The Design of Wide Band Planar Arrays of Spiral
Antennas
Israel Hinostroza, Régis Guinvarc'h
Randy L. Haupt
Supelec, SONDRA
3 Joliot-Curie, 91192 Gif-sur-Yvette, France
israel.hinostroza@supelec.fr
Haupt Associates
State College, PA 16801
Abstract—A method to design planar phased arrays of spiral
antennas is presented. Different shapes of spirals and their
performance in a periodic array are analyzed using this method.
Keywords- planar array; phased array; spiral-like antenna;
cross-polarization rejection.
I.
Our constraints are that XpolR is more than 15dB, VSWR
is less than 2:1, with no grating lobes and a minimum side
lobes rejection level of 10dB. The goal is to determine the best
kind of antenna and lattice that results in the widest bandwidth
for a maximum scan angle of 30°.
II.
INTRODUCTION
An Archimedean spiral antenna is a good candidate in the
design of a wideband planar array due to its wide band
properties. Spiral antennas come in many different shapes (e.g.
standard Archimedean, square, star [1], hexagonal [2], etc.).
These spirals can be loaded (using resistive, capacitive or
inductive charges [3], [4]) and also cavity backed in order to
improve performance [5]. The antennas can be placed in a
planar array using different lattices (triangular, square, etc.). In
any case, the lowest frequency of the bandwidth is limited by
the Cross Polarization Rejection (XpolR) and the Voltage
Standing Wave Ratio (VSWR). These parameters are related to
the dimension of the spiral antenna. The highest frequency is
limited by the presence of grating lobes which are related to the
distance between antennas.
ANALYTICAL STEP
To illustrate this method we consider four antennas:
standard Archimedean spiral, square, hexagonal and star [1].
We only considered two planar periodic lattices: triangular and
square.
1) Lower limit
To obtain the performance of the antenna at lower
frequencies we propose to use the theoretical limit of VSWR
for the Archimedean spiral with a correction factor p:
fL = p
c0
2πR
(1)
fL is the lowest frequency to obtain an acceptable VSWR and
XpolR, c0 the free space light speed, and R is the outer radius
of the spiral.
The final goal of this study is to explore new techniques for
adapting spiral antennas in a chosen lattice for planar arrays. In
order to do that, we must decrease the computation time in
order to make numerical optimization practical.
Coupling can alter both the XpolR and the VSWR but only
to a certain point. The analytical modeling of coupling is
complex and numerical methods are required to determine the
performance of the array. Since there are many shapes of spiral
antennas (archimedean, square, etc.) and lattices, the process
can be very time-consuming. We propose that the lowest
frequency of the bandwidth only depends on the individual
properties of the antenna, and the highest frequency is
determined by the presence of grating lobes.
We introduce a two-step approach. First, coupling is not
considered during the analytical optimization over the
antenna/lattice couples. This first step saves time on the
antenna/lattice selection. Second, a numerical optimization is
carried out using only the selected candidates of the first step.
Coupling is then taken into account and the values obtained
before are used to seed the optimization algorithm. This
approach saves a considerable amount of computation time.
978-1-4244-9561-0/11/$26.00 ©2011 IEEE
609
Figure 1. Gain and XpolR of spiral antenna, FEKO [6] simulation.
According to Fig. 1, the limits at lower frequencies for a
useful XpolR of an Archimedean spiral antenna with R = 7cm,
is 0.95GHz. In the same way, VSWR is useful for frequencies
higher than 0.78GHz. Then we have:
AP-S/URSI 2011
pVSWR −spiral ≈ 1.1 , p AR −spiral ≈ 1.4
(2)
For the other antennas, R is the radius of the circumscribed
circle and it is equal to 7cm. The values obtained are listed in
Table I.
TABLE I.
CORRECTION FACTORS FOR THE ANTENNAS
Standard
Square
Hexagonal
Star
p
1.1
1.3
1.2
1.2
VSWR
1.4
1.6
1.5
1.7
XpolR
2) Upper limit
The presence of grating lobes depends on the chosen lattice
and the distance d between the antennas. The shape of the
antenna plays an important role in the distance as well. Table II
presents the possible distance/radius ratios. A minimum gap of
0.02*R to avoids antennas touching each other.
TABLE II.
Spiral Ÿ,
Ŷ lattice
2.04
POSSIBLE DISTANCE/RADIUS RATIOS
Hexag Ÿ
lattice
1.77
Hexag Ŷ
lattice
1.84
Square
Ÿ lattice
1.68
Star, Square
Ÿ lattice
1.45
Ant
d/R
3) Bandwidth
In order to evaluate the bandwidth (BW), we prefer to
express it as a ratio of the highest frequency which is
determined by the presence of grating lobes (fGL), and the
lowest frequency (fL) :
BW = f GL / f L
(3)
The next expressions present the possible bandwidths for a
scan angle of 30º (worst case):
BW =
c0 4
c
/ p 0 , triangular lattice
2πR
3 3d
(4)
c0 2
c
/ p 0 , square lattice
3d
2πR
(5)
BW =
standard spiral with triangular lattice (BW=1.7) as the less
efficient candidate.
