Open Book

1. Phasor expressions for Hz , E phi , and Hr as functions of radius r are given for a forward propagating TE01 wave in Eqs. 8.9(19) - (20). Give the corresponding instantaneous expressions, Hz (r, z, t), Ephi (r, z, t) and Hr (r, z, t) for

. . . .. . . . . .(a) a propagating wave, w > wc ;

. . . .. . . . . .(b) a cut-off wave, w < wc .

2. . .. .___________________________

.. . . . . . . . . .. . . . . . . . . . .. |

. . . . . . . . .... epsilono ,. ..|. . .epsilon1 = 4 epsilono ,

. . . . . . . . . .. . .muo. . . . . .|. . . . . .. . .muo

. . . . . __________|____________

. . . .. . . . . .. . . . . .. . . . . z = 0

A hollow-pipe waveguide of arbitrary shape has air dielectric up to z=0 and dielectric with epsilonr =4 beyond. Find the frequency for which there is no reflection for a TM mode incident on the junction if cutoff frequency in the air region is 10 GHz.

3. It was shown in class that the TM wave can travel along a surface with a velocity less than that of light in the dielectric if the surface has an inductive surface reactance. This slow wave decays exponentially in the direction normal to the surface.

. . . . . .. . . ..(a) What evanescent decay constant alphax (tau of the text) is required so that 90% of the power is within 10 cm of the surface?

. . . . . .. . . ..(b) What inductive surface reactance Xs is required to obtain this alphax for a frequency of 10 GHz?

4. . . . . .. . .. . . . . . . . . . . . . . . . .. --------------a--->|

. . .... .. ... .. . . ... . .. . . . . . . . . .. ..| --b-->|

. . . . . .. . . ..______________________________ . . . . _

. . . . . .. . . .. |. . . . .. . . . . . . | ep- |. . . . . . |. . . . ... . . .| . . . . ^

. . . . . .. . . . . |.epsilon2. . .|silon1|. . . . . . |. . . . ... . . .| . . . . d

. . . . . .. . . . .|_________|____|_____|_______| . . . . v

A circular-cylindrical resonator of radius a, height d has dielectric epsilon1 for 0<r<b, dielectric epsilon2 for b<r<a. For the mode with no phi or z variations, similar to that of Sec. 10.6, find the equation which determines resonant frequency w of the mode. You need not try to solve the equation.

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