Question

The ABCD parameters of $\frac{\lambda }{2}$length transmission line with $Z_0=50\Omega$ is

• A. $\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1& j\\ j& 1\end{array}\right]$
• B. $$\left[\begin{array}{cc}1& j\\ j& 1\end{array}\right]$$
• C. $$\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$$
• D. $\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]$

Answer 1

The correct option is D $\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]$

$\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]=\left[\begin{array}{cc}cos\beta l& j{Z}_{0}sin\beta l\\ \frac{jsin\beta l}{Z_o}& cos\beta l\end{array}\right]=\left[\begin{array}{cc}-1& j50\left(0\right)\\ \frac{j}{50}\left(0\right)& -1\end{array}\right]$

$(\beta l=\frac{2\pi }{\lambda }.\frac{\lambda }{2}=\pi )$

$\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]$