Impedances of both ports are same for the symmetrical network.Bandres, M.A., Gutiérrez-Vega, J.C.: Airy-Gauss beams and their transformation by paraxial optical systems. It is not necessary that, these circuits are physically symmetrical.įind the Symmetry condition of ABCD parameter, we have to follow two conditions, Symmetry Condition-1 The electrical network is said to be symmetrical if the input impedance is equal to the output impedance. Generally, the network that consists of passive elements (resistor, inductor, and capacitor) only, that network are reciprocal networks and the network that consists of the active element (transistor or generator), that networks are not a reciprocal network.įind the reciprocity condition of ABCD parameter, we have to follow two conditions, Reciprocity Condition-1 Reciprocity Conditions for ABCD ParameterĪ network is said to be reciprocal if the port-2 voltage is due to applied current at port-1 is the same as the port-1 voltage when the applied current is the same as port-2. The value of D, gives us the ratio of sending end current to the receiving end (short-circuit) current. Therefore, the unit of the B parameter is ohm. The value of B, gives us the ratio of sending end voltage to the receiving end (short-circuit) current. And hence the current flowing through the receiving end V R is zero. Now, we consider the second case in which, the terminals of receiving end of a line are short-circuited. The value of C gives us the ratio of sending end current to receiving end (open-circuit) voltage. The value of A gives us the ratio of sending end voltage to the receiving end (open-circuit) voltage. And hence the current flowing through the receiving end I R is zero. Now, we consider the first case in which, the receiving end of the line is open-circuited. And in the second case, we need to short the receiving end terminals and we will get B and D parameter. In the first case, we need to open the receiving end terminals and we will get A and C parameter. To calculate the value of ABCD parameters, we need to perform two cases. ABCD Parameter for Transmission Lineįor the above figure, equations of ABCD parameters are as shown in the below, If we consider that the port-1 is sending end and port-2 is receiving end of a transmission line, then the two-port network of a transmission line is as the below figure. Reciprocity Conditions for ABCD Parameter.In this equation, A, B, C, and D are transmission line parameters and we will derive the values for these parameters. The equations of ABCD Parameters give us the relation between the sending end and receiving end specifications. Therefore, the ABCD parameters are also different for a different type of transmission line.Ĭonsider a below two-port network that has four terminals (two input terminals and two output terminals). And hence, the mathematical models are different for a different type of transmission line.
![abcd matrix abcd matrix](https://d2vlcm61l7u1fs.cloudfront.net/media/0e9/0e9ef2b7-43b7-4bad-964a-76ce2b8bc27c/phpFesNLS.png)
These different types of lines have different behavior in the actual power system network. The mathematical model of the transmission line is used to derive the actual behavior of the transmission line.
![abcd matrix abcd matrix](http://www.ktword.co.kr/img_data/5151_1.jpg)
The power system engineers need to understand the mathematical model of the transmission line and the ABCD parameter helps a lot to research the transmission line.Īs we know according to the length of a line, the transmission lines are classified as Short, Medium, and Long Transmission lines. Hence, a lot of research needed while designing the transmission line. The transmission line is the biggest part of the power system network and it is most prone to fault. Therefore, the two-port network must be four-terminal, linear, passive, and bilateral networks. The transmission line is a four-terminal, linear, passive, and bilateral network. The input voltage and current of the two-port network can be expressed in terms of the output voltage and current of the two-port network. And hence, the ABCD parameter is also known as Transmission Parameter. The ABCD parameters are used to represent the mathematical model of the transmission line in terms of the two-port network.