Chapter 2: Transmission Line Models

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


(2.46)


(2.47)
(2.48)

 

 

 

 

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