Transmission characteristics of cylindrical frequency selective fabrics with Jerusalem-shaped units

Abstract

Two kinds of complementary cylindrical frequency selective fabrics (CFSFs) with Jerusalem-shaped units were designed, constructed and analyzed in this paper. The models were built and simplified based on the thickness and equivalent electromagnetic parameters of the base fabrics. Considering the unit number difference of the models and bending directionality, the simulation processes were separately carried out using the waveguide method in HFSS software. Based on the preparation of preliminary planar prototypes and corresponding bending molds, different CFSF samples with the same planar units and varying bending curvature were fabricated, and the transmission characteristics were measured using the transmission method to study the influences of bending effects. The measured transmission characteristics with and without the curved mold were similar, proving the use of the curved mold exerted a negligible effect on the actual measured results of samples. For the two kinds of complementary structures, the measured and simulated S₂₁ (transmission coefficient) curves had indistinguishable differences, which justified the validity of the modeling and simulation process. Although the bending direction and curvature affected the S₂₁ curves of aperture and patch CFSFs at varying degrees, the transmission characteristics did not show drastic fluctuation and shifting, which could be attributed to the ideal symmetry of Jerusalem-shaped units and good array characteristics.

Keywords

electromagnetic functional fabrics textile modeling electromagnetic simulation transmission characteristics curved frequency selective surface

Frequency selective surfaces (FSSs) are composed of periodic conductive patches or apertures within a conductive screen.¹ When FSSs interact with the electromagnetic (EM) waves, they exhibit band-stop or band-pass spatial characteristics,² which make them desirable for application in products, like airborne radomes, subreflectors, high impedance surfaces, and polarizers.^3,4 Conventional FSSs fabrication methods include electroplating, chemical plating, vacuum deposition and photo-etching,⁵ and the resultant products are mainly rigid plates and composites.^6–9

Textiles are typical flexible materials with advantages of light weight, softness and low bending rigidity over the rigid materials. In addition, textiles are highly cyclical due to the periodic interlacing of warp and weft yarn and the easy insertion of metallic yarns in the weave structure to impart the fabric with conductive properties. Fabric-based FSSs or frequency selective fabrics (FSFs) have attracted extensive research interest and the related works include model building, theoretical calculation and sample preparation methods like coating printing, silk-screen printing and computer embroidery.^10–17 Despite several shortcomings, research on FSFs has made remarkable progress, like the exposition of the systematic research idea. However, the existing studies were mainly focused on the planar FSFs, with no emphasis on the influences of bending effects.

Typical products are often in the form of a curved surface, such as the soft radome, the battlefield command tent, the flexible filtering clothing, to mention just a few. Earlier works on traditional curved FSSs investigated the numerical analysis methods, the fabrication technology, the differences of transmission characteristics between curved and planar FSSs, and so on,^18–21 which could provide reference values, like the simulation setting method and fundamental filtering principle. However, the existing research methods and results could not be completely applied to the soft curved FSFs, especially in model building and experimental design aspects, and related issues need to be originally resolved. Therefore, in this study, cylindrical frequency selective fabrics (CFSFs) with Jerusalem-shaped units, including aperture and patch structures, were designed, constructed and analyzed. By comparing the experimental and simulation results, the validity of the modeling and simulation process was substantiated and the influences of bending effects were accessed.

Modeling and simulation process

Considering the perfect symmetry of Jerusalem-shaped units and existing experimental results,¹³ in this paper the models of two complementary CFSFs with Jerusalem-shaped units were proposed and built, as shown in Figure 1(a) and (c). Figure 1(b) and (d) respectively give a schematic and sectional view of the planar unit cell, in which the key parameters are marked. Considering the sample testing requirements, the model length and chord length were both set as 300 mm, and therefore the proposed models were mainly determined by the bending radius r, radius angle θ, arc length s and unit cell size parameters (p, a, b, c and d).

Figure 1.

Two kinds of complementary cylindrical frequency selective fabric (CFSF) models with Jerusalem-shaped units: (a) aperture CFSF; (b) planar units; (c) patch CFSF; (d) schematic of cross section.

