# Design of Low-Profile Frequency-Selective Rasorbers Based on Three-Legged Loaded Element

Authors: Yu Qiang; Dongfang Zhou; Qikun Liu; Zhenning Yao
Journal: International Journal of Antennas and Propagation
 (2020)

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## Abstract

A novel low-profile dual-polarization frequency-selective rasorber (FSR) with a transmissive window in the absorption band is proposed in this paper. Based on the equivalent circuit model (ECM), the principles of the impedance design are theoretically derived. Then, a two-layer structure model is constructed. The top layer is composed of a lossy three-legged loaded element (TLLE), and the bottom layer is composed of a square ring bandpass frequency-selective surface (FSS). Furthermore, the strips are folded to reduce the unit cell size to stabilize the angular response. The maximum stable response angle increases from 20 to 40° due to the miniaturized design under both TE and TM polarization. The experimental results of the prototype are in good agreement with the simulation results, which validates the rationality of our design.


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## Body

## 1. Introduction

Frequency-selective surface (FSS), regarded as a spatial filter within a certain bandwidth of the resonant frequency corresponding to the periodic unit cell, has been applied in hybrid radomes to transmit the in-band waves and simultaneously reflect the out-of-band waves [1]. The antenna radar cross section (RCS) could be reduced by its frequency selectivity together with a proper shape [2–4]. However, this approach is only for monostatic interrogations as the reflected waves produce lager RCSs in other directions which may still be detected by the bistatic radar system. Consequently, an ideal invisible radome should transmit the operation signals and absorb the out-of-band input power, which contributes to the generation and development of frequency-selective rasorber (FSR) technology.Several research and applications of 2-D FSRs have been studied in the recent few years [5–16]. These FSRs are usually composed of a lossy layer and a metallic lossless bandpass FSS layer. The lossy layer can be implemented by two methods: magnetic loss material [8] and metallic element loaded with lumped resistors [5–7, 9–16]. Thus, the transmission band can be realized by the resonance of the lossy layer and the lossless layer, while the lossy layer is used to achieve absorption characteristics. Originally, the absorption band and the transmission band are separated, which results in only one-side absorption (the absorption band below the passband [5–7] and the absorption band above the passband [8–10]). To achieve a transmission window in the absorption band, some methods have been reported [11–17]. The combination of the square ring array and the crossed-dipole array realized a passband within an absorption band in [11]. Two sets of LC resonators were loaded on metal cross grids in [14]. However, in these two methods, loading too many elements leads to a complex structure. Subsequently, a 3-D FSR was constructed by using a parallel waveguide with a metallic post in the center in [17]. These structures had stable performance at the oblique incidence, but the costs of fabrication were too high.Therefore, compared with the proposed complex structures, a more simple but stable structure by cascading a three-legged loaded element (TLLE) layer and a square ring bandpass FSS layer is proposed in this paper. This paper first elaborates the design principles of the absorption band and passband through the equivalent circuit model (ECM). The simulation results of preliminary design in the HFSS agree well with the simulation results of the ECM in ADS. Furthermore, a miniaturized structure is proposed to improve the performance under oblique incidence. Ultimately, the prototype is fabricated and the experimental results are basically consistent with the simulation results.


