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Citation: De Sabata, A.; Matekovits,
L.; Buta, A.; Dassano, G.; Silaghi, A.
Frequency Selective Surface for UWB
Filtering and Shielding. Sensors 2022,
22, 1896. https://doi.org/10.3390/
s22051896
Academic Editor: Adrian Bekasiewicz
Received: 1 February 2022
Accepted: 24 February 2022
Published: 28 February 2022
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sensors
Article
Frequency Selective Surface for Ultra-Wide Band Filtering
and Shielding
Aldo De Sabata 1, Ladislau Matekovits 1,2,3 , Adrian Buta 1, Gianluca Dassano 2and Andrei Silaghi 1,*
1Department of Measurements and Optical Electronics, Politehnica University Timisoara,
300006 Timisoara, Romania; aldo.de-sabata@upt.ro (A.D.S.); ladislau.matekovits@polito.it (L.M.);
adrian.buta@student.upt.ro (A.B.)
2Department of Electronics and Telecommunications, Politecnico di Torino, 10129 Turin, Italy;
gianluca.dassano@polito.it
3
Istituto di Elettronica e di Ingegneria dell’Informazione e delle Telecomunicazioni, National Research Council,
10129 Turin, Italy
*Correspondence: andrei.silaghi@upt.ro
Abstract:
A frequency selective surface for spatial filtering in the standardized Ultra-Wide Band
(UWB) frequency range is proposed. A very large stop-band of 1.75–15.44 GHz has been obtained,
with good polarization insensitivity and an angular stability of more than 60
◦
and more than 50
◦
in TE and TM incidence, respectively. Circuit models have been devised. The structure has been
assessed by electromagnetic simulation and implemented on an FR4 substrate of 1.6 mm thickness,
with an edge of the square-shaped unit cell of 15 mm. Tests in an anechoic chamber demonstrated
good matching between simulation and experimental results and proper operation of the device.
Keywords:
frequency selective surface; FR4; spatial band-stop filter; ultra-wide band (UWB);
circuit model
1. Introduction
Frequency selective surfaces (FSSs) implemented on single-layer or stacked printed
circuit boards (PCBs) [
1
,
2
] have found multiple applications in the last decade as radomes,
absorbers, polarizers, artificial magnetic conductors, spatial filters and shields, dichroic
reflectors and reflectors for antenna gain enhancement, etc.
With the advent and exponential growth of wireless communications technology in
the last two decades, a special interest in applications of FSSs as spatial filters, screens
and shields has emerged. Screens can be deployed to protect certain spaces, including
rooms and buildings, from electromagnetic waves in some frequency bands, while leaving
unaffected signals from different frequency bands. Electronic high frequency circuits and
equipment can be shielded in selected frequency bands by embedding them into specially
designed boxes with patterned walls. Such functionalities are analog to the radomes one,
which allows the antenna to communicate at the operational frequency while stopping
unwanted signals. Angle independence and polarization insensitivity of the frequency
response to incident electromagnetic waves are required for these kinds of applications [
3
].
Other more specific applications have also been reported, as for example in imaging [
4
] or
in remote sensing in [5].
Several works have been devoted to spatial filtering in some standardized wireless
communication frequency bands by means of FSSs. A single layer, double-metallization
solution, built on FR4 substrate that filters electromagnetic signals from WiMAX, WLAN,
and X-band has been proposed in [
6
]. The miniaturized unit cell (10
×
10 mm
2
) was based
on combinations of square loops and dipoles. The structure has been tested up to a 50
◦
angle of incidence.
A geometry based on a modified circular loop that introduced two notch frequencies
in the ISM band at 2.4 and 5.8 GHz has been introduced in [
7
] in view of mitigating the
Sensors 2022,22, 1896. https://doi.org/10.3390/s22051896 https://www.mdpi.com/journal/sensors
Sensors 2022,22, 1896 2 of 16
mutual interference of indoor adjacent wireless networks. An optimization technique
has been proposed to allow for the independent adjustment of the two frequencies. The
structure offered stable frequency response up to a 30
◦
angle of incidence. Filtering in
the GSM bands has been considered in [
8
]. A proposed square unit cell with a side of
50 mm and consisting of a combination of a square loop resonator and a more complicated
loop-shaped resonator has been demonstrated to filter signals at 942, 1842, and 2142 MHz,
up to a 45
◦
angle of incidence. The small dimension experimental prototype was realized
on an FR4 substrate and contained 4 ×4 elements.
