Introduction to Electric Circuits

9.8 Cascaded two-port networks 223

Nominai-T representation of 'medium length' power
transmission lines

In power transmission lines this T-network is called a nominal-T network. Half
of the line impedance is considered to be concentrated at each end of the line
and the whole of the shunt admittance is placed at the centre of the line.
Replacing the impedance Z by Z/2, where Z is the total series impedance of the
line, gives for the transmission parameters of a nominal-T network:

A = D = I + ZY/2; B- z + zZY/4; C- Y

The ABCD-parameters of a single-phase, two-winding
transformer

The transformer is a very important electrical 'machine', used not only for
voltage and current level changing but also for buffering and matching
purposes. They are manufactured in an enormous range of sizes from a few VA
in electronic circuits to more than 1000 MVA in power systems.

Example 9.11

Determine the ABCD-parameters for the ideal two-winding transformer shown

in Fig. 9.16.

n:l I2 O

V2

N1 N2 o

Figure 9.16

Solution

The ideal transformer shown has a transformation ratio n = N1/N 2. From

transformer theory we have that V1/V2 = I2/I~ - n, so

VI-nV2 and 11=I2/n

These relationships may be written

V 1 = r/V 2 + 0 6 (9.59)

11 = 0V2 + (1/n)I2 (9.60)

Comparing Equations (9.59) and (9.33) we see that A = n and B = 0. Compar-

ing Equations (9.60) and (9.34) we see that C = 0 and D = 1In. In matrix

form