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Equivalent Circuit of Long Transmission Line | π and T network:

So far as the end conditions are concerned, the Equivalent Circuit of Long Transmission Line can be established in the form of a T- or π-network.

The parameters of the equivalent network are easily obtained by comparing the performance equations of a π-network and a transmission line in terms of end quantities.

Equivalent Circuit of Long Transmission Line

For a π-network shown in Fig. 5.15.

Equivalent Circuit of Long Transmission Line

According to exact solution of a long line

Equivalent Circuit of Long Transmission Line

For exact equivalence, we must have

From Eq. (5.50)

Equivalent Circuit of Long Transmission Line

Thus

is the factor by which the series impedance of the nominal-π must be multiplied to obtain the Zparameter of the equivalent-π, Substituting Z’ from Eq. (5.50) in Eq. (5.51), we get

Thus

is the factor by which the shunt admittance arm of the nominal- π must be multiplied to obtain the shunt parameter ( Y’/2) of the equivalent- π.

Note that

Equivalent Circuit of Long Transmission Line

is a consistent equation in terms of the above values of Y’ and Z’.

For a line of medium length

Equivalent Circuit of Long Transmission Line

so that the equivalent- π network reduces to that of nominal- π.

Equivalent Circuit of Long Transmission Line

Equivalent-T network parameters of a transmission line are obtained on similar lines. The equivalent-T network is shown in Fig. 5.16.