Question

A lossless transmission line is used to deliver an AC signal from Liverpool to Wirral. The length of the transmission line is 6 km. The phase velocity is the same as in free space. The transmission line is terminated by a load at the Wirral side with an impedance of 100 Ω. j) If the characteristic impedance of the transmission line is 100 Ω and the AC b) signal has a frequency of 50 Hz, what is the input impedance seen at the Liverpool side? ii) If the characteristic impedance of the transmission line is 20 Ω and the AC signal has a frequency of 50 Hz, what is the input impedance seen at the Liverpool side? iii) If the characteristic impedance of the transmission line is 20 Ω and the AC signal has a frequency of 10 kHz, what is the input impedance seen at the Liverpool side? iv) Use the results obtained from Questions Q1b-i) to Q1b- to explain why the characteristic impedance is generally a very important parameter at high frequencies, but not so important at low frequencies

Answer 1

Given l = 6 km Z_R = 100 Ohm = Load. (i) z_0 = 100 Ohm f = 50 Hz. we know that input impedance of a lossless line is given by z_in = z_0 [z_R + j Z_0 tan beta l/z_0 + j z R tan beta l] beta = 2 pi/lambda. lambda = c/f = 3 times 10^8/50 beta l = 2 pi/lambda (l) = 2 pi times 50/3 times 10^8 times 6 times 10^3 beta l = 6.283 times 10^- 3. Tan (beta l) = 6.283 times 10^- 3.z_in = 100 [100 + j (100) tan beta l/100 + j (100) + tan beta l]. z_in = 100 Ohm. (ii) Given z_0 = 20 Ohm f = 50 Hz. Z_in = 20 [100 + j 20 (6.283 times 10^- 3)/20 + j 100 (6.283 times 10^- 3)] z_in = 20 (4.99 < - 1.72 degree). z_in = 99.8 < - 1.72 degree. (iii) Given z_0 = 20 Ohm