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CHAPTER 6 TWO PORT NETWORKS 1 OBJECTIVES • To understand about two – port networks and its functions. • To understand the different between zparameter, y-parameter, ABCD- parameter and terminated two port networks. • To investigate and analysis the behavior of two – port networks. 2 SUB - TOPICS 6-1 Z – PARAMETER 6-2 Y – PARAMETER 6-3 ABCD – PARAMETER 6-4 TERMINATED TWO PORT NETWORKS 3 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) 4 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. 5 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. I I1 + V1 - V1 z11I1 z12I 2 V2 z 21I1 z 22I 2 2 Z11 Z12 Z21 Z22 + V2 - V1 z11 z12 I1 V z z I z 2 21 22 2 I1 I 2 where the z terms are called the impedance parameters, or simply z parameters, and have units of ohms. 6 V1 z11 I1 and I 2 0 V2 z 21 I1 I 2 0 z11 = Open-circuit input impedance z21 = Open-circuit transfer impedance from port 1 to port 2 V1 z12 I2 and I1 0 V2 z 22 I2 I1 0 z12 = Open-circuit transfer impedance from port 2 to port 1 z22 = Open-circuit output impedance 7 Example 1 Find the Z – parameter of the circuit below. + V1 I2 I1 + 240Ω 120Ω _ V2 _ 40Ω 8 Solution 9 Example 2 Find the Z – parameter of the circuit below I1 + V1 _ 2Ω 10Ω j4Ω + _ I2 + 10I2 -j20Ω V2 _ 10 Solution 11 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 Yparameter is shown below. I2 I1 + V1 - I1 y11V1 y12V2 I 2 y 21V1 y 22V2 Y11 Y12 Y21 Y22 + V2 - I1 y11 y12 V1 V1 I y y V y V 2 21 22 2 2 where the y terms are called the admittance parameters, or simply y parameters, and they have units of Siemens. 12 I1 y11 V1 and V2 0 I2 y 21 V1 V2 0 y11 = Short-circuit input admittance y21 = Short-circuit transfer admittance from port 1 to port 2 y12 I1 V2 and V1 0 y 22 I2 V2 V1 0 y12 = Short-circuit transfer admittance from port 2 to port 1 y22 = Short-circuit output admittance 13 Example 3 Find the Y – parameter of the circuit shown below. + V1 _ I1 5Ω I2 + 20Ω 15Ω V2 _ 14 Solution 15 Example 4 Find the Y – parameters of the circuit shown. I1 + V1 _ 2Ω 10Ω j4Ω + _ I2 + 10I2 -j20Ω V2 _ 16 Solution 17 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 (V1 and I1) in terms of the receiving – end variables (V2 and -I2). • The “black box” that we want to replace with T – parameter is as shown below. I2 I1 + V1 - A11 B12 C21 D22 + V2 - 18 V1 AV2 BI 2 I1 CV2 DI 2 V1 A B V2 V2 I C D I T I 2 1 2 where the T terms are called the transmission parameters, or simply T or ABCD parameters, and each parameter has different units. V A 1 V2 I1 C V2 A=open-circuit voltage ratio I 2 0 I2 0 C= open-circuit transfer admittance (S) V B 1 I2 D I1 I2 V2 0 B= negative shortcircuit transfer impedance () V2 0 D=negative shortcircuit current ratio 19 Example 5 Find the ABCD – parameter of the circuit shown below. I1 2Ω 4Ω + V1 _ I2 + 10Ω V2 _ 20 Solution 21 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. Zg Vg + I2 I1 + V1 - Two – port network + V2 - ZL Terminated two-port parameter can be implement to Z-parameter, Y-parameter and ABCD-parameter. 22 • Zg represents the internal impedance of the source and Vg is the internal voltage of the source and ZL is the load impedance. • There are a few characteristics of the terminated twoport network and some of them are; V1 I1 i) input impedance, Zi ii) output impedance, Zo iii) current gain, A i V2 I2 I2 I1 V2 iv) voltage gain, A v V1 v) overall voltage gain, A g V2 Vg 23 •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, V1 Z11I1 Z12I 2 .......(1) V2 Z21I1 Z22I 2 .......(2) 2) KVL at input, V1 Vg I1Zg .......(3) 3) KVL at the output, V I Z .......(4) 2 2 L •From these equations, all the characteristic can be obtained. 24 Example 6 For the two-port shown below, obtain the suitable value of Rs such that maximum power is available at the input terminal. The Z-parameter of the two-port network is given as Z11 Z 21 Z12 6 Z 22 4 2 4 With Rs = 5Ω,what would be the value of Rs Vs + I2 I1 + V1 - V2 Vs Z + V2 - 4Ω 25 Solution 26 Example 7 The ABCD parameter of two – port network shown below are. 4 0.1S 20 2 The output port is connected to a variable load for a maximum power transfer. Find RL and the maximum power transferred. 27 Solution 28