GSM shielding has been approached again in [
9
], where a 2.5D structure with two
frequency notches at 900 and 1790 MHz has been proposed. The unit cell was based on a
modified double-square loop element knitted on both sides of a PTFE substrate, and inter-
connecting vias, for a dimension of the square-shaped unit cell of 24 mm. Correct operation
has been demonstrated up to an angle of incidence of 60
◦
. A number of five notches are
introduced by the FSS solution proposed in [
10
], covering the GSM, GPS, Bluetooth/Wi-Fi,
Wi-MAX and WLAN bands, designed in view of shielding against smartphone and tablet
electromagnetic signals. The unit cell consisted of five square and modified square rings
imprinted on an FR4 substrate, for dimensions of the unit cell of 27
×
25.7 mm
2
. The
structure has been experimentally tested for incidence angle stability up to an angle of 45
◦
.
Shielding by incorporation of FSS into building elements has been considered in [
11
].
A 20
×
20 mm
2
unit cell has been designed, based on circular and elliptical loops and de-
posited on window glass, affecting transparency only by an amount of 14%. The prototype,
containing 13
×
10 unit cells and operating as a band-stop filter at 2.45 and 5.5 GHz (Wi-Fi
and WLAN), has been demonstrated to be polarization insensitive and angle independent
up to 45
◦
. The interest in stop-band filters for wireless applications is demonstrated also by
the conception of an active surface containing p-i-n diodes as control elements [
12
], with a
unit cell based on ring patches and cross-dipoles, and exhibiting closely spaced resonant
frequencies of 2.36 and 2.89 GHz. The proposed structure, with dimensions of the unit cell
of 21
×
18 mm
2
, has been implemented on an FR4 prototype board with dimensions of
20 ×20 cm2and tested in normal and oblique incidence up to an angle of 40◦.
The evolution of the wireless technology raised the interest in research for wide-band
solutions too. An early design, with a large –10 dB stop-band in the interval 6.5–14 GHz,
has been reported in [
13
]. The unit cell, with dimensions 12
×
12 mm
2
, was based on a
combination of a cross dipole on one face of the PCB and a circular ring on the other one.
The prototype, comprising 36
×
23 unit cells, has been implemented on an FR4 substrate of
3.2 mm thickness, demonstrating functionality up to an angle of incidence of 45◦.
A solution for shielding in the X band, with a central frequency around 10 GHz and
a fractional bandwidth (
∆f
/
f0
) of 48% has been reported in [
14
]. The unit cell pattern
was based on convoluted square loops for better polarization stability. The edge of the
square-shaped unit cell was of 6.8 mm. Two prototypes have been fabricated, one on
a single-sided Rogers/Duroid flexible laminate with a thickness of 0.127 mm in view
of conformal applications, and one on an FR4 substrate with thickness of 1.5 mm for
cost-effectiveness. Oblique incidence has been tested up to an angle of 60◦.
A tunable FSS with circular loops connected by varactor diodes has been proposed
in [
15
]. Depending on the bias of the diodes, the operational frequency varied from 0.54 to
2.50 GHz, with a stop-band width of 1.28 GHz, for a size of the square unit cell of 12 mm.
The experimental board built on an FR4 substrate with a thickness of 1 mm has been
tested up to an incidence angle of 60
◦
, and showed a good polarization stability. In [
16
],
an FSS with two distanced layers having different transmission zeros, with a pattern of
cross dipoles with incurved arms has been considered. Miniaturization of the unit cell
(7.7 ×7.7 mm2)
allowed for good polarization stability and proper operation up to an angle
of 60
◦
in the X-band, for a bandwidth of 3.59 GHz. Experiments have been carried over
with a prototype comprising 21
×
14 elements and having Arlon DiClad 880 of 0.76 mm
thickness for dielectric substrate.
Sensors 2022,22, 1896 3 of 16
A single-layer, single-sided solution having a very large –10 dB stop-band in the range
2.72–13 GHz, intended to be applied as a reflector to enhance the gain of UWB antennas
has been reported in [
17
]. The pattern in the unit cell consisted of modified square rings.
