A Method for Designing Multi-Band Rasorbers for Wideband Applications

Rasorbers with a single passband (narrow or wide) or multiple narrow passbands have been reported for stealth applications over the past few years. In this work, a method of designing the multi-band rasorber with wide passband(s) is proposed for the stealth of wideband antennas. Firstly, the method of designing multi-band FSS is proposed based on the theory of N-band resonator, in which all the passbands exhibit second-order response. Secondly, a parallel resonator combining spiral inductor and interdigital capacitor is proposed to satisfy wide passband requirements at lower frequency of the operating band. Finally, to verify the proposed method, a dual-band rasorber consisting of FSS and resistive layer is fabricated and measured. The measured results illustrate two passbands within 4.9-6 GHz (20.0%) and 8.6-9 GHz (6.3%), respectively. Three absorption bands with 48.4%, 25.7%, and 22.0% fractional bandwidths are also achieved.

Although three-dimensional (3D) rasorbers [15]- [19] exhibit better transmission selectivity and wider absorption bandwidth compared with their two-dimensional (2D) counterparts, the 2D rasorbers [20]- [40] composed of lateral resistive layer and frequency selective surface (FSS) have attracted more attention due to their compact geometry and convenience of manufacturing.
The associate editor coordinating the review of this manuscript and approving it for publication was Muhammad Zubair .
Since rasorbers are mainly used to reduce the radar crosssection (RCS) of antennas, their absorption bandwidths are expected to be as wide as possible to achieve good stealth performance, while the transmission bands are designed according to the operating bands of antennas. In the beginning, rasorbers with a single transmission band below (i.e. T-A type) [20], [21], above (i.e. A-T type) [22]- [24], and on both sides (i.e. A-T-A type) [25]- [27] of the absorption band were developed. The passbands of these rasorbers are achieved by the parallel resonant structures with single-order response in both FSS and resistive layer. Furthermore, by loading the PIN diodes and varactors to control the resonant frequency of parallel resonator, the tunable [28], [29] and switchable rasorbers [30]- [32] were also reported to enhance their stealth ability.
For the broadband applications, rasorbers with a wide passband were proposed [33]- [36] utilizing high-order FSSs [5], [6]. These FSSs exhibit wide passband with secondorder response, resulting in good in-band flatness and excellent roll-off performance on the edges of the passband that enhances the absorption performance of the resultant rasorbers. Besides, since the fractional transmission bandwidth of parallel resonator is inversely proportional to its Q-factor [41], low-Q resonant structures are also adopted in the resistive layer for wide-band rasorber designs. Later, to satisfy the requirements of multi-band applications, rasorbers with double and triple passbands were proposed, resulting in the corresponding A-T-A-T [37], [38], A-T-A-T-A [39] and T-A-T-A-T-A [40] devices. The passbands of these rasorbers are achieved by combining several parallel resonant structures in both FSS and resistive layer, which can be potentially extended to other multi-band designs. However, the existing multi-band devices only exhibit narrow passbands that are not favored for multi-band antennas with wide operating band [42], [43].
Therefore, in this work the method to achieve wide passband(s) in a multi-band rasorber is proposed using highorder multi-band FSS and low-Q parallel resonator. Although several high-order multi-band FSSs have been previously reported [7], [8], a universal method of designing multi-band FSS with wide passband(s) has not been investigated. Hence, based on the theories of dual-behavior resonator filter [44], [45] and N-band resonator [46], a multi-band FSS design method is proposed, in which all the designed passbands exhibit second-order response. In addition, the wide passbands of existing rasorbers are achieved at higher frequencies of their operating bands [33]- [36]. Still, the wide passband may also be required at lower frequencies for dual-band antennas [42], [43]. Therefore, a parallel resonator consisting of spiral inductor and interdigital capacitor is proposed to achieve a wide passband at lower frequency. Moreover, the resultant dual-band rasorber with a wide passband at lower frequency and a narrow passband at higher frequency is fabricated and measured to verify the proposed method.

