The design synthesis of multiband artificial magnetic conductors using high impedance frequency selective surfaces

Abstract

This paper introduces several different design methodologies for multiband artificial magnetic conducting (AMC) surfaces. The paper begins by investigating the multiband properties exhibited by a conventional electromagnetic bandgap (EBG) AMC that consists of a frequency selective surface (FSS) on top of a thin dielectric substrate with a PEC back plane. The higher-order resonances associated with these surfaces have not been discussed in detail to date, as previous research has been concerned only with exploiting the primary resonant frequency. However, it will be shown that by understanding and making appropriate use of these higher order resonances, it is possible to design multiband AMC surfaces that work for nearly any desired combination of operating frequencies. The first multiband AMC design approach that will be considered is based on the introduction of FSS screens that have fractal or nearly fractal unit cell geometries. This is followed by a more general and robust genetic algorithm (GA) technique for the synthesis of optimal multiband AMC surfaces. In this case, a GA is used to evolve multiband AMC surface designs by simultaneously optimizing the geometry and size of the FSS unit cell as well as the thickness and dielectric constant of the substrate material. Finally, several examples of multiband AMC surfaces are presented, including some practical dual-band and tri-band designs genetically evolved for operation at GPS and cellular frequencies, as well as an example illustrating the success in creating a multiband AMC surface with angular stability.

Full text

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8 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 53, NO. 1, JANUARY 2005
The Design Synthesis of Multiband Artificial
Magnetic Conductors Using High Impedance
Frequency Selective Surfaces
Douglas J. Kern, Student Member, IEEE, Douglas H. Werner, Senior Member, IEEE,
Agostino Monorchio, Member, IEEE, Luigi Lanuzza, Student, IEEE, and Michael J. Wilhelm
Abstract—This paper introduces several different design
methodologies for multiband artificial magnetic conducting
(AMC) surfaces. The paper begins by investigating the multiband
properties exhibited by a conventional electromagnetic bandgap
(EBG) AMC that consists of a frequency selective surface (FSS)
on top of a thin dielectric substrate with a PEC back plane. The
higher-order resonances associated with these surfaces have not
been discussed in detail to date, as previous research has been
concerned only with exploiting the primary resonant frequency.
However, it will be shown that by understanding and making
appropriate use of these higher order resonances, it is possible to
design multiband AMC surfaces that work for nearly any desired
combination of operating frequencies. The first multiband AMC
design approach that will be considered is based on the introduc-
tion of FSS screens that have fractal or nearly fractal unit cell
geometries. This is followed by a more general and robust genetic
algorithm (GA) technique for the synthesis of optimal multiband
AMC surfaces. In this case, a GA is used to evolve multiband
AMC surface designs by simultaneously optimizing the geometry
and size of the FSS unit cell as well as the thickness and dielectric
constant of the substrate material. Finally, several examples of
multiband AMC surfaces are presented, including some practical
dual-band and tri-band designs genetically evolved for operation
at GPS and cellular frequencies, as well as an example illustrating
the success in creating a multiband AMC surface with angular
stability.
Index Terms—Artificial magnetic conducting (AMC), electro-
magnetic bandgap (EBG) surface, frequency selective surface
(FSS), metamaterials, multiband, perfect magnetic conductor
(PMC).
I. INTRODUCTION
A. Background
R
not found in nature. Such structures, known as metamaterials,
are deliberately designed to function in ways that ordinary
ECENTLY there has been an interest in developing
materials that exhibit novel electromagnetic properties
Manuscript received October 29, 2003; revised September 3, 2004. This
work was supported in part by a grant from the Defense Advanced Research
Projects Agency (DARPA) via the Metamaterials Program managed by Dr.
Valerie Browning under Grant.
D. J. Kern and D. H. Werner are with the Department of Electrical Engi-
neering, The Pennsylvania State University, University Park, PA 16802 USA
(e-mail: dhw@psu.edu).
A. Monorchio and L. Lanuzza are with the Department of Information Engi-
neering, University of Pisa, I-56122 Pisa, Italy.
M. J. Wilhelm is with Sciperio, Incorporated, Stillwater, OK 74075 USA.
Digital Object Identifier 10.1109/TAP.2004.840540
bulk-scale materials cannot. Some examples of microwave
metamaterials include left-handed media [1]–[5], electro-
magnetic bandgap materials [6]–[10], as well as chiral and
bianisotropic media [11]–[14]. This paper will focus on the
development of a design synthesis methodology for thin, multi-
band artificial magnetic conductors (AMCs), which represent
an important subclass of electromagnetic bandgap (EBG)
metamaterials.
An EBG surface is the microwave analog to a photonic
bandgap (PBG) structure, which operates at or near the visible
region of the electromagnetic spectrum. A PBG structure
exhibits a two-dimensional (2-D) or three-dimensional (3-D)
“band gap” over a specified frequency range, for which the
transmitted wave is greatly diminished. Similarly, an EBG
usually exhibits a 2-D band gap in the microwave region.
