In this paper, a miniaturized and polarization insensitive frequency selective surface filter with large band ratio (BR) is presented. This structure consists of one metal layer and two dielectric layers. The metal layer includes two parts, with the outer square loop providing a lower frequency stopband and the inner pattern providing a higher frequency stopband. The structure has excellent miniaturization characteristics, in particular, the unit size is only 0.054 and the thickness is only 0.014 , where is the wavelength corresponding to the first resonant frequency. Additionally, there is only one layer of metal layer, which greatly reduces the processing complexity and cost. The measurement results show that for TE and TM polarization, the center frequencies of the two stop bands are 2.03 and 18.98 GHz corresponding to a BR of 9.35. It can be used as a spatial dual frequency filter with large frequency band separation. In addition, the proposed structure also possesses advantages such as wideband response, polarization insensitivity, and high angle stability. The simulation results are in good agreement with the measured results.
I. INTRODUCTION
Frequency selective surface (FSS) is a type of microwave device with periodic array structures, which plays the role of spatial filters for electromagnetic waves with different incidence angles and different polarization modes.1 It is widely used in wireless communication, radar and antenna fields, such as various antenna reflectors, radomes, absorbers, shields, polarizers, detector and reduction of radar cross section (RCS), etc.2–11
With the rapid development of wireless communications, radar, and satellite communications, the design and fabrication of dual-band or multi-band FSSs have attracted increasing attention.12 A multi-band FSS facilitates the adjustment of frequency bands, reduces system footprint, and additionally enables stealth capabilities.13There are several main techniques for designing dual-band or multi-band FSSs: (1) fractal elements,14 (2) multiple resonant elements,15 (3) multi-layer structures,16 (4) single-frequency FSSs with resonant primitives,17 and so on. Most of the existing designs focus on applications with closely spaced operating frequency bands.18 These designs rely on coupled resonant structures, where the resonant characteristics of the unit cells are modified to achieve the tightest possible frequency separation between adjacent bands. In practical scenarios, achieving outstanding multi-band responses with a large band ratio (BR), where BR represents the ratio of the resonant frequencies of two band-stop windows, becomes challenging due to harmonic resonances and grating flaps. It has been documented by Li et al. that angular stability degrades rapidly in the majority of multi-frequency band FSSs when the BR is relatively large.19 Researchers need to ensure effective separation of the two resonant frequencies within a limited size by cleverly designing the unit cell shape, coupling mechanisms, and material properties, while preventing interference or overlap between the structures.
In recent years, a number of researchers have attempted to design FSS structures with large band ratio.20–24 For example, in 2014, Li et al.20 proposed a three-dimensional bandpass FSS, consisting of a set of three-layer printed circuit boards and some inserted metal rods and plates, to achieve high frequency dual-band performance, with a BR of 4.2. In 2019, Li et al.21 proposed a three-layer spurious-free structure design to obtain a relatively large BR. However, both of the above FSS are unipolar. Based on the staggered grid structure, Jiang et al.22 combined two square grid FSSs together to enhance the band stop response of FSSs, resulting in a wider bandwidth between the two passbands, thereby increasing BR to 6.2. However, the above structures are three-dimensional, complicated to fabricate, and the BR is not high enough.
Therefore, unlike existing works that employ complex multi-layer or three-dimensional structures, this paper proposes a miniaturized and polarization insensitive FSS filter with large BR, which is a simple single-layer metallic FSS design, making it easier to fabricate. The schema and working principles are illustrated in Fig. 1. Guided by the theory of equivalent circuit model (ECM), the internal complex combination model is designed from the dual square loop model, which increases the BR and improves the angular stability of the structure. Utilizing a configuration that incorporates a metal layer and a double-layer dielectric substrate, the resonant frequency of the low-frequency operating band was reduced, thereby further augmenting the BR. This approach also ensured the durability and stability of the FSS. The reliability of the theoretical analysis and simulation was validated through empirical measurements. This type of FSS filter with a large BR offers advanced spectral filtering capabilities, promising significant advancements in communication systems, radar stealth, satellite communication, and environmental sensing, addressing challenges in electromagnetic compatibility and component miniaturization.
The arrangement of the remaining chapters is as follows: Section II presents the structural description and operating mechanism of the designed FSS. Section III verifies the dual stop band transmission performance through full-wave simulation as well as microwave darkroom testing, and the measured results are in good agreement with the simulated results. Section IV gives the conclusion.
