Topic: Network Theory
Y-parameter of a two port network is $\begin{bmatrix}5 & 2 \\ 1 & 3\end{bmatrix}$. A $1~\Omega$ resistor is connected in parallel to the network as shown. Find out the Y parameter of the whole network.
- A. $\begin{bmatrix}6 & 1 \\ 0 & 4\end{bmatrix}$
- B. $\begin{bmatrix}3 & 1 \\ 1 & 2\end{bmatrix}$
- C. $\begin{bmatrix}4 & 1 \\ 0 & 2\end{bmatrix}$
- D. $\begin{bmatrix}6 & 3 \\ 2 & 4\end{bmatrix}$
Answer: A. $\begin{bmatrix}6 & 1 \\ 0 & 4\end{bmatrix}$
Explanation: When two-port networks are connected in parallel, their Y-parameter matrices add up. The Y-parameter matrix for a series resistor $R=1~\Omega$ connected between input and output ports is $\begin{bmatrix}1/R & -1/R \\ -1/R & 1/R\end{bmatrix} = \begin{bmatrix}1 & -1 \\ -1 & 1\end{bmatrix}$. Adding this to the original matrix gives $\begin{bmatrix}5+1 & 2-1 \\ 1-1 & 3+1\end{bmatrix} = \begin{bmatrix}6 & 1 \\ 0 & 4\end{bmatrix}$.