452 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 57, NO. 2, FEBRUARY 2009
A New Technique for Design of Low-Profile,
Second-Order, Bandpass Frequency
Selective Surfaces
Mudar Al-Joumayly, Student Member, IEEE, and Nader Behdad, Member, IEEE
Abstract—In this study, a new method for designing low profile
frequency selective surfaces (FSS) with second-order bandpass re-
sponses is presented. The FSSs designed using this technique utilize
non-resonant subwavelength constituting unit cells with unit cell
dimensions and periodicities in the order of � ��
�
. It is demon-
strated that using the proposed technique, second-order FSSs with
an overall thickness of
�
�� can be designed. This is considerably
smaller than the thickness of second-order FSSs designed using
traditional techniques and could be particularly useful at lower
frequencies with long wavelengths. To facilitate the design of this
structure, an equivalent circuit based synthesis method is also pre-
sented in this paper. Two bandpass FSS prototypes operating at
X-band are designed, fabricated, and tested. A free space measure-
ment setup is used to thoroughly characterize the frequency re-
sponses of these prototypes for both the TE and TM polarizations
and various angles of incidence. The frequency responses of these
structures are shown to have a relatively low sensitivity to the angle
of incidence. Principles of operation, detailed design and synthesis
procedure, and measurement results of two fabricated prototypes
are presented and discussed in this paper.
Index Terms—Antenna arrays, frequency selective surfaces
(FSSs), periodic structures, radomes, spatial filters.
I. INTRODUCTION
F REQUENCY selective surfaces (FSSs) have been the sub-ject of intensive investigation by many researchers. These
structures are used in a variety of different applications ranging
from microwave systems and antennas to radar and satellite
communications [1]–[11]. A FSS is a periodic structure usually
composed of an assembly of identical elements arranged in a
one or two-dimensional lattice. In their simplest form, these el-
ements can be in the form of metallic patches with a specific
pattern or the complementary of the metal patches having aper-
tures similar to the metallic patches etched in a ground plane.
Similar to microwave filters, frequency selective surfaces can
have low-pass, high-pass, bandpass, or band-stop frequency re-
sponses. However, unlike microwave filters, these responses de-
Manuscript received May 12, 2008; revised August 21, 2008. Current version
published March 20, 2009.
M. Al-Joumayly is with the Antennas, RF, and Microwave Integrated Sys-
tems (ARMI) Laboratory, Department of Electrical Engineering and Computer
Science, University of Central Florida, Orlando, FL 32816-2362, USA.
N. Behdad was with the Department of EECS, University of Central Florida.
He is now with the ECE Department, University of Wisconsin, Madison, WI,
USA (e-mail: behdad@engr.wisc.edu).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TAP.2008.2011382
pend not only on frequency but also on the polarization and
angle of arrival of the incident electromagnetic wave.
Many different techniques have been used to design FSSs.
Traditional FSS design techniques often use periodic arrays of
resonant elements to achieve bandpass or band-stop behavior
as described in [12], [13]. Using these techniques, a periodic
array of slot elements can be designed to demonstrate a first
order bandpass response. To achieve higher order bandpass re-
sponses, multiple FSS panels must be cascaded with a quarter
wavelength spacing between each panel. While this quarter-
wavelength spacing may be useful in certain applications for
structural rigidity, it presents a problem for other applications
including low-frequency FSSs, as well as applications where
conformal FSSs are required to cover structures with moderate
to small radii of curvature. Moreover, using quarter-wavelength
spacers increases the sensitivity of the response of such second
order FSSs to the angle of incidence. While techniques exist that
can circumvent this particular problem, such techniques gener-
ally involve using superstrate dielectric stabilizers that further
increase the overall thickness of the structure [13].