## 2. Equivalent Circuit Analysis

According to the reported FSRs, a basic ECM usually contains three parts: a resistive layer on the top, a bandpass layer at the bottom, and an air dielectric layer in the middle. The shunt impedance between the transmission lines can be used to simulate the resistive layer and bandpass layer of the ECM.In the absorption band of an ideal FSR, the incident waves need to be absorbed as completely as possible. That is,S11=0 and S21=0. Likewise, for the ideal passband, the insertion loss should be as low as possible. That is, S11=0 and S21=1. To achieve a transmission window in the absorption band, the operating frequencies can be divided into three regions: the lower absorption band fA1, the higher absorption band fA2, and the passband fT. The relationship between three frequencies is fA1 < fT < fA2. For the absorption band fA1 and fA2, the ECM of the resistive layer needs to realize two series resonance points, while the ECM of the bandpass layer needs to serve as the ground plane. For the passband fT, the ECMs of the resistive layer and the bandpass layer need to realize parallel resonance at the same point. So, the equivalent circuit of the structure should have at least two series resonance points and one parallel resonance point.Thus, an ECM that satisfies the above conditions is shown in Figure1. Z0 is the characteristic impendence of the free space. ZR and ZB represent the equivalent impendence of the resistive layer and the bandpass layer, respectively, and can be expressed as(1)ZR=R1+jωL1+1jωC1+1jωC2+2/jωL2+R2,ZB=1jωC3+1/jωL3,where ω is the angular frequency. The resonance frequency can be computed by searching for the nulls of the derivation function of the impendence.Figure 1
Equivalent circuit model.In the passband,L2 and C2, L3 and C3 resonate in parallel at fT, which can be obtained as(2)fT=12πL2C2/2=12πL3C3.Thus,ZR ⟶ ∞ and ZB ⟶ ∞. According to [11], S11=0 and S21=1. R2 represents the inevitable loss in the practical design, so it is set as small as possible to achieve an ideal transmission. Therefore, it is an effective method to design a structure in which the resistance layer resonates in parallel in the passband.In the absorption band, sinceZB tends to infinity at the parallel resonance frequency fT of the bandpass layer, Im (ZB) = 0 at the lower series resonant frequency fA1 and higher series resonant frequency fA2, which can be determined by(3)fA1=n−n2−8m/2m2π,fA2=n+n2−8m/2m2π,where(4)m=L1L2C1C2,n=2L1C1+L2C2+L2C1.In conclusion, the bandpass layer performs as the ground plane when the resistive layer achieves absorption characteristics. However, it is difficult to achieve the ideal situation that all the incident waves are absorbed, so a reflection coefficient standardS11<−10°dB is set to evaluate the absorption performance. Since the value of R2 is very small, the real part of ZR is mainly determined by R1. The value of ω is related to frequency, so the value of R1 is set near Z0.


## 3. Design and Performance of the Rasorbers

### 3.1. Preliminary Design and Performance

A 3-D view of preliminary design based on the above ECM analysis is shown in Figure2(a). Each unit includes a resistive layer on the top and a bandpass layer at the bottom, which are separated by air. A lossy metallic TLLE [1] and a lossless square ring bandpass FSS constitute the resistive layer and the bandpass layer, respectively, as shown in Figures 2(b) and 2(c). The lumped resistors are placed near the end of each strip in the TLLE. Both the two layers are printed on Rogers 4350B with a thickness t and a relative dielectric constant εr.Figure 2
(a) 3-D view of preliminary design. (b) Resistive layer on the top. (c) Bandpass layer at the bottom (geometric dimensions:p = 32 mm, h = 13 mm, w1=0.5mm, w2=1.5mm, w3=0.29mm, d1 = 14 mm, d2 = 0.8 mm, R = 100 Ω, w0=1.72mm, l0 = 20 mm, t = 0.508 mm, and εr = 3.48).
(a)
(b)
(c)For the lossy metallic TLLE in the resistive layer, the two oblique strips can be decomposed intox and y directions, respectively. Then, the strips along the direction of the electric field incidence can be equivalent to a series of L1, C1, and R1, while the strips perpendicular to the incident direction of the electric field can be denoted by series-parallel connection of L2, R2, and C2. For the bandpass layer, the lossless square ring FSS are presented by the parallel connection of L3 and C3.The reflection/transmission coefficients of the rasorber with 100 Ω and 0 Ω resistors are shown in Figure3. By inserting resistors of 100 Ω, the reflection coefficient of the absorption band drops sharply due to the ohmic loss, but the transmission coefficient of the passband is basically unaffected. Thus, it implements a transmission window within the absorption band. Moreover, to verify the effectiveness of the FSR, the surface current distributions of the TLLE at different operating frequencies are given in Figure 4. As can be seen, at fT, the surface current density of the TLLE resistances is very small, which means that good transmission is achieved. Conversely, at fA1 and fA2, the surface current density is very large, which means good absorption is achieved. Meanwhile, the surface current density of the resistors on each strip is different, which means that only part of the resistors in a certain absorption band mainly absorbs the incident waves.Figure 3
Reflection/transmission coefficients of the rasorber with 100 Ω and 0 Ω resistors.Figure 4
Surface current distributions of the TLLE at different operating frequencies. (a)fA1: lower absorption frequency, (b) fT: parallel resonant frequency, and (c) fA2: higher absorption frequency.
(a)
(b)
(c)The simulation results of reflection/transmission coefficients based on ECM calculations in the ADS and HFSS are shown in Figure5. From the figure, the two curves are basically in good agreement, which further proves the rationality of our design. Different from the simulation structure in the HFSS, there is only one resistance model in the ECM, and its value is set near Z0. Therefore, the total resistance value in HFSS simulation is larger than R1 in ECM simulation. The slight differences in Figure 5 may be due to the loss of the dielectric substrate, which is not considered in the ECM. It is seen that the bandwidth with a reflection coefficient less than −10 dB covers 2.56 GHz to 7.47 GHz and the transmission coefficient at 4.03 GHz is only 0.24 dB under normal incidence.Figure 5
Simulation results of reflection/transmission coefficients based on ECM calculations and HFSS (circuit parameters:L1 = 3.81 nH, C1 = 0.203 pF, R1 = 390 Ω, L2 = 5.05 nH, C2 = 0.633 pF, R2 = 0.5 Ω, L3 = 2.123 nH, C3 = 0.757 pF, and h = 13 mm, for which the corresponding electrical length is 64° at 4.1 GHz).In addition, the reflection/transmission coefficients at different incident angles under TE and TM polarization are studied, as shown in Figure6. The simulation results under two polarizations are basically the same. However, as the oblique incident angle increases to 20°, the performance of the FSR deteriorates due to the generation of the grating lobe, so the model will be ameliorated to solve the problem next.Figure 6
Simulated results of reflection/transmission coefficients of preliminary design under different oblique incidence angles. (a) TE polarization. (b) TM polarization.
(a)
(b)


