Astandard x-band rectangular waveguide with dimensions a = 0.9 in and b = 0.4 in is filled with lossless polystyrene (er = 2.56). for the lowest-order mode of the waveguide, determine at 10 ghz the following values:

(a) cutoff frequency

(b) guide wavelength

(c) guided intrinsic impedance

(d) guided phase velocity

assume the waveguide of part 1 is to be interfaced with a hollow waveguide of the same dimensions.
to avoid reflections, an additional x-band waveguide (of the same dimensions) a quarter-wavelength long section is inserted between the two.
assume dominant mode propagation and that the operating frequency is 10 ghz.

(a) determine the guided intrinsic impedance of the quarter-wavelength section of waveguide.

(b) determine the dielectric constant of the lossless medium that must be used to fill the quarter-wavelength section waveguide.

(c) determine the length of the quarter-wavelength section waveguide.