Another category of periodic structures which has been in-
vestigated over the years, is dielectric frequency selective sur-
faces (DFSS) similar to those discussed in [14]. In DFSSs, inho-
mogeneous dielectric periodic structures are used. Such struc-
tures have the advantage of low absorption loss as compared to
metallic structures. Generally, the performance of such DFSSs
are affected by the number of layers and the distribution of the
material in the unit cell. However, these structures are more
difficult and costly to fabricate compared to traditional planar
structures. Other techniques for designing frequency selective
surfaces have also been reported. In [15], a FSS based on sub-
strate integrated waveguide (SIW) technology is studied. The
response of this type of FSS depends on resonant frequency of
the SIW cavity. However, these structures are difficult to fabri-
cate, are relatively thick, and are generally narrow-band, since
the SIW cavities are high-Q structures. Another concept in de-
signing FSSs based on microstrip patch antennas has been re-
ported in [16] and [17]. In [16], an FSS is obtained by utilizing
two arrays of patch antennas coupled together using coupling
apertures in their ground planes. In [17], a similar design is used,
except this time the coupling aperture is a resonator (first order
filter) and an antenna-filter-antenna array is obtained. However,
in all these techniques, resonant patch antennas are used in pe-
riodic structures with periodicities in the order of half a wave-
length. This large periodicity is generally undesirable, since it
will lead to an early onset of grating lobes and will also increase
the sensitivity of their responses to the angle of incidence.
0018-926X/$25.00 © 2009 IEEE
AL-JOUMAYLY AND BEHDAD: A NEW TECHNIQUE FOR DESIGN OF LOW-PROFILE, SECOND-ORDER 453
In this paper, a new technique for designing low-profile
frequency selective surfaces, with second-order bandpass
responses, is presented. In this technique, the constituting
elements of the FSS are non-resonant1 structures that are com-
bined to create a second-order bandpass filter. Both the unit cell
dimensions and the periodicity of the structure are considerably
smaller than the wavelength. This helps reduce the sensitivity
of the response of this FSS to the angle of incidence and assures
that no grating lobes can be excited for any real angle of inci-
dence [13]. Furthermore, the overall profiles (thicknesses) of the
second-order FSSs presented in this paper are extremely small
(equal to ). This thickness is considerably smaller than
the overall thickness of a traditional second-order FSS designed
by cascading two first-order FSS panels a quarter-wavelength
apart, which is at least a quarter wavelength. The combination
of subwavelength unit cell dimensions and small period as well
as the small overall thickness of the proposed structure results
in a second-order FSS with a frequency response that is less
sensitive to the angle of incidence of the EM wave compared
to that of a traditional second-order bandpass FSS obtained
by cascading two first-order FSS panels a quarter-wavelength
apart. Such low-profile FSSs can be especially useful at lower
frequencies where the wavelengths are long and traditional
second-order FSSs will be too thick, bulky, and heavy to use.
In what follows, first the design procedure and the principles
of operation of the proposed FSS are presented in Section II.
For a normally incident plane wave, a simple equivalent cir-
cuit model is developed for the proposed FSS and it is shown
that the structure is equivalent to a second-order coupled res-
onator spatial filter. A synthesis procedure along with closed
form formulas are presented that allow for deriving the equiv-
alent circuit model parameters based on the desired response
type, operational bandwidth, and center frequency of opera-
tion. In Section III, the design, fabrication, and measurement
results of two prototypes of the proposed FSS are presented and
discussed. Finally, a few concluding remarks are presented in
Section IV.
II. PRINCIPLES OF OPERATION AND FSS DESIGN PROCEDURE
A. Principles of Operation
Fig. 1 shows the three-dimensional view of different layers
of the proposed FSS. The structure is composed of three dif-
ferent metal layers separated from one another by two very thin
dielectric substrates. The top and bottom metal layers consist
of two, two-dimensional (2-D) periodic arrangements of sub-
wavelength capacitive patches. The center metal layer consists
of a 2-D periodic arrangement of metallic strips in the form of
a wire grid. In its basic and simplest form, the capacitive patch
layers are identical and so are the dielectric substrates. This re-
sults in a structure that is symmetric with respect to the plane
containing the wire grids. The overall thickness of the FSS is
twice the thickness of the dielectric substrates, , used to fabri-
cate the structure on. Fig. 1 also shows the top view of different
1Note: By using the term “non-resonant,” we mean that, if only one single
unit cell of the proposed FSS is considered in free space, it will not be a resonant
structure similar to a resonant dipole or slot antenna. This is different from an
FSS composed of a periodic array of resonant dipole or slot antennas, where the
constituting unit cell is a resonant structure.
Fig. 1. Topology of the low-profile, second-order bandpass FSS presented in
Section II.
