Equivalent π Representation of a Long Line
The π equivalent of a long transmission line is shown in Fig. 2.6. In this the series impedance is denoted by Z¢ while the shunt admittance is denoted by Y¢ From (2.13) to (2.15) the ABCD parameters are defined as
Fig. 2.6 Equivalent p representation of a long transmission line.
Comparing (2.44) with (2.47) we can write
Ω 
(2.49) 
where Z = zl is the total impedance of the line. Again comparing (2.43) with (2.46) we get

(2.50) 
Rearranging (2.50) we get

(2.51) 
where Y = yl is the total admittance of the line. Note that for small values of l , sinh γl = γl and tanh ( γl /2) = γl /2. Therefore from (2.49) we get Z = Z¢ and from (2.51) we get Y = Y¢ . This implies that when the length of the line is small, the nominal p representation with lumped parameters is fairly accurate. However the lumped parameter representation becomes erroneous as the length of the line increases.
Do an example to illustrate this 