The experimental board has been fabricated on an FR4 substrate of 1.6 mm thickness and
comprised 32
×
32 unit cell elements. A claimed 80
◦
angular stability has been reported. A
single layer FSS with parallel convoluted elements patches printed on the opposite faces of
a 1.6 mm thick FR4 substrate has been proposed in [
18
]. For dimensions of the unit cell of
10
×
10 mm
2
, a large –10 dB bandwidth in the range 3.1–13.3 GHz and an angle stability
up to 45
◦
have been obtained. Experiments were performed with a prototype containing
30 ×30 unit cells.
In this paper, an FSS with a very large stop-band, designed to filter electromagnetic
signals in the standardized UWB frequency range (3.1–10.6) GHz, is proposed. To ensure
proper operation, the design provides a stop-band larger than the targeted one (a –10 dB
stop-band is obtained between 1.75 and 15.44 GHz, spanning a 13.69 GHz wide bandwidth).
The solution, which presents a stop-band much larger than the ones reported in the recently
published papers, is implemented on a single-layered, double-face, cost-effective FR4
substrate, of 1.6 mm thickness. The unit cell extends over 15 ×15 mm2. The results of the
numerical simulations have been efficiently verified by experiments, carried out on a board
comprising 30 ×30 unit cells.
The rest of the paper is organized as follows. In the next section, the proposed solution
is presented and the operation is assessed by electromagnetic simulation. Circuit models
for the two faces of the unit cell and for the combination of the two are proposed and
validated in Section 3. Experimental results are reported in Section 4and conclusions are
drawn in the last section .
2. Presentation of the Proposed Structure
The proposed periodic surface is built on a single-layer FR4 substrate (
εr
= 4.3,
tan δ= 0.025
), of thickness
st
= 1.6 mm, with metallization on both faces. The structure of
the unit cell, of dimensions dx=dy=15 mm is reported in Figure 1.
The metal pattern on the upper face of the unit cell, referred to as “Face 1” (Figure 1a),
consists of nine squares, having an edge
L2
= 2.2 mm and lines of width of
w1
= 1 mm and
length
L1
=
dx−d
= 14.9 mm, where
d
= 0.1 mm is the distance between parallel square
rings within adjacent unit cells. The distance between the centers of any two consecutive
squares is L1/3 in both xand ydirections.
Face 2 (Figure 1b) contains four metal squares of edge
Lsq
= 5 mm, with centers
displaced by
T
=
dx/
2
−Lsq
/2
−d
/2 with respect to the center of the unit cell in both
x
and
y
directions and one hollow square, situated at the center of the unit cell, having an
edge L3= 4.5 mm drawn with a line width w2= 0.1 mm.
The CAD model of the unit cell is reported in Figure 1c, with substrate removed to
ensure visibility of the whole metallization. The conception of the structure relied on the
interplay between the rather large dimension of the unit cell, of 15 mm, introduced to
ensure an appropriate response to incident electromagnetic waves at low frequencies, and
the presence of a certain number of small resonators in each unit cell, for providing a good
response at higher frequencies. The resonators introduce several resonances that ensure
the occurrence of a large stopband, as presented and explained next.
The structure has been firstly tested by simulation, in normal incidence of plane waves,
with the E field parallel to the
dy
edge of the unit cell of Figure 1a, a situation called TE
or
S
polarization [
19
]. The frequency domain solver, with periodic boundary conditions
in the
x
and
y
directions has been used, and Floquet ports in the
z
direction have been
defined. In the simulations, the substrate material has been defined as “FR4 (lossy)”. The
TM (
P
) polarization yields the same results in normal incidence, due to the symmetry
of the structure of the unit cell. The simulated transmittance (magnitude of
S21
in (dB))
is reported in Figure 2(the blue, solid line curve). The measured transmittance is also
represented in the same figure, with a red, dotted line for reference. The experimental setup
and measuring procedure will be addressed in Section 4.
Sensors 2022,22, 1896 4 of 16
Figure 1.
Unit cell geometry—CAD model: (
a
) Face 1; (
b
) Face 2; (
c
) rendering with removed
substrate for better visibility.
Figure 2.
Transmittance of the periodic surface in normal incidence: simulated (blue, solid line), and
measured (red, dotted line). The –10 dB line is used to determine bandwidth.
