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Abstract
In this paper, a miniaturized frequency-selective rasorber (FSR) with an ultra-wide transmission band (| S21 | <1 dB) is presented. The FSR is made up of a lossless multi-layer cascaded frequency-selective surface (FSS) with a 2.5-D lossy layer above, separated by an air gap. Modified metallic Jerusalem crosses loaded with lumped resistors serve as the unit cell of the lossy layer. An equivalent parallel LC circuit with high inductance and extremely low parasitic capacitance is introduced by zigzag strips and vias, which broaden the transmission band significantly. The equivalent circuit model (ECM) is constructed to provide further insight into the structure. Simulation results show that the proposed FSR exhibits an ultra-wide transmission band of 1-dB from 6.20 to 17.97 GHz (97.4%) with a minimum insertion loss of 0.074 dB. Meanwhile, an 80% absorption band covering 2.58-4.13 GHz is achieved below the passband. For demonstration, an experimental prototype of the 2.5-D FSR is fabricated and measured, and the simulated and measured results are reasonably consistent.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Frequency-selective surfaces (FSSs) are 2-D infinite periodic arrays that have the ability to tailor the frequency selectivity in transmission or reflection characteristics [1]. Over the past few decades, FSSs have been extensively utilized as hybrid radomes to protect antennas from physical environment and reduce radar cross section (RCS) [2]. However, for traditional FSS-based radomes, signals in band are transmitted with minimal power loss, while out-of-band incoming waves are reflected strongly, making them futile for dual/multi-station RCS reduction [3]. Microwave absorbers have been extensively studied for various scenarios where electromagnetic wave absorption is desired. There are several types of microwave absorbers, such as circuit analog absorbers (CAAs) [4–6], capacitive circuit absorbers (CCAs) [7,8] and metamaterial absorbers [9–11]. To further overcome the challenge of out-of-band reflections, frequency-selective rasorber (FSR), which is a combination of FSS and CAA absorber, was first introduced as an idea in 1995 [12] and presented specifically in 2012 [13].
Instead of reflection, the FSR exhibits the characteristics of absorption for out-of-band incident waves, while still retaining the ability to transmit along the passband with low insertion loss (IL). In recent years, various FSRs have been proposed and can be classified into three main categories as the passband setting above, below and within the absorption band, corresponding to A-T [14], T-A [15] and A-T-A [16,17] rasorbers respectively. Besides, FSRs can also be sorted into 2-D and 3-D types from the structure point of view [18]. However, the cost of profile height and structure complexity cannot be neglected in 3-D FSRs. The attention about FSR mainly focuses on miniaturization [19], multi-polarization [20], wideband [14,21–31], tunability [32] and flexibility [33,34]. It should be pointed out that in the studies of wideband, a considerable number of research articles have made efforts to broaden the 10-dB absorption band, while the transmission band is still narrow [21–23].
With the vigorous development of ultrawide-band (UWB) technology worldwide, the applications of UWB systems are becoming increasingly extensive. Thus, FSRs with an ultra-wide transmission band are essential for certain practical applications. To the best of our knowledge, however, only few studies have been devoted to FSRs with wide transmission band [14,24–31]. Employing the modal interaction pole generated by the cross-dog-bone lossy layer, a FSR with a wide 3-dB transmission bandwidth of 41.3$\%$ is proposed [24]. The wide 1-dB transmission band of the FSRs covering 8.3-11.07 GHz and 9.0-12.63 GHz are achieved by inserting circular spiral resonators [14] and a convoluted resonator [25] in the lossy layer, respectively. In [28], resistors connected in parallel with two lumped series $LC$ circuits are introduced, which lead to a broad transparent window due to the broadband resonance, whereas the FSR is suffering from single polarization. With cascading two 2.5-D parallel resonators (PRs) composed of the interdigitated capacitor and the metal meandered strip-line on both surfaces of the lossy layer, a passband bandwidth of 21.2% is maintained [30]. Although tortuous cross elements in [26,27,31] are also effective for wide transmission passband, they cannot meet the requirements of ultrawide-band scenarios yet.
This paper proposes a novel miniaturized FSR with an ultra-wide transmission band using 2.5-D structures to achieve the UWB stealth and communication responses demonstrated in Fig. 2, schematics and working principles of which are shown in Fig. 1. The Jerusalem cross modified by zigzag strips and vias is adopted as the unit cell element, as well as a lumped resistor is loaded in the center of each side of the layer. By employing a multi-layer FSS with ultra-wide bandpass behavior, an ultra-wide transmission band is achieved above an absorption band, which provides the desired performance within a wide reflection reduction band. At last, an experimental prototype was fabricated and measured to verify the predicted responses. Of all the FSRs that have been presented before, the transmission band of the proposed FSR is the widest.
