Frequency selective surfaces (FSSs) play an important role in wireless systems as these can be used as filters, in isolating the unwanted radiation, in microstrip patch antennas for improving the performance of these antennas and in other 5G applications. The analysis and design of the double concentric ring frequency selective surface (DCRFSS) is presented in this research. In the sub-6 GHz 5G FR1 spectrum, a computational synthesis technique for creating DCRFSS based spatial filters is proposed. The analytical tools presented in this study can be used to gain a better understanding of filtering processes and for constructing the spatial filters. Variation of the loop sizes, angles of incidence, and polarization of the concentric rings are the factors which influence the transmission coefficient as per the thorough investigation performed in this paper. A novel synthesis approach based on mathematical equations that may be used to determine the physical parameters of DCRFSS-based spatial filters is presented. The proposed synthesis technique is validated by comparing results from high frequency structure simulator (HFSS), Ansys electronic desktop circuit editor, and an experimental setup. Furthermore, the findings acquired from a unit cell are expanded to a 2 × 2 array, which shows identical performance and therefore proves its stability.
Spatial filtersdouble concentric ring frequency selective surface (DCRFSS)angle of incidencefinite element method (FEM)polarization anglesIntroduction
Wireless systems are protected by spatial domain selection algorithms against unwanted signals sent by other communication equipment, which can create interference. These filters include a built-in frequency selection that improves the radiation performance of a radiator. Frequency selective surfaces (FSS) have attracted a lot of attention in recent years as a method of constructing spatial filters because they may impart filtering features in the spatial domain [1–5]. Recent study has sought to build and promote a square shaped loop, circumferential ring, ellipsoid, hexagonal geometry, and a cross dipole as geometric patterns that might be employed in the electromagnetic spectrum [6–8]. These filters are used in telecommunications to control electromagnetic radiation. They can, nevertheless, be used for weighing in other fields, such as high-gain antenna sub-reflectors, material processing, and dielectric electromagnetic shielding [9–11]. After looking at the conductive square loops [12], a mathematical analysis was undertaken, and an analogous geometrical shape was given. The behavior of the FSS is investigated using a unit cell from an array. As a result, selecting the proper unit cell shape is crucial for ensuring that the planned structure operates at the desired frequency. The architectural design, patch/slot geometry, spacing between components, and superstrate material are all key aspects in determining crucial FSS features such resonance frequency, bandwidth, and Q-factor [13]. FSS may be employed for energy harvesting and electromagnetic shielding [14–19], as well as for the optimization of the electromagnetic coupling and further providing angular stability with shrinking of unit cells. Multiple layers cascaded together in the FSS design for sub-6 GHz proposed has the downside of increasing overall thickness and complexity [20,21]. Circular frequency selective surface shape is widely used in the upper microwave spectrum for a variety of purposes. A simple synthesis approach for assessing the DCRFSS, which was utilized to construct the structure at 3 GHz, 15 GHz, and 26 GHz resonating frequencies, is described in [22]. The Jerusalem cross FSS complementing structures are devised, which offers efficient electromagnetic shielding in the X-band of the microwave frequency spectrum [23]. Due to their symmetrical geometry, the square loop and concentric circular ring are less sensitive to changes in angle of incidence (AOI) than other shaped structures [24–26]. As detailed in the literature [27–29], the architecture of FSS is represented by an analogous circuit model that aids in the extraction of their electrical properties. The launch of the sub-6-GHz 5G cell spectrum frequency is based on optimizing the existing 4G technology that the industry has previously created. Sub-6 GHz is a turning point in terms of coverage and penetration, and the 5G experience is vastly different from that of mm-wave [30–33]. A novel synthesis approach based on mathematical equations is used to determine the physical parameters of DCRFSS-based spatial filters. The development of a periodic unit cell structure with double concentric ring frequency selective surface (DCRFSS) with band-pass behavior in the sub-6 GHz 5G spectrum is discussed by using a numerical synthesis technique. The synthesis is based on a basic equivalent circuit model analysis approach that allows for massive computations in a short period of time. The lumped circuit characteristics are obtained by using the equivalent circuit modelling (ECM) approach. The simulations are run on the Ansys HFSS simulator, which is based on the finite element method (FEM). The achievements are assessed in terms of providing modelled geometry and a synthesis technique for measuring and estimating the dimensions of the DCRFSS structure. To guarantee that the transmission and reflection coefficients are accurate, the prototype is created and tested. The manuscript is structured around the design of the double concentric ring FSS along with the mathematical analysis which is presented in the Section 2. In part 3, the outcomes are derived from theoretical notions are contrasted to the simulated results. The study is expanded to formation of an array in part 4, and the findings are provided for the DCRFSS structure, with a closing comment in the Section 5.
