Narrow-band frequency selective fabrics: simulation and experiment results

Abstract

In this paper, frequency selective fabrics (FSFs) with narrow-band transmission characteristics were proposed. The square-ring FSF was taken as an instance to illustrate the design principle. Based on the existing theoretical basis and by means of software simulation and optimization, the optimum structures with ideal narrow-band band-stop or band-pass characteristics were obtained. Then, the practical specimens were manufactured through a computer-based carving process and measured using the transmission method in an anechoic chamber. Two structural models were respectively simulated using two different algorithms and the results showed very small differences, primarily verifying the effectiveness of the design methods and reasonability of the model simplification. The measured and simulated transmission characteristics of square-ring FSFs were compared and showed a high consistency, which further verified the validation of the design method. The other two kinds of FSFs, namely Jerusalem-shaped and circle/ring hybrid FSFs, were designed and measured, which showed the narrow-band frequency selective characteristics were quite ideal. This indicates that the proposed design method using simulation software may be applied to many different structures and has directive sense in the related product design and development process.

Keywords

frequency selective surface narrow-band transmission electromagnetic simulation computer-based carving anechoic chamber

The frequency selective surface (FSS) is a periodic spatial filtering structure that has been widely used in many fields.^1,2 Many researchers have carried out relevant research work, mainly focusing on numerical calculation and simulation issues, fundamental algorithms, sample fabrication, etc.^3–5 However, the traditional products based on FSS are principally rigid plates,⁶ rarely involving soft material.

Due to the good periodicity and convenient local metallization process of fabrics, soft frequency selective fabrics (FSFs) have been proposed and studied.^7–12 Textile forming technology, such as weaving, knitting and braiding, could be used to prepare the products in which the periodic conductive patterns are embedded.⁷ Also, methods such as silk-screen printing, computer embroidery technology and the cloth hot stamping process have been used to obtain the periodic conductive pattern on the surface of fabrics,^8–12 serving as the flexible substrates. Actually, two-dimensional (2D) weaving technology is often used to prepare the periodically conductive grid structure and the transmission characteristics are mostly high-pass filtering properties, lacking the ideal band-pass and band-stop characteristics.^7–11 Although more complicated fabric forming processes could be used in the preparation of FSFs, the preparation accuracy as well as efficiency is difficult to satisfy. The finishing technology shows flexible and operable fabrication advantages, which seems to be more suitable for laboratory research.¹²

The influences of various parameters on the frequency response characteristics have been systematically studied in our previous work,^7–9 and the expected transmission performance could be obtained by adjusting the dimension parameters specific to design requirements. In practical applications, such as communication, stealth, radar detection, etc., the bandwidth level is also an extremely important indicator, as it determines the frequency range at which electromagnetic (EM) waves could pass through or be shielded, and then affects the transmitted or reflected information and energy. Considering that the actual application requirements are usually different, there is no definitive boundary to distinguish the bandwidth levels of narrow-band and broad-band characteristics. Taking the aperture FSFs as an example, the reported –0.5 dB bandwidth values are basically greater than 0.3 GHz.^13–15 Existing research works are mostly focused on broad-band absorption,^16–18 but the narrow-band transmission characteristics are seldom thoroughly studied and effective design methods are lacking.

In this paper, the square-ring FSF unit was taken as an instance to illustrate the design principle of narrow-band transmission characteristics. The modeling and simulation methods were adopted for optimal design, and then the FSF samples were fabricated and measured to explore the validity of the design process.

Design procedure

Theoretical basis

Classical FSSs can be classified into different types according to the unit shape and some basic empirical formulas were obtained, which show the approximate relationship between the resonance frequency and the size parameters.¹⁹ By means of the empirical formulas, the range of unit size parameters could be roughly estimated. Also, it is indicated that the size of the bandwidth mainly depends on the unit arrangement, namely the unit distance D. In general, a 10% increase of D in one direction will reduce the FSS bandwidth by 10%, and a 10% increase in both directions will result in a 20% reduction in bandwidth.^19,20 Increasing the value of D effectively reduces bandwidth, while overlarge spacing is likely to cause grating lobes in the FSS, which would cause energy dispersion and misjudgment of the target location, which is detrimental to FSS applications and should be suppressed.