Figure 2reveals the presence of a very large –10 dB stop-band, between 1.59 and
15.76 GHz, spanning a 14.17 GHz wide bandwidth (163.3% with respect to the central
frequency). The simulated values for the stop-band limits have been confirmed by the
Sensors 2022,22, 1896 5 of 16
measured ones, of 1.75 and 15.44 GHz, respectively. Therefore, the periodic surface acts
like a band-stop filter with an ultra-wide bandwidth.
The proposed filter has been devised by first coupling two resonators with comple-
mentary frequency responses, as shown in Figure 3. The transmittance of a periodic surface
having the metal pattern on one side only, namely Face 1 in Figure 1a, is displayed with a
red, solid line in Figure 3. The transmittance presents a large stop-band around a resonant
frequency of 6.87 GHz. This resonance is introduced by the dipoles of length
L1
, as the
field image of the surface current density on Face 1, in TE normal incidence, represented in
Figure 4a shows (metallization on Face 2 was absent when the field image in Figure 4a was
obtained by simulation).
Reactive loading of three of the five dipoles present on the unit cell provides the
possibility to obtain a larger bandwidth. This has been used to optimize the dimensions
of the dipoles and squares to obtain a large bandwidth. Note that the current flowing
on the orthogonal direction (
x
in this case) is very small, so that the cross-pol coupling is
also small.
Figure 3.
Transmittance in normal incidence of periodic surfaces with metal patterns on one face
only, as in Figure 1: Face 1 solid line; Face 2 dotted line.
As it can be seen in Figure 3, the periodic surface with metallization on Face 2 has
only two resonance frequencies at 11.58 and 15.06 GHz. The corresponding field images
are displayed in Figure 4b,c, respectively. Note that the resonance at 11.58 GHz is mainly
determined by the hollow rectangles, while the one at 15.06 GHz is mainly determined by
the capacitive coupling between the metal squares. When metallizations are present on
both sides of the periodic structure, Figure 1c, the resulting periodic surface has resonant
frequencies at 6.74 and 11.59 GHz, which are very close to the resonant frequencies of the
structures based on Face 1 or Face 2 only. However, the resonance around 15 GHz is no
more present. The field image in Figure 4d confirms that the operation of the filter is mainly
determined by the pattern of Face 1 at 6.74 GHz.
A similar image (not reported) demonstrates a similar operation of the FSS at the other
resonance frequency. Therefore, by coupling two band-stop filters, one with a large band-
width at low frequencies and another one with a two-band structure at higher frequencies,
a band-stop filter with an ultra-wide band has been obtained. Optimization was possible
by considering the impact of various geometrical parameters on the frequency response.
The transmission and reflection coefficients in co- and cross-polarization are repre-
sented in Figure 5. The linearly polarized wave is incident from the side of Face 1. The
same figure displays the phase of the reflection coefficient in co-polarization. The almost
linear variation of the phase of the reflection coefficient with frequency is similar to the
Sensors 2022,22, 1896 6 of 16
result reported in [
13
]. To gain a deeper insight into the operation of the proposed FSS, a
circuit model is considered in the next section.
(a) (b)
(c) (d)
Figure 4.
Field images of surface current density for the periodic surface with: (
a
) Face 1 only present,
at 6.87 GHz; (b) Face 2 only present, at 11.58 GHz; (c) Face 2 only present, at 15.06 GHz. (d) View of
Face 1, when both metallizations are present, at 6.74 GHz. The use of 2
×
2 configuration is preferred
since it allows a better appreciation of the field distribution between adjacent unit cells.
Figure 5.
Reflection and transmission coefficients in co- and cross-polarization and phase of reflection
coefficient in co-polarization, when the linearly polarized wave is incident from Face 1 of the FSS.
Sensors 2022,22, 1896 7 of 16
3. Circuit Model
Understanding the frequency response of an FSS is improved by circuit models, which
account for resonances introduced by the structure that affect electromagnetic waves in
normal incidence [
20
]. In this section, we present circuit models for the unit cells on the two
faces of the proposed FSS individually, and for the unit cell of the FSS resulted by putting
the two faces together.
The circuit model for Face 1 is presented in Figure 6a. The incident wave is modeled
by a matched voltage generator connected at the input terminals, having an internal
impedance equal to the wave impedance
Z0
of the free space. The FSS is represented
by the combination of the shunt impedance
Z
, accounting for the metal pattern, and the
transmission line of length
st
, accounting for the substrate. The characteristic impedance
of the transmission line is denoted by
Zc
, and the propagation constant is denoted by
γ
.
