FOUR TERMINAL NETWORKS TWO – PORT NETWORKS Two – ports – are electric circuits with two input and two output terminals as shown I1 I2 V2 V1 Input Port Output Port In two – ports, the input voltage and current (V1 & I1) are related with the output voltage and current (V2 & I2) by the following equations:V1 = Z11 I1 – Z12 I2 V2 = Z21 I1 – Z22 I2 Z – parameters I1 = Y11 V1 – Y12 V2 I2 = Y21 V1 – Y22 V2 Y– parameters V1 = h11 I1 – h12 V2 I2 = h21 I1 – h22 V2 h – parameters V1 = A V2 + B I2 I1 = C V2 + D I2 ABCD parameters The coefficients of the current and/ or voltage on the right – hand side of the above equations are called the parameters of the two-port circuit. If ports can be interchanged without disturbing the values of the terminal currents and voltage then the two-port circuit is called Symmetrical. For Symmetrical two-ports:A=D Also the ABCD parameters are related by the following equation: AD-BC = 1. A and D – no units, B in (ohm), C in (mho). We can find the ABCD parameters in terms of Z – parameters for example as follows:V1 = Z11 I1 – Z12 I2 …………….1 V2 = Z21 I1 – Z22 I2 ……………………..2 From eq (2): V Z I1 2 22 I 2 ……………3 Z 21 Z 21 Sub. for (I1) in eq (1) we get. V Z V1 Z11 2 22 I 2 Z12 I 2 Z 21 Z 21 Z Z Z Z12 Z 21 I 2 V1 = 11 V2 11 22 Z Z 21 21 Since V1 = A V2 + B I2. I1 = C V2 + D I2. A C Z11 Z Z Z12 Z 21 & B 11 22 Z 21 Z 21 Z 1 & D 22 Z 21 Z 21 When interchanging the places between the source and the load in a two-port the following equations should be used:V2 = D V1+ BI1 I2 = C V1 + AI1 ABCD – parameters calculations The ABCD parameters could be found by experiment as well as by calculation when finding the ABCD parameters by calculation, circuit components and their interconnection must be known. For the experimental determination of the parameters we must conduct – 3 – experiments (because we have only – 3 independent parameters). The simplest method used is by conducting short and open circuit experiments. Experiment No. 1 In this experiment the source is connected to the input terminals, the output terminals are open – circuited. I10 I20 =0 V20 V10 ~ V10 = A V20 I10 = C V20 V10 A Z10 I10 C ………………..1 Experiment No. 2 In this experiment the source is connected to the input terminals, the out put is connected to the input terminals, the out put terminals are shortcircuited. ~ I1S I2S V1S V2S V2S = 0 V1S = B I2S I1S = D I2S VI S B Z IS I IS ……………………..2 D Experiment No. 3 In this experiment the source is connected to the out put terminals, the input terminals are short-circuited. I1S I2S V1S = 0 V2S V1S = 0 V2 =DV1 + BI1 I2 = CV1 + AI1 V2S = BI1S I2S = AI1S V2S B Z 2S I 2S A ………………..3 ~ Since we have: AD-BC = 1 1 BC 1 AD AD Z10 Z15 1 Z10 AD 1 Z15 1 Z10 AD …………………..4 Z 25 B D D …………………..5 Z 25 A B A Multiplying eq (4) By eq (5) we get Z 25 Z10 Z15 1 Z15 Z10 A2 A Z10 Z15 Z 25 Z10 Z15 After finding A from eq (6), we can find (C) from eq (1), from eq (3) we can find (B) then (D) can be find from eq (2).