Munk¹⁹ studied the condition for grating lobes and summarizes it in an authoritative book. Table 1 shows the criteria for avoiding grating lobes of three lattice types, where D is the periodic unit distance, λ is the free-space EM wavelength and θ is the incidence angle. In the second column of Table 1, the dark spot represents the conductive unit and the arrange modes could be square, regular triangle or isosceles triangle, which are called lattice types. The grating lobe could be avoided if the mathematical relationships of D, λ and θ meet the conditions listed in the third column of Table 1, which are called grating lobe criteria.^19–22 As the EM wave transmits vertically onto the square array, the unit distance D should be less than λ, 1.15λ and 1.12λ, respectively. It can be concluded that the occurrence probability of the grating lobe could be reduced by replacing the square lattice with a triangular lattice or by reducing the array period unit distance.

Table 1.

Lattice type and grating lobe criterion

Lattice type	Limited condition	θ = 0 º
Square	$\frac{D}{λ} < \frac{1}{1 + sin θ}$	D < λ
Regular triangle	$\frac{D}{λ} < \frac{1.15}{1 + sin θ}$	D < 1.15λ
Isosceles triangle	$\frac{D}{λ} < \frac{1.12}{1 + sin θ}$	D < 1.12λ

During the design procedure, the unit distance D should be adjusted to simultaneously make the bandwidth relatively narrow and avoid the grating phenomenon, but the adjustment directions are opposite and therefore it needs to be systematically considered. Based on the above design idea, designers could roughly define the size range and lattice type. Combined with the unit size estimated by the empirical formula, the FSSs could be designed to meet actual needs through a fast and effective procedure, making them suitable for simple unit structures.

Modeling and simulation process

The finishing technology shows flexible and operable fabrication advantages and it is studied in this paper. Through the rational analysis of the empirical formula and grating lobe criterion, the frequency response characteristics and the dimension parameters could be roughly predicted. However, it is more difficult to quantitatively calculate FSSs with novel and complicated units, and therefore a more elaborate design method is needed. The EM simulation method could be used to calculate the transmission coefficient and reflection coefficient of FSFs when they interact with the EM field, and also the optimum structure parameters could be optimized with the help of EM software. The accurate unit cell model should be first established and then imported into the EM software for further simulation, obtaining the optimized the dimension parameter and ideal frequency response characteristics.

The modeling process of the square-ring FSF unit is taken as an example to illustrate the principle. Figure 1(a) and (b) show the schematics of patch and aperture FSFs respectively, where Dx and Dy are the unit distances and m and n are the side lengths of outer ring and inner ring, respectively. For the general base fabrics, the surface roughness is negligible as the thin conductive metal patch is attached. The thickness values and dielectric parameters of actual fabrics could be measured and assigned to the structure models. To improve the simulation efficiency, the base fabrics could be equivalent to a smooth plate with the same thickness and dielectric properties, as shown in Figure 2(a) and (b). The equivalent process could greatly simplify the simulation model and reduce the simulation difficulty, and its validity will be elaborated in the follow-up comparative analysis of simulation results.

Figure 1.

Two complementary square-ring frequency selective fabrics: (a) patch type and (b) aperture type.

Figure 2.

Patch square-ring frequency selective fabric model and equivalent plate model: (a) fabric substrate and (b) plate substrate.

In order to verify the validity of the simulation method, HFSS software (Finite Element Method) and CST Microwave Studio (Finite Integration Technique) were respectively used to simulate and optimize the FSFs. During the simulation process, the designer only needs to create or import the unit cell model, specify the material properties, correctly assign the model boundary conditions, as well as excitation methods, and accurately define the solution settings, and the software will output the related results.

Figure 3(a) and (b) show simulation schematics of the square-ring patch fabric-based FSFs and plate-based FSSs in HFSS, mainly including the air box, the dielectric substrate, the FSS unit cell, the EM wave incident port (FloquetPort1) and the receiving port (FloquetPort2). The Floquet method was adopted as the CST software simulates the FSFs, and the Periodic Structures-Unit Cell template was used to establish the unit cell structure; the vertical axis boundary Open (add space) is adjusted, and the sweep frequency is set to simulate, as shown in Figure 3(c) and (d).

Figure 3.

Simulation design in two simulation software programs: (a) HFSS simulation – fabric substrate; (b) HFSS simulation – plate substrate; (c) boundary conditions in CST simulation and (d) CST simulation – fabric substrate.

Experimental details

Sample preparation

The FSF samples were prepared through the computer-based carving process, and the plane FSS array should be drawn using mapping software, such as CorelDRAW or Adobe illustrator, and then output commands to control the engraving machine for periodic cutting. In the experiment, adhesive aluminum foil was fitted on top of the base fabric and, after the cutting process was finished, the unnecessary aluminum foil was be stripped off by a utility knife, obtaining the FSFs.