2. Design and analysis of the proposed FSR
2.1 Basic principles of broadening transmission bandwidth
Based on the simple ECM model of basic dual-layer FSR shown in Fig. 3, the transmission coefficient between port1 and port2 ($S_{21}$) is given in [38] as follow.
In Fig. 3, $Z_{0}$ is the characteristic impedance of the free space and $Z_{s}$ is of the dielectric spacer. The equivalent impedance of the lossy layer and the bandpass FSS, respectively, is indicated by the symbols $Z_{R}$ and $Z_{B}$, which can be represented by $Z_{R}=R+jX_{R}$ and $Z_{B}=jX_{B}$. $h$ is spacer’s thickness. Applying foam with air-like dielectric characteristics causes $Z_{s}=Z_{0}$. With the bandpass FSS, its equivalent impedance $Z_{B}$ is infinite in the passband.
Formula (1) is the same as the transmission coefficient equation of a single lossy layer, which means that the low insertion loss characteristics of the FSR are only determined by the lossy layer since the bandpass FSS is equivalent to an open circuit in the operation band. In case of impedance $Z_{R}$ resonating to infinity, there will be a perfect transmission near the resonance frequency.
In the design of the lossy layer, An LC parallel circuit is adopted in order to achieve low insertion loss in the transmission band, while a RLC series circuit is used for sufficient absorption performance. Wide transmission band FSR requires as large L as possible and as low C as possible [14].
2.2 Design of the proposed FSR
Figure 4 illustrates the 3-D geometrical topology of the proposed FSR unit cell. The lossy layer and the lossless layer are separated by a 13mm thick air spacer. The lossy layer and the bandpass FSS are both processed on the Rogers 5880 with $\varepsilon _{r}=2.2$.
Fig. 4. 3-D geometrical topology of the proposed FSR. (a) Overall structure view. (b) Details of layers. ($p$=8 mm, $t_{1}$=0.508 mm, $t_{2}$=1.524 mm, $h$=13 mm, $s$=4 mm, $w$=0.2 mm, $g$=0.2 mm, $r_{1}$=0.5 mm, $r_{2}$=1 mm, $r_{3}$=0.5 mm, $l_{1}$=1 mm, $l_{2}$=2.7 mm, $l_{3}$=0.6 mm, $d_{1}$=0.2 mm, $d_{2}$=0.4 mm, $cr_{1}$=1.9 mm, $cr_{2}$=2.05 mm, $gt$=0.075 mm)
The unit cell of the lossy layer is based on a lumped-resistor-loaded Jerusalem cross modified by zigzag strips and vias. The zigzag strips alternate on both sides of the dielectric substrate and are connected by vias. Among them, the metal patterns on the upper surface and that on the lower one of the lossy layer are 90$^{\circ }$ rotationally symmetric. The center of each side of the layer is where a lumped resistor is mounted.
The bandpass FSS is a triple-layer structure composed of two identical circular rings coupled by a central layer of square apertures. Its structure comprises of two layers of dielectric substrate, with the aperture array etched on the interface of the two layers and the ring arrays printed on the upper and bottom surfaces.
Normal incident waves propagate along the $-z$-axis. As this design utilizes rotation-symmetrical structures, the following work focuses only on responses under TE-polarized ($y$-axis) incident wave conditions.
2.3 Analysis and simulation results
Figure 5(a) shows a detailed analysis of the equivalent circuit effects under TM polarization of the proposed lossy layer. Metallic via is equivalent to inductance $L_v$ and equivalent capacitance $C_v$ exists between adjacent vias [39]. The strips along the direction of incident wave polarization is equivalent to inductance $L_{11}$ and $L_{12}$. $C_{11}$ is the equivalent capacitance between the loading arms of adjacent cells. $R$ depends on the resistance value of the lumped resistor used. Due to the metallic strips are zigzagged and alternatively placed on each side of the substrate, there are equivalent capacitance $C_s (C_{s1}, C_{s2})$ between parallel strips on both sides. As the symmetry of the structure, the equivalent circuit on the right arm is the same as the left arm and the labels have been omitted for simplicity.