A. EQUIVALENT CIRCUIT MODEL OF FREQUENCY SELECTIVE SURFACE
The equivalent circuit model (ECM) of the proposed N -band FSS is shown in Fig. 1(a). N (≥ 2) series L-C resonators are loaded in the first and third layers of FSS, and a single series L 0 -C 0 resonator is loaded in the second layer. The resonant frequencies of each resonator are represented as In order to illustrate the operating mechanism of FSS, two equivalent transformations are implemented as shown in Fig. 1(a)-(c). Firstly, the transmission lines within the red dashed boxes of Fig. 1(a) are transformed into the π networks within the red dashed boxes of Fig. 1(b). By letting the ABCD matrices [41] of transmission line and π network equal to each other, L u and C u are derived as and µ 0 , 0 , and Z 0 are the permeability, permittivity, and characteristic impedance of free space, respectively. 1 and h are the relative permittivity and thickness of the dielectric substrates that are modeled as the transmission lines. Secondly, by ignoring the small capacitor C u , the T network within the blue dashed box of Fig. 1(b) is transformed into the π network [41] within the blue dashed box of Fig. 1 is inductive at frequencies above f 0 (i.e. f > f 0 ), and ω = 2πf is the angular frequency. Since a series L-C resonator is capacitive (or inductive) below (or above) its resonant frequency, for f 0 ≤ f ≤ f 1 it is easy to know that in the green dashed boxes of Fig. 1(c), Thus, a transmission pole can be achieved when the reactances of capacitive and inductive parts cancel each other.
It is worth noting that though N can be any integer greater than one theoretically, the number of passbands for a practical FSS is limited due to the size restriction of its unit cell. To demonstrate the performance of the proposed FSS, four examples (i.e. FSS I, II, III, and IV) are presented, and Fig. 2 gives the S-parameters of each FSS where the circuit parameters are optimized through manual tuning. As shown in Fig. 2(a)-(c), when N = 2 dual-band FSSs with adjustable transmission bandwidths is achieved. Fig. 2(d) indicates that when N = 3 a tri-band FSS is obtained. Hence, two or more passbands with second-order response can be achieved following the proposed method. Besides, in each case the transmission zeros induced by series L n -C n (0 ≤ n ≤ N ) are observed on both sides of all passbands, which improves the roll-off performance of FSS and can potentially help to enhance the absorption bandwidth in rasorber design.

B. EQUIVALENT CIRCUIT MODEL OF RASORBER
The ECM principle of the resistive layer presented in [39] and [40] can be extended to design rasorbers with two or more passbands. As examples, the resistive layer whose ECM is designed following [39] and the FSSs presented in Fig. 2(a)-(c) are used for rasorber design. The resultant ECM of the dual-band rasorber is shown in Fig. 3. In resistive layer, series R s -L s -C s is optimized to match the air impedance for the absorption of rasorber. Parallel L p1 -C p1 and L p2 -C p2 exhibit infinite impedances at their resonant frequencies. Thus, two passbands with low insertion loss of resistive layer are achieved. Since parallel L-C resonator with low (or high) Q-factor produces wide (or narrow) passband [41], the Q-factors of L p1 -C p1 and L p2 -C p2 are adjusted to match the transmission bandwidths of FSSs. Fig. 4(a)-(c) give the calculated S-parameters of the proposed dual-band rasorbers where the circuit parameters are optimized through manual tuning. It is found that to achieve wide passband at lower frequency, the parallel L-C resonator with high inductance and relatively high capacitance  is needed. Since there are few researches on the rasorber with wide passband at lower frequency of the operating band, rasorber I is chosen for the following design.

