University of California
College of Engineering
Department of Electrical Engineering
and Computer Science

T.K. Gustafson	Spring 1997
EECS 117b	4 units

Electromagnetic Fields and Waves

T.K. Gustafson 183M Cory , 2-3139, Office hours 10-11 M & Th, or by arrangement
e-mail: tkg@diva

Problem Set No. 4

Problem No. 1

Show that for the Interface mode between a vacuum and a metal that the propagation constant, is given by   where is the dielectric coefficient for the metal. Plot this for .

Problem No. 2
(a) From the expression for the dielectric coefficient for a metal including collisions, estimate the value of the d.c. conductivity. Take radians per second and , the electron density, approximately the numbers for aluminum.

(13.3c) Neglect the last three sentences (Refer to Eqs. (6),(7) and (8)).

Problem No. 3 (13.3d) Neglect the last sentence.

Problem No. 4 (9.9d)

Problem No. 5 Consider the periodic structure modelled as a transmission line with alternating inductors , in series and with capacitors C shunting the nodes between inductors with ground.

Show that the dispersion curve has two branches and that there is a stop band, the width of which is determined by and .

Design a travelling wave filter with a stop band between 9 and 10 GHz (if farads/cm) and also a pass-band from 10-15 GHz (i.e., choose , and a).

*** correction: pass-band will be determined by stop-band; impose an
*** independent condition that the group velocity of the lower band at
*** k_z = 0 is equal to half the velocity of light in vacuum.