### 3.2. Miniaturized Design and Performance

To eliminate the problem of performance degradation of the preliminary design at oblique incidence, the strips are folded to reduce the unit cell size, as shown in Figure7. Folding strips are introduced at the bottom of the three legs, which essentially increases the electrical length of the element. Also, the bandpass FSS is replaced by the Jerusalem bandpass FSS, which has a tighter structure. Therefore, its response stability at oblique incidence is improved.Figure 7
(a) Resistive layer on the top of the miniaturized design. (b) Bandpass layer at the bottom of the miniaturized design (geometric dimensions:p = 22 mm, h = 13 mm, w1=0.5mm, w2=1.5mm, w3=0.3mm, d1 = 6 mm, d2 = 0.8 mm, l1 = 8.8 mm, l2 = 2.5 mm, R = 100 Ω, w0=1.96mm, l0 = 18 mm, d0 = 10 mm).
(a)
(b)The performance of the miniaturized design under TE and TM polarization is shown in Figure8. Under normal incidence, the insertion loss is 0.28 dB at 4.16 GHz and 0.22 dB at 4.18 GHz and the fractional width with a reflection coefficient less than −10 dB is 100.1% from 2.47 GHz to 7.5 GHz and 100.9% from 2.57 GHz to 7.8 GHz, for TE and TM polarization, respectively. The results exhibit that the miniaturized structure has a stable response with the incidence angle up to 40°, both for TE and TM polarization. Moreover, the curves have some slight fluctuations around 4.5 GHz due to harmonic resonance at oblique incidence, but anyway, it has little effect on transmission and absorption performance of the FSR.Figure 8
Simulated results of reflection/transmission coefficients of miniaturized design under different oblique incidence angles. (a) TE polarization. (b) TM polarization.
(a)
(b)