One particularly interesting EBG structure is that of the AMC
surface. The use of an EBG AMC structure as a substrate for a
low-profile conformal antenna is one particular application of
interest, and by aligning the resonant frequency of the antenna
with the band gap of the EBG surface it is possible to improve
antenna performance and reduce surface waves within the
substrate [15]–[17].
An ideal AMC, also known as a perfect magnetic conductor
(PMC), is a surface that exhibits a reflectivity of
posed to a PEC, which has a reflectivity of
speaking, the AMC condition is characterized by the frequency
or frequencies where the phase of the reflection coefficient is
zero degrees (i.e., where the reflected wave is in phase with the
incident wave). The AMC structure has also been shown to re-
duce the effects of unwanted surface waves, thereby providing
a means for achieving more desirable antenna radiation patterns
andreducedcouplinginanarrayenvironment[15]–[17].Unfor-
tunately, such a structure does not exist in nature, and so it must
be created by artificial means if an AMC ground plane is to be
incorporated into the design of a low-profile antenna system.
This paper specifically addresses the subclass of metamate-
rials known as EBG surfaces, which can be designed to act as
an AMC ground plane over a desired narrow frequency range.
Moreover,thetypeofAMCgroundplanethatwillbeconsidered
here is based on a planar architecture, without the need for vias,
which incorporates a high impedance Frequency Selective Sur-
face (FSS) into its design. Various methods are investigated for
exploiting the higher order resonances of these high impedance
FSS with the goal of designing multiband AMC ground planes.
One approach that will be considered for achieving a multiband
response involves using fractal geometries for the FSS screen
, as op-
[18]. Strictly
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KERN et al.: DESIGN SYNTHESIS OF MULTIBAND ARTIFICIAL MAGNETIC CONDUCTORS9
Fig.1.
corresponding unit cell.
OriginaluniplanarcompactPBGgeometryincludinggroundplaneand
elements. A robust genetic algorithm (GA) optimization proce-
dure will also be discussed for the synthesis of multiband AMC
surface designs that can have nearly any desired combination of
resonant frequency bands.
B. High Impedance Ground Plane
An EBG structure can be used to design a high impedance
ground plane that acts as a thin AMC metamaterial capable of
reducing surface waves near resonance. One of the first EBG
ground plane designs to incorporate an FSS was that proposed
in [6]. This design, referred to as the uniplanar compact PBG
(or sometimes uniplanar compact EBG) structure, consists of a
2-D FSS lattice with each cell composed of metal pads and four
connecting microstrip lines etched atop a dielectric substrate,
which in turn is backed by a standard PEC ground plane. The
advantage of this geometry is that it acts as a high impedance
magnetic conducting surface over a specific frequency range.
The geometry of this structure is shown in Fig. 1 along with a
single FSS unit cell.
One application of an AMC EBG structure is to create a high
surface impedance and reduce leaky waves in a conventional
coplanar waveguide (CPW) [6]. Additionally, the uniplanar
compact PBG structure was shown to reduce the surface-wave
losses and improve the broadside gain of an aperture-coupled
patch antenna mounted on top of it [8]. Another application
that has been demonstrated for the uniplanar compact PBG
technology was to create a TEM waveguide which gives a
relatively uniform field distribution along the waveguide cross
sectionforfrequenciesbetweenapproximately9.4and10.4GHz
[7]. It has also been shown in [15] that by placing thin strips
of an AMC surface between microstrip patch antennas allows
for the reduction in mutual coupling due to the suppression
of surface waves between the antenna elements.
C. Original Uniplanar Compact PBG Geometry
The geometry of the original uniplanar compact PBG meta-
material structure first introduced in [6] is shown in Fig. 1. The
surface consists of a doubly periodic metallic pattern (i.e., a
frequency selective surface) etched onto a thin dielectric sub-
strate material, backed by a conventional PEC ground plane.
A simple equivalent circuit model for the structure shown in
Fig. 1 can be derived and explained by examining the ge-
ometry of the unit cell. The thin conducting microstrip lines
connecting adjacent cells give rise to an inductive component.
The capacitive component consists of the one central square
patch with four additional smaller patches connected to its
corners. Thus, the structure can be viewed as behaving like a
parallel tuned LC circuit, with a resonant frequency given by:
(1)
where
respectively, associated with the periodic metallic screen. This
resonant frequency is precisely where the high impedance and
AMC conditions occur. By altering the unit cell geometry the
values for
and , and therefore the resonant frequency, can
be modified accordingly.
The surface impedance and reflection coefficient for the uni-
planar compact PBG structure shown in Fig. 1 can therefore be
estimated based on this parallel LC equivalent circuit configu-
ration. Hence, the surface impedance may be represented as
andare the equivalent inductance and capacitance,
(2)
where is given by
(3)
The reflection coefficient for normal incidence [18] is typically
used, along with the above equations, to illustrate the AMC
condition by plotting its magnitude and phase as a function of
frequency.