III. STRUCTURAL DESIGN AND FABRICATION A. MODELING AND FULL-WAVE SIMULATION
To verify the proposed method, a single-polarized device following the ECM of rasorber I is designed. The unit cell structure of the corresponding FSS (i.e. FSS I) is shown in Fig. 5. In each layer, series L-C resonators are realized with rectangular patches and a pair of parallel strips are added in the middle layer to achieve C 0 . Periodic boundary conditions are set for the unit cell and Floquet Ports are used for excitations in full-wave simulation. Fig. 6 demonstrates the S-parameters of the FSS, in which the results achieved from calculation and simulation agree well with each other. The results reveal a wide passband (|S 21 | ≥ −1 dB) covering 4.64-5.92 GHz (24.2%) and a narrow passband within 8.31-8.8 GHz (5.7%). Fig. 7 demonstrates the unit cell structure of rasorber I. The parallel strip capacitor in the center of resistive layer is C s , and L s is realized by meander inductors. The lumped resistors VOLUME 9, 2021  R s are loaded between C s and L s . A commonly used interdigital resonator with high Q-factor is adopted to realize L p2 -C p2 . Since spiral inductor and interdigital capacitor exhibit relatively high inductance and capacitance densities among the printed lumped elements, respectively [47], a resonant structure consisting of rectangular spiral inductor and interdigital capacitor is proposed to realize L p1 -C p1 , which attains low Q-factor and low resonant frequency. The dimension of spiral inductors can be estimated as [48] L(nH) = 6.35×10 6 ×µ 0 n 2 t D av [ln where and n t is the number of turns. The dimension of interdigital capacitor can be estimated as [47] C(pF) = ( r + 1)l[(n f − 3)4.4 + 9.9] × 10 −3 , where l and n f are the length and number of fingers. Fig. 8(a) and (b) give the simulated S-parameters of the proposed rasorber under different oblique EM wave incidence. It is found that the transmission/absorption  performances of rasorber remain stable below 7 GHz for incident angle ≤ 40 • . Although the transmission band is reduced with the increase of incident angle at higher frequencies, a narrow transmission band is still observed under an incident angle of 40 • . Moreover, the current distributions of resistive layer are demonstrated in Fig. 9 to provide a better understanding of the operation mechanism of the proposed device [49]. Within two transmission bands, e.g., 5.2 and 8.5 GHz, strong resonant currents are observed around the parallel LC structures. Hence, transmission bands with low insertion loss are achieved. Within the absorptin bands, e.g., 10 GHz, strong surface currents are observed around the lumped resistors, resulting in efficient EM energy absorption.

B. FABRICATION AND MEASUREMENT
As shown in Fig. 10(a)-(d), the rasorber consisting of 15 × 15 unit cells with an overall dimension of 240 × 240 mm 2 is   Taconic RF-35 (ε r = 3.5, tanσ = 0.0025) are used for resistive layer and FSS, respectively. The thickness of whole device is 13.3 mm. Free-space measurement [50] shown in Fig. 10(e) and (f) are carried out to test the frequency response of the proposed device. Fig. 11 gives the S-parameters of rasorber achieved from full-wave simulation and free-space measurement. The simulation results indicate that the device exhibits wave transmission (|S 21 | ≥ −1 dB) within 4.74-5.75 GHz and 8.3-8.69 GHz, and 80% wave absorption within 2.63-3.85, 6.19-7.88, and 9.15-11.06 GHz. Good agreements are achieved between measured and simulated results at lowfrequency band, while a frequency shift is observed at higher frequencies. This might because of the manufacturing and measuring errors that are more sensitive at higher frequencies.
The measured performances of the proposed rasorber and other existing multi-band rasorbers are summarized in Table 1. It can be seen that the proposed method enables a rasorber with both wide (20%) and narrow (6.3%) transmission bands. The device also exhibits 96.1% fractional absorption bandwidth thanks to the improved roll-off performance of the NBR-based FSS. VOLUME 9, 2021

IV. CONCLUSION
In this work, the method for achieving wide passband(s) in multi-band rasorber is proposed. A convenient approach for multi-band FSS design is presented by coupling two N -band resonators. In addition, a spiral-interdigital resonator with low Q-factor and low resonant frequency is designed to realize the wide passband at lower frequency of the operating band. A dual-band rasorber with both wide and narrow passbands is designed and fabricated to validate the proposed method. This method can be potentially used in other multiband rasorber designs to fulfill the stealth requirements of antennas with diverse operating bands.