Question

Two passive two-port networks \( P \) and \( Q \) are connected as shown in the figure. The impedance matrix of network \( P \) is \( Z_P = \begin{bmatrix} 40 \, \Omega & 60 \, \Omega \\ 80 \, \Omega & 100 \, \Omega \end{bmatrix} \). The admittance matrix of network \( Q \) is \( Y_Q = \begin{bmatrix} 5 \, S & -2.5 \, S \\ -2.5 \, S & 1 \, S \end{bmatrix} \). Let the ABCD matrix of the two-port network \( R \) in the figure be \( \begin{bmatrix} \alpha & \beta \\ \gamma & \delta \end{bmatrix} \). The value of \( \beta \) in \( \Omega \) is ______ (rounded off to 2 decimal places).

 

Hint:

For cascaded two-port networks, use the relation \( [A B; C D]_R = [A B; C D]_P \times [A B; C D]_Q \).

Answer 1

Correct Answer: -19.9