Fig. 2. A simple equivalent circuit model for the low-profile FSS shown in
Fig. 1 and discussed in Section II.
layers of the unit cell of the proposed FSS. Each unit cell has
maximum physical dimensions of and in the and
directions, respectively, which are also the same as the period
of the structure in the and directions. Each capacitive patch
in the capacitive layer is in the form of a square metallic patch
with side length of , where is the separation between the
two adjacent capacitive patches. The top view of the inductive
strips used in the middle layer of the unit cell of the FSS is also
shown in Fig. 1. As is observed from this figure, the structure
maintains its original shape as it is rotated by 90 . This ensures
that the frequency response of the structure is polarization in-
sensitive for normal incidence. Assuming that the structure has
the same period in and directions, the inductive layer will
be in the form of two metallic strips perpendicular to each other
with a length of , and width of .
To better understand the principles of operation of this struc-
ture, it is helpful to consider its simple equivalent circuit shown
in Fig. 2, which is valid for normal incidence. The patches in the
first and third metallic layers are modeled with parallel capac-
itors ( and ), while the wire grid layer is modeled with
parallel inductor . The substrates separating these metal
layers are represented by two short pieces of transmission lines
with characteristic impedances of and
and lengths of and , where and are the
dielectric constants of the substrates and is the free
space impedance. The half-spaces on the two sides of the FSS
are modeled with semi-infinite transmission lines with charac-
teristic impedances of and , where
and are normalized source and load impedances and
454 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 57, NO. 2, FEBRUARY 2009
Fig. 3. (a) Simplified equivalent circuit model of the FSS presented in Fig. 1.
(b) By converting the T-network composed of � , � , and � into a �-net-
work composed of � , � , and � , the simplified equivalent circuit shown in
(a) is converted to a classic second-order coupled resonator filter utilizing in-
ductive coupling between the resonators.
for free space. This equivalent circuit can be further sim-
plified to obtain the one shown in Fig. 3(a). In this circuit, the
short transmission line sections are replaced with their equiva-
lent circuit model composed of a series inductor and shunt ca-
pacitor. This circuit is a second-order coupled resonator band-
pass filter. The second-order nature of this filter can be clearly
observed if one converts the T-network composed of inductors
, , and in Fig. 3(a) to a -network composed of the
inductors , , and as shown in Fig. 3(b) [18]. As can
be observed, the circuit shown in Fig. 3(b) is composed of two
parallel LC resonators coupled to one another using a single in-
ductor, . This circuit is a classic example of a second-order
coupled-resonator bandpass filter as described in [18]. The two
circuits shown in Fig. 3(a) and (b) are both second-order cou-
pled resonator structures and are completely equivalent to each
other. The equations relating the values of the inductors ,
, and to those of , , and are also provided in
Fig. 3(b). Since the equivalent circuit shown in Fig. 3(a) is an ap-
proximated version of the one shown in Fig. 2, the proposed FSS
structure will act in a manner similar to that of a second-order,
coupled-resonator bandpass filter.
B. Design Procedure
The FSS presented in this paper can be designed using a
simple and systematic approach. The design procedure starts
with the equivalent circuit model shown in Fig. 3(a). The frac-
tional bandwidth of the FSS, , its center frequency of opera-
tion, , and the response type are generally known a priori.
In the coupled resonator filter topology presented in Fig. 3, the
normalized loaded quality factor of the resonators, and ,
the normalized coupling coefficient between the two resonators,
, and the normalized source and load impedances, and ,
are determined by the desired response type (e.g., Butterworth,
TABLE I
NORMALIZED QUALITY FACTORS AND COUPLING COEFFICIENT
FOR REALIZING DIFFERENT FILTER RESPONSES
etc.). The values of these parameters are provided in [18] and
also given in Table I for a number of common second-order re-
sponses. The classical equations used for the design of second-
order coupled-resonator filters of the type shown in Fig. 3(b) can
be found in [18]. In this case, we have used these equations and
after some simple algebraic manipulations and with the aid of
the reverse transformation equations provided in Fig. 3(b), we
have obtained the element values of the equivalent circuit model
shown in Fig. 3(a). This way, from the values of , , , ,
, , and , the values of inductors , , and can
be determined using the following equations:
(1)
(2)
(3)
where is the fractional bandwidth of the structure
and is the 3 dB transmission bandwidth of the filter. As
mentioned in the previous subsection, and are the se-
ries inductors representing the short transmission lines on both
sides of the inductive layer, as shown in Fig. 2. The value of this
inductance can be calculated from the value of the inductance
per unit length of the short transmission line. Using the Teleg-
rapher’s model for TEM transmission lines, is simply equal
to , where is the permeability of free space, is the
relative permeability of the dielectric substrate used and is the
length of the transmission line (equal to the thickness of the di-
electric substrate). Therefore, the thickness of the substrates,
and can be calculated from:
(4)
(5)
Using a procedure similar to the one used to obtain the values
of , , and , the values of the capacitances and
can be calculated from
(6)
(7)
AL-JOUMAYLY AND BEHDAD: A NEW TECHNIQUE FOR DESIGN OF LOW-PROFILE, SECOND-ORDER 455
Fig. 4. Calculated transmission and reflection coefficients of the equivalent cir-
cuit model of the second order FSS, shown in Fig. 2, and the simplified circuit
model, shown in Fig. 3 for the example studied in Section II.
