A novel wideband, low-profile and second-order miniaturized band-pass frequency selective surfaces

A novel wideband, low-profile and second-order miniaturized band-pass frequency selective surface (FSS) made of metallic mesh and its complementary structures with skewed arrays of modified triples is presented in this paper. Compared with traditional second-order bandpass FSSs obtained using λ / 4 apart from one another, the novel FSS with an overall thickness of λ / 18 is composed of three metallic layers (the outside and middle layers are complementary) separated by two electric thin dielectric substrates. This arrangement can shorten the inter-element spacing and increase the bandwidth, while the up and bottom metallic layers can constitute a symmetric biplanar FSS and thus realize ability of maximally flat second-order bandpass response. The novel FSS has a − 3 dB bandwidth about 8.2 GHz (6.9 -15.1 GHz) and a fractional bandwidth exceeds 75%. Moreover, such an FSS has the merits of stable performance for incident angles within 50 ◦ and di ff erent polarizations. The principles of operation along with guidelines for the design of the proposed FSS, the simulated results by vector modal matching method, and the experimental values of the fabricated prototype are also presented and discussed. C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http: // dx.doi.org / 10.1063 / 1.4927502]


I. INTRODUCTION
Frequency Selective Surface (FSS) is an artificial periodic structure, which is arranged by two dimensional array of metallic patches or apertures on dielectric layer(s).In traditional FSS design techniques, periodic arrays of resonant elements are often used to achieve band-pass or band-stop behavior depending on the element type (i.e.aperture or patch).Because of its superior performance, FSS has been the focus of intensive investigation for decades.And it has been widely used on satellites, radomes and aircrafts.2][3][4][5] The demand for broadband radome is rising along with the improvements in wideband radar and satellite communications systems.
Nowadays, there are two methods to design broadband radome.The first one is based on the theory of multilayer film, and the designed structure is comprised of multilayer dielectric materials.It is feasible in theory, but its fabrication is limited by some difficulties.Moreover, a multilayer film in radar range is not suitable for practical application due to the constrains in thickness and weight.The other method is based on the technique of FSS.The radome can have a wideband, by adding a FSS structure.Many methods are taken to design wideband FSS, such as changing the FSS elements or period, increasing the thickness of the supporting dielectric layer. 6To achieve a desired bandwidth, a combination of these techniques is often adopted.The −3 dB bandwidths achieved by using convoluted and interwoven FSS elements are 64.1% and 63% in Refs.7 and 8 respectively.However, these single layer structures still have some deficiencies, such as the narrow top of the stop-band with a small attenuation, and the unstable performance with different incident angle.To a Author to whom correspondence should be addressed.Electronic mail: xnxlzhy999@126.com2158-3226/2015/5(7)/077157/6 5, 077157-1 © Author(s) 2015 increase the Q value of radome, sometimes, a maximally flat (Butterworth) response with broad flat top and sharp cut-off is required.It can be achieved by cascading multiple FSS panels.As reported, a symmetric bi-planar FSSs was built by mounting two identical layers behind each other. 1 Only at crucial coupling, the system can have a desired maximally flat (Butterworth) response.The symmetric multilayer FSS which was discussed in Ref. 9 results in good transmission property with a broad flat top and a −3 dB fractional bandwidth of 22%.In addition, the FSS with three different metallic layers that based on coupling mechanism can also produce a maximally flat (Butterworth) response.
A second-order and a three-order FSS were designed, 10,11 with −3 fractional bandwidths of only about 20% and 22%, respectively.In this paper, we design a wideband FSS with three complementary metallic layers.It has a maximally flat (Butterworth) response and stable performance.Its −3 dB bandwidth is about 8.2 GHz (from 6.9 GHz to 15.1 GHz) and the fractional bandwidth exceeds 75%.By changing the parameters of the dielectric layers, the −3dB bandwidth can reach up to 10.6 GHz (from 8.9 GHz to 19.5 GHz) and the fractional bandwidth exceeds 72%.These results are more satisfactory than those in Refs.7-11.