Both quantities are determined by the material properties of the substrate (FR4). These
parameters are calculated as follows:
Zc=rµ0
ε0εr(1−δ)(1)
γ=ωqµ0ε0εr(1−δ)(2)
where
µ0
represents the value of the absolute permeability in vacuum and
ε0
represents the
value of the absolute permittivity in vacuum.
A matched load equal to the free space impedance is connected to the output terminals.
The S21 parameter of the two-port in Figure 6a is given by:
S21 =2zp
1+zp
1+Γ
eγd+Γe−γd(3)
where
Γ=Z0−Zc
Z0+Zc(4)
Z0=rµ0
ε0
(5)
and
zp=zzin
z+zin
; (6)
z=Z
Z0
; (7)
zin =Zc
Z0
Z0+Zctanh(γd)
Zc+Z0tanh(γd)(8)
The circuit model for Face 2 is obtained from the schematic in Figure 6a by feeding the
two-port at the terminals from the right and terminating the left port by a matched load.
However, Equations (3)–(8) for calculating the
S21
parameter still apply, due to reciprocity.
Both faces of the FSS introduce resonances, as reported in Figure 3. Since the resonances
are widely separated in frequency, the shunt impedance
Z
in Figure 6a consists of several
uncoupled resonant circuits, as shown in Figure 6b. The presence of the dissipating elements
Ri
in Figure 6b is motivated by the losses introduced by the FR4 substrate in near field. The
propagation of the waves in the substrate also introduces losses. However, propagation
losses are negligibly small, as calculation of
S21
performed by alternatively considering
or neglecting losses in the transmission line of very small length
st
(the thickness of the
substrate) in Figure 6a reveals.
Sensors 2022,22, 1896 8 of 16
(a)
(b)
Figure 6. Equivalent circuits: (a) unit cell; (b) impedance Z.
To estimate the order of magnitude of the circuit elements, well-known approximation
formulas can be considered as a starting point. The inductance
L
of a thin metal strip of
length sand width wis given by
L=µ0
s
2πln2s
w(9)
Then, the capacitance
C
of the resonant circuit can be calculated from the resonant
frequency fraccording to:
fr=1
2π√LC (10)
For example, the calculated inductance of a strip having
s
= 5 mm and
w
= 1 mm,
belonging to the strip resonator in Figure 4a, is 2.28 nH. For
s
= 4.5 mm and
w
= 0.1 mm,
corresponding to the edge of the hollow rectangle that bears a high current density in
Figure 4b, the calculated inductance is 4.04 nH.
Equations (3)–(8) have been implemented in a Matlab
TM
script and the obtained
transmittance has been compared with the one obtained by simulation. The values of
the circuit elements have been found in a few iterations. The values obtained for the two
values of the inductance mentioned above have been 0.62 and 3.29 nH, respectively. The
resistances in the circuits have the role to ensure an appropriate Q value.
The circuit elements for the two faces are listed in Table 1. The second column
contains the circuit elements and resonant frequencies associated with the unit cell of Face
1. The third column contains the same elements associated with Face 2. Three resonant
frequencies, denoted
fri
, have been considered for Face 1 (
n
= 3 in Figure 6b) and four
resonant frequencies for Face 2 (
n
= 4 in Figure 6b). Note that the frequency
fr4
lies outside
the operating frequency range of the FSS; however, simulations have indicated its presence.
Sensors 2022,22, 1896 9 of 16
This resonant frequency impacts the frequency response of the FSS in the operational
frequency range.
The transmittance obtained with the circuit model for Face 1 is represented in
Figure 7a
,
together with the transmittance obtained by simulation with CST for comparison. A similar
representation for Face 2 is reported in Figure 7b. Both results indicate a good match.
Table 1. Elements of the circuit models for the unit cells.
