MA Xin, LIU Yunzhe, WAN Guobin, and PAN Aigang

1. School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710129, China;2. School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China

Abstract: A miniaturized periodic element for constructing bandpass frequency selective surface (FSS) independent of incident angles and polarizations is presented. An interdigital resonator (IR) with one extending finger to connect the two separate parts of the interdigital capacitor is explored to achieve parallel resonance. The equivalent circuit model (ECM) and electric field distributions are introduced to explain frequency performance of FSS. The whole structure has only one layer and possesses a low profile (a thickness of 0.001 5λ , where λ represents the resonant wavelength in free space) as well as a small size (0.03λ × 0.03λ). This FSS performs as a spatial bandpass filter which exhibits a great angular stability with incident angles ranging from 0° to 80° for both transverse electric (TE) and transverse magnetic (TM) polarizations. As an example, a prototype of one proposed FSS is fabricated and tested. The measured results show a good angular stability.

Keywords: frequency selective surface (FSS), angular stability,bandpass filter.

1. Introduction

Frequency selective surfaces (FSSs) have attracted a myriad of attentions due to extensive applications in manipulating the propagation of impinging waves. Their widespread applications include antenna reflectors [1],radomes, absorbers [2], electromagnetic shielding [3], polarization selectors [4] and satellite platforms [5] in the microwave and millimeter-wave regimes. The classic application is the integration of bandpass FSS with a protective radome in stealth technology to reduce the radar cross section of the enclosed antenna outside its operating band [1]. Due to limited space for practical applications, miniaturized FSSs are proposed to achieve large element numbers in a certain area to act as an infinite FSS with less distortion of elements. In addition, FSSs should have more consistent performance at the operating frequency under incident waves with different angles and polarizations.

Recently, numerous efforts have been exerted to obtain miniaturized FSS with angular stability. Many approaches including cross-layer capacitance [6,7], meandering wires [8,9] and fractal elements [10] have been employed to obtain better angular performance for stopband FSS. In the view of bandpass FSS, numerous attentions have been focused on the multilayer technique to obtain angular stability [11-22]. A larger coupling capacitance is brought in each overlap area between the square-loop slots and patches to reduce the dimension to 0.035λ ×0.035λ with angular stability up to 45° [17].Similarly, different geometric patterns overlaid with another layer are introduced to increase the equivalent capacitance of the bandpass FSS, thus leading to a lower resonance frequency. In this way, the angular stability is up to 60° [18-21]. For easy design and manufacture, two identical FSS screens with relative lateral displacement are cascaded to realize better angular stability (up to 80°)[22]. As an advanced multilayer structure, 2.5-dimensional elements are proposed to obtain stable frequency responses [23]. However, this method is explored for stopband FSS. For passband filter, two identical metallic convoluted cross slot layers with vertical metal vias are used to realize great angular stability up to 75° for both transverse electric (TE) and transverse magnetic (TM)polarizations [24]. In addition, the integration of outer dielectric bonding having a low dielectric constant helps in stabilizing the resonace frequency of double-layers FSS structure [25]. However, in practical manufacture and applications, especially in applications of curve surface with significant curvature, multilayer structures are prone to cause misalignment problems. Limited by the manufacturing process, upper and lower layers cannot be aligned completely, which not only affects the coherence of resonance, but also increases the transmission loss,thus resulting in design performance variation. To our best knowledge, there are few reports about the angular stability of single-layer bandpass FSS. Two kinds of singlelayer FSS integrated with convoluted wires are explored to realize angular stability ranging from 0° to 60° [26,27].

In this paper, a single-layer bandpass FSS with miniaturized unit cells is proposed to achieve superior performance in angular insensitivity. The FSS mounted on a thin substrate is composed of interdigital-resonator array by extending one finger of the interdigital resonator (IR).The proposed element has two merits: small dimension(0.03λ × 0.03λ) and better angular stability (up to 80° both for TE and TM polarizations). Finally, the superiorities of the proposed FSS are verified by both simulation and measurement.