Illustrated in Fig. 5(b), an equivalent circuit model (ECM) is created and simplified based on analysis above to further clarify the workings of the design. The series connection of a series RLC circuit ($R$, $L_{1}$ and $C_{1}$) and a shunt LC circuit ($L_{2}$ and $C_{2}$) can be used to mimic the lumped-resistor-loaded modified Jerusalem cross on the lossy layer. Among them, $L_1$ is equivalent to the series connection of $L_{11}$ and $L_{12}$, $C_1$ is equivalent by $C_{11}$. $C_s$ and $C_v$ in shunt are equivalent to $C_2$, where $C_s$ is a series connection of $C_{s1}$ and $C_{s2}$. $L_2$ is a series of $L_v$. The series of metallic vias contributes to a higher equivalent inductance $L_2$, while the series of $C_{s1}$ and $C_{s2}$ makes the equivalent capacitance $C_2$ much smaller. As a result, the bandwidth of the transmission band can be significantly enhanced. A series LC circuit ($L_{3}$ and $C_{3}$) and an inductor $L_{4}$ can be used to represent the bandpass FSS’s cricular ring layers and square aperture layer, respectively. The characteristic transmission line impedances $Z_{0}$, $Z_{s}$ and $Z_{d}$ are used to represent vacuum, the substrate and the air spacer, respectively.
Equivalent circuit models for many FSS elements have been extensively and thoroughly investigated by many researchers [35,36]. For the strips perpendicular to the electric-field vector polarization, the capacitive susceptance can be given by
The frequency responses of the proposed 2.5-D FSR are simulated by High-Frequency Structure Simulator (HFSS) and Advanced Design System (ADS), corresponding to electromagnetic simulation and circuit simulation, respectively. The master-slave boundary conditions are used along the X-axis and Y-axis in the full-wave simulation to idealize the proposed FSR as an infinitely large periodic structure. Meanwhile, Floquet ports are set at both ends of the air cavity. The circuit diagram of the ECM is drawn and simulated in ADS. Good agreements are realized between the ECM theoretical results and full-wave simulation results, as illustrated in Fig. 6. It is seen that under the normal incidence, the ultrawide transmission bandwidth with IL less than 1 dB is 97.4$\%$ from 6.2 to 17.97 GHz, and the minimum IL is 0.074 dB at 8.9 GHz. Absorptvity of the FSR are also depicted in Fig. 6. An absorption band of 2.58-4.13 GHz (46.2$\%$) is covered by over 80$\%$ absorptivity. Meanwhile, with a fractional operational bandwidth of 150.7$\%$, the 10 dB reflection reduction band is accomplished from 2.52 to 17.94 GHz. The slight discrepancy between the ADS and HFSS simulation results is due to the neglect of some parasitic capacitance and inductance in the ECM, such as the effect of the structure along TM polarization direction under TE polarization conditions and vice versa. The influence of more than one Floquet harmonic at higher frequencies is also ignored in this ECM.
Fig. 6. Reflection/transmission coefficients and Absorptivity of the proposed FSR under normal incidence.
The frequency responses of the lossy layer in 2-D form and 2.5-D form without the ground is shown in Fig. 7(a). It is clear that the use of metallic vias significantly widens the low-IL transmission bandwidth and shifts the resonance frequency to around 7 GHz, enabling even more miniaturization. The impedance of the lossy layer is also depicted in Fig. 7(b), it can be seen clearly that parallel resonance occurs at nearby 7 GHz and the real part of impedance nearly maintains to zero, which reveals the low insertion loss characteristic. Figure 7(c) illustrates the frequency response of the bandpass FSS structure. With utilizing non-resonant elements, a second-order 1-dB passband ranging from 7.1 GHz to 17.5 GHz is realized. In Fig. 7(d), the multi-resonance of the proposed FSR are intuitively seen from the imaginary part of the impedance, while the loss characteristics in the absorption band and the lossless characteristics in the passband are implied by the real part. The real part of the impedance at infinity near the resonant frequency of the parallel connection should be ignored due to the calculation error [14].
Fig. 7. The frequency responses and impedance curves of different layer structures of the proposed FSR.
Fig. 8 shows the influence of four key parameters on the proposed FSR, which are: the length of loading arm $s$, the length of the zigzag strips $l_2$, the height of air gap between the lossy layer and the lossless layer $h$, and the outer radius of the circular rings of the lossless layer $cr_2$. In general, the $S_{21}$ is very stable at different parameters, except for the significant effect of $cr_2$ at higher frequencies. The changes in $s$ and $l_2$ mainly affect the absorption band located at low frequencies. With the increase of $s$, the resonance frequencies have a tendency to move lower, while the $S_{11}$ at higher frequencies has been raised. The trend of $S_{11}$ with $l_2$ is basically the same as $s$, but its effect is smaller compared to $s$. $h$ is a very sensitive parameter for the performance of the whole structure and its variation will significantly affect the $S_{11}$. As $h$ increases, the second resonance point in the passband will move to lower frequencies and the third resonance point will gradually disappear, while the first resonance point will remain almost constant. Moreover, the change of $h$ is fatal to the performance of the absorption band. An increase in $h$ within a certain range can enhance the bandwidth of the absorption band, but its effect is limited. The reduction in $cr_2$ expands the passband bandwidth ($\left | S_{21}\right |$ <1 dB) significantly toward high frequencies, however, this comes at the cost of a deterioration in $S_{11}$.