In consideration of the complicated fabric structure and the bending effect, the EM calculation process would be very time-consuming. Consistent with the subsequent experiment sample, the substrate should be a plain polyester fabric. To simplify the proposed model, the base fabric was equivalent to a smooth plate with the same thickness as the fabric (about 0.2 mm) and equivalent EM parameters (roughly equal to the vacuum as the frequency is greater than 1 GHz), and the simplified model was imported into the corresponding EM software for further simulation. The conductive layer was set as 0.8 mm and the texture was set as aluminum, the same with the experimental material. In addition, the proposed models were composed of 15 × 15 units (Figure 1), and they certainly could be reduced to be fewer units without altering the bending curvature and unit size, such as 8 × 8 units and 5 × 5 units.

The simulation process was performed using the waveguide method in HFSS software, and the simulation schematics are shown in Figure 2. Figure 2(a) shows the four boundary conditions were perfectly matched layers and Figure 2(b) reveals the two lumped ports were set as waveports. The design method was based on the features of plane wave and curved array structure, and related settings were completed in the internal components of the software. Different from the symmetric planar structure, the CFSF has obvious directionality. As the electric field (or magnetic field) is also directional, the electric field direction may be perpendicular or parallel to the bending axial direction, which is called circumferential direction or axial direction, respectively. The schematic of circumferential direction bending is shown as an example in Figure 2(b). In two circumstances, the transmission characteristics are different and should be separately explored.

Figure 2.

Schematic of simulation process using waveguide method: (a) perfectly matched layers (PML) boundary condition; (b) waveguide port excitation.

Based on the modeling and simulation design, the simulation results could be obtained. Figure 3 gives the simulation results of different unit number models, from which we could see the influences of unit number on the transmission characteristics. The simulation results of the planar structure are also shown in Figure 3 for comparison.

Figure 3.

Comparison of simulation results for different unit number models (r = 150 mm, circumferential direction).

In Figure 3, the frequency response characteristics of proposed CFSFs were different from the planar structure, and the S₂₁ (transmission coefficient, which is the inverse of the shielding effectiveness)¹⁰ curves moved towards the lower positions on the whole. The resonance frequency remained basically unchanged, but the resonance peak decreased obviously, making the bandwidth value slightly reduced. The above phenomenon should be attributed to the poor array characteristics of CFSFs, so that the phase difference between two adjacent units could not be well coupled. As the EM wave is perpendicularly incident to the surface of CFSFs, the effect could be equivalent to the multi-angle incidence to the planar FSFs, and then multiple new scattering spectrums occur, especially for the simulated S₂₁ curves of the 8 × 8 unit model. The intensity of reflection waves and multiple mode diffracted waves change rapidly, and surface scattering effects increase sharply and then central band transmittance decreases accordingly.

Compared with the 5 × 5 unit model, the simulation S₂₁ curve of the 8 × 8 unit model fluctuated more severely, but the general tendencies of the two curves were consistent, having no significant difference. In order to improve the simulation efficiency, the simulation results of the 5 × 5 unit model were regarded as the prediction results of the bending model with the specific curved curvature, and the relevant results in this paper were all calculated based on the 5 × 5 unit model.

Experiment

Sample preparation

The planar FSF samples were fabricated using a computer-based carving method.¹¹ The plain polyester fabric was selected as the substrate: the linear densities of warp and weft yarn were both 14.8 tex; the fabric counts for warp and weft directions were 286 and 224 per 10 cm, respectively; the areal density of the fabric was 178 g/m²; the equivalent thickness was 0.2 mm. The thickness of the conductive aluminum was 0.8 mm. As the planar samples were prepared, they were put closely onto the surface of the molds with different curvature, thus forming the final CFSFs, as shown in Figure 4.

Figure 4.

Sample pictures of cylindrical frequency selective fabric (CFSF): (a) aperture CFSF; (b) patch CFSF.