Structure
This section outlines the architectural design of the DCRFSS. By using the mathematical formulas provided by Marcuvitz [34] for conductive strips, an efficient approach employing equivalent circuit model (ECM) is applied to examine the intended shape. The equivalent circuit approach is more efficient to employ when paired with computational optimization techniques because of the ease of the attempts substituted for the realization with little computational effort. The angle of incidence (AOI) is a critical metric that must be considered while determining design specifications. The technique for evaluating periodic gratings proposed by Marcuvitz has been initially tested on square loop FSS structures [35–37]. In addition, a correction term was included in [38] to eliminate the inaccuracy of this technique for oblique angles of incidence. Due to its simplicity and ability to drastically save time and computational effort when compared to the full wave technique, equivalent circuit model (ECM) analysis and construction of an FSS is an easily accepted solution. It also gives the proposed structure a clear electromagnetic comprehension. The resonant frequencies may be calculated by using principle of the LC circuits which are demonstrated in the Eqs. (1) and (2) as shown below:
fr1=12πL1C1
fr2=12πL2C2where f_{r1} and f_{r2} are the resonance frequencies of each ring construction, and L_{1}, C_{1}, L_{2} & C_{2} are the inductance and capacitance values associated with each concentric ring. At the resonance frequencies, the FSS achieves maximum current distribution, resulting in a transmission null as all incident power is radiated back. Marcuvitz [34], who devised formulae for deriving estimated values of inductances and capacitances of periodic conductive strips, is credited with the foundation of the ECM approach. The inductive impedances and capacitive susceptibility values are defined as follows:
ωrLZ0=lpcosθ∗F(p,t,λ,θ)
F(p,t,λ,θ)=p′λ[lncsc(πt2p)+G(p,t,λ,θ)]
ωrCY0=4lpsecϕ∗F(p,g,λ,ϕ)∗εeffwhere εeff is the effective permittivity of the surface.
F(p,g,λ,ϕ)=pλ[lncsc(πg2p)+G(p,g,λ,ϕ)]where p’ and t’ depicts the value of the periodicity and thickness of the conductive ring respectively; θ and ϕ represents the incidence angles; λ denotes the wavelength of incident radiations; and G(.) denotes a function for incorporating a correction term (CT). The parameters of the DCRFSS structure, such as the circumference of the ring (d), unit cell periodicity (p), and thickness of the metal conductor, are used to extract lumped circuit components such as inductance and capacitance (t), gap between the adjacent rings (g), angle of incidence (θ for TE and ϕ for TM) and the wavelength of the incident ray (λ) by using equivalent circuit model analysis approach. In the Fig. 1, a copper sheet (dark blue color) with thickness (t_{c}) of 0.002 cm and conductivity (σ) of 5.8 × 10^{7} S/m is engraved and deposited over the Flame Retardant 4 (FR4) dielectric substrate.
Schematic of DCRFSS unit cell
However, to achieve resonance at the necessary frequencies with the desired bandwidth, it is advisable to define the parameters together with the periodicity for the circular ring in the creation of DCRFSS structure. In the literature, [19] and [22] provide an effective synthesis procedure that allowed us to create a precise mathematical analysis by utilizing the ECM approach. The electrons on the metallic sheet vibrate when the incidence plane wave contacts the surface of the metallic patches. When the electric field is parallel to the surface of the metallic strip, an inductive component emerges; when it is perpendicular to the plane of the metallic strip, a capacitive component emerges. Using this method, an equivalent circuit can be constructed for the FSS which can show low, high, band-pass, or band-stop filter behavior depending on the chosen shape. In the case of the circular ring FSS, the diameter and periodicity of the structure must be determined to calculate the resonant frequency of operation. The meta-analysis presented provides only provide the information about the values of inductance (L) and capacitance (C) for a circular ring structure but analyzing the geometrical relationship of lumped circuit elements with the model parameters at the specified resonance frequency is a difficult task. The analysis is expanded to the construction of a new equivalent circuit for the suggested concentric ring circular aperture, as shown in the Fig. 2b, and an array depiction of 2 × 2 cells is shown in the Fig. 2a.
