Inverse Transmission Parameters

The transmission parameter and the inverse transmission parameter are duals of each other.

If, instead of quantities [tex]{V_1}[/tex] and [tex]{I_1}[/tex], quantities [tex]{V_2}[/tex] and [tex]{I_2}[/tex] are expressed in terms of [tex]{V_1}[/tex] and [tex]{I_1}[/tex], the resulting parameter [tex](A',B',C',D')[/tex] are called inverse transmission parameter.

The inverse transmission parameters of the two port network in figure having direction of voltages and current as shown,are given by

[tex]{V_2} = A'{V_1} + B'( - {I_1})[/tex]

[tex]{I_2} = C'{V_1} + D'( - {I_1})[/tex]

in matrix form,

\[\left[ \begin{array}{l}
{V_2}\\
{I_2}
\end{array} \right] = \left( {\begin{array}{*{20}{c}}
{A'}&{B'}\\
{C'}&{D'}
\end{array}} \right)\left[ \begin{array}{l}
{V_1}\\
 - {I_1}
\end{array} \right]\]

The inverse transmission parameters can be defined as

[tex]A' = \frac{{{V_2}}}{{{V_1}}};{I_1} = 0[/tex] forward voltage ratio with sending end open circuited.

[tex]C' = \frac{{{I_2}}}{{{V_1}}};{I_1} = 0[/tex] transfer admittance with sending end open circuited.

[tex]B' = \frac{{{V_2}}}{{ - {I_1}}};{V_1} = 0[/tex] transfer impedance with sending end short circuited.

[tex]D' = \frac{{{I_2}}}{{ - {I_1}}};{V_1} = 0[/tex] forward current ratio with sending end short circuited.