Question

SET 1 1. A lossless transmission line of length 1-0.3? is terminated with complex load impedance ZL- 30 + j20 ? and characteristic impedance Z0-75 ?. Using formulae, calculate (7 Marks) (4 Marks) (5 Marks) (14 Marks) i. The input impedance to the line Zin in ?; The input admittance to the line Yin in S; i The distance to first minimum from the load; Use Smith Chart to all above parameters iv.

Answer 1

l = 0.3 lambda Z_L = 30 + j 20 ohm Z_0 = 75 ohm Z_ln = Z_0 [Z_L (cos Bl + j Z_0 sin Bl)/Z_0 cos Bl + j Z_L sin Bl] Bl = 2 pi/lambda times 3 lambda = 3 pi/5 cos (Bl) = -0.31 ohm -0.3 sin (Bl) = 0.95 Z_ln = Z_0 [(30 + j 20) (-31) + j 75 times 0.95]/75 times (-0.31) + j (30 + j 20) times 0.955 = 75 [- (9 + j 6) + j 71.2/-22.5 + 28.5 J - 19] = 75 [-9 + j 65.2/-41.5 + j 28.5] \r\n Z_ln = 75 { (-9 + j 65.2) (-41.5 - j 28.5)/1722.25 + 812.25 = 75/2534.5 [373.5 + j 256.5 - j 2705.8 + 1858.2] = 75/2534.5 [2232 + (-j) 2450 Z_ln Approximatelyequalto 66 - j 72 ohm Impact admittance y_in = 1/Z_ln s y_in = 1/66 - j 72 = 66 + j 72/4356 + 5184 y_ln = 66 + j 72/9540 =