In fact, the proposed molds in this paper consist of hardboard, brown paper, scotch tape, double-faced adhesive tape, etc. These materials may cause the test errors and thus, in order to ensure the validity of the testing results, the influences of fabricated molds on the transmission characteristics need to be explored.

Testing procedure

Consistent with the testing procedure of planar samples, the transmission coefficient and reflection coefficient testing of CFSFs were performed in the anechoic chamber, as shown in Figure 5. The two horn antennas (2–18 GHz) system consists of transmitting antennas (Tx) and receiving antennas (Rx), and they are connected by an Agilent N5230C vector network analyzer. In order to eliminate the influence of background noise, a two-step calibration was implemented. The transmission coefficients T₀ (in dB) were first measured without sample and then the transmission coefficients T₁ (in dB) were measured with CFSF, and the actual transmission characteristic T (in dB) could be calculated by T = T₁ – T₀.

Figure 5.

Measurement setup in the microwave anechoic chamber: (a) circumferential direction; (b) axial direction.

Due to the fact that the bending effect has directivity, the actual electric field could be along the circumferential or axial direction of CFSF, as shown in Figure 5. Therefore, two sets of testing results could be obtained, and the influences of the bending direction are analyzed in the following section.

Experimental design

To explore the influence rules of bending effects, a series of samples were designed (listed in Table 1), in which θ, s and r have the same meaning with the parameters in Figure 1.

Table 1.

Design of cylindrical frequency selective fabrics with different curvature

No.	θ (°)	s (mm)	r (mm)	k = 1/r (mm⁻¹)	Dimension parameter
1#	180	471	150	6.67 × 10⁻³	a = 8.5 mm
2#	150	406.5	155.3	6.44 × 10⁻³	b = 12 mm
3#	120	362.8	173.2	5.77 × 10⁻³	c = 1.5 mm
4#	0	300	∞	0	d = 15 mm p = 20 mm

r = bending radius; s = arc length.

It is worth noting that all the samples in Table 1 are with the same planar unit cell and each sample has two kinds of complementary structures. The transmission characteristics of the aperture and patch structures of CFSF 1# are explored in the subsequent section.

Analysis and discussion

Influence of test mold

Before discussing the influences of bending effects, the validity of the measured results should be studied. By comparing the experiment results of pure air and curved mold, the effect degree of the mold on the transmission characteristics could be obtained, as shown in Figure 6.

Figure 6.

Measured results comparison of pure air and curved mold (r = 150 mm).

In Figure 6, the two upper curves respectively represent the S₂₁ difference values of the pure air testing and the curved mold in two directions. Figure 6 shows that the testing results of the curved mold in circumferential as well as axial direction are both very close to the air test results, especially in the frequency ranges of 2–9 GHz and 14–18 GHz. As for the mold test in circumferential direction, the difference values with air test are almost zero on the whole frequency band. For the mold test in axial direction, there are some differences in the frequency range of 9–14 GHz and the difference values reach maximum (about 5 dB) in roughly 12 GHz.

According to the testing results, it seems that the introduction of the curved mold does not significantly exert an influence on the transmission characteristics, which guarantees the effectiveness of the test results. In order to further reduce the mold interference effect, the testing results of the curved mold were selected as the environmental values.

Comparison of measured and simulated results

To verify the validity of the modeling and simulation process, the measured and simulated results were compared and are shown in Figure 7, from which we could see the measured results of two complementary CFSFs are both consistent with the simulated results on the whole.

Figure 7.

Comparison of measured and simulated results for cylindrical frequency selective fabric (CFSF): (a) aperture CFSF; (b) patch CFSF (1#: r = 150 mm, circumferential direction).

