An_FSS-based_Conformal_Band-stop_Filter_Design_for_Planar_and_Non-planar_Surfaces.pdf

• To introduce the basic concepts of DC and AC circuits behavior

1. An FSS-based Conformal Band-stop Filter Design
for Planar and Non-planar Surfaces

Akhila Gouda
1
, Rabindra K. Mishra
2
, and Saptarshi Ghosh
3

1,3
Department of Electrical Engineering, Indian Institute of Technology Indore, Madhya Pradesh – 453552, India
2
Department of Electronic Science and Technology, Berhampur University, Odisha – 760007, India
1
[email protected],
2
[email protected], and
3
[email protected]
Abstract—This paper presents a frequency selective
surface (FSS)-based conformal bandstop filter design for use
in different types of planar and non-planar surfaces. The unit
cell of the proposed geometry is based on a single metallic
square loop printed on a dielectric substrate. The overall
structure exhibits a bandstop response in the frequency range
of 6.68 to 12.66 GHz, with a center frequency at 9.53 GHz.
The topology is initially analyzed with respect to circuit
modeling, surface current distribution, and parametric
variation. Afterward, the structure is studied under different
types of non-planar surfaces (x -axis curve, y-axis curve, xy-
axis curve, hemispherical surface) using the finite element
boundary integral (FEBI) method, and the bandstop filter
response is observed across the operating band (with
transmission coefficient < –10 dB) for all cases. The matching
between the planar and non-planar responses confirms the
conformal behavior of the proposed FSS structure.
Keywords— Conformal, Finite element boundary integral,
Frequency selective surfaces
I. INTRODUCTION
Frequency selective surfaces (FSS) find extensive
applications in defense technology, wireless network, RF
energy harvesting, satellite communication, antenna
parameter enhancement, etc. [1]–[6], owing to their ability
to exhibit various electromagnetic (EM) characteristics,
such as filter, absorber, polarizer, reflector, and so on.
These FSSs are made of periodic structures arranged in
two-dimensional (2-D) arrays, where the shapes of the unit
cells regulate the EM operation.[7], [8] Along with
displaying various types of passive EM behavior, these
FSSs are also used in reconfigurable devices due to their
ease of integration with PIN diodes, varactor diodes, and
other lumped components.[9]–[12] One of the primary
applications of FSS is its highly selective shielding
properties, which are often exploited to protect any
electronic/ electrical device from its nearby interference.
Over the last decade, several types of FSS-based shielding
operations have been reported in the literature [13], [14]. A
few geometries are used for single-band shielding, whereas
a few others are focused on multi-band and wideband
shielding [15]. Researchers have also achieved wide band
coverage, polarization insensitivity, and angular stability in
those shielding devices. A four-fold symmetrical topology
helps an FSS geometry to achieve polarization
insensitivity, [16], [17] whereas miniaturized elements can
produce good angular stability [18]. Multi-layer or/and
resistive-conductive ink patterns can achieve wide
bandwidth. Reconfigurable shielding operations have also
been found in various works, where PIN diodes and
varactors diodes are used to regulate the shielding
operations across various frequency ranges.
With the advent of time, the use of FSS has increased
exponentially, where the structures need to be implemented
on different planar and non-planar surfaces. Defense
applications, in particular, require conformal FSSs for
various purposes, such as reducing radar cross-sections,
improving radome designs, and improving shielding
performance. However, the research on FSS designs has
been mostly limited to the planar structure. A few
geometries have considered single axis curvature
(cylindrical shape) [19]–[22], while a handful of articles
have shown investigation on double curvature shapes [23].
But most researchers are either limited to experimental
demonstration or restricted simulation modeling. An in-
depth analysis of FSS geometry for different types of non-
planar surfaces is yet to be achieved.
This paper presents an FSS-based bandstop filter for
shielding applications. Different non-planar surfaces, like
cylindrical shapes, elliptical paraboloids, and hemispherical
shapes, are studied along with planar geometry, and their
performance is compared with one another. The Floquet
port boundary condition is used to study the unit cell. In
contrast, the FEBI setup has been used to design those
planar and non-planar surfaces [24]. Finally, the responses
are compiled together to demonstrate the validation of the
simulation setups, thereby confirming the shielding
behavior of the proposed FSS.
II. DESIGN AND ANALYSIS OF UNIT CELL FSS
Fig. 1(a) shows the proposed unit cell geometry of the
FSS structure, which consists of a copper metallic square
loop pattern (brown color) printed on a Polylactic acid
(PLA) based dielectric substrate (blue color), having a
dielectric constant of 2.1 and a loss tangent of 0.07. The
copper thickness has been considered as 0.035 mm. The
dimensions of the geometry are as follows: a = 10 mm, b =
8.8 mm, w = 1 mm, and th = 0.5 mm. The metal square loop
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2022 IEEE Microwaves, Antennas, and Propagation Conference (MAPCON) | 978-1-6654-5203-8/22/$31.00 ©2022 IEEE | DOI: 10.1109/MAPCON56011.2022.10047603
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2. provides the inductance along the incident electric field
direction, and the gap between the neighboring unit cells