It is useful at this point to define a method of determining
the percent bandwidth of AMC operation, which can be speci-
fied as the frequency range for which the phase of the reflection
coefficient is within some limit. For the purposes of this paper,
the usable bandwidth will be taken to be where the phase of the
reflection coefficient is between
bandwidth is defined as
. Therefore, the percent
% (4)
where
equals
phase equals
reflection phase equals 0 .
Previous research has been concerned only with the primary
resonant frequency for various cell geometries. However, by
usinga full-waveperiodicmoment method(PMM) codeto sim-
ulate the structure in Fig. 1, higher resonant frequencies are
shown to exist. The frequency response for the uniplanar com-
pact PBG structure, along with the active region of the unit cell
geometry, is illustrated in Fig. 2.
As can be seen in Fig. 2, the original structure actually has
three resonant frequencies. Each frequency corresponds to a
different capacitive portion of the unit cell geometry. At the
lowest frequency, the entire unit cell contributes to the overall
capacitance. However, at the higher frequencies, only portions
of the unit cell contribute to the capacitance of the structure.
The second resonance has a capacitive component given by the
center square of the unit cell, while the third resonance occurs
due to the capacitance of the four smallest squares located on
the corners of the central square patch.
is the upper frequency such that the reflection phase
is the lower frequency where the reflection
, and is the center frequency where the

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10 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 53, NO. 1, JANUARY 2005
Fig. 2.
introduced in [6] showing multiple resonant frequencies.
Frequency response for the original uniplanar compact PBG structure
D. Optimization Methodology
The genetic algorithm synthesis methodology introduced
in this paper is intended to evolve optimal multiband high
impedance frequency selective surfaces (which we call GA-de-
signed high impedance FSS) for any desired combination of
operating frequencies. The majority of the multiband designs
presented here assume an incident wave normal to the surface
of the high impedance FSS structure. The final design presented
in this paper uses a slightly different approach to synthesize
a multiband GA-designed high impedance FSS structure that
has a wide stability range with respect to the incident angle of
illumination [19], [20].
II. HIGHER ORDER RESONANCES OF A HIGH IMPEDANCE FSS
A. Fractalized High Impedance FSS
The original uniplanar compact PBG structure can be modi-
fied to include even higher resonant frequencies by introducing
a fractalized structure for the unit cell. The new geometry is
based on the original uniplanar compact PBG unit cell with
slight modifications. The smallest square patches in the uni-
planar compact PBG unit cell are now altered to include three
additional smaller patches attached to each square to form a
repetitive, reduced scale version of the original. Thus, the new
unit cell has a nearly fractal capacitive structure for 3 iterations,
consisting of the original central square, four smaller squares
addedtothecentralsquare,andthenthreesmallersquaresadded
to each of those squares. The size of each square is modified
from the original uniplanar compact PBG geometry in order to
keep the overall unit cell size the same. The four original induc-
tive metal strips are included in the fractalized design to main-
tain the same inductance for this structure. The new fractalized
unit cell and a portion of the corresponding periodic metallic
sheet for this design are shown in Fig. 3, along with a plot of the
reflection phase response.
This structure can now be analyzed in much the same way
as the original uniplanar compact PBG structure and it is rec-
ognized that five different capacitive areas can be distinguished
Fig. 3.
periodic metallic sheet with reflection phase response versus frequency.
Fractalized uniplanar compact PBG unit cell and corresponding
for this modified geometry. As such, it would be expected that
five distinct resonant frequencies should be apparent when the
reflection coefficient phase is plotted versus frequency. This is
indeed the case, as can be seen in Fig. 3. Thus it can be con-
cluded that by simply changing the geometry of the periodic
metallic sheet in an appropriate way, the corresponding reso-
nant frequencies can also be modified and controlled.
In an attempt to verify whether simply changing the unit cell
geometry can influence the resonant frequency of the uniplanar
compact PBG structure, an alternative geometry was studied,
which is shown in Fig. 4, along with its corresponding reflec-
tion phase response. This geometry was obtained by separating
the four smaller square patches from the larger central patch in
the unit cell structure of the uniplanar compact PBG shown in
Fig. 1. The overall size of the patches was also slightly reduced
in order to fit within the same unit cell dimensions as used in
the original uniplanar compact PBG structure. This modifica-
tion was performed as a validation of the observations made to
explain the multiband behavior of the uniplanar compact PBG
structure. In other words, by modifying the original uniplanar
compactPBGgeometryinthisway,itisexpectedthatthelowest
resonant frequency should be eliminated. Only the two higher
resonances from Fig. 2 should be remaining, with a slight fre-
quency shift due to the change in size of the center and four
separated corner patches.
These results serve to illustrate the important multiband
aspects of uniplanar compact PBG and related AMC structures.