II. FSS STRUCTURE AND FABRICATION
The important factor in determination of FSS bandwidth is the inter-element spacing.By choosing appropriate FSS elements and arrays, we can shorten inter-element spacing and enhance the bandwidth of FSS.As a rule, the loop element has a smaller inter-element spacing than the centerconnected element, which increases the bandwidth and delay the onset of grating lobes.Hence, the loop element is preferred over to the center-connected element.At normal incident, the unit cells of an inductive surface can be equal to an inductor L, while the unit cells of capacitive surface can be equal to a capacitor C. Thus, metallic elements of modified triples were chosen, as shown in Fig. 1(a).The legs of the modified triples are longer enough to connect with the legs of the surrounding elements.According to the FSS structure, on one hand, the complementary bi-planar FSS can obtain miniaturization property through the coupling mechanism, which can effectively reduce the inter-element spacing.On the other hand, the symmetric bi-planar FSS at crucial coupling can have maximally flat (Butterworth) response with a wideband.Based on the studies of the complementary and symmetric structures, we design a novel FSS structure with wider bandwidth in this paper, as shown in Fig. 1(b).
As showed in Fig. 1(b), the middle layer is consisted of a two-dimensional periodic array of metallic strips with modified triples elements.It corresponds to an inductor in a circuit model and stores magnetic energy, since it acts as an inductive surface.The top and bottom complementary structures of the middle layer store electric energy and act as capacitive surfaces.The three FSS layers are fabricated on thin flexible polyimide substrates with a thickness d 1 = 0.025 mm, dielectric constant ε r 1 = 3.0 and loss tangent tan δ 1 = 0.005.The bonding film layers are characterized by d 2 = 0.04 mm, ε r 2 = 2.45 and tan δ 2 = 0.0035.The parameters ε r 3 , d 3 of the dielectric layers are selected according to the conditions of critical coupling.The four layers between the metallic arrays can be called as coupling media.
The capacitive and inductive surfaces, with the overall size of 400 mm × 400 mm, is fabricated through a standard etching of copper on 0.025-mm-thick polyimide substrates (ε r 1 = 3, d 1 = 0.025 mm, tan θ = 0.005), as shown in Fig. 2. The dimensions of the FSS units, as shown in Fig. 1(a), are D x = 4 mm, D y = 3.466 mm, l = 2.32 mm, w 1 = 0.5 mm, and w 2 = 0.373 mm.The parameters of dielectric layers are ε r 3 = 3.17, d 3 = 1 mm and tan θ = 0.008 also with the dimensions of 400 mm × 400 mm.Finally the three metallic layers on polyimide substrates are adhered to the dielectric layers together as shown in Fig. 1(b) by aerial bonding films (ε r 2 = 2.45, d 2 = 0.04 mm and tan θ = 0.0035) with accuracy alignment.

