Question

Find coefficient of reflection and the fractions of the incident power that are transmitted down the lines with impedances Z2 and Z3

Z1 . Consider a junction of three co-axial transmission lines of impedances Z1, Z2, and Zs whose inner and outer conductors are connected as shown in the diagram. Suppose that a signal is incident on the junction along the line whose impedance is Z. Show that the coefticient of reflection is and that the fractions of the incident power that are transmitted down the lines with impedances Z2 and Zs are T3

Answer 1

"Given In case of T-function (or) parallel lines The free body diagram is as follows: The equivalent circuit for the above figure is For parallel linear, v"" is a constant and I"" varies i.e v"" = v + v' v' = v"" - v (1) I"" = I""_2 + I""_3 = I + I' (1) Now v""/zs_2 + v""/zs_3 = v/zs_1 - v""/zs_1 (2) From (1) in (2) v"" [1/zs_2 + 1/zs_3] = v/zs_1 - (v"" - v/zs_1) v"" [1/zs_2 + 1/zs_3] = v/zs_1 - [v""/zs_1] + [v/zs_1] v"" [1/zs_2 + 1/zs_3] + v""/zs_1 = 2v/zs_1 v"" [1/zs_1 + 1/zs_2 + 1/zs_3] = 2v/zs_1 v"" [1/zs_1 + 1/zs_2 + 1/zs_3] = 2v/zs_1 T_v = v""/v = 2/zs_1/(1/zs_1 + 1/zs_2 + 1/zs_2)"