Moreover, these findings suggest that a desired multiband
frequency response could be obtained for these structures by

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KERN et al.: DESIGN SYNTHESIS OF MULTIBAND ARTIFICIAL MAGNETIC CONDUCTORS11
Fig. 4.
andreflectionphaseresponseforthemodifieduniplanarcompactPBGgeometry
designed to eliminate the lowest resonant frequency.
Modified uniplanar compact PBG unit cell, corresponding FSS screen,
appropriately modifying their geometry. This result has many
potential applications, namely the ability to design a specific
periodic geometry to correspond to the desired frequencies
for multiband AMC operation, and even in the design of
thin electromagnetic absorbers [21], [22]. However, designing
such a structure by trial and error or by employing simple
circuit analysis techniques can prove to be quite difficult and
tedious. For this reason a robust genetic algorithm optimization
procedure will be introduced as a useful design synthesis tool
for multiband EBG AMC surfaces.
B. Tunable High Impedance Structures
There are many ways to modify the resonant frequency of
a standard high impedance FSS structure by either designing
for a completely different frequency response, or by tuning
the original response to a nearby frequency band. One of the
simplest methods to alter the resonant frequency is to increase
the inductance or capacitance of the metallic FSS screen placed
above the substrate. This requires a slight modification of the
original unit cell design in one of two ways. For an increased
inductance design, the standard inductive metal strips can be
replaced with a meandering metal strip to connect the same
two points on the unit cell. Thus, the original capacitance is
maintained while the overall length of the metal connecting
strips, and hence the inductance, is increased. Similarly, the
inductance can be held fixed and the capacitance can be
increased by introducing an interdigitated edge between the
Fig. 5.
sheet, and frequency response for original uniplanar compact PBG geometry
and modified uniplanar compact PBG structure with interdigitated capacitance.
The interdigitated uniplanar compact PBG structure has a lower resonant
frequency for the same geometric footprint.
Interdigitated unit cell geometry with corresponding periodic metallic
square patches in adjacent unit cells. By increasing the surface
areabetween adjacentcells,thecapacitance isincreasedand the
resonantfrequencycanbereducedforthesameunitcellsizeand
substrate parameters. An example of adding an interdigitated
capacitance to the original uniplanar compact PBG unit cell
is shown in Fig. 5, along with a portion of the corresponding
periodic metallic sheet. The frequency response for the original
uniplanar compact PBG structure, along with the frequency
response of the interdigitated uniplanar compact PBG, is shown
in Fig. 5 as well. As can be seen, the use of an interdigitated
capacitance reduces the resonant frequency for each band while
maintaining the same geometric footprint.
An alternative approach to tune the high impedance FSS
structure is to modify the characteristics of the dielectric
substrate, rather than the FSS screen geometry. This can be
performed most effectively by utilizing a tunable dielectric
material that changes its permittivity with an induced electric
field applied to the substrate. By varying the permittivity of
the dielectric substrate, the resonant frequency can be similarly
tuned. One way to interpret this behavior is to recognize that
the capacitive part of the resonant LC equivalent circuit model
for the high impedance FSS is dependent upon the dielectric
constant of the substrate material. Hence, the capacitance of
the high impedance FSS, and therefore its resonant frequency,
can be influenced by changes in the value of the dielectric

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12 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 53, NO. 1, JANUARY 2005
constant of the substrate material. Another method of tuning
the capacitance of an EBG is through the use of varactor
diodes. By periodically loading an EBG structure with these
tunable capacitors, it is possible to utilize the EBG surface
to steer a reflected beam and provide greater bandwidth than
conventional reflectarray structures [23].
III. HIGH IMPEDANCE FSS DESIGN PROCEDURE
A. Periodic Method of Moments Analysis
By altering the unit cell geometry for the original uniplanar
compact PBG design, a more general structure is obtained that
achieves high surface impedance, and therefore acts as an arti-
ficial magnetic conductor, over a desired frequency range. This
more general structure will be referred to as a high impedance
FSS. The first step to generalizing the unit cell geometry is to
encode the unit cell as a 16
16 square grid of pixels, each rep-
resenting either the presence or absence of metal. The unit cell
isanalyzedusingafull-wavePMMcodethatemploysFloquet’s
theorem and rooftop basis functions [24]–[27].
B. GA Optimization of High Impedance FSS Designs
In this section an optimization methodology is introduced for
synthesizing multiband high impedance FSS structures. Due to
the complex nature of the problem, conventional optimization
methods were not considered in favor of a more robust GA ap-
proach, which mimics the evolutionary process of biological
species [28]–[31]. The use of a GA allows for simultaneous
optimization of the FSS unit cell size and geometry as well
as the dielectric constant and thickness of the substrate mate-
rial. Previous research has utilized a GA optimization to design
FSS structures for conventional applications [32]–[35]. How-
ever, this paper takes a different approach, by using the GA op-
timization to determine the shape and dimensions of the FSS
screen required to realize a metamaterial structure that behaves
as an AMC at the desired frequency bands of operation.
