Introduction to Electric Circuits

224 Two-port networks

V1 0

[Ii1=[~ X,/nl[~ 2] (9.61)

Example 9.12

Obtain the ABCD-parameters for a practical transformer.

Solution
A practical transformer has resistance and leakage inductance associated with
its windings and these are taken into account by lumped series impedances in
series with each 'perfect' winding. For the purposes of analysis it is usual to
refer the whole of this impedance to one side of the transformer.
A real transformer also has losses due to hysteresis and eddy currents and
these are taken into account using a shunt conductance. This, together with a
shunt susceptance used to take account of the need for a magnetizing current,
gives a shunt admittance Y. The equivalent circuit then takes the form shown in
Fig. 9.17.

I

V1

o

Z

1

I2

0

V2

n'] ....^0

Figure 9.17

The diagram shows that the practical transformer equivalent circuit may be

considered to be made up of a series impedance cascaded with a shunt

admittance and then a perfect transformer. Using the transfer matrices

developed in Examples 9.4, 9.7, and 9.11 we have

Multiplying the first two transfer matrices we obtain

Finally, multiplying the remaining two transfer matrices we get

11 Yn 1/n_

V2] (9.62)