Figure 4 shows a schematic of the sample preparation process. In the experiment, the cutting speed as well as cutter pressure should be debugged repeatedly, considering the physical properties of the fabric covered with metal foil material, and the engraving patterns and sizes. The final process parameters could be determined by observing the edge flatness of the sample unit cell, thus improving the precision for sample preparation. In this paper, polyester fabric-based FSFs were prepared. To achieve the best cutting effect, the cutting pressure was maintained at 14 g and the speed was set at 200 mm/s. The sample size was cut into 300 mm × 300 mm for the following test for transmission characteristics.

Figure 4.

Sample preparation process.

Plain weave polyester fabric was selected as the substrate of FSFs. The linear densities of the warp and weft yarn were both 14.8 tex; the fabric counts for the warp and weft directions were 256 and 224 per 10 cm; the areal density of the fabric was 180 g/m². The permittivity test was accomplished using a Dielectric Constant Tester, and the dielectric constant was found to be around 1.25 when the frequency of the electric field was set to 1 GHz. The thickness of the upper adhesive aluminum foil was roughly 0.08 mm. All of the above values were used as the corresponding parameters in the structural model for simulation.

Transmission characteristics testing

The testing of transmission characteristics was performed in a microwave anechoic at Nanjing University of Aeronautics and Astronautics using the transmission method. As shown in Figure 5, the entire testing system mainly includes a transmitting antenna, receiving antenna and absorbing wall.

Figure 5.

Testing procedure of frequency selective fabric samples.

In the test setup, two horn antennas Tx and Rx were respectively used for transmitting signals and receiving signals, and connected with an Agilent N5230C vector network analyzer. The absorbing wall is removable and made of pyramidal construction units, and the sample with the square size of 300 mm × 300 mm could be placed in the middle to test the transmission performance. As the horn antennas are placed as in Figure 4, the polarization mode is transverse magnetic (TM) mode, and the transverse electric (TE) mode could be easily realized by rotating the horn antennas by 90°. The testing principle and method were illustrated in the previous paper.¹²

Analysis and discussion

Analysis of simulation results

HFSS and CST software have different simulation principles but similar processes. In both software programs, the EM transmission or reflection characteristics could be obtained by accurately setting the solution frequency and the sweep range. The dimension parameters can be optimized according to the expected resonance frequency. The square-ring FSFs were taken as an example for optimization design, and the parameters values were m = 10 mm, n = 8.6 mm, Dx = Dy = 18 mm. The conductivity of the conductor is 3.8 × 10⁷ S/m (aluminum) and the thickness is 0.08 mm. The dielectric constants of the fabric and equivalent plate were both 1.25 and the thickness was 0.48 mm. The sweep range is 5–15 GHz, as the EM wave was perpendicularly incident. Figure 6(a) and (b) show the simulation results comparison of two models in two kinds of software, in which the title for the vertical coordinates is the transmission coefficient (S₂₁) or reflection coefficient (S₁₁), and the plotted curves are called S₂₁ curves or S₁₁ curves. In Figures 7–10, the meanings of the notations are exactly the same.

Figure 6.

Comparison of simulation results: (a) simulation results – two kinds of models and electromagnetic software and (b) simulation results – two kinds of complementary structures. FSF: frequency selective fabric.

Figure 7.

Comparison of measured and simulated results for square-ring frequency selective fabrics: (a) patch type and (b) aperture type.

Figure 8.

Array structures of two other frequency selective fabrics: (a) Jerusalem-shaped units and (b) circle/ring hybrid units.

Figure 9.

Measured results under two polarization modes for Jerusalem-shaped frequency selective fabrics: (a) patch type and (b) aperture type. TE: transverse electric; TM: transverse magnetic.

Figure 10.

Measured results under two polarization modes for circle/ring hybrid frequency selective fabrics: (a) patch type and (b) aperture type. TE: transverse electric; TM: transverse magnetic.

It can be seen from Figure 6(a) that the simulation results of the fabric-based model and the flat-based model show little difference. Taking the HFSS simulation results as an example, the resonance frequencies of the fabric-based model and the flat-based model are 10.14 and 10.01 GHz, respectively, and the two resonance peaks are –47.66 and –48.26 dB, respectively, showing it is totally feasible to predict the transmission characteristics of fabric-based FSFs using plate-based FSSs. The simulation results of the identical FSF model in two kinds of EM software are also very close. Taking the fabric-based FSF model as an example, the resonance frequencies in HFSS and CST software are 10.14 and 10.25 dB, respectively, and the resonance peaks are –47.66 and –48.74 dB, respectively, with no significant differences. The same structure shows very close frequency response characteristics under two different algorithms, and the result verifies the effectiveness of the theoretical design.