Face 1 Face 2 FSS
fr1(GHz) 6.87 11.65 6.72
fr2(GHz) 16.73 15.05 9.80
fr3(GHz) 12.48 16.55 11.57
fr4(GHz) - 20.34 12.63
fr5(GHz) - - 18.3
R1(Ω)0.74 27.52 0.74
R2(Ω)20.73 5.65 32.04
R3(Ω)263.89 94.25 0.42
R4(Ω)- 0.42 13.31
R5(Ω)- - 0.4
C1(fF) 860 8.80 980
C2(fF) 5.50 34.0 75.5
C3(fF) 1.00 2.80 85.0
C4(fF) - 41.0 105.0
C5(fF) - - 75.0
L1(nH) 0.62 21.21 0.57
L2(nH) 16.45 3.29 3.49
L3(nH) 162.63 33.03 2.23
L4(nH) - 2.26 1.51
L5(nH) - - 1.01
When the two faces are put together to form the FSS, various couplings between
constituting elements occur. These couplings are intricate and hard to identify individually,
due to the large number of resonators that are present in the unit cell. The effect of the
coupling can be referred to the input or the output of the transmission line that is present
in the circuit model, or to both.
We have adopted the solution to refer the effect of coupling to the input, such that
circuit elements and resonances are modified, and additional resonances might be present
at the input (Face 1) due to the impact of the output (Face 2). This approach is motivated
by the fact that the large resonance that occurs above 6 GHz when only Face 1 is present in
the simulation (see Figure 3) also occurs when both faces are present, as revealed by the
simulation and measurement results reported in Figure 2.
Sensors 2022,22, 1896 10 of 16
(a)
(b)
Figure 7.
Transmittance of structure with metal pattern on one face only: calculated with the circuit
model of the unit cell (dashed line) and obtained by simulation (solid line): (a) Face 1; (b) Face 2.
The selected circuit model has been therefore the one represented in Figure 6a, with
the impedance
Z
having the structure in Figure 6b. In this case,
n
= 5 resonances had to be
considered, such that five series RLC circuits connected in parallel entered the structure of
the impedance Z.
Equations (1)–(8) have been used again to calculate the
S21
parameter of the circuit,
and several iterations have been performed to calculate the values for the parameters,
knowing the orders of magnitude from (9) and (10). The best fit has been obtained for the
resonance frequencies and parameter values listed in the last column from Table 1. The
transmittance obtained with the circuit model is represented in Figure 8. The transmittance
obtained by simulation with CST is also reported in the same figure, for comparison. It can
be seen that the transmittance calculated with the circuit model matches the one obtained
by simulation in a reasonable way in the –10 dB stop-band, which is the frequency band of
interest. Moreover, the band limits are correctly assessed by the circuit model.
Sensors 2022,22, 1896 11 of 16
Figure 8.
Transmittance of the full structure: calculated with the circuit model of the unit cell (dashed
line) and obtained by simulation (solid line).
4. Experimental Validation
The proposed periodic structure has been realized as a prototype of FR4 printed circuit
board (PCB) comprising 30 unit cells in each of the two orthogonal directions for a total
extension of 450
×
450 mm
2
. A photograph of the Face 1 of the prototype in presented in
Figure 9a, whilst Face 2 is visible in Figure 9b. Measurements have been performed in an
anechoic chamber, Figure 9c, by means of the same substitution method and equipment
described in [21].
The transmittance of the prototype built on PCB has been measured in a full anechoic
chamber, of dimensions 6
×
3
×
3 m
3
, having the metal walls, ceiling, and floor covered
with absorbing pyramids working for frequencies higher than 1 GHz. The substitution
method has been applied, by using a Keysight N5227A vector network analyzer (VNA)
and two types of R&S HF906 double-ridged horn antennas. The distance between the two
horn antennas was 2.8 m (the measured object being placed half-way and rotated around
an axis passing through the middle of the structure).
First, the
S21
parameter of the system formed by the emitting and receiving horns, con-
nected to the VNA has been measured in the case when the antennas have been separated
by a tinfoil covered plywood having an empty window for inserting the sample,
Figure 9c.
Then, the measurements have been repeated with the sample inserted, Figure 9d. The
transmittance of the sample in dB could be calculated by taking the difference of the results
from the second and first measurements described above. A simple mechanism has been
devised for allowing the rotation of the screen at prescribed angles in view of measuring
the transmittance at different incidence angles. It consists of a fix pedestal and a rotating
panel with the hole (mentioned above with reference to Figure 9c). The extension of the
tinfoil covered plywood is the maximum available for the normal incidence, corresponding
to an infinite ground plane. When rotated, some space between it and the tips of the
cones appear, but the diffraction from the edges are cancelled by the calibration process
(difference method described above). The accuracy is of 1
◦
, but, during the measurements,
a 5◦step sequence has been considered, since the rotation has been performed by hand.
