Question

The ABCDparameters, which are in general complex numbers, haveunits 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.

${\mathit{V}}_{\mathbf{s}}\mathbf{=}\mathit{A}{\mathit{V}}_{\mathbf{R}}\mathbf{+}\mathit{B}{\mathit{I}}_{\mathbf{R}}$ ……. (1)

${\mathit{I}}_{\mathbf{S}}\mathbf{=}\mathit{C}{\mathit{V}}_{\mathbf{R}}\mathbf{+}\mathit{D}{\mathit{I}}_{\mathbf{R}}$ ……. (2)

Here,$V_S$and $V_R$ are sending end and receiving end voltages, $I_s$ and $I_R$ are sending end and receiving end currents.

Here, $A$, $B$, $C$ 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).

$$\begin{gathered} A=1+\frac{ZY}{2} \\ B=Z \\ C=Y\left(1+\frac{ZY}{4}\right) \\ D=1+\frac{ZY}{2} \end{gathered}$$

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.