2OBJECTIVES 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.
3SUB - TOPICS 6-1 Z – PARAMETER 6-2 Y – PARAMETER 6-3 ABCD – PARAMETER 6-4 TERMINATED TWO PORTNETWORKS
4TWO – 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)
5One 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.
66-1 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.
7z11 = 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
8Example 1 Find the Z – parameter of the circuit below. 40Ω 240Ω 120Ω + V1_V2I1I2
9Solution When I2 = 0(open circuit port 2). Redraw the circuit. Ia I1 + 40Ω240Ω120Ω+V1_V2I1IaIb
10When I1 = 0 (open circuit port 1). Redraw the circuit. 40Ω240Ω120Ω+V1_V2IyI2IxIn matrix form:
11Example 2 Find the Z – parameter of the circuit below + _ V1 V2 -j20Ω 10Ωj4Ω2Ω10I2I2I1
12Solution i) I2 = 0 (open circuit port 2). Redraw the circuit. + V1 _ j4Ω2ΩI1V2I2 = 0
13ii) I1 = 0 (open circuit port 1). Redraw the circuit. +_V1V2-j20Ω10Ω10I2I2I1 = 0
146-2 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.
15y11 = 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
16Example 3 Find the Y – parameter of the circuit shown below. 5Ω 15Ω 20Ω+V1_V2I1I2
19Example 4 Find the Y – parameters of the circuit shown. V1 V2 -j20Ω +_V1V2-j20Ω10Ωj4Ω2Ω10I2I2I1
20Solution i) V2 = 0 (short – circuit port 2). Redraw the circuit. V1 +_V110Ωj4Ω2Ω10I2I2I1
21ii) V1 = 0 (short – circuit port 1). Redraw the circuit. +_V2-j20Ω10Ωj4Ω2Ω10I2I2I1
226-3 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
23where 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
24Example 5 Find the ABCD – parameter of the circuit shown below. 2Ω 10Ω +V2_I1I2V14Ω
276-4 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.
28Zg 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;
29The 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.
30Example 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
31Solution 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,
32To find at max. power transfer, voltage drop at Z1 is half of VsFrom equations (3), (4), (5) & (6),Overall voltage gain,
33Example 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.