28 December, 2011

Medium Transmission lines representation

Medium transmission lines are represented in two ways 


1) nominal - T Representation
2) nominal - π Representation
Nominal - T Representation
In this representation the shunt admittance is placed in the middle and the series impedance is divided into two equal parts and these parts are placed on either side of the shunt admittance. The nominal-T representation is shown in Fig below.

               Nominal-T representation

In this figure
Vs ,Is             - Sending end voltage & current
Vr,Ir         - Receving end voltage & current
Z/2          - half of the lumped series impedance of the line
Y             -lumped shunt admittance of the line
VM          -mid point voltage
Then the application of KCL at the midpoint results in
(1)






Rearranging the above equation can be written as
(2)





Now the receiving end current is given by
(3)





Substituting the value of VM from (2) in (3) and rearranging we get
(4)





Furthermore the sending end current is
(5)





Then substituting the value of VM from (2) in (5) and solving
(6)





Then the ABCD parameters of the T-network are
(7)
(8)
(9)

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