Question

The ABCDparameters, which are in general complex numbers, have units of __________, __________, __________, and __________,respectively.

Short answer

Therefore,The ABCDparameters, have units of dimensionless, ohm, Siemens, and dimensionless, respectively.

Step-by-step solution

Determine the relation between sending end and receiving end quantities.

Write the relation between sending end and receiving end quantities in terms of transmission parameters.

${\mathbf{V}}_{\mathbf{S}}\mathbf{=}{\mathbf{AV}}_{\mathbf{R}}\mathbf{+}{\mathbf{BI}}_{\mathbf{R}}$ ……. (1)

${\mathbf{I}}_{\mathbf{S}}\mathbf{=}{\mathbf{CV}}_{\mathbf{R}}\mathbf{+}{\mathbf{DI}}_{\mathbf{R}}$ ……. (2)

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.

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

Determine the units of transmission parameters.

Write $A$, $B$, $C$ and $D$ are parameters in terms of transmission line parameters $Z$(impedance) and $Y$ (admittance).

$\mathrm{A}=1+\frac{\mathrm{ZY}}{2}$

$\mathrm{B}=\mathrm{Z}$

role="math" localid="1655357566439" $\mathrm{C}=\mathrm{Y}\left(1+\frac{\mathrm{ZY}}{\text{4}}\right)$

$\mathrm{D}=1+\frac{\mathrm{ZY}}{2}$

From above equations, the parameters $A$ and $D$ are dimensionless.

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

Therefore,The ABCDparameters, have units of dimensionless, ohm, Siemens, and dimensionless, respectively.