III. RESULTS AND DISCUSSION
An equivalent circuit model is used to study the principles of FSS design. of the FSS can be shown as in Fig. 3, in which the free space impedance Z 0 = 377 Ω. Z, Z 1 , Z 2 and Z 3 are the intrinsic impedances of the coupling medium, the polyimide substrate, the thin bonding film and the dielectric layer, respectively.Z 1 = Z 0 /(ε r 1 ) 1/2 , Z 2 = Z 0 /(ε r 2 ) 1/2 , Z 3 = Z 0 /(ε r 3 ) 1/2 , and the intrinsic impedance Z of the coupling medium is equal to the series combination of Z 1 , 2Z 2 and Z 3 .Fig. 3, it can be seen that the FSS structure is a second-order band-pass filter with a parallel C-L-C circuit, and a wide band can be achieved by coupling the electric and magnetic field of the incident wave between C and L. To exactly calculate the transmittances of this FSS structure, we used the vector modal matching method, which is one of the stable convergent full-wave numerical analysis methods. 12-14Fig. 4 shows the transmission of FSS at normal incidence.This structure has a maximally flat (Butterworth) response with flat top and sharp cut-off.The flat top has a very small valley with a depth of −0.57dB at 10.8 GHz, located between two peaks at 8.8GHz (−0.12 dB) and 13GHz (−0.18 dB).The frequency response from 7.6 GHz to 14.2 GHz remains above −1 dB, so the -1 dB fractional bandwidth is about 60.55%.The transmission of the FSS from 6.9 GHz to 15.1 GHz is higher than -3 dB, indicating the −3 dB fractional bandwidth is about 75.93%.
Regarding the period size of the FSS, it can be obtained that D x and D y are only about 0.144λ and 0.125λ, respectively, where λ is the wavelength at the central frequency of the pass-band.The FSS has a miniaturization ability, which can decrease the inner-element spacing to increase the bandwidth of the structure.In conclusion, the proposed FSS has an excellent maximally flat (Butterworth) response at the whole X-band.
In Fig. 4, there is a small valley in the middle of the pass-band, because the parameters of the structure do not meet the conditions of critical coupling very well.This case is called overcritical coupling.When the two dielectric layers (ε r 3 = 3.17, tan θ = 0.008 and d 3 = 1 mm) are changed to foam material layers (ε r 3 = 1.1, tan θ = 0.003 and d 3 = 1 mm), a curve with a flatter top is obtained, as shown in Fig. 5.In such case, the small valley in the top of the pass-band disappears, the structure meets the conditions of critical coupling well than before.The new structure has a maximally flat (Butterworth) response at the whole Ku-band, and the −1 dB and −3 dB fractional bandwidths are about 52.74% (10.3 GHz-18 GHz) and 72.6% (8.9 GHz -19.5 GHz), respectively.
In fact, for many practical applications the valley in Fig. 4 is too small to have severe consequence.And by changing the dielectric layers, we can obtain a desired wide pass-band with a maximally flat (Butterworth) response at least at X or Ku-band.
In order to further reveal the properties of the FSS, we studied its transmission at oblique incident angles (from normal to 50 • ) for both TE and TM polarizations, the structure with ε r 3 = 3.17, tan θ = 0.008 and d 3 = 1 mm as example are shown in Fig. 6.
For TE polarization (Fig. 6(a)), from scan angle increases from 0 • to 50 • , the pass-band shifts slightly to a high frequency with the width of the flat top increases and the −3 dB bandwidth remains constant, while the depth of the valley increases from −0.57 dB at 10.8 GHz to −2.14 dB at 11.8 GHz.As for TM polarization in Fig. 6(b), with the scan angle increases from 0 • to 50 • , the width of the flat top and the −3 dB bandwidth increase, while the depth of the valley gradually decreases and the flat top becomes more visible.Finally the valley disappears when the scan angle is above 50 • .As showed in Fig. 6, the structure is less sensitive to the incident angle and polarization, and it always has an excellent wide pass-band with flat top and sharp cut-off.
The fabricated prototype is measured in a free-space environment using an Agilent N5244A vector network analyzer.And the measurement environment is shown in Fig. 7.Besides the vector network analyzer is a pair of lens antennas, a bearing bracket and a rotatable table.
Fig. 8 shows the frequency response characteristics to compare and contrast the measured and simulated results for TE polarization from 0 • to 50 • .It can be seen that the measured curves show band shifts to the high frequency, and the widths of the flat tops and the −3dB bandwidths of the measured results are larger than that of the simulated results, and the valleys of the measured results are smaller than that of the simulated results.This was mainly due to that the thicknesses of the dielectric layers used in the experiment are slightly thinner than 1mm.In addition, there are some errors during the fabrication of the FSS and testing process.Neglecting the influences of all the  factors, we consider that the measured and simulated results have a good agreement from 0 • to 50 • .It experimentally verifies the accuracy of the numerical analysis.

IV. CONCLUSIONS
In this paper, a novel wideband, low-profile and second-order miniaturized band-pass FSS was proposed with stable performance for varying incident angles within 50 • and different polarizations.They are made of three metallic layers and can act as second-order filter.In this paper, the equivalent circuit model of the FSS is used for performance analysis, and the structure is simulated by the vector modal matching method.Its −3 dB bandwidth is about 8.2 GHz (6.9 GHz -15.1 GHz) and the fractional bandwidth exceeds 75%.And the measurement results for the fabricated prototype using lithography are in good agreement with the simulated values, which experimentally verify the accuracy of the numerical analysis.The proposed structure can be used to design wideband, low-profile and second-order miniaturized band-pass FSSs with flat top, sharp cut-off and stable performance for varying incident angles within 50 • and different polarizations.
FIG. 1.(a) Elements of inductive and capacitive surfaces (b) Structural diagram of the FSS.