The surface current distributions and E-field distributions along thickness direction of the lossy layer under TE and TM polarized incident waves are shown in Fig. 9 to shed light on the mechanism of absorption and low IL. As can be seen, the excited current flows through the lumped resistor at 3.2 GHz in the absorption band, allowing the absorption behavior to be achieved. From the E-field distributions, the electric field intensity is greatly reduced after the incident wave passes through the lossy layer at 3.2 GHz, proving that the EM waves are consumed. On the contrary, at 8.9, 14.2, 17.6 GHz within the transmission band, there is practically no current on the resistor-loaded arms and the electric intensity of the incident waves after passing through the lossy layer is almost no attenuation. Thus, low IL is achieved in these scenarios.
Figure 10 investigates and displays the transmission and absorption responses under both TE-polarized and TM-polarized oblique incidences. As the incident angle increases up to 30$^{\circ }$, the transmission coefficient of the proposed FSR remains very stable, while the reflection coefficient deteriorates gradually under TE polarization. Note that a null is generated nearby 14.5 GHz at TM-polarized oblique incidences due to the “bent mode" of the Jerusalem cross [1], however, it may be tolerable under such an ultrawide-band scenario.
3. Experimental measurement
To verify the proposed 2.5-D FSR’s transmission and reflection performance, a prototype of 28$\times$28 unit cells with the size of 250mm$\times$250mm is manufactured and measured as shown in Fig. 11. The bandpass FSS is processed on a Rogers 5880 that is 1.524 mm thick, while the lossy layer is processed on a Rogers 5880 that is 0.508 mm thick. The metallic strips are soldered with chip resistors in the 0402 package. Eight nylon screws are used to fix the polymethacrylimide (PMI) foams that separate and support the lossy layer and the lossless layer.
Fig. 11. Photograph of the fabricated prototype. (a) Integrated FSR, lossy layer and lossless layer. (b) Measurement setup.
The comparison of the proposed FSR’s simulated and measured performance is shown in Fig. 12. The measured results demonstrate that the 1-dB transmission band is achieved from 6.3 to 17.8 GHz with a fractional bandwidth of 95.4$\%$ and the band with $S_{11}$ < −10 dB is covered over 2.4–17.8 GHz. Measured results are in good agreement with the simulated results. The modest disparity between the results of the simulation and the measurements is mainly due to the tolerance in the fabrication and measurement peocesses. For example, the parasitic parameters of the lumped resistors and the error of the soldering process can cause an uncertain resonance frequency shift as well as an increase in the insertion loss. And the inherent loss of the connecting cables may be to blame for the overall lower $S_{11}$ parameter. Besides, the experimental prototype is a finite periodic structure, whose edge effects may also have an impact on the difference between simulation and measurement.
Table 1 compares the proposed FSR with existing FSRs that have been published. The proposed FSR produces the largest 1-dB transmission bandwidth with a minimum IL and 10-dB reflection reduction band when compared to the other reported studies. The lossy layer’s unit cell includes the fewest number of lumped resistors overall.
Table 1. Comparison between the proposed FSR and earlier works.
4. Conclusion
This paper has proposed, measured, and validated an ultra-wide transmission band FSR employing 2.5-D miniature structures. A lossy layer and a bandpass FSS layer made up the FSR. The zigzag stripes and vias on a metallic Jerusalem cross loaded with lumped resistors have been used to create an absorption band and an ultrawide transmission band. The transmission band of the lossy layer has been matched by the bandpass FSS. According to the observed results, it was able to simultaneously produce an ultrawide -10-dB reflection band from 2.4 to 17.8 GHz and 1-dB transmission band in the desired passband from 6.3 to 17.8 GHz. The lossy layer’s lumped resistors are used in lower amounts than in other published FSRs, and the proposed FSR produces the widest relative bandwidth, suggesting the possibility of ultra-wideband stealth and communication.
Funding
National Natural Science Foundation of China (61471117).
Acknowledgments
The authors would like to thank Prof. Zongxin Wang, from Southeast University, Nanjing, for fruitful discussions about the structure design in this letter. The authors would also like to express their sincere gratitude to the anonymous reviewers for their constructive comments on this paper.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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