# IOWA STATE UNIVERSITY

```IOWA STATE UNIVERSITY
College of Engineering
OF SCIENCE AND TECHNOLOGY
and Computer Engineering
Problem Set No. 5
Spring Term 1998
Department of Electrical
EE 313
Issued: 980217T
Due:
980224T
Problem 1
Calculate the cutoff frequencies for the lowest 5 modes guided in a parallel-plate waveguide for which the upper and lower plates are separated by 5 cm, and the permittivity of
the medium between the two plates is &sup2; = 2 &sup2;o .
Problem 2
Consider a parallel-plate waveguide filled with a dielectric material for z &gt; 0 , as shown.
The dielectric material has permittivity &sup2;1 . The operating frequency is 30/(2π) GHz.
√
(a) Let d = 2 3π cm and consider the empty waveguide case when &sup2;1 = &sup2;o (in the absence
of the dielectric). Which TEm and TMm modes can propagate in this waveguide?
(b) Find expressions for the E and H fields for the TM2 mode.
√
(c) Let &sup2;1 = 3 &sup2;o and d = 2 3π cm. For waves propagating in the +z -direction, for which
values of m will the TMm modes be totally reflected at the dielectric boundary? Why?
x
d
&micro;o , &sup2; 1
&micro;o , &sup2; o
z
z=0
Problem 3
An air-filled parallel-plate waveguide has a plate separation of 1 cm. At what frequencies
can the modes TE1 , TE2 , TM0 , TM1 , and TM2 propagate? What are the phase velocities
for the TE1 mode at 20 GHz? Near 15 GHz?
```