The measured transmittance in normal incidence is represented in Figure 2with a
red, dotted curve, together with the simulated one, in order to reveal the good matching
between the two. The simulated transmittance for TE incidence for colatitudes (angle
θ
in
spherical coordinates) between 0 and 60
◦
and the measured ones are reported in Figure 10.
Measurements have been limited to an angle of incidence of 60
◦
as the effective
aperture for the incident waves decreases by 50% with respect to normal incidence. The
same curves but for TM incidence are represented in Figure 11. This set of results is
sufficient for assessing the variability of the transmittance at oblique incidence, due to the
symmetry of the metal pattern in the unit cell.
Sensors 2022,22, 1896 12 of 16
(a) (b)
(c) (d)
Figure 9.
Experimental validation: PCB prototype Face 1 (
a
), and Face 2 (
b
); measurement setup
without (c), and with (d) prototype inserted.
Figure 10. Transmittance in oblique incidence of TE waves: simulated vs. measured.
The reported data show a good agreement between simulation and measurement
results. Some minor differences exist for small values of the transmittance, i.e., in the
stop-band that are caused by variations in the geometry and irregularities in the dielectric
of the PCB, by tolerances in the metallization and by higher order modes that are launched
as surface waves, which can radiate when reaching the bounds of the PCB. The last
phenomenon might be significant at some frequencies only, for large angles of incidence.
Possible leakage of energy due to propagative modes must also be evaluated. At an
angle of incidence of 15
◦
, modes TE(–1,0) and TM(–1,0) become propagative at a frequency
of 15.88 GHz. However, the transmittance is below –25 dB for all considered frequencies.
The same modes become propagative at 13.33 GHz for
θ
= 30
◦
, at 11.71 GHz for
θ
= 45
◦
, and
at 10.72 GHz for
θ
= 60
◦
. However, the maximum values of the transmittance are
–35 dB
Sensors 2022,22, 1896 13 of 16
in the first two cases, and –40 dB in the last one, making the leakage due to propagative
modes other than TE(0,0) and TM(0,0) negligibly small.
Figure 11. Transmittance in oblique incidence of TM waves: simulated vs. measured.
To illustrate the impact of higher order modes, we present in Figure 12 the magnitudes
of the
S21
parameters corresponding to the modes listed in Table 2, for TE(0,0) incidence
(Figure 12a) and TM(0,0) incidence (Figure 12b), at an angle
θ
= 30
◦
and azimuth
φ
= 0.
The Rayleigh frequencies are also listed for convenience in Table 2. The results have been
obtained by simulation with [19].
Table 2. Mode numbering for incidence at θ= 30◦(φ= 0) and corresponding Rayleigh frequencies.
Mode nr. 1 2 3 4 5 6 7 8 9 10
Mode TE TM TE TM TE TM TE TM TE TM
(0,0) (0,0) (0,1) (0,1) (0,−1) (0,−1) (1,0) (1,0) (−1,0) (−1,0)
Rayleigh frequency (GHz) 0 0 23.08 23.08 23.08 23.08 39.97 39.97 13.32 13.32
The reported results indicate that, indeed, the only propagating modes in the frequency
range of interest are TE(
−
1,0) and TM(
−
1,0) for TE and TM incidence, respectively, and
the corresponding transmittances are below –10 dB. Furthermore, evanescent modes have
negligibly small transmittances in the operating frequency band of the FSS.
The transmittance of the structure has been further measured in TE and TM incidence
for angles of incidence between 0 and 60
◦
with a 5
◦
increment and the stop-band has been
determined in each case, since it is the most important parameter of the proposed filtering
surface. Results are reported in Figure 13, the stop-band for the TE case being denoted by
[fLTE;fHTE] and for the TM case by [ fLTM ;fHTM ].
Results in Figure 13 reveal that the stop-band is practically constant in TE incidence
up to an angle of incidence of 60
◦
(
fLTE
varies from 1.75 GHz at 0
◦
to 1.66 GHz at 60
◦
and
fHT E
increases from 15.44 GHz at 0
◦
to values above 20 GHz between 45
◦
and 60
◦
).
