Misalai ABCD parameters (ko da ake kira misalai chain ko kuma misalai transmission line) suna da cikakken circuit constants wadanda ake amfani da su don taimaka kan model transmission lines. Duk da haka, misalai ABCD parameters suna amfani a two port network representation of a transmission line. The circuit of such a two-port network is shown below:
Wani babban bahaushe na engineering na power system ya shiga a transmission of electrical power daga wata wurin (misali generating station) zuwa wata wurin (misali substations ko homes) ta hanyar mafi karfi.
Saboda haka, yana da kyau game da malamai na mathematical modeling of how this power is transmitted. Misalai ABCD parameters and a two-port model suna amfani don haɗa wannan cacewa mai zurfi.
Don in ba da cikakken wannan mathematical model, transmission lines suna sauƙa da uku types: short transmission lines, medium transmission lines, and long transmission lines.
Formula for these ABCD parameters zai canza kadan bayan iyakokin transmission line. Wannan ita ce da ya shafi saboda wasu electrical phenomena – such as corona discharge and the Ferranti effect – only come into play when dealing with long transmission lines.
Ko da sunan, wani two-port network na da 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.
Now the ABCD parameters of the transmission line provide the link between the supply and receiving end voltages and currents, considering the circuit elements to be linear in nature.
Thus the relation between the sending and receiving end specifications is given using ABCD parameters by the equations below.
Now in order to determine the ABCD parameters of the transmission line let us impose the required circuit conditions in different cases.
The receiving end is open-circuited meaning the receiving end current IR = 0.
Applying this condition to equation (1) we get,
Thus it’s implied 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 dimensionless parameter.
Applying the same open circuit condition i.e IR = 0 to equation (2)
Thus it’s implied that on applying open circuit condition to ABCD parameters of a 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 = IS ⁄ VR mho.
Receiving end is short circuited meaning receiving end voltage VR = 0
Applying this condition to equation (1) we get,
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. 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 = VS ⁄ IR Ω.
Applying the same short circuit condition i.e VR = 0 to equation (2) we get
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. Since dimension wise D is a ratio of current to current, it’s a dimensionless parameter.
∴ The misalai ABCD parameters of the transmission line can be tabulated as:
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