## 3.1. Preliminary Design and Performance

A 3-D view of preliminary design based on the above ECM analysis is shown in Figure2(a). Each unit includes a resistive layer on the top and a bandpass layer at the bottom, which are separated by air. A lossy metallic TLLE [1] and a lossless square ring bandpass FSS constitute the resistive layer and the bandpass layer, respectively, as shown in Figures 2(b) and 2(c). The lumped resistors are placed near the end of each strip in the TLLE. Both the two layers are printed on Rogers 4350B with a thickness t and a relative dielectric constant εr.Figure 2
(a) 3-D view of preliminary design. (b) Resistive layer on the top. (c) Bandpass layer at the bottom (geometric dimensions:p = 32 mm, h = 13 mm, w1=0.5mm, w2=1.5mm, w3=0.29mm, d1 = 14 mm, d2 = 0.8 mm, R = 100 Ω, w0=1.72mm, l0 = 20 mm, t = 0.508 mm, and εr = 3.48).
(a)
(b)
(c)For the lossy metallic TLLE in the resistive layer, the two oblique strips can be decomposed intox and y directions, respectively. Then, the strips along the direction of the electric field incidence can be equivalent to a series of L1, C1, and R1, while the strips perpendicular to the incident direction of the electric field can be denoted by series-parallel connection of L2, R2, and C2. For the bandpass layer, the lossless square ring FSS are presented by the parallel connection of L3 and C3.The reflection/transmission coefficients of the rasorber with 100 Ω and 0 Ω resistors are shown in Figure3. By inserting resistors of 100 Ω, the reflection coefficient of the absorption band drops sharply due to the ohmic loss, but the transmission coefficient of the passband is basically unaffected. Thus, it implements a transmission window within the absorption band. Moreover, to verify the effectiveness of the FSR, the surface current distributions of the TLLE at different operating frequencies are given in Figure 4. As can be seen, at fT, the surface current density of the TLLE resistances is very small, which means that good transmission is achieved. Conversely, at fA1 and fA2, the surface current density is very large, which means good absorption is achieved. Meanwhile, the surface current density of the resistors on each strip is different, which means that only part of the resistors in a certain absorption band mainly absorbs the incident waves.Figure 3
Reflection/transmission coefficients of the rasorber with 100 Ω and 0 Ω resistors.Figure 4
Surface current distributions of the TLLE at different operating frequencies. (a)fA1: lower absorption frequency, (b) fT: parallel resonant frequency, and (c) fA2: higher absorption frequency.
(a)
(b)
(c)The simulation results of reflection/transmission coefficients based on ECM calculations in the ADS and HFSS are shown in Figure5. From the figure, the two curves are basically in good agreement, which further proves the rationality of our design. Different from the simulation structure in the HFSS, there is only one resistance model in the ECM, and its value is set near Z0. Therefore, the total resistance value in HFSS simulation is larger than R1 in ECM simulation. The slight differences in Figure 5 may be due to the loss of the dielectric substrate, which is not considered in the ECM. It is seen that the bandwidth with a reflection coefficient less than −10 dB covers 2.56 GHz to 7.47 GHz and the transmission coefficient at 4.03 GHz is only 0.24 dB under normal incidence.Figure 5
Simulation results of reflection/transmission coefficients based on ECM calculations and HFSS (circuit parameters:L1 = 3.81 nH, C1 = 0.203 pF, R1 = 390 Ω, L2 = 5.05 nH, C2 = 0.633 pF, R2 = 0.5 Ω, L3 = 2.123 nH, C3 = 0.757 pF, and h = 13 mm, for which the corresponding electrical length is 64° at 4.1 GHz).In addition, the reflection/transmission coefficients at different incident angles under TE and TM polarization are studied, as shown in Figure6. The simulation results under two polarizations are basically the same. However, as the oblique incident angle increases to 20°, the performance of the FSR deteriorates due to the generation of the grating lobe, so the model will be ameliorated to solve the problem next.Figure 6
Simulated results of reflection/transmission coefficients of preliminary design under different oblique incidence angles. (a) TE polarization. (b) TM polarization.
(a)
(b)


## 3.2. Miniaturized Design and Performance

To eliminate the problem of performance degradation of the preliminary design at oblique incidence, the strips are folded to reduce the unit cell size, as shown in Figure7. Folding strips are introduced at the bottom of the three legs, which essentially increases the electrical length of the element. Also, the bandpass FSS is replaced by the Jerusalem bandpass FSS, which has a tighter structure. Therefore, its response stability at oblique incidence is improved.Figure 7
(a) Resistive layer on the top of the miniaturized design. (b) Bandpass layer at the bottom of the miniaturized design (geometric dimensions:p = 22 mm, h = 13 mm, w1=0.5mm, w2=1.5mm, w3=0.3mm, d1 = 6 mm, d2 = 0.8 mm, l1 = 8.8 mm, l2 = 2.5 mm, R = 100 Ω, w0=1.96mm, l0 = 18 mm, d0 = 10 mm).
(a)
(b)The performance of the miniaturized design under TE and TM polarization is shown in Figure8. Under normal incidence, the insertion loss is 0.28 dB at 4.16 GHz and 0.22 dB at 4.18 GHz and the fractional width with a reflection coefficient less than −10 dB is 100.1% from 2.47 GHz to 7.5 GHz and 100.9% from 2.57 GHz to 7.8 GHz, for TE and TM polarization, respectively. The results exhibit that the miniaturized structure has a stable response with the incidence angle up to 40°, both for TE and TM polarization. Moreover, the curves have some slight fluctuations around 4.5 GHz due to harmonic resonance at oblique incidence, but anyway, it has little effect on transmission and absorption performance of the FSR.Figure 8
Simulated results of reflection/transmission coefficients of miniaturized design under different oblique incidence angles. (a) TE polarization. (b) TM polarization.
(a)
(b)