II. DESIGN AND ANALYSIS OF THE FSS
A. Structure description
The proposed FSS structure is a single layer structure with a thin dielectric layer above and below the main metal layer in the center as shown in Fig. 2. It mainly consists of two dielectric layers with a patch-type metal layer in the middle. This FSS is assembled by a parallel tightly arranged along the x and y directions, which provides polarization insensitivity. Based on the basic single-layer FSS, a tightly fitting dielectric substrate is added to further reduce the operating range of the low-frequency stop band, thereby increasing the BR, and also protecting the intermediate metal layer to improve its durability.
The structure of each unit is shown in Fig. 3, which mainly consists of an outer metal loop and an inner center-symmetric structure. The centrosymmetry of the inner layer is a combination of a group of concentric rings and an improved swastika, and Fig. 4 illustrates the evolution of the internal structure design. The evolution process begins with the classical swastika-shaped structure composed of four bent branches, on each of which a smaller rectangular fractal is added. Next, a T-shaped structure is split from the ends of the four branches. Finally, a dual-ring patch is connected in series. This design approach enhances the effective path of the internal complex pattern, thereby achieving a miniaturized unit. This FSS uses FR-4 with a relative permittivity and loss tangent as the substrate, and the metal layer is made of copper.
B. Operation principle
(a) Equivalent circuit model of general two square Loop FSS. (b) Equivalent circuit model of the proposed FSS. nH, pF, , nH, pF.
(a) Equivalent circuit model of general two square Loop FSS. (b) Equivalent circuit model of the proposed FSS. nH, pF, , nH, pF.
The inductance value of the swastika structure is the series sum of the four identical curved segments. The coupled inductance of the double ring is the parallel value of the two rings. Therefore, the rough value of is the inductance value of the swastika structure and the double ring structure connected in series. Then, the advanced design system (ADS) is used for curve fitting and optimization to obtain all parameters. The frequencies of two different stopbands can be calculated using formula (1).
Simulate the equivalent circuit using ADS, the capacitance and inductance values obtained through curve fitting optimization are shown in Fig. 5. The S-parameters obtained from CST simulation and the ECM are shown in Fig. 6(a). From the results, it can be seen that the two stopbands are located at 2.03 and 18.98 GHz, respectively, and the equivalent circuit model results are generally consistent with the full wave simulation results.
(a) Comparison of the S-parameters under normal incidence. Full wave electromagnetic simulation results and ECM prediction results are provided. (b) Comparison of S-parameters in TE and TM polarization modes.
(a) Comparison of the S-parameters under normal incidence. Full wave electromagnetic simulation results and ECM prediction results are provided. (b) Comparison of S-parameters in TE and TM polarization modes.
C. Design of dual-stopband FSSs
Based on the analysis of the basic dual loop model, this paper proposes a dual-stopband FSS filter. The outer layer of a very slender square loop metal can provide a very small resonant frequency band. The inner layer is made of a modified swastika-shaped graphic, which ensures the axial and central symmetry of the structure, thus improving the angular stability as well as the polarization insensitivity. Designing such complex internal structures can improve the stability of FSSs at large BR and increase the level of miniaturization. The upper dielectric substrate can further reduce the low resonant frequency, thereby improving BR, and also protect the middle metal layer to improve the durability of FSSs.
Figure 7 displays the variation of the calculated transmittivity with increasing incidence angle at TE and TM polarizations. The results indicate that the transmittivity remains stable when the incident angle increases from 0 to 45 . The transmittivity can be calculated as .
The transmittivity of the proposed FSS varying with incident angle. (a) TE polarization; (b) TM polarization.
The transmittivity of the proposed FSS varying with incident angle. (a) TE polarization; (b) TM polarization.
III. RESULTS AND DISCUSSION
In order to verify the performance of the proposed FSS, the insertion loss at different polarization angles was simulated. Figure 6(b) shows the simulated frequency response characteristics of dual-stopband FSS under TE and TM polarization at normal incidence. The results indicate that compared to the ordinary dual-loop FSS, this structure has a wider passband bandwidth, achieving a passband above 16.9GHz, and achieving a stopband window with insertion loss less than 10dB in the range of 1.25–3.11 GHz and 18.70–19.20 GHz. The simulation results show that the center frequencies of the first and second stopbands are 2.03 and 18.98 GHz, respectively. The passband range of 10dB or more between two stopbands is 3.11–18.70 GHz, with a relative bandwidth of 143.0%. Moreover, the FSS maintains polarization insensitivity.