DCRFSS array illustrating (a) 2 × 2 array, (b) equivalent circuit of a unit cell
Fig. 2b depicts the suggested equivalent circuit, which consists of a capacitive branch (C1) that represents the gap between two outer neighboring rings. The branch (C2-L1) represents the reactance’s associated with copper conductor of the outer ring and the gap between the two concentric rings apertures. The branch (C3-L2) represents the interactions between the inner concentric ring and the gap lying within the ring. The lumped circuit elements are extracted by using the equations which are given by:
BC1Y0=4sec(ϕ)F(p,d1−2CT,λ,ϕ)
XL1Z0=1εeff[(XL1intZ0)+(XL1int2Z0)]
XL2Z0=1εeff[(XL1int2Z0)+(XL2intZ0)]
BC2Y0=(BC2intY0)+d3+g2+2CTt1(BC1Y0)
BC3Y0=(10)(BC3intY0)+d3−2t2+g3+2CTt1(BC3intY0)
where(BC2intY0)=pπ(d22)F(p,2t2,λ,ϕ)
(BC3intY0)=(2π)(pd3−2t2)F(p,d3−2t2,λ,ϕ)
(XL1intZ0)=F(p,d1−2CT,λ,θ)
(XL1int2Z0)=F(d1−t1,t1,λ,θ)
(XL2intZ0)=2F(d3−t2,t2,λ,θ)
The series of Eq. (7) up to Eq. (15) gives the inductive and the capacitive behaviors of the ring apertures for the designed geometry. The value of C_{1} is evaluated by the Eq. (7). The value of C_{2} is extracted by the interaction of inner ring aperture of effective thickness t_{2} and the outer ring aperture of thickness t_{1} and the gap between the two rings as g_{2} as illustrated in Eq. (10). Further, the value of C_{3} is evaluated in the Eq. (11) and contains the numeric value attained by the capacitive reactance of the inner circular ring (multiplied by an amplification factor of 10 due to its high influence). In the Eq. (8), the value of L_{1} is computed considering the inductance offered by outer conductive loop. For the value of L_{2}, the Eq. (9) is used for calculating inductive impedance offered by inner concentric ring. The subscript int is used to indicate an intermediate variable for obtaining the final parameter. It is important to define the added term CT which denotes the correction term and is related to the average value of g_{1}, in accordance with the diameter chosen for making the conductive ring and is given as:
CT=∫−d2d2|(d2)−(d2)2−x2|ddx
The Eq. (17) gives the correction term average value which is related to the diameter of the ring and it has proven to be an interesting approach in providing accurate results of the proposed ECM. In Eqs. (8) and (9), the term used ε_{eff} denotes the values of effective relative permittivity of the dielectric substrate explained in [35] and given as:
εeff=εr+(εr−1)(−1eMN)where M = 10h’/p’ in which h’ signifies the effective thickness of the substrate, ɛ_{r} represents the relative permittivity and the constant term N is dependent on the geometry and is related to the amount of conductive element present in the geometry [37]. The value of N is obtained according to the methodology given by [39] for different geometries. On generalizing the Eq. (18), the expression reduces to:
εeff=ε1+ε22; forh∼0.02λo
In the above equation ε1 takes the value of εr for the FR4 substrate i.e., 4.4 and ε2 is substituted with the dielectric permittivity of the air which has the value of unity. The dimensions of the parameters such as thickness of the ring (t) are calculated for different values of (t/λ) and the periodicity (p) is evaluated by using grating lobe condition given by:
p(1+sinθ)<λεeff
It has been stated that a generalized equation for linking the aforementioned parameters can be derived after additional simplification.
p=Mλwhere M denotes the constant of proportionality whose values lies in between 0 and 1. Considering the modal analysis of thin concentric rings dispersed periodically along any two skewed coordinates are revealed with an incident plane wave of any polarization striking at any of the oblique angles, as seen in the Fig. 3. It is important to get noted that the spacing between the ring elements should always be less than or equal to λ/2.
