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Synthesis of artificial magnetic conductors by using multilayered frequency selective surfaces - Antennas and Wireless Propagation Letters 196
IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 1, 2002
Synthesis of Artificial Magnetic Conductors by Using
Multilayered Frequency Selective Surfaces
Agostino Monorchio, Member, IEEE, Giuliano Manara, Senior Member, IEEE, and Luigi Lanuzza
AbstractIn this letter, the combination of a multilayered di-
electric structure, a capacitive frequency selective surface (FSS)
and a perfectly electric conducting (PEC) ground plane is proposed
for realizing high-impedance surfaces. These surfaces behave like
an artificial magnetic conductor (AMC) in a specific frequency
range; the inclusion of the dielectric layers allows us to enhance the
angular properties of the AMC as well as the frequency bandwidth
of the device. In order to obtain the proper values of the design pa-
rameters, a genetic algorithm (GA) is employed that makes use of
an electromagnetic solver based on the method of moments (MoM)
to evaluate the scattering properties of the structure. A key step in
the design procedure is the inclusion in the fitness function of the
electromagnetic response of the high-impedance surface with re-
spect to the illumination angle. The synthesized structure shows
the desired frequency performance and reveals robust as concerns
the stability of the solution with respect to a wide interval of illu-
mination angles.
Index
TermsArtificial
magnetic
conductors,
frequency
selective surfaces, genetic algorithms, metamaterials, photonic
bandgap.
I. I
NTRODUCTION
I
T is well known that a hypothetical perfect magnetic con-
ductor might be very useful in a large variety of microwave
applications; for instance a magnetic ground plane can improve
the performance of printed dipole antennas, creating their
equiverse image currents. Recently, photonic bandgap (PBG)
structures have been widely investigated for their behavior as
artificial magnetic conductors (AMC) at the corresponding
stopband frequency, considerably reducing the tangential
magnetic field component. Either three-dimensional [1] or
two-dimensional [2] structures have been proposed to realize
this goal, both dielectric and metal-dielectric. In particular, a
two-dimensional structure can be realized by using a frequency
selective surface (FSS) screen backed by a perfectly electric
conducting (PEC) ground plane. This configuration is desirable
for its low-cost manufacturing and for the easy integration
in microwave devices. In this work, we propose to insert the
FSS screen in a multilayered dielectric arrangement in order
to obtain the desired reflecting properties of the AMC at wide
incidence angles as well as for wide frequency bands. However,
the design of such a complex structure is not an easy matter,
because it involves the optimization of many parameters, as
for instance, the FSS screen basic periodicity cell shape and
dimensions, as well as the dielectric layers thickness and
Manuscript received August 5, 2002; revised September 18, 2002.
The authors are with the Department of Information Engineering,
University of Pisa, I-56126 Pisa, Italy (e-mail: a.monorchio@iet.unipi.it;
g.manara@iet.unipi.it; l.lanuzza@iet.unipi.it).
Digital Object Identifier 10.1109/LAWP.2002.807956
electric properties. Genetic algorithms are global stochastic
search methods that are very suitable to this purpose [3]. They
are able to determine a global minimum (or a maximum) of a
multivariables function representing the problem to be solved,
by evolving proper populations of solutions. The chromosomes
associated with the individuals of these populations are a set of
genes, representing coded versions of the optimization parame-
ters. As shown in the recent literature (see for instance [4][9]),
a genetic algorithm (GA) evolutionary strategy can be suitably
applied to design FSS filters. In this work, GA is employed
to determine the shape and the dimensions of the metallic
elements of the FSS screen, as well as the permittivity and the
thickness of each dielectric layer for realizing an AMC in the
pertinent frequency band. A key step in the design procedure
is the inclusion in the fitness function of the electromagnetic
response of the high-impedance plane with respect to the
incidence angle. The synthesized structure shows the desired
frequency behavior and reveals robust as concerns the stability
of the solution with respect to wide angles of illumination. An
example of a designed high-impedance surface is presented
and numerically tested to demonstrate the effectiveness of the
optimization procedure.