For aperture CFSF, the two S₂₁ curves show greater deviations at the beginning and end of the testing frequency band, especially at the lower frequencies (about 3–5GHz), which could be attributed to the following aspects: namely, the test errors including the sample preparation errors; the limited size of actual sample; the signal loss during cable transmission; and the simulation errors caused by the reduced units in the model. The measured results were valid because the deviations do not affect the characteristic indexes, including the resonance frequency, resonance peak and bandwidth, as marked in Figure 7(a). For patch CFSF, the measured S₂₁ curve coincides with the simulated S₂₁ curve in the whole frequency range. Although the resonance peaks of patch CFSF have distinct differences in numerical data in Figure 7(b), both of the shielding effectiveness in the resonance frequency are over 20 dB, respectively 25.84 dB and 20.62 dB, meaning 99% of EM waves could be shielded and the actual differences were very small.

For two kinds of complementary structures, the measured and simulated S₂₁ curves are not exactly coincident, suggesting that the simulation model should be more elaborate. But the differences do not affect the critical characteristics of S₂₁ curves, which verified the effectiveness of the modeling and simulation process. On this basis, the correlation analysis of the parameters' influences on the transmission characteristics could be performed.

Influence of bending direction

On account of the bending directionality, the frequency response characteristics are different and need to be separately studied. Aperture and patch CFSFs were tested under two kinds of bending conditions, and the measured results are shown in Figure 8. In order to quantitatively analyze the influences of the bending direction, the transmission characteristics of the corresponding planar FSF were tested and are displayed in Figure 8 for comparison.

Figure 8.

Measured results under two kinds of bending directions of cylindrical frequency selective fabric (CFSF): (a) aperture CFSF; (b) patch CFSF (1#: r = 150 mm).

It could be easily seen from Figure 8 that the bending direction really exerts an influence on the transmission characteristics, for two kinds of complementary CFSFs. For aperture CFSF, the shape of S₂₁ curves remains basically the same on the whole, and the resonance frequencies have little changes, but the resonance peaks gradually decrease. For patch CFSF, the S₂₁ curves have some minor changes, especially in the lower and higher frequency ranges, but the fluctuations do not affect the whole variation trend of S₂₁ curves. To analyze the influence degree of bending direction, the characteristic indexes of S₂₁ curves in Figure 8(a) and (b) were extracted, and these are listed in Tables 2 and 3.

Table 2.

Eigenvalues of S₂₁ curves under different bending directions (aperture cylindrical frequency selective fabric)

Bending direction	Resonance frequency/GHz	Resonance peak/dB	−3 dB bandwidth/GHz
Planar structure	5.91	0	1.22
Circumferential	5.76	–1.19	0.96
Axial	5.63	–2.14	0.64

Table 3.

Eigenvalues of S₂₁ curves under different bending directions (patch cylindrical frequency selective fabric)

Bending direction	Resonance frequency/GHz	Resonance peak/dB	−10 dB bandwidth/GHz
Planar structure	5.91	–24.51	0.48
Circumferential	5.76	–20.19	0.93
Axial	5.75	–23.02	0.82

Tables 2 and 3 show that as the bending direction changes the frequency response characteristics of two complementary FSFs with Jerusalem-shaped units both make certain changes. For aperture FSF, the values of resonance frequency and resonance peak under the axial bending testing condition are smaller, respectively 5.63 GHz and –2.14 dB. Compared with the planar testing results, the bandwidths of –3dB under circumferential and axial bending testing conditions are slightly smaller, 0.96 and 0.64 GHz respectively. For patch FSF, the measured S₂₁ curves under two kinds of directions have no obvious differences on the whole. Specifically, the resonance frequency keeps stable at 5.76 GHz, and the bandwidths of –10 dB under circumferential and axial bending testing conditions are 0.93 and 0.82 GHz, respectively. The bending direction has different effects on the transmission characteristics of aperture and patch CFSFs, and therefore the frequency characteristics should be separately explored aiming at different requirements.

The above experimental results show that the circumferential direction bending has a larger impact on the frequency response characteristics, which could be ascribed to worse unit coupling characteristics of FSFs, leading to the larger fluctuations of EM transmission characteristics compared with planar FSFs. Although the bending effect exerts a certain influence on the frequency response characteristics of Jerusalem-shaped FSFs, the S₂₁ curves do not show greater fluctuation and deviation, especially the patch structure. The Jerusalem-shaped unit cells have super symmetry and show high stability to the EM incident angle as well as polarization mode, which could be widely used in related products.