Geometrical placement of circular ring FSS
As demonstrated in the Fig. 3, a plane wave with propagation vector k strikes an array of rings which are distributed along the skewed coordinates s_{1} and s_{2} respectively. The distribution of the rings is such that the angle between k and the normal to the surface is denoted by θ and the angle between projection vector s_{1} and k is given by ф. The positioning of the electromagnetic fields in the vicinity of the array of FSS must meet the Floquet theorem's periodicity criterion. The scalar wave equation by using the Floquet’s theorem is given by [40]:
ψmn=e−j(Umnx+Vmny+Wmnz)
whereUmn=ksinθcosΦ+2πmdx
Vmn=ksinθcosΦ+2πndy−2πmdxtanα
Wmn={k2−Tmn2 for k2>Tmn2−jTmn2−k2 for Tmn2>k2and the term Tmn2 is given by:
Tmn2=Umn2+Vmn2
In the above equations, m and n denotes the Floquet indices. The term W_{mn} indicates the propagation constants of the incident rays which attain positive values for propagating modes and exhibits negative imaginary values for evanescent modes. The components pertaining to the electric field distribution which are transverse to the z axis can be expressed in terms of the factor ψ as given below:
Δmn TE=1dx dy(VmnTmnx˙−UmnTmny˙)ψmnTE modes
Δmn TM=1dx dy(UmnTmnx˙+VmnTmny˙)ψmnTM modes
The above mentioned fields are related to each other as given below:
ηmn TE=kη0Wpq
ηmn TM=Wpqη0k
The incident plane wave consisting of unit intensity electric field propagating in the direction of (θ, ϕ), can be expressed by the addition of the E and H polarized plane waves. The incident plane waves correspond to the TE and TM Floquet modes consisting of values m, n=0. Hence, the values of the incident electric and magnetic fields:
E˙i=∑r=12A00rΔ00r
H˙i=∑r=12A00rΔ00r(z˙×Δ00r)
In the above expressions, the term r denotes the TE and TM modes. The factor A_{00r} denotes the magnitude of the component. The scattered fields can be expressed in terms of the reflection coefficient R_{mnr} as given below:
E˙s=∑m∑n∑r=12RmnrΔmnr
H˙s=−∑m∑n∑r=12Rmnrηmnr(z˙×Δmnr)
The value of the unknown reflection coefficient R_{mnr} is given by:
Rmnr=ηmnr∬z˙×H˙s.Δmnr∗da
The analysis of the electromagnetic behavior of the circular ring is completed by signifying the boundary conditions which are given by:
E˙s+E˙i=0for each loop
(H˙s+H˙i)2z˙=K^
Now, substituting the Eq. (35) in Eq. (33) and incorporating the values of Eqs. (31) and (33) into the Eq. (36) we get:
∑r=12A00rΔ00r=−∑m∑n∑r=12ηmnrΔmnr∬z˙×H˙s.Δmnr∗da
For simplification of the Eq. (38), the induced current, −z˙×H˙s is replaced by another set of orthonormal mode functions which are compatible to the geometry of circular rings and also satisfy boundary conditions as shown below:
−z˙×H˙s=∑m∑n∑l=12(Bmnlψmnl)+BTEMψTEM
The limits for the mode coefficients ranges from l = 1 to l = 2 which denotes TE and TM modes respectively. The terms ψmnl and ψTEM for circular rings can be expressed as [41]:
ψmnTE=ρˇnρZn(kcmn′ρ)sinnϕ+ϕˇkcmn′Zn′(kcmn′ρ)cosnϕ
ψmnTM=ρˇkcmnZn′ˇ(kcmnρ)sinnΦ+ΦˇnρZnˇ(kcmnρ)cosnΦ
ψTEM=1ρlnba[x´cosnΦ+y´sinnΦ]where the simplified terms Zn and Znˇ are given by:
Znˇ=πεn2(Jn(kcmnb)Jn(kcmna))−1×(Yn(kcmna)Jn(kcmnρ)−Jn(kcmna)Yn(kcmnρ))where the terms k_{cmn} and k′_{cmn} is the m^{th} root of the equations as given below :
(Yn′(kc′)Jn′(kc′ba)−Jn′(kc′)Yn′(kc′ba))=0∀k cmn
(Yn(kc)Jn(kcba)−Jn(kc)Yn(kcba))=0∀k cmn′
On multiplying, both sides of the Eq. (39) by the complex conjugate of the coefficients ψmnl and ψTEM and integrating the finalized product value over the circular ring, the results are retrieved as [38]:
∑r=12A00rC00r*ABL=−∑m∑n∑r=12ηmnrCmnr*ABL∬z˙×H˙s.Δmnr∗da where the coefficient terms Cmnr*TEM and Cmnr*ABL are given by:
Cmnr*ABL=∬ψABL.Δmnr∗da
Cmnr*TEM=∬ψTEM.Δmnr∗da
Hence, the integral equation can be generalized into:
[ZMNLmnl][Bmnl]=[Dmnl]where Z denotes the square matrix in which the row index is designated by M,N,L and the column matrix is designated by m,n,l. The unknown coefficients B_{mnl} and B_{TEM} must be evaluated from the Eq. (51) and substituted in the Eq. (40) for evaluation of the reflection coefficient R_{mnr}, as suggested in [7].
