Transmission of power from generating unit to distributing units can be done through the transmission line. During transmission, many losses occur in the transmission line which decreases the efficiency of a line. For improving the proficiency of the transmission, two port networks are used.
A network having two input and two output terminals is known as a two port network. The network shown below has four terminals in which A and B represents the input port where as C and D represents the output port.
Vs = sending end voltage
Is = sending end current
Vr = receiving end voltage
Ir = receiving end current
A, B, C and D are the constants also known as the transmission parameters or chain parameters. These parameters are used for the analysis of an electrical network. It is also used for determining the performance of input, output voltage and current of the transmission network.
The above equations can also be written in a matrix form for easy calculations shown below
ABCD parameters for open circuit
From above equations, we get the value of A parameter which is the ratio of sending end voltage to the receiving end voltage. It is a dimensionless constant because their ratio has the same dimension.
Similarly, if Ir =0 is substituted in current equation,
ABCD parameters for short circuit
Similarly, if we put Vr= 0 in current equations,
Relation between ABCD parameters
For determining the relation between various types of network, like passive or bilateral network reciprocity theorem is applied. The voltage V is applied to the sending end, and the receiving end is kept short circuit, so the voltage becomes zero. Since, under short circuit the receiving end voltage is zero, the voltage and current equations become
Combining the above equations give,
For a symmetrical network, the input and output terminal may be interchanged without affecting the network behaviour.