ABCD Parameters of Transmission Line

ABCD Parameters

The ABCD parameters of generalized constant of the transmission line is find out by sending end current and sending end voltage equation. In order to find out ABCD parameters of the transmission line, it is considered that (1) The receiving end of the transmission line is open circuited and (2) Receiving end of the transmission line is short circuited.

V_S = AV_R + BI_R

I_S = CV_R + DI_R

Where

V_S = Sending end voltage

I_S = Sending end current

V_R = Receiving end voltage

I_R = Receiving end current

A, B, C and D = Constant

The generalized constant of the transmission line is found out by

Receiving end of the transmission line open circuited, receiving end current I_R = 0

ABCD Parameters: Receiving End Open Circuited

Constant A

V_S = AV_R

A = V_S / V_R and

The constant A is defined as the ratio of sending end voltage to the receiving end voltage when receiving end of the line is open circuited. It is also called as reverse voltage gain. It is unitless.

Constant C

I_S = CV_R

C = I_S / V_R

The constant C is defined as the ratio of sending end current to the receiving end voltage when receiving end of the line is open circuited. Its unit is 1 / ohm or mho.

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Receiving end of the transmission line is short circuited, when receiving end voltage V_R = 0

ABCD Parameters: Receiving End Short Circuited

Constant B

V_S = BI_R

B = V_S / I_R

The constant B is defined as the ratio of sending end voltage to the receiving end current when receiving end of the transmission line is short circuited. Its unit is ohm.

Constant D

I_S = DI_R

D = I_S / I_R

The constant D is defined as the ratio of sending end current to the receiving end current when receiving end of the transmission line is short circuited. It is also called as reverse current gain. It is unit less.

ABCD Parameters: Summary

Transmission line parameters	How to Find out?	Formula	Unit	Better known as
A	Receiving end of transmission line is open circuited	VS / VR	Unit less	Reverse voltage gain
B	Receiving end of transmission line is short circuited	VS / IR	ohm
C	Receiving end of transmission line is open circuited	IS / VR	mho
D	Receiving end of transmission line is short circuited	IS / IR	Unit less	Reverse current gain