1) Consider travelling waves in a waveguide of rectangular cross section. The width of the guide...

Transcribed Image Text:

1) Consider travelling waves in a waveguide of rectangular cross section. The width of the guide is g and height is h. Assume that the guide is in the x direction with height in the y direction and width in the z direction. The equation for the field in this medium is given 2 Z as; 0² Ey at² The field that satisfies this equation is independent of y and is given by; Ê(x,z, t) = Eo sin(лz/g) cos(wt - kx)ĵ Here c denotes the speed of light and wo = (cπ/g) a) Find the dispersion relation b) Find the phase speed vo 0² Ey əx² = c². c) Find the group speed vg d) Are these waves dispersive or nondispersive (i.e. is v = vg)? de - w Ey A square pulse of width I given by; Ê(x, z = g/2,t = 0) = Eo for 0<x<I Ê(x, z = g/2,t=0) = for x < 0 and x > l e) Transform this signal to the Fourier domain formally (write but do not evaluate the integrals) f) Find Ak and Aw. This part IS NOT during the exam but to be sent by mail by Friday 11.59 pm. Do part (e) using MATLAB or Python and plot the results g) h) Re create the wave at time t = T and plot it using MATLAB or Python. 1) Consider travelling waves in a waveguide of rectangular cross section. The width of the guide is g and height is h. Assume that the guide is in the x direction with height in the y direction and width in the z direction. The equation for the field in this medium is given 2 Z as; 0² Ey at² The field that satisfies this equation is independent of y and is given by; Ê(x,z, t) = Eo sin(лz/g) cos(wt - kx)ĵ Here c denotes the speed of light and wo = (cπ/g) a) Find the dispersion relation b) Find the phase speed vo 0² Ey əx² = c². c) Find the group speed vg d) Are these waves dispersive or nondispersive (i.e. is v = vg)? de - w Ey A square pulse of width I given by; Ê(x, z = g/2,t = 0) = Eo for 0<x<I Ê(x, z = g/2,t=0) = for x < 0 and x > l e) Transform this signal to the Fourier domain formally (write but do not evaluate the integrals) f) Find Ak and Aw. This part IS NOT during the exam but to be sent by mail by Friday 11.59 pm. Do part (e) using MATLAB or Python and plot the results g) h) Re create the wave at time t = T and plot it using MATLAB or Python.

Answer rating: 100% (QA)

Explanation In waveguides the dispersion ... View the full answer