II. F
ORMULATION
In Fig. 1, we show the structure of the multilayered FSS
screen backed by a PEC ground plane that has been used as a
working example. Indeed, a single dielectric FSS screen is not
able to provide the proper reflecting behavior in wide frequency
bands and/or wide intervals of incidence angles. To this aim, the
thickness and the dielectric permittivity of each layer, together
with the shape and the dimensions of the unit periodicity cell,
can be used as additional parameters to be optimized in order
to get the desired frequency response [4]. Each parameter has
been codified in a binary string to form a chromosome, repre-
senting the whole structure, as shown in Fig. 2. To achieve a
realistic design, the permittivities of the dielectric layers were
selected from among a set of 16 commercially available prod-
ucts, together with some hypothetical (but still realistic) ex-
ploratory values. The maximum number of different dielectric
layers has been initially fixed to eight, being the layers placed
indifferently above or below the FSS screen. However, extended
numerical experiments showed that satisfactory results can be
found by using only two or three dielectric layers over the FSS
screen and one layer as substrate. The basic periodicity cell is
subdivided into elementary pixels coded as 1s or 0s depending
on whether they are covered by a printed metal element or not
(see Fig. 2); either symmetric or asymmetric shapes of the ele-
mentary cell have been considered [4], [5].
1536-1225/02$17.00 © 2002 IEEE MONORCHIO et al.: SYNTHESIS OF ARTIFICIAL MAGNETIC CONDUCTORS
197
Fig. 1.
Configuration used for realizing the high-impedance surface.
Fig. 2.
(a) Design parameters and (b) chromosome structure.
To evaluate the frequency and angular electromagnetic be-
havior of the surface, an electromagnetic solver based on the
method of moments (MoM) has been used, which is particularly
suited for the analysis of doubly periodic multilayer screens [8].
Since the MoM formulation is nothing but conventional, it will
be not discussed further for the sake of brevity.
The evaluation criterion of the structure performance has
been chosen as the root mean square difference between
the actual and the desired electric field reflection coefficient
for both TE and TM modes; i.e.,
j for a
PMC (this condition has been imposed separately on both the
real and the imaginary parts). To improve angular stability, two
analyses have been performed, one in the frequency domain
and the other by varying the incidence angle at the central
frequency of the band. As far as the frequency behavior is
concerned, we calculate the fitness function as
e
m
(1)
where
is the total number of frequencies
in the desired
band. A similar quantity is computed for different incidence
angles
e
m
(2)
where
is the total number of incidence angles
consid-
ered at the central frequency of the desired band. In order to
ensure symmetry, we have imposed equal dimensions along the
periodicity directions for the unit cell. We note that the separa-
tion of the reflection coefficient into its real and imaginary part
allows us to maximize the amplitude of
also in the presence
of losses in the dielectric materials or in the conductor.
To get the global fitness value of the structure, a simple av-
erage between TE and TM responses is performed (ensuring
good polarization performance), while a weighted average is 198
IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 1, 2002
(a)
(b)
Fig. 3.
(a) GA synthesized basic periodicity cell. (b) Complete view of the
FSS screen. Dark areas correspond to printed metallic elements.
evaluated between the frequency and incidence angle fitness
data, i.e.,
(3)
with
. A single point crossover has been used,
with probability
. The specific GA adopted in
this work employs a standard proportionate selection also called
the weighted roulette wheel selection scheme [3]. Moreover,
to improve the algorithm speed of convergence, a new kind of
selection strategy has been introduced. It is well known that
best results are usually found if GA starts from a good ini-
tial population. In our case, we build the initial population by
using the best chromosomes of several trial populations; once
the evolution has started, the next generations are created by
inserting only new chromosomes showing fitness values lower
than the older ones. In this way, overlapping generations are in-
volved, resulting in a hybrid scheme between generational and
steady-state GAs [3]. A faster convergence might result in a
loss of genetic information, prematurely removing overall unfit
chromosomes, which, h