In the TM incidence case, the stability of the stop-band can be considered reasonable up
to an angle of incidence of 50
◦
(
fLTM
increases from 1.75 GHz at 0
◦
to 2.87 GHz at 50
◦
,
3.34 GHz at 55
◦
and 4.00 GHz at 60
◦
, and
fHT M
varies from 15.44 GHz at 0
◦
to 17.78 GHz
at 45
◦
and 17.13 GHz at 60
◦
). Nevertheless, the stop-band remains ultra-wide for all angles
of incidence.
Sensors 2022,22, 1896 14 of 16
(a)
(b)
Figure 12.
Transmittances of 10 modes for
θ
= 30
◦
: (
a
) TE incidence of mode 1; (
b
) TM incidence of
mode 2.
Figure 13. Stop-band limits versus incidence angle.
A response that is more dependent on the angle in TM incidence than in TE incidence
has been noticed in other works too [
15
]. This can be explained by considering the interac-
tion of the electric and magnetic field intensities of the incident wave with metal dipoles
and loops placed on the two sides of the PCB. In TE incidence, as the incidence angle
θ
increases, the length of the projection of the E vector on the surface remains constant and
the projection of the H vector on the
z
-axis, which is perpendicular to the surface of the
loops increases, and so does the interaction between the two.
Sensors 2022,22, 1896 15 of 16
On the other hand, in TM incidence, as the incidence angle
θ
increases, the projection
of the E vector on the surface of the FSS decreases, making the interaction with the dipoles
smaller, while the H vector remains parallel to the surface of the loops. The interaction of
the H field with the FSS is achieved in this case through the loops that are perpendicular to
the structure (parallel to the
z
-axis) that are closed by capacitive effect between the metal
patches on the two faces of the FSS.
5. Conclusions
In this paper, an FSS operating as a band-stop spatial filter with a very large stopband,
intended for filtering in the UWB frequency range, with good polarization insensitivity and
angle stability has been proposed. The structure has been implemented on a cost-effective
FR4 substrate. A very large stopband has been obtained, in the range of
1.75–15.44 GHz.
This compares favorably with other works reported in the literature having similar tar-
gets.
Table 3
contains a comparison with similar works (
λc
is the free-space wavelength
corresponding to the mid-band frequency, and
λ0
corresponds to the lower frequency of
the stopband).
Table 3. Comparison with other works.
Stop-Band d/λcd/λ0Angle Substrate Substrate
(GHz) Sensitivity Type Thickness (mm)
[13] 6.5–14 0.41 0.26 45◦FR4 3.2
[17] 2.72–13.23 0.21 0.07 80◦FR4 1.6
[18] 3.1–13.3 0.27 0.1 45◦FR4 1.6
Present 1.75–15.44 0.43 0.09 60◦TE, >50◦TM FR4 1.6
work
The first line summarizes an older solution, which raised the interest in wideband
FSSs. The next two lines are from works dedicated to filtering in the UWB frequency range,
similarly to the proposed solution. The last line reports parameters of the solution proposed
in this paper. The largest bandwidth has been obtained in our case. However, the necessity
to decrease the lower bound of the stopband imposed a larger dimension for the unit cell,
which somehow impacted the angle stability, which is lower than the one reported in [
17
].
As explained in Section 2, for the correct operation at higher frequencies, smaller resonators
have been inserted in the unit cell.
The proposed structure has been assessed by simulation, circuit model and mea-
surement in an anechoic chamber. The obtained results demonstrated a good agreement
between theory and experiments.
Author Contributions:
Conceptualization, A.D.S. and A.S.; methodology, L.M. and A.D.S.; software,
A.B. and A.S.; validation, G.D. and L.M.; formal analysis, A.D.S. and A.S.; investigation, A.B. and
A.S.; resources, L.M., A.S. and A.D.S.; data curation, A.D.S., A.B. and A.S.; writing—original draft
preparation, A.B. and A.S.; writing—review and editing, A.D.S. and L.M.; visualization, G.D., A.B.
and A.S.; supervision, L.M. and A.D.S.; project administration, A.S.; funding acquisition, L.M. and
A.S. All authors have read and agreed to the published version of the manuscript.
Funding:
This work was partly supported by a grant from the Romanian Ministry of Research
and Innovation, CCDI-UEFISCDI, project application number PN-III-P1-1.1-PD-2021-0010/within
PNCDI III.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
Sensors 2022,22, 1896 16 of 16
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