A Horn-Fed Reflector Optimized with a Genetic Algorithm
Randy L. Haupt
The Pennsylvania State University
Applied Research Laboratory
P. O. Box 30
State College, PA 16804-0030
haupt@ieee.org
Abstract
Designing reflector antennas to minimize the effects of spillover and feed
blockage requires optimization of accurate numerical models. A FEKO [1] model
of a horn-fed parabolic reflector is optimized for maximum directivity using a
genetic algorithm (GA).
Introduction
The design of a horn fed parabolic dish antenna involves many design parameters.
There are two very important considerations when placing a horn antenna at the
focal point of a parabolic dish antenna. First, the horn radiation pattern should be
concentrated on the reflector surface to reduce spillover and have the desired edge
taper. Second, the horn should be designed to reduce blockage, hence gain, of the
antenna. Spillover and edge taper is typically handled through horn design [2],
and blockage is remedied through offset reflectors. The computational
horsepower necessary for optimizing a full wave analysis of the horn fed reflector
was not available during early efforts to optimize the horn feeds for reflectors [3].
This paper presents results of maximizing the directivity of a 12λ diameter
reflector through optimizing the horn size and placement as well as the focal
length.
Objective Function Formulation
Figure 1 is the reflector antenna model. The waveguide dimensions and dish
diameter are specified while the other variables have the range limits indicated
below.
h = waveguide height = 0.75λ
w = waveguide width = 0.375λ
D = reflector diameter = 20λ
v = distance of paraboloid vertex to origin
h ' = horn height: a ≤ a ' ≤ 5a
w ' = horn width: b ≤ b ' ≤ 5b
L = horn length: 0.5λ ≤ A ≤ 4.5λ
f = focal length of paraboloid: 3.125λ ≤ f ≤ 6.25λ
δ f = v − f : 0 ≤ δ f ≤ 4λ
©2005 ACES
A GA written in MATLAB calls the FEKO program to calculate the directivity of
the antenna. MATLAB writes reflector design variables to a text input file for
FEKO. FEKO reads these variables then writes directivity values to a file that can
be read by MATLAB.
Figure 1. Model of the horn fed reflector antenna.
Results.
The GA had a population size of 8 and a mutation rate of 20%. Convergence
stalled after 39 generations as shown in Figure 2. The maximum directivity
obtained was 31.2 dB. Figure 3 shows the resulting E plane and H plane pattern
cuts for the final design. The optimized variables had values given by
h ' = 1.7λ
w ' = 1.3λ
L = 4.2λ
f = 22λ
δ f = 3.8λ
The f / D ratio is 1.83. In addition, the δ f = 3.8λ moves the horn even farther
from the reflector. Thus, the antenna design has a high directivity at a cost of not
being very compact. It would be possible to further limit or fix the focal length of
the reflector and optimize on the horn antenna if a certain size constraint had to be
imposed.
Figure 2. The directivity increases as the GA progresses. The first few
generations show dramatic improvement.
Figure 3. The E plane and H plane cuts of the optimized reflector antenna.
Conclusions
The GA found the optimum horn design and focal point for the reflector antenna
that resulted in maximum directivity for a 12λ diameter dish. Interfacing a GA to
FEKO produces a powerful tool for designing horn-fed reflector antennas.
Acknowledgments
I want to thank C. J. Reddy and Vivek Ramani of EM Software & Systems (USA)
Inc for helping me with the FEKO model.
References
[1] FEKO Suite 4.1, EM Software and Systems (www.feko.info), 2003.
[2] A.D. Olver, et.al., Microwave Horns and Feeds, New York: IEEE Press,
1994.
[3] W. Truman and C. Balanis, "Optimum design of horn feeds for reflector
antennas," AP-S Trans., Vol. 22, No. 4, Apr 1974, pp. 485-586.