Equivalent Circuit of a Long Line

Equivalent Circuit of a Long Line:

So far as the end conditions are concerned, the Equivalent Circuit of a Long 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 a Long Line

For a π-network shown in Fig. 5.15.

Equivalent Circuit of a Long Line

According to exact solution of a long line

Equivalent Circuit of a Long Line

For exact equivalence, we must have

Equivalent Circuit of a Long Line

From Eq. (5.50)

Equivalent Circuit of a Long LineThusEquivalent Circuit of a Long Line

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

Equivalent Circuit of a Long Line

ThusEquivalent Circuit of a Long Line

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 thatEquivalent Circuit of a Long Line

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

For a line of medium length

Equivalent Circuit of a Long Line

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

Equivalent Circuit of a Long Line

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

Updated: March 21, 2020 — 11:33 pm