Furthermore, the main parameters of complex structure have also been varied to study the change in the resonance behavior. It can be observed from Fig. 8 that effective inductance increases with increases from 1.3 to 1.6 mm, the high-frequency decreases from 18.98 to 17.17 GHz. This leads to a reduction of frequency band ratio from 9.35 to 8.46. Similarly, as decreases from 0.5 to 0.1 mm, the performance changes are the same as . Simultaneously, the first stopband can also be tuned by adjusting the dimensions of the outer square loop. By multiplying Eqs. (2) and (3), the calculation formula for can be obtained, further revealing that . Consequently, as increases (as the outer square loop becomes thicker), the value of decreases. According to Eq. (1), this results in a higher resonant frequency for the first stopband. Similarly, , indicating that is monotonically decreasing with respect to . This implies that as the spacing between the outer square loops increases, the resonant frequency also rises. Through the study of parameters, a more comprehensive analysis of the electromagnetic behavior of the FSS can be achieved. The optimized parameters chosen for proposed miniaturized FSS are presented in Table I.
The simulated transmission spectrums of the proposed FSS. (a) For different values of , and (b) for different values of .
The simulated transmission spectrums of the proposed FSS. (a) For different values of , and (b) for different values of .
Physical parameters of the FSS in Fig. 3.
Parameter | D | h | l1 | l2 | l3 | R1 | R2 |
Value (mm) | 8 | 1 | 1.3 | 0.7 | 0.3 | 0.9 | 0.7 |
Parameter | R3 | R4 | w1 | w2 | d1 | d2 | d3 |
Value (mm) | 0.6 | 0.4 | 0.1 | 0.2 | 0.4 | 0.1 | 0.05 |
Parameter | D | h | l1 | l2 | l3 | R1 | R2 |
Value (mm) | 8 | 1 | 1.3 | 0.7 | 0.3 | 0.9 | 0.7 |
Parameter | R3 | R4 | w1 | w2 | d1 | d2 | d3 |
Value (mm) | 0.6 | 0.4 | 0.1 | 0.2 | 0.4 | 0.1 | 0.05 |
To further validate the simulation results, FSS has been fabricated and measured. The prototype consists of unit cells, with a total size of 340 340 mm. The diagram of the measuring device is shown in Fig. 9. The transmitting and receiving antennas are both linearly polarized horn antennas used for transmitting and receiving electromagnetic wave signals. The transmitting antenna is located on the mechanical rocker arm above, and the receiving antenna is located on the mechanical rocker arm in the orange small darkroom below. The rotation angle is controlled by a computer, and the transmitting and receiving antennas are always in the same straight line as the prepared FSS during measuring. The transmitted and received signal levels were analyzed by Vector Network Analyzer (VNA) to calculate the transmittance of the FSS. In the measurement process, in order to verify the angular stability of the FSS, the computer control the tilt angle of the robotic arm simultaneously, so as to change the tilt angle theta of the transmitting and receiving antennas. To verify the polarization insensitivity of FSS, measurements were made by rotating two antennas at , using time-domain gating technology to eliminate multipath interference during testing.
Photos of measuring devices (transmitting–receiving antennas) and fabricated FSSs.
Photos of measuring devices (transmitting–receiving antennas) and fabricated FSSs.
Figures 10 and 11 show the simulated and measured insertion loss of the dual-stopband FSS under TE and TM polarization oblique incidence. For TE polarization, as theta increases, the first stopband always maintains good stability and the range remains basically unchanged. The bandwidth of the second stopband is widened, but the frequency position is shifted slightly forward. From the measurement results, it can be seen that when the incident angle theta=30 , the frequency range of the second stopband is 17.96–18.68 GHz, and the center frequency is 18.32 GHz. When theta = 45 , the frequency range of the second stopband is 17.10–17.90 GHz, and the center frequency is reduced to 17.50 GHz. However, at this time, its BR is 8.6, which still maintains a large band ratio. When theta increases, there is some deviation in the S-parameters, which can be attributed to factors such as phase variations, increased penetration depth, and multi-mode effects. For TM polarization, as theta increases, the first and second stop bands always maintain good stability. From Figs. 10(b) and 11(b), it can be seen that the measurement results and simulation results are consistent within the error range. The reason for the error is due to the immature sample processing technology and defects in the testing environment. Overall, this FSS structure maintains good angular stability.