2. Structure and operating principle

2.1 Structure description

The angular stability of the FSS concerns both geometry of the unit cell and interelement spacing [1]. In general,small interelement spacing leads to a stable frequency response with incident angles. The size of the unit cell for bandpass FSS can be shrunk down manifestly by periodic elements comprised of a parallel effective inductor and a capacitor, whose dimensions are much smaller than the wavelength at the resonant frequency, instead of an element of resonant type with a comparable size to a half of the wavelength at the resonant frequency. The traditional cross-slot element, as shown in Fig.1(a), which can be characterized by a parallel effective inductor and a capacitor, is widely used for bandpass FSS. An IR constructed by extending one finger of a strip-type interdigital capacitor to connect the two separate parts of the capacitor,shown in Fig.1(b), is explored to realize parallel resonance with a small size. In order to make full use of geometric space, we propose an improved IR (IIR), whose geometry is given in Fig. 1(c).

Fig. 1 Evolution of the element and equivalent circuit model

2.2 Equivalent circuit model (ECM)

The extended finger acts as an inductorLIand the coupling between other fingers still plays the role of a capacitorCI.Theinterdigitalcapacitorbecomesaparallel resonatorcoinedas IR[28].TheECMofIR is exactly the same with that of cross-slot FSS，as shown in Fig. 1(d).

The capacitance and the inductance values of the IR [28-30] can be evaluated as

wherelfis the length of fingers andnis the number of fingers.lsandws1are the length and the width of the extended finger, respectively.lf,ls,ws1andt(thickness of metal) are in meter.wf1is the width of fingers. It is seen that the equivalent circuit of an IR unit cell contains one parallel resonator, which resonates at

Due to the introduction of high capacitance generated by IR, the lower resonance frequency can be obtained. From Fig.1(d), it is obvious that when the impedance of the parallel resonator is capacitive, one transmission zero can be produced at its series resonantwithL.Therefore,the transmission zerofzis approximatelyevaluatedby

Based on the calculated equivalent inductances and capacitances of the proposed FSS structure, the circuit simulation is conducted with the following optimized values:CI=2.06 pF,LI=3.055 nH,L=0.777 nH. The dimensions of IR unit cell areP1=10 mm,l1=2.5 mm,ws1=0.2 mm,wf1=0.2 mm,lf=4.9 mm,n=17. FSS is printed on a dielectric slab with εr= 2.65, tan σ = 0.001 5, and thickness of 0.5 mm. Fig. 2 compares the simulated frequency responses for the proposed FSS using CST Microwave Studio and those obtained from the equivalent circuit in Fig. 1(d). A perfect agreement can be found. As a comparison, the frequency responses of cross-slot FSS having the same period with IR are plotted in Fig. 2. The dimensions of the cross slot areP=10 mm,l=2.5 mm,w=0.2 mm. The resonant frequencies of IR and cross slot are 2 GHz and 11.2 GHz, respectively.

Fig. 2 S parameters of IR FSS, cross-slot FSS and IIR FSS under normal incidence

One can note that IR reduces the unit size from 0.37λ to 0.066λ compared to the resonant wavelength due to a higher capacitance. The frequency responses of IIR FSS having the same period with IR are also plotted in Fig. 2.Dimensions of the designed IIR unit cell areP3=10 mm,s1=0.35 mm,s2=0.04 mm,wf=0.2 mm,ws=0.1 mm,n=31. One can see that the full utilization of the geometrical space makes the values of both capacitance and inductance of IR increase dramatically. Therefore, compared with IR, the resonance frequency of IIR is much lower, resulting in a shorter electrical length.

To obtain a better insight, the electric field distributions of IR and IIR at their corresponding resonance frequencies under normal incidence for both TE and TM polarizations are portrayed in Fig. 3 and Fig. 4, respectively. The directions of the incident electric field for TE and TM polarizations are alongyandxaxis, respectively. Strong coupling of IR and IIR can be observed when the fingers of IR are parallel to the polarization of the incident electric field.