For the normal incidence designs considered here, the fitness
function (FF) is defined in terms of the maximum reflection co-
efficient phase
for each frequency of interest as follows:
(5)
where
uate the fitness function. The maximum reflection coefficient
phase is then the larger of the TE and TM reflection coefficient
phase angles. By optimizing for the larger reflection phase, it
is guaranteed that the other polarization will have an equal or
better fitness function.
The GA used to synthesize the high impedance FSS struc-
tures presented in this paper employs a real-valued encoding
scheme for the design parameters. The maximum population
size is 1000, the maximum number of chromosomes is 300, and
themaximumnumberofparametersis24.Tournamentselection
isusedforchoosingtheparents,and bothsingle-pointcrossover
and mutation are used in exploring the cost surface.
is the total number of frequency points used to eval-
C. Design Constraints and Operating Frequencies
One of the main applications for this type of high impedance
FSS design is to realize a thin AMC ground plane that can be
usedtoimproveantennaperformance,especiallyincaseswhere
low-profile antenna designs are required. To this end, by com-
bining a multiband or broadband antenna with a properly de-
signed multiband AMC surface, it is possible to improve the
antenna radiation characteristics, as well as reduce the max-
imum required antenna height with respect to a conventional
PEC ground plane. We introduce and compare in this paper
a number of different designs for multiband high impedance
FSS surfaces. Specific bands of practical interest have been tar-
geted for several of the high impedance FSS designs that were
evolved using a GA. For example, some possible frequency
bands considered for these designs include the GPS L1 fre-
quencyof1.575GHz,andthecellularbandscovering880MHz,
1.85–1.91 GHz and 1.93–1.99 GHz. In the actual designs, the
two higher cell phone bands are approximated by their center
frequencies of 1.88 and 1.96 GHz. The primary goal here is to
obtain a dual- or tri-band design for use at the GPS frequency
and either one or two of the three cellular bands.
For fabrication purposes, the designs were limited to a max-
imum dielectric thickness of 5.08 mm, a maximum dielectric
constant of 13, and a maximum unit cell size of one tenth of a
wavelength at 1.575 GHz (i.e., 1.9 cm). The unit cell is always
a square and contains 8-fold symmetry in order to guarantee the
same response to a TE or a TM polarized incident wave. The
above parameters will allow for a relatively thin, inexpensive
structure to be fabricated that has a small unit cell size with re-
spect to wavelength.
IV. MULTIBAND GA-DESIGNED HIGH IMPEDANCE
FSS RESULTS
A. Multiband Results for Arbitrary Frequency Bands
The GA optimization approach introduced in this paper can
beusedtodesignmultibandhighimpedanceFSSstructureswith
nearlyany arbitrary separationbetween theoperating frequency
bands. By allowing for large separation between frequency
bands, it is possible to achieve a relatively wide bandwidth
about the center frequency of each band. The result presented
here is a dual-band GA-designed high impedance FSS structure
optimized for operation at 8 and 23 GHz. These frequencies
were chosen because there is a large spacing between the
frequency bands to allow for a solution to be obtained with a
reasonably large bandwidth. The multiband GA-designed high
impedance FSS synthesis procedure evolved a surface with
the parameters given in Table I.
The advantages of this design are the relatively low dielectric
constantofthesubstratematerialaswellasthewidebandwidths
that can be achieved for both bands. The main disadvantage
is the fact that this particular design requires a fairly thick
substrate in terms of a wavelength at 8 GHz (i.e.,
or ). The unit cell, corresponding screen geometry,
and reflection coefficient phase versus frequency are shown
in Fig. 6. This reflection phase curve is perhaps a nearly
optimal response in the sense that the transition from PEC
to PMC (or AMC) conditions is very gradual and thus leads
to a large resonant bandwidth. The percent bandwidths for

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KERN et al.: DESIGN SYNTHESIS OF MULTIBAND ARTIFICIAL MAGNETIC CONDUCTORS13
TABLE I
PARAMETERS FOR DUAL-BAND 8 AND 23 GHz GA-DESIGNED
HIGH IMPEDANCE FSS
Fig. 6.
dual-band8and23GHzGA-designedhighimpedanceFSS,withcorresponding
plot of reflection phase versus frequency.
Unit cell geometry and corresponding periodic metallic sheet for
this design are 67.2% at 8 GHz, and 18.8% at 23 GHz. This
example serves to demonstrate that the GA approach can be
used to successfully design dual-band high impedance FSS
structures with relatively large bandwidths, provided that the
two frequency bands are not spaced too close together.
A tri-band high impedance FSS design has also been simu-
lated previously, operating at 3.7, 11, and 18 GHz [36]. This
design demonstrates that the multiband optimization process is
capable of obtaining more than two resonances with large oper-
ating bandwidths. The following designs illustrate an additional
capability of the optimization procedure; namely, the design of
multiband high impedance FSS structures with very little sepa-
ration between the operating frequencies.
