Size Constraint inn Design of Concentric Ring
R
Array
Pedro Mendes Ruiz, Israel Hinostroza aand Régis
Guinvarc’h
upt
Randy L. Hau
Electrical Engineering and Computer Science
Colorado School off Mines
Golden, Colorado 804
401, USA
SONDRA
SUPELEC
Gif-sur-Yvette, France
israel.hinostroza@supelec.fr
Abstract—In an earlier work a dual-polarized un
niform concentric
ring array had a diameter of 4 m and 224 sp
piral antennas, it
covered a bandwidth from 1 GHz – 2 GHz. In tthe present paper,
the additional constraint of space is introducced. Keeping the
same characteristics of the previous work, th
he new proposed
array has a diameter of 2.2 m (70% space reeduction) and 148
antennas (34% element number reduction). T
The design of the
array was carried out using Genetic Algorithms optimization.
I.
INTRODUCTION
Two-arm Archimedean spiral antennas aree mono-polarized
wideband elements and can be used in the dessign of wideband
arrays. The highest frequency of the array iis limited by the
appearance of the grating lobes which aree related to the
distance between the antennas and the lattice of the array. For
dual-polarization capabilities, the introductioon of spirals of
opposite polarizations is needed. This neeed introduces an
additional distance between same-polarized elements, hence
reducing the bandwidth. To overcome this issuue, a sparse array
approach has been proposed in [1] [2]. Inn this work, the
additional constraint of maximum aperture forr a dual-polarized
planar array of spiral antennas is explored.
II.
AY
CONCENTRIC RING ARRA
A. Previous Array
In a previous work [2] a uniform concentrric ring array was
chosen to design a 4-ring dual-polarized arrray keeping the
radius of the first ring of the array at 15 cm. Thhe resultant array
had a diameter of 4 m. The relative sidelobee level (RSLL) is
less than -10 dB for scan angles, from broaadside, less than
θ=30º and frequencies less than 2 GHz. Beinng dual-polarized,
the array was composed of 112 antennas peer polarization (a
total of 224 antennas).
be optimized, but that would mean having
h
a variable number of
parameters in the optimization. In order to keep the problem
simple, the number of rings is choseen to be 4 and the maximum
radius accepted is 1.2 m.
C. GA optimization
The parameters to be optimized, to obtain a maximum
RSLL of -10 dB with a maximum raadius of 1.2 m, are shown in
Fig.1. The optimization is carried out
o using isotropic sources.
The description of the parameterrs for the n-th ring is as
follows:
•
ween the rings and Δ0 is the
Δn is the distance betw
radius of the first ring.
•
t ring from the reference
Fn is the rotation of the
j=0º
In order to have a uniform distribution of antennas per ring,
the number of elements in each ring for each polarization is
nce by the minimal distance
obtained by dividing its circumferen
between consecutive elements (24 cm) and applying the floor
function, meaning that the angular distance (Pn) between
elements of each ring varies acccordingly but it is not a
parameter to be optimized. As for th
he position of the elements,
the RH spiral antenna is by defau
ult placed so that the first
element of the innermost ring is the reference to calculate the
angular position of the other elemen
nts and to apply the rotation
of the other rings. The elements aree then uniformly distributed
in each ring in such a manner that the
t RL elements are placed
in the middle of two consecutive RH
H elements.
The spirals had a diameter of 10.5 cm. As the antennas in
each ring have alternately right (RH) and left (LH) hand
polarizations, the minimum distance between two consecutive
antennas of the same polarization was set to 244 cm.
B. Additional constraints for size reduction
To reduce the size of the array, additionaal constraints are
considered in this work. The minimal distannce between two
rings is set to 20 cm. The innermost (first ringg) ring must have
a variable radius of at least 12 cm, so thhat it is able to
accommodate at least 3 radiating elements for each polarization
(to be able to use the sequential rotation teechnique [3]). It
would be possible to use the number of rings as a parameter to
978-1-4799-7815-1/15/$31.00 ©2015 IEEE
2455
Fig. 1. Rotation angles and distancces between the rings of the
array to be optimized. Circles witth cross and filled circles
represent spirals with RH and LH polarization, respectively.
AP-S 2015
To ensure a maximum RSLL of -10 dB, for frequencies
lower than 2 GHz, the optimization was carriedd out at 2 GHz. It
was performed using the Matlab GA toolbox. The optimization
was realized 8 times and only the best result oof the 8 runs was
kept.
process a new array, working in thee same bandwidth and even
larger, has been proposed, but this tiime with a maximum radius
of 1.15 meters, 32 % of the area of the
t original array. Thanks to
this size reduction, the number of ellements was also reduced to
66 % of the original. The new arraay keeps its good RSLL for
scan angles lower than θ=30º from broadside.
b
REFERENCES
[1]
[2]
[3]
Fig. 2. Elements positions in previous work [2] design (left)
and in this work design (right). Crosses andd circles are the
positions of the RH and LH spirals, resspectively.
Fig. 3. Maximum rejection of sidelobe levvel (RSLL) of
optimized array for scan angles lower thann θ=30º from
broadside.
D. Results
In Fig. 2 we can appreciate the compariison between the
sizes of the reference array [2] and the optimized array
presented in this work. The maximum radius of the new array
is 1.15 m whereas for the reference array itt is 2.04 m. This
corresponds to an area reduction of 68 %. Bessides, the number
of antennas was reduced from 112 to 74, per polarization,
which corresponds to an element number reducction of 34 %.
Although the optimization was carried outt at 2GHz, Fig. 3
shows that the RSLL is still good up to 3 GHz..
CONCLUSIONS
In a previous work [2], a concentric rinng array working
from 1 GHz to 2 GHz, with a maximum radiuss of 2 meters, was
conceived. Imposing space constraints in the optimization
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ual polarization interleaved spiral
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