Question

The mathematical expression for a voltage wave on a transmission line is given as: V(z,t) = 5e-azsin(41x10ºt – 2012) (V/m) where z is the distance from the generator and a is an unknown constant. At z = 2 meters the amplitude of the voltage oscillation is measured to be 1 Volt. a) (2 pts) Find the linear frequency of the wave b) (3 pts) Find the wavelength c) (3 pts) Find the phase speed d) (3 pts) Find the value of the constant a e) (2 pts) Find the direction of propagation f) (2 pts) Find the lossy TL current wave equation on the equation sheet and write it down g) (3 pts) Briefly explain the principles for designing a quarter-wave matching network h) (2 pts) Under what circumstances does it become necessary to use transmission line theory?

Answer 1

I Sol Given line Voltage Wave of the transmission VCz,t) = 5edz Sin (haxlo't "Haxlott - 2002) (ulni m the equation = HAX109 aaf wax 10 = 2 GHz i Linear frequency = a bettz 6 have length = 20 from the equation ß = 204 7 - 8 205 = 0.4 m ③ Phase Velocity Up - w = xf Up = 0. 1x 2x 109 = 0.ax109 m/s & given z=2 At t=0, , V=1 1=56-2a Sin (-40A) e QA = 1- 4.061 Apply In on both sides 2x = 1.4011 (R=0.70057

with - E compared of propagation us tz U+- Ate-re is compared given equation I . Direction of propagation To find Current equation we Characterstic umpedence Velocity factor = Ž = 1 K Relative permitivity - = 0.2x 10.9 mis 3x108 mis. = 225 O V K = 2 = 2.25 20- 276 = 184 1 (z, t) = 5 e-az Sin (wax lo t-2002) 184 I (z, t = 0.027 e-az sin (HR x 10 t - 2002) .