![abcd matrix abcd matrix](https://i.stack.imgur.com/AGph9.png)
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. 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. 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.
![abcd matrix abcd matrix](https://www.mikrocontroller.net/attachment/295251/ABCD-Matrix.jpg)
![abcd matrix abcd matrix](https://www.rfwireless-world.com/images/abcd-matrix-to-S-matrix.jpg)
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. Since dimension wise D is a ratio of current to current, it’s a dimensionless parameter.The ABCD parameters are used to represent the mathematical model of the transmission line in terms of the two-port network. Thus it’s implied 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. Thus B is the short circuit resistance and is given byĪpplying the same short circuit condition i.e V R = 0 to equation (2) we get Since dimension wise B is a ratio of voltage to current, its unit is Ω. Thus it’s implied 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’s current. Receiving end is short circuited meaning receiving end voltage V R = 0Īpplying this condition to equation (1) we get,