## 4. Experimental Verification and Discussion

For verification, a prototype of miniaturized design is fabricated using the printed circuit board (PCB) technology, as shown in Figure9. The prototype consists of 1 × 6 unit cells with a size of 22 mm × 132 mm. The unit cell dimensions follow the previous design with a periodic boundary condition. Both the resistive layer and bandpass layer are printed on a 0.508 mm thick Rogers 4350B substrate individually with a relative dielectric constant of 3.48 and a loss tangent of 0.0037. Six chip resistors (CRCW0603100RFKEAC) are soldered to the metal strips of each resistive unit cell. Two substrates are fixed by plastic screws with 13 mm thick air in the middle.Figure 9
Photos of the fabricated rasorber. (a) Assembled structure with plastic screws. (b) Resistive layer on the top (c) Bandpass layer at the bottom.
(a)
(b)
(c)Using a TEM cell, the sample with six unit cells is tested, which is an efficient method to characterize the periodic structures [18]. A photo of the measurement setup in a TEM cell is shown in Figure 10. An Agilent vector network analyzer (VNA) is used for the test. The tapered structures ensure that the tips of the wave top plate are connected to the input and output ports, which have subminiature type A (SMA) connectors. Measurement and simulation results under the normal incidence are shown in Figure 11. For TE polarization, the passband of the FSR sample moves to 4.32 GHz with an insertion loss of 0.73 dB and the fractional width with a reflection coefficient less than −10 dB is 99.5% from 2.65 GHz to 7.9 GHz. For TM polarization, the passband of the FSR sample moves to 4.34 GHz with an insertion loss of 0.71 dB and the fractional width with a reflection coefficient less than −10 dB is 98.2% from 2.73 GHz to 8 GHz. The differences between the simulation and measurement results may be due to the fabrication tolerance of the PCB and the inevitable loss in the test.Figure 10
Photograph of the measurement setup in a TEM cell.Figure 11
Measurement and simulated results under the normal incidence. (a) TE polarization. (b) TM polarization.
(a)
(b)To better understand the performance of our design, the insertion loss of the transmission band, fractional bandwidth (FBW) of −10 dB reflection, periodicity, number of lumped elements in one unit cell, and angular stability are compared with similar designs in the latest literature, as shown in Table1. Our design, comparatively, has the lowest insertion loss in the transmission band and the least lumped elements in a unit cell, which means our rasorber has a good transmission performance and simple structure. Moreover, our rasorber has minimal periodicity except for the 3-D structure in [17], meaning a smaller profile and a more stable angular response. However, the only drawback is that the FBW of our designed rasorber is not the biggest, meaning that the absorption band is not the widest, which also needs to be further improved in the future research.Table 1
Performance comparison.
Reference
Transmission band (fT)/IL
FBW (%)
Periodicity
Number of lumped elements
Angular stability
[11]
4.42 GHz/−0.68 dB
92.3
0.37λt
18
0–30°
[12]
3.54 GHz/−0.92 dB
116.9
0.3λt
8
0–40°
[14]
6.62 GHz/−0.4 dB
98.8
0.44λt
16
0–45°
[15]
4.25 GHz/−0.26 dB
101
0.35λt
8
0–30°
[16]
10.3 GHz/−0.3 dB
108.3
0.52λt
8
0–45°
[17]
2.2 GHz/−0.5 dB
114.1
0.18λt
8
0–40°
This work
4.18 GHz/−0.22 dB
101
0.31λ
t
6
0–40°
Ref. = reference number, IL = insertion loss, FBW = fractional bandwidth of −10 dB reflection, andλt = free space wavelength at the transmission frequency fT.


## 5. Conclusions

A novel simple and stable low-profile rasorber with good transmissive property within a wide absorption band is proposed in this paper. The ECM is firstly analyzed which provides more insight into the FSS behavior. A lossy metallic TLLE is then chosen to implement the resistive layer, thus avoiding complex and expensive structures. Furthermore, the use of folded strips and Jerusalem structure reduces the size of the unit cell, making the angular response of the FSR more stable. Finally, the prototype is fabricated and the agreement between the measurement results and the simulation results proves the correctness of our design.



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*Source: 9878607-2020-01-09.xml*