Introduction to Electric Circuits

9. 7 The inverse transmission parameters 215

V 2 = A'V 1 + B'I 1 (9.40)

I2 = C'V~ + D'I~ (9.41)

In matrix form we have

A' B'

Ic

A', B', C' and D' are called the inverse transmission parameters or the inverse
ABCD-parameters and they are measured with the input port either open
circuited or short circuited. They are defined as follows"
9 A' is measured as V2/V1 with I~ - 0 and is a dimensionless ratio of two
voltages:
A' = (Vz/V1)I/,= o (9.43)
9 B' is measured as V2/I1 with V~ = 0 and its unit is the volt per ampere. It
therefore has the dimensions of impedance:
B' - (Vz/I1)lv,:o (9.44)
9 C' is measured as I2/V~ with 11 = 0 and its unit is the ampere per volt. It
therefore has the dimensions of admittance:

C' = (I2/Vl)ll,= 0

9 D' is measured as I2/It with V1 = 0 and is a dimensionless ratio of two

currents:

(9.45)

D' = (12/I1)]v,= o (9.46)

Example 9.4

Determine the ABCD-parameters of the series impedance network shown in

Fig. 9.8.

I1 Z I2

+o ,,....- | | r o-1-

T

--0 O--

Figure 9.8

Solution

To find A and C we open circuit the output port to make 12 = 0. Then V 1 - V 2

and I~ = 12 - 0. From Equation (9.36), A - Vt/V2 - 1. From Equation (9.38),

c- I,/V - o.