Question

A two-port network, shown in figure, is described by the following equations:

$I_1=Y_{11}{E}_1+Y_{12}{E}_2$
$I_2=Y_{21}{E}_1+Y_{22}{E}_2$


The admittance parameters, $Y_{11}{Y}_{12},Y_{21}and{Y}_{22}$ for the network shown are

• A. $0.5\mho ,1\mho ,2\mho ,and1\mho$ respectively
• B. $\frac{1}{3}\mho ,-\frac{1}{6}\mho ,-\frac{1}{6}\mho and\frac{1}{3}\mho$ respectively
• C. $0.5\mho ,0.5\mho ,1.5\mho and2\mho$ respectively
• D. $-\frac{2}{5}\mho ,-\frac{3}{7}\mho ,\frac{3}{7}\mho and\frac{2}{5}\mho$ respectively

Answer 1

The correct option is B $\frac{1}{3}\mho ,-\frac{1}{6}\mho ,-\frac{1}{6}\mho and\frac{1}{3}\mho$ respectively

Using KVL,
$E_1=2I_1+2(I_1+I_2)$

Again using KVL,

$E_2=2I_2+2(I_1+I_2)$

$\Rightarrow \left[z\right]=\left[\begin{array}{cc}4& 2\\ 2& 4\end{array}\right]$

$\left[y\right]=[z{]}^{-1}$

$=\frac{1}{(4\times 4)-(2\times 2)}\left[\begin{array}{cc}4& -2\\ -2& 4\end{array}\right]$

$\left[\begin{array}{cc}{Y}_{11}& Y_{12}\\ Y_{21}& Y_{22}\end{array}\right]=\left[\begin{array}{cc}1/3& -1/6\\ -1/6& 1/3\end{array}\right]$$\mho$