(c)
Fig. 1. (a) Unit cell geometry, (b) Equivalent Circuit diagram, and (c) S-
parameter of the proposed structure and its equivalent circuit model.
results in the capacitance. A small resistance also resulted
from the finite conductivity of copper metal (σ = 5.8 × 10
6

S/m). In addition, the PLA dielectric gives the transmission
line effect. Fig. 1(b) shows the complete equivalent circuit
diagram of the proposed unit cell FSS. The series L-C
circuit generates a bandstop filter response, whose
properties rely on the geometric dimensions. The unit cell
geometry is simulated using the Floquet port boundary
condition in Ansys high frequency structure simulator
(HFSS) software. Bandstop filter response is obtained at
9.53 GHz, as shown in Fig. 1(c). The −10 dB bandwidth
covers 6.68 to 12.66 GHz, with a fractional bandwidth of
62.74%. The equivalent circuit has also been modeled in
the Advanced Design System software, and the optimized
circuit parameter values are obtained as L = 1.79 nH, C =
0.15 pF, and R = 3 Ω. The length of the transmission line
is 0.5 mm. While comparing the responses of the unit cell
and its equivalent circuit model with the optimized
parameters, a reasonable agreement is observed in Fig.
1(c).
The proposed FSS geometry is parametrically studied in
Fig. 2 concerning different geometric dimensions. While
increasing the width of the metallic loop (w), the inductance
is decreased, resulting in a right shift of the resonance
frequency, as observed in Fig. 2(a). Similarly, on increasing
the length of the square loop (b), the inductance and
capacitance increase, thus causing a downward shift in the
frequency, as depicted in Fig. 2(b). The dimensions are thus
optimized accordingly to get the bandstop response at the
X-band (8−12 GHz). The structure is further investigated
with respect to the polarization angle for both transverse
electric (TE) and transverse magnetic (TM) modes. While
varying the polarization angle from 0
o
to 90
o
, the responses
are almost identical in Fig. 3, with a maximum variation of
0.34 GHz for both the modes. This confirms the
polarization-insensitive nature of the proposed FSS. The
angular stability of the geometry has also been studied. In
the case of TE mode, the bandwidth is slowly increased
with higher angles, as shown in Fig. 4(a). On the contrary,
the bandwidth decreases with increasing the angle of
incidence in the case of TM mode, as depicted in Fig. 4(b).
For both cases, the angular stability is achieved up to 60
o
.