B. GA-Designed High Impedance FSS Results for GPS and
Cell Band Applications
We next consider a specific design goal with practical ap-
plications, namely, the optimization of a dual- or tri-band high
TABLE II
PARAMETERS FOR DUAL-BAND GPS AND CELLULAR GA-DESIGNED
HIGH IMPEDANCE FSS
impedance FSS to operate at a GPS frequency of 1.575 GHz
and one or more of the cellular frequency bands of 880 MHz,
1.85–1.91 GHz and 1.93–1.99 GHz. It is anticipated for designs
ofthistype,wherethebandsarespacedrelativelyclosetogether,
that all of the design constraints may not be simultaneously sat-
isfied. As such, the constraints on maximum dielectric constant
and maximum substrate thickness will be maintained whenever
possible to ensure that fabrication can be achieved using com-
mercially available materials.
It should be noted that different polarizations are needed for
operating an antenna at both the GPS and cellular frequencies.
While the simpler case of linear polarization is clearly possible
for an antenna placed above an EBG surface, the question arises
as to whether or not a circularly polarized antenna will func-
tionproperlyoveranEBGgroundplane.Previousresearchcon-
cerningaconformalcurlantennaplacedaboveamushroom-like
EBG surface [37] has shown that circular polarization is pos-
sible, and in fact the axial ratio can be improved compared
to a conventional PEC ground. Thus, two antennas operating
with different polarizations above the same properly optimized
EBG surface will allow for GPS reception as well as cellular
communications.
The first example presented is a dual-band GPS/cellular high
impedanceFSSsurface. Thisdesign hasa thinner substratethan
the maximum allowable value, with a relative permittivity of
13. However, the unit cell size must be larger than the tenth of
a wavelength goal in order to achieve a successful design. The
parameters for the resulting structure are listed in Table II.
This design was optimized for operation at 1.575 and
1.96 GHz, the GPS L1 frequency and the highest of the
three cellular frequencies. This structure, being the first true
GA-designed high impedance FSS to achieve such a dual-band
response, was also fabricatedand tested. Thefabricated surface,
along with a plot of the simulated versus measured data for this
design, is shown in Fig. 7. The reflection phase plot illustrates
thatthetargetedresonantfrequencieswereachieved,withaper-
cent bandwidth of 4.43% at 1.575 GHz and 2.2% at 1.96 GHz.
The phase plot also shows very good agreement between the
PMM simulation and the measurements of the actual fabricated
surface. This surface does not achieve a bandwidth as large as
the first dual-band GA-designed high impedance FSS structure
presented in Fig. 6. However, the separation between frequency
bands is drastically reduced for the result shown in Fig. 7 and,
hence, the GA-designed high impedance FSS must transition
from a PEC to PMC condition and back over a much smaller
frequency range, thus effectively reducing the PMC bandwidth.
In this case, there is still sufficient separation between the
bands, as the surface will act as a PEC between about 1.65 and
1.9 GHz.

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14 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 53, NO. 1, JANUARY 2005
Fig. 7.
dual-band GPS and cellular GA-designed high impedance FSS. The FSS unit
cell geometry is shown as an inset on the reflection phase response plot. A
photograph of the actual GA-designed high impedance FSS ground plane that
was fabricated and tested has also been included at the top of the figure.
Simulated versus measured reflection coefficient phase for the
TABLE III
PARAMETERS OF TRI-BAND GA-DESIGNED HIGH IMPEDANCE FSS FOR GPS
L1 AND TWO CELLULAR FREQUENCIES
The nextexample to be considered involves thesynthesis of a
tri-band high impedance FSS for operation at GPS L1 and two
cellular bands. In this case, one of the cell bands is below the
GPS L1 band and the other is above it. The parameters for a
tri-band high impedance FSS optimized using the GA design
technique are given in Table III.
The corresponding unit cell, screen geometry, and reflection
phase response are shown in Fig. 8 for the tri-band design. No-
tice that, in this case, the unit cell size for the GPS band is
slightly larger than a tenth of a wavelength and the resulting
dielectric constant was found to be 36, a higher value than that
found for the previous design. However, the unit cell size is ac-
tually quite small for the lowest operating frequency.
Fig. 8.
GA-designed high impedance FSS, with corresponding reflection phase
response. The targeted center frequencies are 880 MHz, 1.575 GHz, and 1.88
GHz.
Unit cell geometry and corresponding metallic screen for a tri-band
The resonant frequencies for this design are 880 MHz,
1.575 GHz, and 1.88 GHz. Thus, the lower of the two cellular
bands was achieved, along with a lower primary resonance
that can be useful for communication applications even in the
900 MHz range. The bandwidths for these frequency bands
are 6.29%, 2.85%, and 1.97%, respectively. This particular
design demonstrates that it is possible to successfully synthe-
size practical high impedance FSS designs for low-frequency
applications, i.e., applications below 1 GHz.