Parametric Variations
The synthesis technique is validated by presenting a diagnosis as described. The physical measurements of the concentric circular ring based FSS spatial filter to be used in operation from 3 to 4.5 GHz are accessed by using the architecture equations. The Eqs. (6) to (15) are utilized for calculating the lumped circuit elements of the ECM from the parameters of the physical model and the reflection coefficient is predicted by using the Eqs. (22) to (35). In addition to the mathematical calculations, the results retrieved are validated by conducting simulations in the ANSYS tools of HFSS v20 and the ECM is performed on Electronic Desktop Circuit Editor. After the validation of the ECM, the design is authenticated by reporting the measurement results of the designed prototype. Theoretical research and existing studies indicate that, because to its symmetrical construction, DCRFSS provides the optimum performance; nevertheless, when the incidence angle of the wave striking it varies, its properties alter substantially after a certain angle. The FSS unit cell was examined at 0° in the first step, deriving its dimensions according to Tab. 1.
Unit cell dimensions of DCRFSS
Parameters
Values
f_{r1}
3.13 GHz
f_{r2}
5.18 GHz
p
0.55 λ_{mid}
t_{1}
0.0069 λ_{mid}
t_{2}
0.013 λ_{mid}
d_{1}
0.207 λ_{mid}
d_{2}
0.20 λ_{mid}
d_{3}
0.09 λ_{mid}
where the terms f_{r1} denote the lower resonant frequency, f_{r2} signifies the higher resonant frequency, λ_{mid} denotes the centre operating frequency wavelength, p denote the periodicity of DCRFSS structure, d_{1} is the diameter of the outer part of external ring, d_{2} is the diameter of the inner part of external ring and d_{3} is the diameter of the outer part of internal ring, t_{1} is the effective thickness of the outer ring of DCRFSS and t_{2} is the effective thickness of the inner ring of DCRFSS. The band pass behaviour of the DCRFSS is illustrated in the Fig. 4. To retrieve its value at the appropriate resonant frequencies of activity without ignoring the grating lobes, the Eq. (19) must be satisfied. Thus, for normal angle of incidence, Eq. (19) reduces to:
p<λεeff;p<λ for εeff≈1;
Also, a dedicated expression for the outer ring conductor is extracted from the Eq. (20) in the sub-6 GHz band as given below:
p≈λ2.4for outer ring conductor (in the sub−6GHz bands)
p=0.41λfor outer ring conductor (in the sub−6GHz bands)
Illustrations of band pass characteristics from the plot of transmission coefficient <italic>vs</italic>. frequency in sub-6 GHz range
After fixing the value of M and the ring diameters, the effective thickness of both conducting rings is evaluated (i.e., d_{1} and d_{2} by varying t/λ values) using an Eq. (54) which are mentioned in the Tab. 2 for 3 GHz frequency and in the Tab. 3 for 5 GHz frequency. The percentage deviation is also reported which indicates the difference between the simulated and from a fixed desired value. Further to have more clarity, the graphical illustration is plotted in the Figs. 5 and 6 to have an insight of this design. Also, the inner conductive ring possesses the dimensions at the operating frequency i.e., 5 GHz and at normal angle of incidence, the Eq. (19) reduces to:
p<λ;p≈λ1.5for inner ring conductor (in the sub−6GHz bands)
Also the expression is reduced from the Eq. (20) for the inner ring in the sub-6 GHz range as:
p=0.66λfor inner ring conductor (in the sub−6GHz bands)
It should be remembered that the resonant frequency measured in the simulation process is taken at the level where transmission coefficient decreases to −3 dB value. By fixing the value of p, the variations of the characteristics at different values of t/λ is illustrated in the Tabs. 2 and 3.
