Question

Consider a TL under the open circuited condition. (a) Find the expressions for IV(z) and I(z). (b) Sketch V(z)l and |I(z)]. (c) Find VSWR on this line.

TL = transmission line

Answer 1

(a) Find the Expressions for Vertical-bar v (z) and Vertical-bar I (z) Vertical-bar : - A transmissions line is short-circuited Short circuited i.e zL = 0 EM Equation is nabla^2 E = r^2 E nabla^2 M = r^2 H Partialdifferential^2 epsilon_2/squareroot z^2 = Partialdifferential^2 Ex Partialdifferential^2 Hy/Partialdifferential z^2 = Partialdifferential^2 Hy given short circuited transmission line is H = 1/eta [E] where E = epsilon^+- e^z + epsilon^- e^+ gamma z H = 1/eta [epsilon^+ e^-gamma z - E^- e^+ gamma z] \r\n where gamma = propagation Constant gamma = (alpha + jp) Partialdifferential^2_v/Partialdifferential z^2 = gamma^2 v Equation of transmission line v(z) is given by Therefore v(t) = v^+ e^gamma z + v^- e^-gamma z v^+ - forward wave v^- = reflected wave similarly Partialdifferential^2 I/Partialdifferential z^2 = gamma^2 I Similarly Partialdifferential^2 I/Partialdifferential z^2 = gamma^2 I I (z) = 1/z_0 [v^+ e^-gamma_z -v^- e^+ gamma z we know that gamma = alpha + jB alpha = attenuation constant