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 SUB - TOPICS 6-1 Z – PARAMETER 6-2 Y – PARAMETER 6-3 ABCD – PARAMETER 6-4 TERMINATED TWO PORTNETWORKS
4 TWO – PORT NETWORKSA 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 One port or two terminal circuit Two port or four terminal circuitIt is an electrical network with two separate ports for input and output.No independent sources.
6 6-1 Z – PARAMETERZ – 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-I1I2V2Z11Z21Z12Z22where the z terms are called the impedance parameters, or simply z parameters, and have units of ohms.
7 z11 = Open-circuit input impedance z21 = Open-circuit transfer impedance from port 1 to port 2z12 = Open-circuit transfer impedance from port 2 to port 1z22 = Open-circuit output impedance
8 Example 1 Find the Z – parameter of the circuit below. 40Ω 240Ω 120Ω + V1_V2I1I2
9 Solution When I2 = 0(open circuit port 2). Redraw the circuit. Ia I1 + 40Ω240Ω120Ω+V1_V2I1IaIb
10 When I1 = 0 (open circuit port 1). Redraw the circuit. 40Ω240Ω120Ω+V1_V2IyI2IxIn matrix form:
11 Example 2 Find the Z – parameter of the circuit below + _ V1 V2 -j20Ω 10Ωj4Ω2Ω10I2I2I1
12 Solution i) I2 = 0 (open circuit port 2). Redraw the circuit. + V1 _ j4Ω2ΩI1V2I2 = 0
13 ii) I1 = 0 (open circuit port 1). Redraw the circuit. +_V1V2-j20Ω10Ω10I2I2I1 = 0
14 6-2 Y - PARAMETERY – 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-I1I2V2Y11Y21Y12Y22where the y terms are called the admittance parameters, or simply y parameters, and they have units of Siemens.
15 y11 = Short-circuit input admittance y21 = Short-circuit transfer admittance from port 1 to port 2y12 = Short-circuit transfer admittance from port 2 to port 1y22 = Short-circuit outputadmittance
16 Example 3 Find the Y – parameter of the circuit shown below. 5Ω 15Ω 20Ω+V1_V2I1I2
19 Example 4 Find the Y – parameters of the circuit shown. V1 V2 -j20Ω +_V1V2-j20Ω10Ωj4Ω2Ω10I2I2I1
20 Solution i) V2 = 0 (short – circuit port 2). Redraw the circuit. V1 +_V110Ωj4Ω2Ω10I2I2I1
21 ii) V1 = 0 (short – circuit port 1). Redraw the circuit. +_V2-j20Ω10Ωj4Ω2Ω10I2I2I1
22 6-3 T (ABCD) PARAMETERT – 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.+V1-I1I2V2A11C21B12D22
23 where the T terms are called the transmission parameters, or simply T or ABCD parameters, and each parameter hasdifferent units.B= negative short-circuit transfer impedance ()A=open-circuit voltage ratioC= open-circuit transfer admittance (S)D=negative short-circuit current ratio
24 Example 5 Find the ABCD – parameter of the circuit shown below. 2Ω 10Ω +V2_I1I2V14Ω
27 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-I1I2V2ZgZLVgTwo – port networkTerminated two-port parameter can be implement to z-parameter,Y-parameter and ABCD-parameter.
28 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 two-port network and some of them are;
29 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.
30 Example 6 For the two-port shown below, obtain the suitable value of Rs such that maximum power is available at the inputterminal. The Z-parameter of the two-port network is given asWith Rs = 5Ω,what would be the value of+V1-I1I2V2Rs4ΩVsZ
31 Solution Z-parameter equation becomes; KVL at the output; Subs. (3) into (2);Subs. (4) into (1);Hence, the input impedance;For the circuit to have maximum power,
32 To find at max. power transfer, voltage drop at Z1 is half of VsFrom equations (3), (4), (5) & (6),Overall voltage gain,
33 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 RL and the maximum power transferred.