Outer ring parameters for 0° AOI at 3 GHz
Parameters
Values
t_{1}/λ_{1}
0.005
0.015
0.026
0.036
p
0.55 λ_{mid}
0.55 λ_{mid}
0.55 λ_{mid}
0.55 λ_{mid}
d_{1}
0.20 λ_{mid}
0.22 λ_{mid}
0.23 λ_{mid}
0.24 λ_{mid}
t_{1}
0.0069 λ_{mid}
0.020 λ_{mid}
0.034 λ_{mid}
0.048 λ_{mid}
f_{r1}(simulated)
3.13 GHz
3.46 GHz
3.72 GHz
3.91 GHz
λ_{1}
1.32 λ_{mid}
1.32 λ_{mid}
1.32 λ_{mid}
1.32 λ_{mid}
% deviation of f_{r1} from 3 GHz
4.3
15.3
24
30
Inner ring parameters for 0° AOI at 5 GHz
Parameters
Values
t_{2}/λ_{2}
0.005
0.015
0.026
0.036
p
0.55 λ_{mid}
0.55 λ_{mid}
0.55 λ_{mid}
0.55 λ_{mid}
d_{3}
0.087 λ_{mid}
0.095 λ_{mid}
0.104 λ_{mid}
0.112 λ_{mid}
t_{2}
0.004 λ_{mid}
0.012 λ_{mid}
0.021 λ_{mid}
0.029 λ_{mid}
f_{r2} (simulated)
5.30 GHz
5.15 GHz
5.05 GHz
4.83 GHz
λ_{2}
0.83 λ_{mid}
0.83 λ_{mid}
0.83 λ_{mid}
0.83 λ_{mid}
% deviation of f_{r2} from 5 GHz
6
3
1
3.4
Effect of varying t/λ of the DCRFSS with respect to the resonant frequency for (a) outer conducting ring, (b) inner conducting ring
A significant outcome of this analysis is that the relative deviation percentage of the resonant frequency from the predicted value is reported for different values of the p by varying the t/λ ratio. It is interpreted from the Figs. 5a and 5b that the resonant frequencies due to both the concentric rings shows the variation at a certain rate in terms of an increase in the transmission bandwidth at a normalized incidence angle (0° in our design) with the variation of t/λ ratio. The effect of the variation of the periodicity is also reported for the proposed design of DCRFSS geometry. As the value of the periodicity is increased, the frequency drift is visualized on both higher and the lower ends. The bandwidth enhancement is reported by the variation of the periodicity as depicted in the Tab. 4 and illustrated in the Fig. 6.
Effect of varying periodicity on the transmission coefficient of the DCRFSS
Parameters
Values
p
0.50 λ_{mid}
0.55 λ_{mid}
0.61 λ_{mid}
0.66 λ_{mid}
f_{r1} (simulated) (GHz)
3.13
2.76
2.75
2.75
% deviation of f_{r1} from 3 GHz
4.3
8
8.33
8.33
f_{r2} (simulated) (GHz)
5.18
5.35
5.39
5.28
% deviation of f_{r2} from 5 GHz
3.6
7
7.8
5.6
Effect of varying periodicity (p) on the transmission response of the DCRFSS
The synthesis approach aids in the determination of equivalent circuit characteristics like as inductance and capacitance, as shown in Fig. 3b in the sub-6 GHz FR1 spectrum and listed in Tab. 5.
Lumped circuit parameters extracted from ECM
Parameters
Values
f_{r1}
3.13 GHz
f_{r2}
5.18 GHz
p
0.55 λ_{mid}
t_{1}
0.0069 λ_{mid}
t_{2}
0.013 λ_{mid}
d_{1}
0.207 λ_{mid}
d_{3}
0.09 λ_{mid}
Input →Output
L_{1} Mathematically evaluated
5.385 nH
L_{2} Mathematically evaluated
8.624 nH
C_{2} Mathematically evaluated
0.483 pF
C_{3} Mathematically evaluated
0.109 pF
As seen in the DCRFSS frequency response model, the transmission coefficient (S_{21}) reaches a very low level at the two resonant frequencies (f_{r1} and f_{r2}). The resonance frequencies, f_{r1} and f_{r2}, are discussed and are controlled by adjusting the thickness of the outer and inner rings. It can be observed that the outer ring expresses the inner resonant frequency, and the inner ring geometry represents the outer resonant frequency. It is clear from the Tab. 6, that the percentage deviation is less than 1% for the resonant frequencies extracted from the mathematical analysis. The lumped circuit parameters are then entered into the ANSYS circuit editor, and simulation is performed for validating the design by extracting the transmission characteristics.
