Question

1. The parameters of a certain transmission line operating at 6 x 10$ rad/s are L = 0.4uH/m, C = 40 pF/m, G= 80 mS/m, and R= 2 092/m. a) Find y, a, ß, 2, and Zo: b) If a voltage wave travels 20 m down the line, by what percentage is its amplitude reduced, and by how many degress is its phase shifted?

Answer 1

For the given values of resistance, inductance, capacitance, conductance the required parameters are calculated as below :

Inductance leads to reactance and capacitance leads to Susceptance. So inductance aids with resistance and capacitance with conductance.

1 Given parameters are w = 6x 108 rad/sec and indectance, L-0.4 u Hon = (6.4x106) Capacitance, C = 40 pF/m, = 40x1512 Flm Conductance, G = 80 4 s/m = 80x106 slm Resistance, R = 2011 m. Constant, 7 = rzy ✓ (R + jco L) (G tjoc) (20 +jC6 <18)(0.4x176)) ((soxio“) +(6x18)(4oxid?) 0. 103+32.42 m2 As 7=&tip 30, 1X = 0.103 Nplm 2.42 rad/n เล = IB 2 T1 2.6 m As x = 25 = 2.6m B 2.42 Zo N/A R + JOL G+ juc 20+(30.4 x 106 x6x109) (80x106) +j (6*10*x40x102 So, 7o - 100-34 M o&L =e e Voltage wave travels, L-20m. As, he V. V20 -(0.103) (20) To = 0.131 = 13% omplitude change. phase shift, $ = BL ( o = (2.42)(20) [30] = 2° 4x vědagat

So if voltage wave travels for 20 m along the line with given parameters the amplitude change is 13% and phase shift is as above.