or simply z-parameters Copyright © 2012 Ahmad Nauman. All Rights Reserved

5. Linear Network V 1 I 1 I 2 =0 _ + V 2 The values of the parameters can be evaluated by setting I 2 = 0 (output port open-circuited). Copyright © 2012 Ahmad Nauman. All Rights Reserved

6. Linear Network V 1 I 1 =0 The values of the parameters can be evaluated by setting I 1 = 0 (output port open-circuited). V 2 I 2 _ + Copyright © 2012 Ahmad Nauman. All Rights Reserved

7. Open Circuit Transfer impedance from port 1 to port 2. Open Circuit Transfer impedance from port 2 to port 1. Copyright © 2012 Ahmad Nauman. All Rights Reserved

8. Since the z-parameters are obtained by open-circuiting the input or output port, they are also called the open-circuit impedance parameters . Since they are obtained as a ratio of voltage and current. And the parameters are obtained by open-circuiting port 2 ( I 2 = 0) or port1 ( I 1 = 0). Units of z-parameter are in ohms’ ( Ω ) Copyright © 2012 Ahmad Nauman. All Rights Reserved

9. Impedance parameters are commonly used; In the synthesis of filter. They are also useful in the design and analysis of impedance-matching networks. A nd power distribution networks. Usage: Copyright © 2012 Ahmad Nauman. All Rights Reserved

10. T-network + _ _ + V 1 V 2 I 1 I 2 General form is Copyright © 2012 Ahmad Nauman. All Rights Reserved

11. T-network + _ _ + V 1 V 2 I 1 I 2 Find the z-parameters. Copyright © 2012 Ahmad Nauman. All Rights Reserved

12. + _ V 1 I 1 Applying KVL in loop 1 I 2 But we also know that Copyright © 2012 Ahmad Nauman. All Rights Reserved

13. _ + V 2 I 1 I 2 Applying KVL in loop 2 But we also know that

14. + _ _ + V 1 V 2 I 1 I 2 And the z-parameters are Copyright © 2012 Ahmad Nauman. All Rights Reserved

15. D-Problem 17.8(a) - Hayt + _ _ + V 1 V 2 Figure 17.19 (a) Find the z-parameters. Copyright © 2012 Ahmad Nauman. All Rights Reserved

16. + _ _ + V 1 V 2 Solution: As we know that z-parameters in T Network are So from above figure Copyright © 2012 Ahmad Nauman. All Rights Reserved

17. + _ _ + V 1 V 2 Solution: AnsweR Copyright © 2012 Ahmad Nauman. All Rights Reserved

18. Series connection Network A + _ _ + V 1 V 2 I 1 =I 1A Network B I 1 =I 1B I 1 + + _ _ I 2 =I 2 A I 2 =I 2B + + _ _ I 2 V 1A V 1B V 2A V 2B If each two-port has common reference node for its input and output, and if the references are connected together as indicated in Figure. Copyright © 2012 Ahmad Nauman. All Rights Reserved

19. Series connection I 1 flows through the input ports of the two networks in series. A similar statement holds for I 2 . Thus, ports remain ports after the interconnection. It follows that I = I A = I B. And So Where Copyright © 2012 Ahmad Nauman. All Rights Reserved

20. _ + V 2 I 2 Thévenin Equivalent From this circuit (a) Copyright © 2012 Ahmad Nauman. All Rights Reserved

21. As we know that From eq. (a) We also know that (b) (c) Copyright © 2012 Ahmad Nauman. All Rights Reserved

22. Thus output impedance in terms of z-parameters Copyright © 2012 Ahmad Nauman. All Rights Reserved

23. _ + V 2 I 2 If the generator impedance is zero, the simpler expression Copyright © 2012 Ahmad Nauman. All Rights Reserved

24. D-Problem 17.9 - hayt + _ _ + V 1 V 2 Figure 17.19 (c) I 1 I 2 Copyright © 2012 Ahmad Nauman. All Rights Reserved

25. Applying KVL in loop 1 + _ V 1 I 1 I 2 (a) Solution: Copyright © 2012 Ahmad Nauman. All Rights Reserved

26. _ + V 2 I 1 I 2 Applying KVL in loop 2 (b) Solution: Copyright © 2012 Ahmad Nauman. All Rights Reserved

27. Substituting equation (b) into (a), we get; From equation (c) and (b), we get; (c) As we know that Solution: Copyright © 2012 Ahmad Nauman. All Rights Reserved

28. We know z-parameters are So [z] will be AnsweR Solution: Copyright © 2012 Ahmad Nauman. All Rights Reserved