Verification of ECM model by extracting resonant frequencies
Parameters
Values
L_{1 (nH) Mathematically evaluated}
5.385
L_{2 (nH) Mathematically evaluated}
8.624
C_{2 (pF) Mathematically evaluated}
0.483
C_{3 (pF) Mathematically evaluated}
0.109
Input →Output
f_{r1} GHz _{(as per Eq. (1))}
3.12
f_{r2} GHz _{(as per Eq. (2))}
5.19
% deviation of first resonant frequency
4
% deviation of second resonant frequency
3.8
Fig. 7a depicts the circuit diagram of the suggested DCRFSS design, which clearly depicts the operating principle of a two-port network whereas the graphical comparison for the transmission coefficient curves is depicted in the Fig. 7b. The transmission coefficient graphs retrieved from this analysis are in line with the graphs of HFSS simulator which authenticate our design for sub-6 GHz FR1 spectrum. The deviation in the resonant frequency is reported from the results extracted from the two simulation models and is illustrated in the Tab. 7.
DCRFSS structure (a) circuit schematic, (b) transmission coefficient graphs extracted from HFSS (FEM) and circuit editor (ECM)
It is clearly indicated in the Tab. 7 that the graphs with higher and lower resonant frequencies as retrieved from the two modeling techniques are in line with each other. The percentage deviation is retrieved equal 10 percent for lower resonant frequency and 3.2 percent for the higher resonant frequency. The DCRFSS has the intrinsic quality of having equal output characteristics within a particular range of incidence angle and is also polarization independent, as demonstrated by the study in the Tabs. 6 and 7 respectively. The response of transmission coefficient is reported at different polarization angles in the Fig. 8a and at oblique angles of incidence in the Fig. 8b.
Comparative analysis of the resonant frequencies retrieved from ECM and FEM techniques
Parameters
Values
f_{r1 (HFSS)}
3.13 GHz
f_{r2 (HFSS)}
5.18 GHz
FEM vs. ECM
f_{r1 (Circuit Editor)}
3.47 GHz
f_{r2}_{(Circuit Editor)}
5.01 GHz
% deviation in ECM compared to FEM
10
% deviation in ECM compared to FEM
3.2
Transmission response of the DCRFSS (a) at polarization angles, (b) at oblique AOI’s
The polarization conversion ratio (PCR) is an important parameter to be considered while designing the proposed DCRFSS. The values of the transmission and reflection polarization conversion ratios must be identified for reporting of polarization insensitive behavior. In contrast to the traditional metal-ground transmissive polarization converter, the suggested DCRFSS is designed to be incorporated as a superstrate over an antenna, and hence, its reflection coefficient is not zero. Hence, when calculating the values of the transmissive polarization conversion ratio (TPCR), the reflection and transmission ratios of y-to-x and y-to-y polarization conversions should be taken into mind. The term TPCR is expressed in terms of the reflection and the transmission ratios as shown:
TPCR=|txy|2(|rxy|2+|ryy|2+|txy|2+|tyy|2)
The value of TPCR is above 96% for the entire frequency spectrum within the desired operating band. Also, the values reported in the Tab. 8 clearly indicate that the designed DCRFSS is polarization insensitive as the resonant frequencies attains the same value for different angle ‘ϕ’ ranging from 0° to 90°. As illustrated in Fig. 8b, the intended structure of DCRFSS is synthesized for various oblique incidence angles. The limit of AOI for this design to operate is up to 30° for satisfying the Eq. (20) as given below:
p(1+sin30)<λεeff
Response of DCRFSS as a band pass filter at different polarization angles
The average bandwidth is essentially unaffected by angle fluctuation, and for high incidence angles such as 30°, the structure retains appropriate performance, as shown in Tab. 9.
