(a) The series expansions of the hyperbolic functions are given by

\[
\begin{aligned}
& \cosh \theta=1+\frac{\theta^{2}}{2}+\frac{\theta^{4}}{24}+\frac{\theta^{6}}{720}+\cdots \\
& \sinh \theta=1+\frac{\theta^{2}}{6}+\frac{\theta^{4}}{120}+\frac{\theta^{6}}{5040}+\cdots
\end{aligned}
\]

For the \(A B C D\) parameters of a long transmission line represented by an equivalent \(\pi\) circuit, apply the above expansion considering only the first two terms, and express the result in terms of \(Y\) and \(Z\).

(b) For the nominal \(\pi\) and equivalent \(\pi\) circuits shown in Figures 5.3 and 5.7 of the text, show that

\[
\frac{A-1}{B}=\frac{Y}{2} \quad \text { and } \quad \frac{A-1}{B}=\frac{Y^{\prime}}{2}
\]

hold good, respectively.

Figure 5.3

Figure 5.7

Transcribed Image Text:

Vs HH NI 11 N Z = z ww X12 la Ja 1