It can be seen from Figure 6(b) that the frequency response characteristics of FSFs with two kinds of complementary structural units are opposite but not completely symmetrical. In other words, the S₂₁ curve of the patch FSF does not completely coincide with the S₁₁ curve of the aperture FSF. This could be attributed to the fact that the proposed FSF consists of the base fabric and the upper conductive layer, different from the classical free-standing FSSs. The thickness of the dielectric layer and that of the conductive layer were not infinitesimal, which could not meet the conditions of using Babinet's theorem.

Validation of the design method

To further verify the effectiveness of the design method, the specific samples were prepared based on the optimized dimension parameters, and the transmission characteristics of the fabricated samples were measured using the transmission method. Figure 7(a) and (b) show a comparison of the measured and simulated results for patch and aperture square-ring FSFs, respectively.

In Figure 7, it can be seen that the measured and HFSS software simulated results have high anastomosis for two kinds of complementary square-ring FSFs. To quantitatively compare the differences between the two kinds of results, the eigenvalues of the S₂₁ curves in Figure 7 are extracted and compared, which are listed in Table 2, where the bandwidth values of the patch and aperture FSFs are calculated at threshold values of –0.5 and –10 dB, respectively.

Table 2.

Eigenvalues of measured and simulated S₂₁ curves (square-ring shaped frequency selective fabrics)

FSS type	Resonance frequency/GHz		Resonance peak/dB		Bandwidth/GHz
FSS type	Measured	Simulated	Measured	Simulated	Measured	Simulated
Patch	10.35	10.14	–45.50	–47.66	1.36	1.18
Aperture	10.01	9.74	–0.08	–0.03	0.68	0.87

FSS: frequency selective surface.

Table 2 shows that for the patch square-ring FSF, the measured and simulated resonance frequencies shift by 0.21 GHz, and the difference values of resonance peaks and the –10 dB bandwidths are 2.16 dB and 0.18 GHz, respectively. For the aperture square-ring FSF, the difference between the measured and simulated resonance frequencies is 0.27 GHz, that between two resonance peaks is 0.05 dB and that between the –0.5 dB bandwidth values is 0.19 GHz. For patch FSFs and aperture FSFs, the reasons for the differences are basically the same, namely they could be attributed to the inevitable random errors produced in the sample preparation process, resulting in the change of size as well as material parameters and then making differences with the assignment values in the simulation process. The sample size is not infinite, which may produce diffraction effects of EM waves around the sample edge, causing the data fluctuation or curve shift. Environmental errors may also exert an influence, for instance, signal loss during cable transmission may occur due to aging effects.

For two kinds of FSFs, although the measured and simulated S₂₁ curves do not coincide exactly, the deviations are not very obvious. Considering the experimental errors, the proposed design method is considered to be effective. The bias should be allowed as the EM simulation method is used to predict the transmission characteristics, and the deviation law could be regressed and further used for data modification, improving the consistency between simulation and experimental results.

Applicability of the design method

To further explore the applicability of the design method, two other kinds of FSFs were proposed and simulated, and also the actual samples were fabricated and measured. Figure 8(a) and (b) show the array structures of Jerusalem-shaped units and circle/ring hybrid units separately, in which the colored and shaded areas could be conductive or non-conductive.

If the colored area represents the conductor, the shaded area signifies the non-conductor, and the proposed FSFs are patch types. If the colored area is non-conductive and the shaded area is conductive, the proposed FSFs are aperture types. The Jerusalem-shaped FSFs were optimized specifically to 6 GHz, and the values of parameters were set as follows: a = 15 mm, b = c = 1.5 mm, d = 8.5 mm, D = 20 mm. The corresponding fabricated samples were measured and the results under two polarization modes are shown in Figures 9(a) and (b), respectively.

In Figure 9(a), the transmission characteristics of patch Jerusalem-shaped FSFs under two polarization modes are highly consistent, with nearly identical resonance frequencies and peaks. In the low frequency and high frequency region, the two S₂₁ curves show some fluctuations and produce certain differences. In Figure 9(b), the aperture FSF presents conspicuous band-pass characteristics, and the S₂₁ curves under two polarization modes show some small deviations. To further explore the influences of the polarization mode on the transmission characteristics, the eigenvalues of S₂₁ curves were extracted and are listed in Table 3.

Table 3.

Eigenvalues of measured and simulated S₂₁ curves (Jerusalem-shaped frequency selective fabrics)

Eigenvalues	Patch		Aperture
Eigenvalues	TE	TM	TE	TM
Resonance Frequency/GHz	5.90	5.97	5.90	5.81
Resonance peak/dB	−25.96	−27.78	0	0
Bandwidth/GHz	0.51	0.42	0.38	0.29

TE: transverse electric; TM: transverse magnetic.