where the second terms in (6) and (7) represent the capacitance
values of the shunt capacitors, and , which are part of
the simplified model used for the short transmission line sec-
tion. Also, note that and in (4)–(7) are design parame-
ters that can be chosen freely and are determined by the type of
the dielectric substrate used (although generally , since
most dielectric substrates are non-magnetic). As an example, the
above formulas are used to design a second-order Butterworth
filter with center frequency of and a fractional
bandwidth of (i.e., ) using a dielec-
tric substrate with and . The desired values
for the capacitor, inductor, and substrate thickness are found
using (1)–(7) to be , ,
and , respectively. Using these values, the
frequency responses of the two filters shown in Figs. 2 and 3
are calculated and presented in Fig. 4. As can be seen, a very
good agreement between the two results is observed. The minor
discrepancies observed between the two is attributed to the ap-
proximate model used for short lengths of transmission lines.
This model is generally valid so long as the electrical length of
the line is less than 30 or , where is the free
space wavelength.
The next step in the design procedure is to map the desired in-
ductor, , and capacitors, and , values obtained from the
above formulas to geometrical parameters of the periodic struc-
tures. Due to the close proximity of the three metal layers, the
presence of the inductive layer will affect the capacitance of the
capacitive layer and vice versa. Therefore, the exact dimensions
of the capacitive patches and inductive wire grid should be op-
timized using numerical EM simulations. Nevertheless, a first
order approximation in a closed form formula can be used as
a starting optimization point for the full-wave EM simulations.
The effective capacitance value of a 2-D periodic arrangement
of square metallic patches with side lengths of and the
gap spacing of can be calculated using [19]
(8)
Fig. 5. A unit cell of the proposed FSS is placed inside a waveguide with pe-
riodic boundary conditions to simulate the frequency response of the infinitely
large second-order FSS.
where is the free space permittivity, is the effective per-
mittivity of the medium in which the capacitive patches are lo-
cated, is the unit cell size, and is the spacing between two
adjacent capacitive patches. This formula provides a first order
approximation for the capacitance values and can be used to
determine the period of the structure, , once the spacing be-
tween the patches, , and the capacitance values, and ,
are determined. The gap spacing, , is mainly determined by
the minimum feature that can be fabricated using the fabrica-
tion technology of choice. In low-cost lithography fabrication
techniques, minimum features of 150 can be easily fab-
ricated on high-frequency microwave laminates. As a general
guideline, reducing the gap spacing will result in reduction of
the period of the structure, , which is desirable. Once the
is determined, the initial width of the inductive strips can be ap-
proximated using the following formula [19]
(9)
where is the period of the structure, is the free space per-
meability, is the effective permeability, and is the strip
width. Similar to the previous case, this formula is also valid
only when the inductive wire grid is placed in a homogeneous
medium away from any metallic objects or scatterers. Therefore,
the value of the strip width, , obtained from (9) must only be
used as the first-order approximation and a starting point for the
full-wave optimization of the structure.
Starting with the initial dimensions of the structure obtained
using the procedure mentioned above, the frequency response
of the structure can then be obtained using full-wave EM simu-
lation. In this paper, the simulations are carried out using the
finite element method (FEM) method in Ansoft’s High Fre-
quency Structure Simulator (HFSS
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