ABCD Parameters of Transmission Line

 

Generalized Constant of the transmission line is given by sending end voltage and sending end current equation

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 circuit, receiving end current     I_R = 0

Transmission Line Parameter 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.

Transmission Line Parameter 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

Transmission Line Parameter 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.

Transmission Line Parameter 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.

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