Question

Determine the Z parameters of the network shown below and check the symmetry and reciprocity of the network. Also find the h parameters of the network. 

Answer 1

We know that

$V_1=z_{11}I_1+z_{12}I_2$

$V_2=z_{21}I_1+z_{22}I_2$

$h_{11}=\frac{V_1}{I_1},V_2=0$

$h_{21}=\frac{I_2}{I_1},V_2=0$

$V_2=0$

$z_{21}I_1+z_{22}I_2=0$

$h_{21}=\frac{I_2}{I_1}=-\frac{z_{21}}{z_{22}}$

$h_{11}=\frac{z_{11}z_{22}-z_{12}z_{21}}{z_{22}}=\frac{∆_z}{z_{11}}$

$V_1=z_{12}I_2$

$V_2=z_{22}I_2$

$h_{12}=\frac{V_1}{V_2},I_1=0$

$h_{22}=\frac{I_2}{V_2},I_1=0$

$h_{12}=\frac{V_1}{V_2}=\frac{z_{12}}{z_{22}}$

$h_{22}=\frac{I_2}{V_2}=\frac{1}{z_{22}}$

$\begin{bmatrix} h_{11} & h_{12} \\ h_{13} & h_{14} \end{bmatrix}$ $=\begin{bmatrix} \frac{∆_z}{z_{22}} & \frac{z_{12}}{z_22}\\ -\frac{z_{21}}{z_{22}} & \frac{1}{z_{22}} \end{bmatrix}$