V. MODIFICATIONS AND RESULTS FOR ANGULAR STABILITY
A. Fitness Function Modification Within GA
To improve angular stability, two simulations have been per-
formed; one in the frequency domain and the other by varying
the incidence angle at the center frequency. The fitness function
for the frequency domain is calculated according to
(6)

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KERN et al.: DESIGN SYNTHESIS OF MULTIBAND ARTIFICIAL MAGNETIC CONDUCTORS 15
Fig. 9.
angularly stable GA-designed high impedance FSS, with corresponding
reflection coefficient response. The targeted center frequencies are 1.575 and
1.96 GHz.
Unit cell geometry and corresponding metallic screen for dual-band
where
band and
quantity is computed for different incidence angles
is the total number of frequencies
is evaluated at normal incidence. Then, a similar
in the desired
(7)
where
tral frequency of the desired band. It is useful to note that the
separation of the reflection coefficient into real and imaginary
parts allows for the maximization of the amplitude of
presence of losses in thedielectric materials or the metallic con-
ducting FSS screen.
To obtain the fitness value for each frequency band, the TE
and TM responses are averaged, while a weighted mean is used
for the frequency and incidence angle fitness data. For each fre-
quency band, the fitness function is calculated as
is the total number of incidence anglesat the cen-
in the
(8)
where
ture resonates and
isthenumberoffrequencybandswherethestruc-
is the weight assigned to the fre-
quencyfitnessfunction.Theglobalfitnessfunctioniscalculated
by averaging the values obtained in (8) from each band.
B. Dual-Band Design With Angular Stability
The structure presented in this section has been designed for
wide-angle dual-frequency use, with the operating bands cen-
teredattheGPSfrequencyof1.575GHzandatthestandardcell
phone frequency of 1.96 GHz. In this case a dielectric material
with permittivity
and a thickness value
has been imposed, corresponding to a commercially-available
substrate. The evaluation points in frequency have been set to
with equal sampling around the central frequency of
each band, while the evaluation points for illumination angle
have been set to
, in the interval between
incidence) and
(grazing angle). Moreover, a weight
of
has been imposed in (8). A symmetric shape to-
gether with equal dimensions along the periodicity directions
have been chosen for the elementary cell.
The dimensions of the unit cell were found to be
cm. The unit cell geometry, a complete view of the re-
sulting FSS screen, and the reflection coefficient response are
provided in Fig. 9. The relative bandwidths are 8.5% in the first
band and 2.14% in the second. The angular performance of the
dual-band AMC structure is shown in Fig. 10. It is worth noting
that a properly tuned GA optimization procedure can provide
very robust solutions with respect to the variation of the inci-
dence angle; in our case, we obtained phase values well below
up to an incidence angle of
frequencyaswellasovertheentirefrequencyband(seeFig.10).
To better appreciate the angular performance of the optimized
AMC, two additional curves are included in Fig. 10 for compar-
ison purposes. They include the response of simpler structures
consisting of a
dielectric slab (designed at the central fre-
quency of the band) backed by a PEC ground plane with
and.
cm
(normal
, both at the central
VI. CONCLUSION
The designs presented within this paper have successfully
demonstratedtheabilitytosynthesizemultibandAMCsurfaces.
An investigation into a conventional uniplanar compact PBG
type of AMC has revealed the existence of higher order
resonances associated with the geometrical configuration and
size of these structures. By understanding and accounting
for these higher order resonances, it has been shown that
multiband AMC surfaces can be designed for nearly any
desired combination of operating frequencies. The first AMC
surface design methodology introduced was based on FSS
unit cell geometries that exploit the self-similar property of
fractals in order to achieve the desired multiband performance.
Next, a versatile and robust GA optimization technique was
introducedforthedesignsynthesisofmultibandAMCsurfaces.
The GA was used to simultaneously optimize the geometry
and size of the FSS unit cell, as well as the thickness and
relativedielectricconstantof thesubstrate.Optimized dual-and
tri-band designs were also presented for operation at GPS and
cellular frequencies. Finally, an example has been shown that
demonstrates how the GA high impedance FSS optimization

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16 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 53, NO. 1, JANUARY 2005
Fig. 10.
analysis is performed at (a) ? ? ????? GHz and (b) ? ? ???? GHz.
Angular response of the synthesized structure shown in Fig. 9. The
technique can be used to successfully obtain a multiband
solution that exhibits angular stability without imposing any
additional physical complications to the design of an EBG
AMC surface. The optimization approach introduced in this
paper could also be applied in future research to improve upon
strip-loaded metamaterials in order to obtain better soft or hard
surfaces. For example, periodicities within the strips could be
utilized to eliminate unwanted strip modes and possibly even
increase the operating bandwidth of such a structure.
