10.4 ABCD OR TRANSMISSION PARAMETERS

If we select V ₂ and I ₂ as independent variables, the two-port equations may be written as

Now if V ₂ = 0, the output port is short circuit,

Figure 10.8: Determination of ABCD parameters

If I ₂ = 0, output port is open circuit,

As per convention, the currents entering the upper terminals of the ports are taken as positive. In a power transmission network the output current I ₂ is coming out of the upper terminal of the output port. Hence, the reference direction of the output current I ₂ is opposite to that shown in the figure.

The ABCD parameters are defined as follows:

open circuit reverse voltage transfer ratio

= short circuit reverse transfer impedance

open circuit reverse transfer admittance

short circuit reverse current transfer ratio.

It is seen that all the four parameters are transfer functions. The ABCD parameters are widely used in transmission line calculations.

In transmission line theory, the input port is called the sending input and the output port is called the receiving end.

Example 10.3

Determine the ABCD parameters of the given network as shown in Figure 10.9

Solution: Loops equations are

Figure 10.9

or

or

Now the standard equations for ABCD parameters

Rearrange Equation (2) into the form of Equation (4),

Putting the value of I ₁ from Equation (2a) into Equation (1),

Now comparing Equations (5) and (2a) with Equations (3) and...