Band-pass response of DCRFSS at different oblique incident angles
Parameters
Values
Angle (ϕ) (degree)
0°
5°
10°
15°
20°
25°
30°
f_{r1} (GHz)
3.13
3.07
3.05
3.02
3.00
2.99
2.97
f_{r2} (GHz)
5.18
5.16
5.15
5.14
5.14
5.13
5.12
Bandwidth (MHz)
2050
2090
2100
2120
2140
2140
2150
% FBW
49.33
50.78
51.21
51.96
52.57
52.70
53.21
% deviation of f_{r1} from 3.13 GHz
0
1.9
2.5
3.5
4.1
4.4
5.1
% deviation of f_{r2} from 5.18 GHz
0
0.38
0.57
0.77
0.77
0.96
1.15
As shown in Figs. 8a and 8b, the graphs virtually correspond with each other, making this design stable in terms of polarization and AOI by presenting same features up to 30 degrees of incident angles and 90 degrees for the polarization angles.
Array Modeling and Experimental Set-up
According to Floquet theory, the frequency selective surfaces have identical characteristics in when extended to an array made by combinations of a unit cell [39]. The dimensions of the unit cell are duplicated for all array items. Using this theory, the analysis was extended to create a 2 × 2 DCRFSS array that can be generalized into an N × N array. The designed prototype is illustrated in the Fig. 9a. A unique DCRFSS schematic is utilized to create a prototype with the needed properties. This DCRFSS is constructed utilizing a straight-forward design of single surface layers. At sub-6 GHz frequency ranges of operation, the structure has a low insertion loss. The prototype's frequency response is evaluated for both normal incidence and oblique incidence angles. The measuring investigation is completed by putting together an experimental setup, as shown in Fig. 9b and the measurement set-up in an anechoic chamber for reporting the design characteristics is illustrated in the Fig. 9c. The retrieved measurement findings under the free space environment circumstances are compared with the simulated ones, in the Fig. 9d.
Illustration of the DCRFSS (a) fabricated prototype, (b) experimental set up, (c) 2 × 2 DCRFSS placed in an anechoic chamber, (d) comparative analysis of simulated and measured S-parameters
The proposed DCRFSS design's benefits are compared to the state-of-the-art literature as illustrated in the Tab. 10. The comparison is based on design factors such as substrate thickness, size, and dielectric constant, as well as bandwidth performance. The proposed design in this publication has demonstrated very excellent bandwidth with an ultra-thin design.
State of art comparison of the proposed DCRFSS
Citedwork
Substrate thickness
Cell size
εr
−10 dB FBW (%)
Elements used
Remarks
[9]
---
0.175λ × 0.175λ
2.1
37
Double square and cross loops (DSCL)
Limited bandwidth
[10]
0.046λ
0.18λ × 0.18λ
2.2
34
Double square with gridded loops
Includes highstructural complexity
[11]
0.003λ
0.26λ × 0.26λ
3.5
46
Modified DSL
Not suited for large power applications
[15]
0.13λ
1.67λ × 1.67λ
4.4
32.5
Square loop with grids
Substantial thickness of substrate
[42]
0.01λ
Not specified
2.2
46
Tunable Meta surfaces
Angular stability not studied
[43]
0.06λ
0.2λ × 0.2λ
2.2
24
Jerusalem cross surface
Limited bandwidth
Proposed work
0.022λ
0.20λ − outer loop0.09λ − inner loop
4.4
49.33
Double Concentric Ring structure
Wide bandwidth with angular and polarization stability
Conclusion
A unique numerical synthesis approach for creating a simple, miniaturize, and a broadband FSS that may be employed in the construction of microwave spatial filters in the sub-6 GHz FR1 frequency region is described. Spatial filters are created using double concentric ring frequency selective surface structures, which have high bandwidth and polarization independence. For the estimate of physical dimensions, a unique numerical synthesis approach is suggested. The effect of the variation of periodicity, loop diameters, polarization angles and incident angles with respect to wavelength is analyzed in this study. The prototype is used to validate the synthesis of the proposed structure. In addition, an analogous circuit analysis is offered for examining the intended work in terms of its electrical behavior to demonstrate the filtering process. The suggested structure is polarization insensitive, with a steady transmission response at incidence angles spanning from 0° to 30°. The suggested spatial filters based on the concentric ring design of the FSS proves to be a viable option to be placed as a superstrate with the antenna in sub-6 GHz 5G applications for improving the radiation characteristics.
Funding Statement: Authors have received no specific funding for completing this study.
Conflicts of Interest: Authors hereby declare that they have no conflicts of interest to report regarding the present study.
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