# ABCD Parameters of Transmission Line

on 24/2/2012 & Updated on Saturday 28th of April 2018 at 03:57:28 PM**two port network**for the sake of easier calculations.

The circuit of a 2 port network is shown in the diagram below. As the name suggests, a 2 port network consists of an input port PQ and an output port RS. In any 4 terminal network, (i.e. linear, passive, bilateral network) the input voltage and input current can be expressed in terms of output voltage and output current. Each port has 2 terminals to connect itself to the external circuit. Thus it is essentially a 2 port or a 4 terminal circuit, having

Given to the input port PQ.
Given to the output port RS.
As shown in the diagram below.
Now the **ABCD parameters** or the transmission line parameters provide the link between the supply and receiving end voltages and currents, considering the circuit elements to be linear in nature.

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Thus the relation between the sending and receiving end specifications are given using **ABCD parameters** by the equations below.
Now in order to determine the ABCD parameters of transmission line let us impose the required circuit conditions in different cases.

## ABCD Parameters, When Receiving End is Open Circuited

The receiving end is open circuited meaning receiving end current I_{R}= 0. Applying this condition to equation (1) we get,

Thus its implies that on applying open circuit condition to ABCD parameters, we get parameter A as the ratio of sending end voltage to the open circuit receiving end voltage. Since dimension wise A is a ratio of voltage to voltage, A is a dimension less parameter.
Applying the same open circuit condition i.e I_{R} = 0 to equation (2)
Thus its implies that on applying open circuit condition to ABCD parameters of transmission line, we get parameter C as the ratio of sending end current to the open circuit receiving end voltage. Since dimension wise C is a ratio of current to voltage, its unit is mho.
Thus C is the open circuit conductance and is given by

C = I_{S} ⁄ V_{R} mho.

## ABCD Parameters, When Receiving End is Short Circuited

Receiving end is short circuited meaning receiving end voltage V_{R}= 0 Applying this condition to equation (1) we get, Thus its implies that on applying short circuit condition to ABCD parameters, we get parameter B as the ratio of sending end voltage to the short circuit receiving end current. Since dimension wise B is a ratio of voltage to current, its unit is Ω. Thus B is the short circuit resistance and is given by

B = V

_{S}⁄ I

_{R}Ω. Applying the same short circuit condition i.e V

_{R}= 0 to equation (2) we get

Thus its implies that on applying short circuit condition to ABCD parameters, we get parameter D as the ratio of sending end current to the short circuit receiving end current. Since dimension wise D is a ratio of current to current, it’s a dimension less parameter. ∴ The

**ABCD parameters of transmission line**can be tabulated as:-

Parameter | Specification | Unit |

A = V_{S} / V_{R} | Voltage ratio | Unit less |

B = V_{S} / I_{R} | Short circuit resistance | Ω |

C = I_{S} / V_{R} | Open circuit conductance | mho |

D = I_{S} / I_{R} | Current ratio | Unit less |

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