Consider a section of a uniform transmission line of length , characteristic impedance Z0...

Consider a section of a uniform transmission line of length , characteristic impedance Z0 , and propagation constant γ between terminal pairs 1- 1' and 2- 2' shown in Fig. 9- 44(a). Let (V1, I1) and ( V2 , I2) be-the phasor voltages and phasor currents at terminals 1-1' and 2- 2', respectively.

(a) Use Eqs. a and b to write the equations relating Let (V1, I1) and ( V2 , I2) in the form

Equation (a):

Determine A, B, C, and D, and note the following relations:

Equaion(b):

A= D

Figure:

Figure (a): A line section of length .

Figure (b) : An equivalent two-port symmetrical T-network.

And

Equation (C):

AD - BC =1.

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b) Because of Eqs. a, b, and c, the line section in Fig (a) can be replaced by an equivalent two-port symmetrical T-network shown m Fig(b). Prove that

and