III.
NUMERICAL STEP
The results obtained in the analytical optimization are used
here as a starting point to reach the bandwidth that was
estimated before. We use arrays composed by 18 antennas in
free space. The optimization parameters are the number of
turns and the distance between the antennas (ref. Table IV).
The initial value of the radius of the antennas is 7cm. Initial
values of XpoR and VSWR are not acceptable throughout the
estimated bandwidth. For each array two sets of spirals were
used, those with a constant radius and those with a variable
radius. The size of the spirals are determined by the number of
turns to keep the same density of lines of the spirals. Doing
this, we keep low the level of side lobes.
TABLE IV.
INITIAL VALUES AND RANGES
Spiral Ÿ latt
Hexag Ÿ latt
Squa Ÿ latt
Antennas
14.4
12.53
11.9
Ini. dist(cm)
6/6
6/6
6/6
Ini. #turns
[14.13, 14.67]
[12.26,12.8 ]
[11.59, 12.21]
range dist(cm)
[5.5, 6.5]
[5.5, 6.5]
[5.5, 6.5]
range #turns
These two parameters will influence on the coupling. The
distance will modify, slightly though, the frequency at which
the grating lobes appear. Table V and Fig. 2 presents the
results using FEKO and its optimization tool OPTFEKO.
TABLE V.
Spiral Ÿ
lattice
1.65 / 1.7
1.56 / 0.95
14.76
6.13/5.98
5
BW OBTAINED BY NUMERICAL OPTIMIZATION
Hexagonal Ÿ
lattice
1.78 / 1.8
1.82 / 1.02
12.71
6.37/6.31
26
Squa Ÿ
lattice
1.77 / 1.8
1.94 / 1.1
11.88
6.42/6.31
17
Antennas
BW opt/theory
fGL(GHz) / fL(GHz)
distance(cm)
#turns
#iterations
Using the values of table I and II along with expressions (4)
and (5), we can choose the best candidates.
TABLE III.
ANALYTICALLY ESTIMATED BANDWIDTHS
Spiral
Ÿ latt
Spiral
Ŷ latt
Hexag
Ÿ latt
Hexag
Ŷ latt
Squa
Ÿ latt
Squa
Ŷ latt
Star
Ŷ latt
1.7
1.5
1.8
1.5
1.8
1.8
1.7
Ant
&
latt
BW
According to table III, in bold font, there are three top
candidates. In order to demonstrate our method of estimating
the bandwidth of the antenna/lattice, we will select the two best
candidates and another less efficient candidate. We chose the
hexagonal spiral with triangular lattice and the square spiral
with triangular lattice (BW=1.8) as best candidates and the
610
Figure 2. XpolR for scan angle ș=30º, ij=0º (worst case).
which validates the proposed method. According to the
analytical estimations, there is no need to study the remaining
cases (ref. Table III) which means a large amount of time is
saved on the global optimization. Also, the seeding of the
optimization algorithms greatly help to reduce the optimization
time.
The proposed approach would be also applied to WAVES
method (Wideband Array with Variable Element Sizes [1]) to
study and design planar array with wider bandwidth.
REFERENCES
[1]
[2]
Figure 3. Optimized hexagon array, for scan angle ș=30º, ij=0º.
[3]
The bandwidth obtained by numerical optimization is close
to the estimated bandwidth. The optimization would not have
converged if we had tried to optimize the array for a much
wider bandwidth than the one estimated in the analytical step.
IV.
[4]
[5]
CONCLUSION
The results of the numerical optimization show that the
analytical optimization is close enough to obtain a 5% of error
611
[6]
E. Caswell, “Design and Analysis of Star spiral with Applications to
Wideband Arrays with Variable Element Sizes”, PhD Dissertation,
Virginia Polytech Institute and State University, 2001.
I. Hinostroza, R. Guinvarc'h, R. L. Haupt, “Improving Axial Ratio of a
Planar Phased Array of Spirals”, Antennas and Propagation Symposium
(APSURSI), 2010 IEEE.
H. Nakano, H. Mimnaki, J. Yamauchi, K. Hirose, “A low profile
Archimedean spiral antenna”, Antennas and Propagation Society
International Symposium, 1993 IEEE.
J.L. Volakis, M.W. Nurnberger, D.S. Filipovic, “Slot spiral antenna”,
IEEE Antennas and Propagation Magazine, vol. 43, no. 6, December
2001.
H. Nakano, T. Igarashi, H. Oyanagi, Y. Iitsuka, J. Yamauchi,
“Unbalanced-Mode Spiral Antenna Backed by an Extremely Shallow
Cavity”, IEEE Antennas and Propagation, Transactions, vol. 57, no.6,
June 2009.
FEKO, EM Software & Systems-S.A., 32 Techno lane, Technopark,
Stellenbosch,
7600
South
Africa,
2004.