Comparison of transmission coefficients under different incident angles. (a) TE mode, simulation. (b) TE mode, measuring.
Comparison of transmission coefficients under different incident angles. (a) TE mode, simulation. (b) TE mode, measuring.
Comparison of transmission coefficients under different incident angles. (a) TM mode, simulation. (b)TM mode, measuring.
Comparison of transmission coefficients under different incident angles. (a) TM mode, simulation. (b)TM mode, measuring.
The performance comparison is shown in Table II. Compared with the work in the references, the FSS proposed in this paper has advantages such as miniaturization, large BR, dual polarization, and ultra wide passband. Moreover, most of the FSS in the literature are 3D structures, which are relatively complex to manufacture and have limitations in practical application. However, the FSS proposed in this article is a single-layer structure based on PCB technology, with low cost and easy production. The upper dielectric substrate can further protect the core structure of FSS, improving its durability.
Performance comparison with existing designs.
Reference . | Unit element size . | Thickness . | Polarization . | Angular stability . | Numbers of layers . | Relative bandwidth . | BR . |
---|---|---|---|---|---|---|---|
19 | 0.072λ0 | 0.034λ0 | Single | 45° | 3D | 116.7% | 5.0 |
20 | 0.083λ0 | 0.045λ0 | Single | 40° | 3D | 109.7% | 4.2 |
22 | 0.081λ0 | 0.139λ0 | Dual | 40° | 3D | 116.6% | 6.2 |
23 | 0.090λ0 | 0.033λ0 | Dual | 30° | 3 | 60.0% | 5.4 |
24 | 0.147λ0 | 0.019λ0 | Single | NA | 2 | 66.7% | 3.5 |
This work | 0.054λ0 | 0.014λ0 | Dual | 45° | 1 | 143.0% | 9.4 |
Reference . | Unit element size . | Thickness . | Polarization . | Angular stability . | Numbers of layers . | Relative bandwidth . | BR . |
---|---|---|---|---|---|---|---|
19 | 0.072λ0 | 0.034λ0 | Single | 45° | 3D | 116.7% | 5.0 |
20 | 0.083λ0 | 0.045λ0 | Single | 40° | 3D | 109.7% | 4.2 |
22 | 0.081λ0 | 0.139λ0 | Dual | 40° | 3D | 116.6% | 6.2 |
23 | 0.090λ0 | 0.033λ0 | Dual | 30° | 3 | 60.0% | 5.4 |
24 | 0.147λ0 | 0.019λ0 | Single | NA | 2 | 66.7% | 3.5 |
This work | 0.054λ0 | 0.014λ0 | Dual | 45° | 1 | 143.0% | 9.4 |
IV. CONCLUSION
This paper presents a miniaturized and polarization insensitive FSS filter with large BR. The proposed FSS offers significant advantages, including a large BR, polarization insensitivity, ultra-wideband characteristics, simple fabrication, and high durability. The measurement results of the fabricated FSS are generally consistent with the simulation results within the margin of error, demonstrating stable performance at large frequency band separations. This type of FSS with large BR holds substantial application potential in wideband communication and stealth technology.
ACKNOWLEDGMENTS
The authors would like to thank the reviewers for their valuable comments and suggestions. This work was supported by the Postdoctoral Fellowship Program of CPSF (No. GZC20232050), Fundamental Research Funds for the Central Universities (No. 20106244406), and Aeronautical Science Foundation of China (No. 20240025081001).
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Yi Li: Conceptualization (equal); Data curation (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Ruize Xu: Conceptualization (equal); Data curation (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Peng Ren: Conceptualization (equal); Formal analysis (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). Baoyi Xu: Conceptualization (equal); Funding acquisition (equal); Resources (equal); Writing – review & editing (equal). Minrui Wang: Conceptualization (equal); Data curation (equal); Funding acquisition (equal); Investigation (equal); Project administration (equal); Resources (equal); Validation (equal); Writing – review & editing (equal). Chen Chen: Data curation (equal); Investigation (equal); Software (equal); Validation (equal). Keqing Chen: Data curation (equal); Investigation (equal); Software (equal); Validation (equal); Visualization (equal). Zheng Xiang: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Project administration (equal); Resources (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal).
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.