Consider a transform-limited pulse of center frequency f = 10 GHz, and of full-width 2T = 1.0 ns. The pulse propagates in a lossless single-mode rectangular guide which is air-filled and in which the 10 GHz operating frequency is 1.1 times the cutoff frequency of the TE₁₀mode. Using the result of Problem 13.24, determine the length of guide over which the pulse broadens to twice its initial width. What simple step can be taken to reduce the amount of pulse broadening in this guide, while maintaining the same initial pulse width? Additional background for this problem is found in Section 12.6.

In Problem

Show that the group dispersion parameter, d²Î²/dω², for a given mode in a parallel-plate or rectangular waveguide is given by

where ω_c is the radian cutoff frequency for the mode in question [note that the first derivative form was already found, resulting in Eq. (57)].

Eq. (57)

Transcribed Image Text:

d²B We\27-3/2 do? Ост sin Om ---=) 1 – Vgm ||