Influence of bending curvature

In actual application, the FSFs would suffer different degrees of bending. To quantitatively investigate the influences of bending effect, the transmission characteristics of CFSFs with different bending radii of curvature were measured and the results are shown in Figure 9.

Figure 9.

Measured results under different bending curvature for cylindrical frequency selective fabric (CFSF): (a) aperture CFSF; (b) patch CFSF (circumferential direction).

Figure 9 shows that the transmission characteristics of CFSFs were indeed affected by the bending curvature, although the influence degree was not so significant. To analyze the influences in more detail, the characteristic indexes of S₂₁ curves in Figure 9(a) and (b) were extracted, and these are listed in Tables 4 and 5.

Table 4.

Eigenvalues of S₂₁ curves under different curvature (aperture cylindrical frequency selective fabric)

Bending radius	Resonance frequency/ GHz	Resonance peak/dB	–3 dB bandwidth/ GHz
4# (r = ∞)	5.91	0	1.22
3# (r = 173.2 mm)	5.53	–0.31	1.69
2# (r = 155.3 mm)	5.78	–0.95	1.25
1# (r = 150 mm)	5.76	–1.19	0.96

Table 5.

Eigenvalues of S₂₁ curves under different curvature (patch cylindrical frequency selective fabric)

Bending radius	Resonance frequency/ GHz	Resonance peak/dB	−10 dB bandwidth/ GHz
4# (r = ∞)	5.91	–24.51	0.48
3# (r = 173.2 mm)	5.93	–22.21	0.58
2# (r = 155.3 mm)	5.75	–23.49	0.64
1# (r = 150 mm)	5.76	–20.19	0.82

Tables 4 and 5 show that the bending curvature indeed exerts an influence on the frequency response characteristics, but the influence degree is not significant, consistent with the influences of bending direction. For the aperture CFSF, as r decreases or the bending curvature increases, the shape of S₂₁ curve becomes fat and the whole curve gradually moves down. Specifically, the resonance peak decreases from 0 dB to –1.19 dB and –3 dB bandwidth decreases from 1.22 GHz to 0.96 GHz. For the patch CFSF, the frequency response characteristics are relatively stable as the bending curvature changes. However, as the curvature degree increases, –10 dB bandwidth increases gradually from 0.48 GHz to 0.82 GHz.

Based on the above analysis, we know the frequency response characteristics of CFSFs are affected by the bending effects, and the reason for this phenomenon is the same with Figure 3. In fact, as the plane wave is vertically incident to the surface of planar FSFs, the induced current with a well-coupled phase difference would be generated on the adjacent unit cells, which makes the FSFs radiate energy in the same direction and then produce a resonance phenomenon, obtaining the maximum transmission coefficient. The bending effect weakens the good array characteristics of FSFs, making the surface scattering enhanced and the resonance peak reduced. However, the inherent excellent symmetry of Jerusalem-shaped units counteracts the bending effect, and that is why the proposed FSFs are insensitive to the cylindrical bending effect on the whole.

Conclusion

The CFSFs with Jerusalem-shaped units were proposed in this paper, and the systematic modeling and simulation process were illustrated. By comparing the simulation results of different unit number models, the 5 × 5 unit model was selected for further calculation. The results showed that in the given frequency range of 2–18 GHz, the introduction of the mold basically has no influence on the transmission characteristics of CFSFs samples. Both the bending direction and curvature could affect the frequency response characteristics of aperture and patch CFSFs, but the influence degrees are not exactly the same, and the bending effects have a more significant impact on the transmission characteristics of aperture CFSFs. On the whole, the S₂₁ curves of Jerusalem-shaped FSFs do not show drastic fluctuation and shifting at certain degrees of bending, which could be attributed to the good stability of the array characteristics.

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 Quanzhou Home-bay Recruitment Program of Global Talents (2017ZT002) and the Quanzhou City Science & Technology Program of China (2018K002).

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