Fig. 3 Electric field distribution of IR FSS under normal incidence at 2 GHz

Fig. 4 Electric field distributions of improved IR FSS under normal incidence at 0.944 GHz

3. Simulation and performance evaluation

The incoming wave having different polarizations or incident angles changes the frequency response of FSS.Therefore, it is worth investigating the sensitivity of its frequency response under different polarizations and incident angles (denoted as θ). Fig. 5 and Fig.6 illustrate the transmission and reflection coefficients of the IR FSS and IIR FSS (same dimension with that in Fig. 2) for both TE and TM polarizations under various oblique incident angles, respectively. It is seen that the transmission poles of the proposed FSSs do not change significantly for both TE and TM polarizations under oblique incidence of angles in the range from 0° to 80°. IIR has a better performance of angular insensitivity for the transmission poles, especially for 80° incident waves.

Fig. 5 S parameters of IR FSS under different incident angles

For the TE incidence, as the angle of incidenceθ changes, the wave impedance varies asZ0/cosθ . Here,Z0is the free space impedance. Therefore, as the incident angle increases, the loaded quality factor of the parallel resonators of Fig. 1(d) increases, which brings about decrease of the FSS bandwidth. The wave impedance for the TM polarization, however, changes asZ0cosθ. Therefore, as the incident angle increases, the loaded quality factor decreases for the TM mode, resulting in the broadening of the FSS bandwidth. These are evident from Fig. 5 and Fig. 6. The same behavior can also be observed in[17-19]. The bandwidth angular stability of FSS can be realized by bonding with a low dielectric constant [25].

Fig. 6 S parameters of IIR FSS under different incident angles

In order to illustrate the novelties clearly, the performance comparisons of the proposed FSS against previously reported FSS in some literatures are shown in Table 1. We denotedas thickness of the whole structure,f0as the resonance frequency of FSS for normal incidence, andnlas the number of FSS layers. Compared with the normal incidence scenario, the deviations of the resonance frequency at different incident angles for both TE and TM modes, are shown in the table. It can be seen that a great angular stability is achieved with the proposed structure which is formed by a single FSS layer.

Table 1 Comparisons with other works regarding thickness and deviation of FSS

4. Experimental verification

To experimentally verify the operating principle and the design procedure described above, the designed FSS is fabricated and then measured. It should be noted that in the design described in this paper, the thickness and relative permittivity of the substrate used to support the metallic strips are 0.5 mm and 2.65, respectively. The physical dimension of the fabricated prototype is 50 cm ×60 cm.Limited by measurement conditions, a prototype of the aforementioned IR FSS fabricated by printed circuit board lithography techniques is experimented. The geometrical dimensions of the IR FSS prototype are the same with the geometrical dimensions in Fig. 2. The topology of the fabricated FSS and measurement setup are shown in Fig. 7. The performance of the proposed FSS is experimentally verified by a free-space measurement setup. The experiment is conducted in a microwave anechoic chamber. To measure the frequency response of the fabricated FSS, the screen is placed between the transmitting and receiving antennas which are both connected to a network analyzer (PNA-N5244A). The measurements are carried out in two steps. First, the transmitted coefficients of the screen without the FSS and the reflected coefficients of the conductor panel of the same size with FSS are measured respectively for calibration. Then, the FSS is placed between two antennas and its transmitted coefficients and reflected coefficients are measured respectively once again. The frequency responses are obtained by using these measurement results from two steps. Oblique incidence is achieved by rotating the relative position of the antennas and FSS. Fig. 8 shows the measured results of the proposed FSS for oblique incidence angles for the TEand TM-polarized incidence. The measured results confirm great angular stability of the proposed FSS for different incident angles. Compared with the simulated results which are shown in Fig. 2 and Fig. 5, a small deviation of the resonance frequency has been observed which can be explained due to the manufacturing and measurement limitation.

Fig. 7 Fabricated prototype and measurement setup

Fig. 8 Measured results of IR under different angles of incidence angles

5. Conclusions

One-layer miniaturized FSS with angular stability is proposed in this paper. The application of IR can produce a higher capacitance, which miniaturizes the dimension of unit cell effectively to 0.03λ. The operating principles of the proposed FSS along with the ECM are presented. The simulated and measurement results are compared in this paper. The results show that the proposed FSS reduces the sensitivity to the variation of incident angles up to 80°for both TE and TM modes. The presented structure can be practical for designing angularly-stable bandpass FSS with fewer layers.