UDC 621.372.853.1 : 621.396.677.73
Indexing Terms: Antennas, horn, Electromagnetic waves, scattering
Scattering by a dielectric discontinuity
in an H-plane sectoral horn
Z. A. DELECKI, MSc*
M. HAMID, PhD, FIEE, FIEEEt
and
A. Z. ELSHERBENI, PhD, MIEEE*
* Dept of Electrical Engineering, University of Manitoba, Winnipeg,
Manitoba, Canada R3T 2N2
t University of Manitoba; on leave at the Dept of Electrical
Engineering, University of Central Florida, Orlando, Florida 32816,
USA
t Dept of Electrical Engineering, University of Mississippi,
Mississippi 38677, USA
SUMMARY
Scattering of an electromagnetic wave at a transverse
discontinuity created by an imperfect dielectric in a long H-
plane sectoral horn fed by parallel plate waveguide is solved
by the method of transformation into an equivalent plane
wave (TEPW). An analytical method of matching fields of
both waveguides is developed in order to be consistent with
the TEPW method. The results are compared with data based
on classical and experimental methods.
1 Introduction
Dielectrically loaded horn antennas have been experi-
mentally investigated by a number of authors.
1
"
4
The
simplest structure employing a horn antenna is an H-plane
sectoral horn connected to parallel plate waveguide and
embedded in a dielectric medium. In order to solve the
scattering problem in such a structure the scattering at
both the dielectric discontinuity and the waveguide
junction must be considered. It is well known that such
discontinuities have no exact solution due to the fact that
regions associated with them cannot in most cases be
described in a single coordinate system. Many researchers
have contributed a great deal of work to determine
analytically the scattering by such junctions. Among these
are Stevenson,
5
Leonard and Yen,
6
Hamid,
7
Lewin,
8
Iskander and Hamid.
9
In spite of the fact that they have
based their solutions on different concepts and theories,
this question seems to be still open for an exhaustive
treatment. The previous attempts discuss the case where in
the interior of the horn (or sectoral waveguide) only
outward propagating modes exist. The goal of this paper is
to solve the problem of scattering at the dielectric
discontinuity as well as the scattering at the waveguide
junction discontinuity resulting in a single reflection
coefficient to be monitored in the feed waveguide.
The configuration of the dielectric loaded waveguide
system under consideration is shown in Fig. 1. The parallel
plate waveguide feeds the H-plane sectoral waveguide,
which is assumed to be long and to have an arbitrary flare
angle a. The fields diffracted at the outer edges of the
sectoral waveguide do not interact with those existing on
the transversely oriented internal dielectric surface due to
the fact that the dielectric is assumedHossy and the sectoral
waveguide is semi-infinite in length.
It is further assumed that the waveguide supports a
single TE
p0
mode, where p = 1, 2, 3,..., in the forward
direction (see Fig. 1). The effect of a discontinuous
boundary at the junction causes a diffracted field with an
infinite number of modes travelling in both directions of
the junction.
Journal of the Institution of Electronic and Radio Engineers, Vol. 58, No. 5, pp. 235-243, July/August 1988
2 Behaviour of the Electromagnetic Field in the
Transition Region
Considering that the parallel plate waveguide feeds the
horn-like waveguide and that the tangential electric field
across boundaries is continuous, the unknown total
reflection coefficient F
m
may be found by substituting the
solution of the Helmholtz equation in the parallel plate
region Rj (with the undetermined reflection coefficient of
interest) into the corresponding region of the sectoral
waveguide.
Let us take the solution of the Helmholtz equation for
the electric field with provision that it is expressed in polar
coordinates of the form
8
sin
(1)
where the index p denotes an arbitrary single mode
supported by the parallel plate waveguide. In order to
make use of equation (1) its partial derivatives must be
found. Upon finding and substituting these into the
Helmholtz equation expressed in polar coordinates we
obtain, after lengthy routine calculations, the following
partial differential equation for the unknown reflection
coefficient F
m
valid for
h,
cos
a , a
2
r
2
cos
0+
w
+ 2
mn
ap tan
mrr sin
cos (j)— j
©1988 IERE