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Douglas Kern (S’01) received the B.S. and M.S. degrees in electrical engi-
neering from The Pennsylvania State University, University Park, in 2001 and
2003, respectively, where he is currently working toward the Ph.D. degree in
electricalengineeringinthe ComputationalElectromagneticsandAntennasRe-
search Lab (CEARL).
From August 2001 to August 2004, he was a National Defense Science and
Engineering Graduate (NDSEG) Fellow. His research interests include electro-
magnetic bandgap structures, artificial magnetic conductors, and conformal an-
tenna design, as well as electromagnetic modeling techniques.
Douglas H. Werner (S’81–M’89–SM’94) received
the B.S., M.S., and Ph.D. degrees in electrical en-
gineering and the M.A. degree in mathematics from
The Pennsylvania State University (Penn State),
University Park, in 1983, 1985, 1989, and 1986,
respectively.
He is a Professor in the Department of Electrical
Engineering, Penn State. He is a Member of the
Communications and Space Sciences Lab (CSSL)
and is affiliated with the Electromagnetic Com-
munication Research Lab. He is the Director of
the Computational Electromagnetics and Antennas Research Lab (CEARL)
http://labs.ee.psu.edu/labs/dwernergroup/. He is also a Senior Scientist in
the Electromagnetics and Environmental Effects Department of the Applied
Research Laboratory at Penn State. He has published numerous technical
papers and proceedings articles and is the author of nine book chapters. He is
an Editor of Frontiers in Electromagnetics (Piscataway, NJ: IEEE Press, 2000).
He also contributed a chapter for Electromagnetic Optimization by Genetic
Algorithms (New York: Wiley Interscience, 1999) as well as Soft Computing in
Communications (New York: Springer, 2004). He is a former Associate Editor
of Radio Science. His research interests include theoretical and computational
electromagnetics with applications to antenna theory and design, microwaves,
wireless and personal communication systems, electromagnetic wave interac-
tions with complex media, meta-materials, fractal and knot electrodynamics,
neural networks, genetic algorithms and particle swarm optimization.
Dr. Werner is a Member of Eta Kappa Nu, Tau Beta Pi, Sigma Xi, the
American Geophysical Union (AGU), the International Scientific Radio Union
(URSI) Commissions B and G, and the Applied Computational Electromag-
netics Society(ACES). He waspresented with the 1993 Applied Computational
Electromagnetics Society (ACES) Best Paper Award and was also the recipient
of a 1993 International Union of Radio Science (URSI) Young Scientist Award.
In 1994, he received The Pennsylvania State University Applied Research
Laboratory Outstanding Publication Award. He was the recipient of a College
of Engineering PSES Outstanding Research Award and Outstanding Teaching
Award, in March 2000 and March 2002, respectively, and was recently pre-
sented with an IEEE Central Pennsylvania Section Millennium Medal. He has
also received several Letters of Commendation from Penn State’s Department
of Electrical Engineering for Outstanding Teaching and Research. He is an
Editor of the IEEE ANTENNAS AND PROPAGATION MAGAZINE.
Agostino Monorchio (S’89–M’96) was born in Italy
on March 16, 1966. He received the “Laurea” degree
in electronics engineering and the Ph.D. degree in
“methods and technologies for environmental mon-
itoring,” from the University of Pisa, Italy, in 1991
and 1994, respectively,
In 1995, he joined the Radio Astronomy Group
at the Arcetri Astrophysical Observatory, Florence,
Italy, as a Postdoctoral Research Fellow, working
in the area of antennas and microwave systems. He
has been collaborating with the Electromagnetic
Communication Laboratory, The Pennsylvania State University (Penn State),
University Park, since 1997, when he was awarded a Summa Foundation
fellowship and, successively in 1999, in the context of a NATO Senior
fellowshipprogramme. He has also beena Visiting Scientist at the University of
Granada, Spain, and he is affiliated with the Computational Electromagnetics
and Antennas Research Laboratory of Penn State University. He is currently
an Associate Professor in the School of Engineering of the University
of Pisa, and an Adjunct Professor at the Italian Naval Academy and the
Department of Electrical Engineering, Penn State. His research interests
include the development of novel numerical and asymptotic methods in applied
electromagnetics, both in frequency and time domains, with applications
to the design of antennas and microwave systems, the analysis and the
design of frequency selective surfaces and novel materials and the definition
of electromagnetic scattering models from complex objects and random
surfaces for remote sensing applications.
Luigi Lanuzza (S’04) was born in Milazzo, Italy,
in 1973. He received the degree in electronics en-
gineering from the University of Messina, Messina
Sicily, in 2001.
In 2001, he joined the Department of Information
Engineering, University of Pisa, as a Research Asso-
ciate, working mainly in the development of genetic
algorithms for the design of high performance fre-
quencyselectivesurfaces,artificialmagneticconduc-
tors, and waveguide filters.
Michael J. Wilhelm, photograph and biography not available at the time of
publication.