Example$-1$

Consider a dielectric filled parallel plate wave guide

with d$=2$cm$.$ The permeability of the dielectric is $($$0)$

and the permittivity is $(2.25)$ the $($$0).$ Find:

$(1)$ The propagation velocity if the electromagnetic Waves.

$(2)$ The minimum Cutoff Frequency.

$(3)$ Which TE$\_($m$)$ and TM$\_($m$)$ nodes can propagate for

$12$ GHz signal $?$

$(4)$ Calculate the associated cutoff wavelengths in

each case?

Example $2$

Repeat example $1,$ if the dielectric between the

plates is Teflon and has r of $2\mathrm{.}1$ for

an electromagnetic wave of a frequency of

$4$ GHZ $.$