(a)

(b)
Fig. 2. S-parameters of the unit cells (a) width variation and (b) square
loop length variation (solid line = S11 and dotted line = S21) (c) S-parameter
of the unit cell and its equivalent circuit.
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3. III. DESIGN AND ANALYSIS OF FINITE PLANAR AND NON-
PLANAR FSS
A. Finite FSS Designs
In order to study the non-planar FSS geometries, Floquet
port simulation setup is insufficient, and a different method
known as FEBI is exploited to study the non-planar
structures. Before analyzing the non-planar designs, the
proposed FSS is investigated under a planar configuration
with a finite size. The dimensions of the planar FSS are
considered as 250 mm × 250 mm, consisting of 25 × 25
unit cells, as shown in Fig. 5. Two antennas, one acting as
a transmitting antenna and another behaving as a receiving
antenna, are also designed and placed on the two sides of
the geometry. The antennas are designed to operate in the
X-band frequency range. The antennas are placed in far-
field conditions with respect to the FSS, and the normal
incidence is maintained.

(a)

(b)
Fig. 3. Transmittance of FSS geometry with different polarization angles:
(a) TE mode and (b) TM mode.

(a)

(b)
Fig. 4. Transmittance of FSS geometry with different incidence angles. (a)
TE mode and (b) TM mode.

Three boundary boxes enclose the FSS and the two
antennas. The boundary separation is optimized to
accelerate the computational speed. The overall setup is
illustrated in Fig. 5, along with the zoomed view of the unit
cells, while the simulation is carried out in Ansys HFSS
using the FEBI setup.
In the subsequent steps, different types of non-planar
surfaces are used to study the curvilinear effect of the
proposed structure. Fig. 6(a) shows the cylindrical FSS
surface bent along the x-axis, whereas the bending on y-axis
is shown in Fig. 6(b). In both cases, the length and radius of
the cylinder are maintained as 250 mm and 80 mm,
respectively, and the bending angle is 180
o
. In the next step,
an elliptical paraboloid surface is designed using Equation
1, which is presented in Fig. 6(c), and the same number of
unit cells (25 × 25) are maintained.
Lastly, a hemispherical surface with a radius of 100 mm
is considered in Fig. 6(d). As required, other types of
conformal surfaces can also be designed based on the
different equations.
2 2
, where 2, 125 mm , 125 mmz ax ay a x y= + = − ≤ ≤
------ (1)
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4. Fig. 5. Planar FSS structure contains (25 × 25 unit cells)

(a)

(b)

(c)

(d)
Fig. 6. Conformal FSS structure. (a) cylinder x-axis curve (25 × 25 unit
cells), (b) cylinder y-axis curve (25 × 25 unit cells), (c) xy-axis curve (25 ×
25 unit cells), and (d) hemispherical surface.
B. Results and Analysis
The transmission coefficients of the finite FSS structures
are calculated using two steps. In the first step, the response
is recorded without the FSS structure. In the next step, the
response is recorded with the FSS geometries under
consideration, and their difference gives the required
transmittance. Fig. 7 compares the transmission responses
of all the finite FSS structures (studied using the FEBI
setup) with the unit cell simulation (made using Floquet
port). It is observed that the responses are almost coincided
in the frequency range of 7 to 13 GHz. A small shift towards
the higher frequency is observed in the finite FSSs due to
their finite size limitation. In the case of the hemispherical
FSS design, periodicity is disturbed at the apex, which
deteriorates the bandstop response and reduces the
bandwidth. A different mapping technique can further
improve the overall response.


Fig. 7. Comparison transmittance plot.
IV. CONCLUSION
In this paper, a square loop based FSS has been
designed to exhibit the band stop characteristic in X-band
frequency for planar as well as non-planar surfaces. The
proposed geometry has initially been studied with unit cell
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5. setup and later the analysis has been extended for various
types of nonplanar finite size surfaces. The bandstop
response remains similar for different arrangements,
although there is an upward frequency shift of around 0.5
GHz for the hemispherical pattern, owing to a lower value
of packing efficiency. Improvement of packing efficiency
as well as fabrication of FSS structures using 3D printing
technology and followed by free space measurement are
the scope of future works.
ACKNOWLEDGEMENT
The authors wish to acknowledge the University Grants
Commission (UGC), Government of India for providing
financial assistance through Junior Research Fellowship
program.
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