1. 1 TWO PORT NETWORKS CHAPTER 6

2. 2 OBJECTIVES To understand about two – port networks and its functions. To understand the different between z- parameter, y-parameter, ABCD- parameter and terminated two port networks. To investigate and analysis the behavior of two – port networks.

3. 3 SUB - TOPICS  6-1 Z – PARAMETER  6-2 Y – PARAMETER  6-3 ABCD – PARAMETER  6-4 TERMINATED TWO PORT NETWORKS

4. 4 TWO – PORT NETWORKS A pair of terminals through which a current may enter or leave a network is known as a port. Two terminal devices or elements (such as resistors, capacitors, and inductors) results in one – port network. Most of the circuits we have dealt with so far are two – terminal or one – port circuits. (Fig. a) A two – port network is an electrical network with two separate ports for input and output. It has two terminal pairs acting as access points. The current entering one terminal of a pair leaves the other terminal in the pair. (Fig. b)

5. 5 One port or two terminal circuit Two port or four terminal circuit It is an electrical network with two separate ports for input and output. No independent sources.

6. 6 6-1 Z – PARAMETER Z – parameter also called as impedance parameter and the units is ohm (Ω) The “black box” is replace with Z-parameter is as shown below. +V1-+V1- I1I1 I2I2 +V2-+V2- Z 11 Z 21 Z 12 Z 22 where the z terms are called the impedance parameters, or simply z parameters, and have units of ohms.

7. 7 z 11 = Open-circuit input impedance z 21 = Open-circuit transfer impedance from port 1 to port 2 z 12 = Open-circuit transfer impedance from port 2 to port 1 z 22 = Open-circuit output impedance

8. 8 Example 1 Find the Z – parameter of the circuit below. 40Ω 240Ω 120Ω +V1_+V1_ +V2_+V2_ I1I1 I2I2

9. 9 Solution

10. 10 Example 2 Find the Z – parameter of the circuit below +_+_ +V1_+V1_ +V2_+V2_ -j20Ω 10Ω j4Ω 2Ω2Ω 10I 2 I2I2 I1I1

11. 11Solution

12. 12 6-2 Y - PARAMETER Y – parameter also called admittance parameter and the units is siemens (S). The “black box” that we want to replace with the Y- parameter is shown below. +V1-+V1- I1I1 I2I2 +V2-+V2- Y 11 Y 21 Y 12 Y 22 where the y terms are called the admittance parameters, or simply y parameters, and they have units of Siemens.

13. 13 y 11 = Short-circuit input admittance y 21 = Short-circuit transfer admittance from port 1 to port 2 y 12 = Short-circuit transfer admittance from port 2 to port 1 y 22 = Short-circuit output admittance

14. 14 Example 3 Find the Y – parameter of the circuit shown below. 5Ω5Ω 15Ω 20Ω +V1_+V1_ +V2_+V2_ I1I1 I2I2

15. 15 Solution

16. 16 Example 4 Find the Y – parameters of the circuit shown. +_+_ +V1_+V1_ +V2_+V2_ -j20Ω 10Ω j4Ω 2Ω2Ω 10I 2 I2I2 I1I1

17. 17Solution

18. 18 6-3 T (ABCD) PARAMETER T – parameter or also ABCD – parameter is a another set of parameters relates the variables at the input port to those at the output port. T – parameter also called transmission parameters because this parameter are useful in the analysis of transmission lines because they express sending – end variables (V 1 and I 1 ) in terms of the receiving – end variables (V 2 and -I 2 ). The “black box” that we want to replace with T – parameter is as shown below. +V1-+V1- I1I1 I2I2 +V2-+V2- A 11 C 21 B 12 D 22

19. 19 where the T terms are called the transmission parameters, or simply T or ABCD parameters, and each parameter has different units. A=open-circuit voltage ratio C= open-circuit transfer admittance (S) B= negative short- circuit transfer impedance (  ) D=negative short- circuit current ratio

20. 20 Example 5 Find the ABCD – parameter of the circuit shown below. 2Ω2Ω 10Ω +V2_+V2_ I1I1 I2I2 +V1_+V1_ 4Ω4Ω

21. 21 Solution

22. 22 6-4 TERMINATED TWO – PORT NETWORKS In typical application of two port network, the circuit is driven at port 1 and loaded at port 2. Figure below shows the typical terminated 2 port model. +V1-+V1- I1I1 I2I2 +V2-+V2- ++ ZgZg ZLZL VgVg Two – port network Terminated two-port parameter can be implement to Z-parameter, Y-parameter and ABCD-parameter.

23. 23 Z g represents the internal impedance of the source and V g is the internal voltage of the source and Z L is the load impedance. There are a few characteristics of the terminated two- port network and some of them are;

24. 24 The derivation of any one of the desired expression involves the algebraic manipulation of the two – port equation. The equation are: 1) the two-port parameter equation either Z or Y or ABCD. For example, Z-parameter, 2) KVL at input, 3) KVL at the output, From these equations, all the characteristic can be obtained.

25. 25 Example 6 For the two-port shown below, obtain the suitable value of R s such that maximum power is available at the input terminal. The Z-parameter of the two-port network is given as With R s = 5Ω,what would be the value of +V1-+V1- I1I1 I2I2 +V2-+V2- ++ RsRs 4Ω4ΩVsVs Z

26. 26 Solution

27. 27 Example 7 The ABCD parameter of two – port network shown below are. The output port is connected to a variable load for a maximum power transfer. Find R L and the maximum power transferred.

28. 28 Solution