Question

As applied to linear, passive, bilateral two-port networks, the ABCD parameters satisfy$\mathbf{AD}\mathbf{-}\mathbf{BC}\mathbf{=}\mathbf{1}$.

(a) True

(b) False

Short answer

Therefore, the correct option is (a) True.

Step-by-step solution

Determine the relation between sending end and receiving end quantities.

Draw the two-port network.

Here,${\mathrm{V}}_{\mathrm{S}}$and ${\mathrm{V}}_{\mathrm{R}}$ are sending end and receiving end voltages, ${\mathrm{I}}_{\mathrm{S}}$ and ${\mathrm{I}}_{\mathrm{R}}$are sending end and receiving end currents.

Write the relation between sending end and receiving end quantities in matrix form.

$\left[\begin{array}{c}{V}_S\\ I_S\end{array}\right]\mathbf{=}\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]\mathbf{}\left[\begin{array}{c}{V}_R\\ I_R\end{array}\right]$ ……. (1)

Here, $A$, $B$, $C$ and $D$ are parameters that depends on transmission line parameters.

Determine the correct option.

The parameters $A$ and $D$are dimensionless.

The unit of $C$ is Siemens and the unit of $B$ is ohm.

For passive, linear, bilateral, two-port network, the relation in transmission parameter is,

$\mathrm{AD}-\mathrm{BC}=1$ …… (2)

Therefore, the correct option is (a) True.