In Table 3, the values of the resonance frequency, resonance peak and bandwidth are compared quantitatively. According to the specific numbers, it can be clearly seen that the distinctions are very small. For the patch FSF, the resonance frequencies under the two polarization modes are 5.90 and 5.97 GHz, respectively, the resonance peaks have a slight difference, namely –25.96 and –27.78 dB, respectively, and the –10 dB bandwidths are fairly close, that is, 0.51 and 0.42 GHz, respectively. For the aperture FSF, the resonance frequencies, the resonance peaks and the bandwidths are not exactly same, but the differences are negligible. For instance, the bandwidths are respectively 0.38 and 0.29 GHz under TE and TM polarization modes, with the difference value of merely 0.09 GHz. The stable transmission characteristics rely on the excellent symmetrical characteristics of Jerusalem-shaped units and the result fluctuations could be attributed to variation of the size parameters for the actual specimen caused by fabrication errors, the edge diffraction effect of EM waves resulting from non-infinite sample size and environmental errors caused by the bending loss of the radio frequency cable, etc.

The above square-ring unit, as well as the Jerusalem-shaped unit, is a single structural unit. To explore the applicability of the design method to FSFs with complex conductive units, FSFs with circle/ring hybrid units were proposed, simulated and optimized specifically to 3 GHz, and the values of the parameters were set as follows: R = 25 mm, r = 21 mm, r₁ = 6 mm, D = 65 mm. The corresponding samples were fabricated and measured. Figures 10(a) and (b) show the measured results under two polarization modes, patch and aperture FSFs.

In Figure 10, we can see that the S₂₁ curves under the two polarization modes are highly consistent throughout the whole test band, for the patch as well as the aperture FSF. There are certainly some fluctuations at some particular bands, for example, a large difference value of S₂₁ appears at 5.6 GHz for the aperture FSF, but the local fluctuations would not significantly affect the characteristic transmission performance. To further explore the influences of polarization modes, the eigenvalues of circle/ring hybrid FSFs have been extracted and are listed in Table 4.

Table 4.

Eigenvalues of measured and simulated S₂₁ curves (circle/ring hybrid frequency selective fabrics)

Eigenvalues	Patch		Aperture
Eigenvalues	TE	TM	TE	TM
Resonance frequency/GHz	3.03	3.03	3.00	2.98
Resonance peak/dB	–18.97	–18.94	–0.48	–0.20
Bandwidth/GHz	0.35	0.27	0.02	0.04

TE: transverse electric; TM: transverse magnetic.

In Table 4, the specific values of characteristic indexes, including resonance frequencies, resonance peaks and bandwidths, are listed for comparison. For the aperture FSF, the resonance frequencies under the two polarization modes are 3.00 and 2.98 GHz, respectively, the resonance peaks are slightly different, respectively –18.97 and –18.94 dB, and also the –0.5 dB bandwidths show a small difference, respectively 0.02 and 0.04 GHz. In addition, the differences of the patch FSF could be compared quantitatively. For example, the resonance frequencies under two polarization modes are completely identical, that is, 3.03 GHz. The resonance peaks and the bandwidths are not exactly the same, and the reason is similar to the above-mentioned Jerusalem-shaped FSFs.

Both of the Jerusalem-shaped FSFs and circle/ring hybrid FSFs show ideal narrow-band transmission characteristics under the two polarization modes, that is, the resonance frequency, resonance peak and bandwidth could meet expectations. The experimental results show that the design method using simulation software could be applied to many different structures in the related product design and development process.

Conclusion

In this paper, narrow-band FSFs were designed and fabricated. Modeling and EM simulation methods were adopted in the theoretical design process. The computer-based carving process and transmission method were used for sample fabrication and measurement. By comparing the simulation results of two structural models in two software programs, the validity of the design methods was primarily verified. The measured and simulated resonance frequencies shift insignificantly, and the differences of resonance peaks and the –0.5 or –10 dB bandwidths were acceptable. Although the characteristic indices were not completely identical, the differences were within the error range, showing the validity of the design method. Jerusalem-shaped and circle/ring hybrid FSFs were also designed, fabricated and the measured. The results showed that the narrow-band transmission characteristics were quite ideal, verifying the wide applicability of the design method.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Quanzhou Home-bay Recruitment Program of Global Talents (2017ZT002) and the Quanzhou City Science & Technology Program of China (2018K002).

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