Table 1 gives the conversion formulas between the 4 two-port networks presented in this chapter. $\Delta_Y$, $\Delta_Z$, $\Delta_H$, and $\Delta_T$ refer to determinants of the $Y$, $Z$, $H$ and transmittance-parameter matrices (e.g. $\Delta_Y=y_{11}y_{22}-y_{12}y_{21}$, ...).

To convert from one set of parameters to another, first write the current-voltage characteristics of the network using the first set and define the variables of the second set as new unknowns. Then solve the resulting system of two equations in the new unknowns.

For instance, assume we know the y-parameters of a network and want to find the h-parameters. First write the current-voltage characteristics of the network using the y-parameters $$\begin{equation}I_1=y_{11}{\color{red}V_1} + y_{12}V_2\end{equation}$$ $$\begin{equation}{\color{red}I_2}=y_{21}{\color{red}V_1} + y_{22}V_2\end{equation}$$ Then, since we want to compute the values of the h-parameters, we need to solve the above system of equations for ${\color{red}V_1}$ and ${\color{red}I_2}$. We obtain $$\begin{equation}{\color{red}V_1}=\frac{I_1}{y_{11}} -\frac{y_{12}}{y_{11}}V_2\end{equation}$$ $$\begin{equation}{\color{red}I_2}=\frac{y_{21}}{y_{11}}I_1 + (y_{22}-\frac{y_{12}y_{21}}{y_{11}})V_2\end{equation}$$ which can be written as $$\begin{equation}\begin{bmatrix}{\color{red}V_1}\\{\color{red}I_2}\end{bmatrix} = \begin{bmatrix}\frac{1}{y_{11}} & -\frac{y_{12}}{y_{11}}\\\frac{y_{21}}{y_{11}} & \frac{y_{22}y_{11}-y_{12}y_{21}}{y_{11}}\end{bmatrix} \begin{bmatrix}I_1\\V_2\end{bmatrix}\end{equation}$$ The $2\times 2$ matrix on the right-hand side of the last equation can be identified as the matrix of hybrid parameters (see also Table 1).