Introduction to Electric Circuits

9.6 The transmission or ABCD-parameters 213

Therefore

h21-~. 12/1, = -Z3/(Z2 + Z3)

Putting in the impedance values,

h21 = -5/10 = -0.5

From Equation (9.30)

g21 = 1/h21 = --2

From Equation (9.21), h22 - I2/V2 with I1 = 0. With

I 1 = 0, I 2 -- V2/(Z 2 + Z 3)

SO

h22 : 12/1/'2 : 1//(Z2 + Z3)S

Putting in the impedance values

h22 : 1/(5 + 5) : 0.1 S

From Equation (9.32)

g22 = 1/h22 = (Z2 + Z3) : (5 + 5) = 10 D,

From Equation (9.20), h12 -- V1/V 2 with 11 -- 0. Now with the input port open

circuited to make 11 = 0, V 1 = IeZ 3 and 12 = V2//(Z2 + Z3),

V 1 : V2Z3/(Z 2 -[-- Z3)

It follows that

hi 2 --- Vl/V 2 -- Z3/(Z2 + Z3)

Putting in the impedance values we have

hi2--- 5/(5 "+" 5) -- 5/10 = 0.5

From Equation (9.31)

g12 : 1//h12 = 1/0.5 = 2

9.6 THE TRANSMISSION ORABCD-PARAMETERS

Set 5: The fifth set, which leads to the so-called transmission or ABCD-

parameters, has 1/2 and 12 as the independent variables and V~, I1 as the

dependent variables. The output port current flows out of the positive terminal

which is the opposite direction to the conventional direction considered in the

previous four sets of equations. This is shown in Fig. 9.7.

These equations are used extensively for the analysis of transmission systems