Design of 2.5D Miniaturized Broadband Absorber for Ultrahigh-Frequency Band

Abstract

A broadband metamaterial absorber (MA) structure for Ultrahigh-Frequency (UHF) band was proposed, and the miniaturization of the unit was realized by combining the method of bending metal wires and loading metal vias. The size of the unit cell is 0.040 λ_L × 0.040 λ_L × 0.075 λ_L (λ_L is the wavelength corresponding to the lowest frequency of 0.5 GHz). The simulation results show that the bandwidth of the MA is from 0.50 GHz to 1.33 GHz, and the relative bandwidth is 90.7%. Polarization insensitivity of the MA was realized through assembling a 2 × 2 orthogonal array. TE and TM polarizations maintain more than 80% of the absorptance in the range of 40° at oblique incidence. The consistency of full-wave simulation, circuit simulation and measured results is high, which verifies the broadband absorption characteristics of the proposed MA.

1. Introduction

Since Landy successfully designed the first MA [1], rich research results of MAs have been accumulated in terms of structural forms and design principles. However, current researches on stealth materials mainly focus on X and Ku bands [2,3,4], while researches on UHF band are less. It is because the attenuation constant of the material decreases significantly at low frequency, and the electrical size corresponding to the low frequency is relatively large, which is difficult to meet the need for miniaturization in practical applications.

Combined with current research, the low-frequency technology of MAs can be divided into two categories. One is to lower the position of the resonance point by lumped elements, and the other is to use the convolution geometry method to increase the length of metal wire by bending, winding, etc. In 2017, Xuan K B et al. proposed a design method of absorbers loaded by capacitors [5]. Four lumped capacitors embedded between metal patches effectively lower the resonant frequency. Experimental results show that the structure achieves perfect absorption at 102 MHz, and the unit size is reduced to 35 × 35 mm². Then, in order to verify the contribution of capacitors to the resonant frequency regulation, two capacitors with different capacitance values were loaded into the unit [6] so that the MA realized double absorption peaks at 304.9 MHz and 358.5 MHz. Inductors were also applied in low-frequency technology research of MAs. Jeong H et al. [7] connected the metal square ring with four inductors and indicated that the absorption frequency was inversely proportional to the inductance value of the inductors. In addition, Buitung S innovatively proposed an hourglass-type absorber structure on the basis of curved lines [8], which can obtain a narrow-band absorption peak near 377 MHz. Araneo R et al. designed a complex helical unit structure by using tightly arranged helical lines to enhance the coupling effect in MA [9] and achieved perfect absorption at 395 MHz. Although the above designs achieve low-frequency absorption, it is a common problem that the bandwidths of designed MAs are not wide enough. In 2016, a compact MA for the UHF band was designed in [10], and it bends the square metal ring loaded with resistors inward several times. Without affecting the frequency response, it reduces the unit size to a quarter of the metal square ring, but the absolute bandwidth of the MA is only 150 MHz. In order to improve the bandwidth, the bending method of metal wires, the number of lumped resistors and the thickness of the air layer were further optimized in [11], thereby introducing more resonance points in MA. The research successfully realizes a low-frequency broadband MA operating from 0.8 GHz to 2.7 GHz.

The above research results enrich the design ideas of low-frequency MAs, but they are all optimized based on traditional 2D structures. In recent years, 3D structures [12,13] and 2.5D structures [14,15,16,17] have been widely used in the design of metamaterials. Unlike 3D structures, 2.5D structures show wide-band and low-frequency characteristics without changing the profile height. Typical structures of 2.5D are proposed in [14,15]. Metal vias can increase the capacitance and inductance in the equivalent circuit. In addition, it can connect a longer circuit in MA, which is conducive to the realization of low-frequency. With a systematic study of the equivalent circuit with metal vias [16], Yi-min et al. introduced vertical vias into the design of frequency selective surface and proposed the calculation formula of equivalent capacitance and equivalent inductance. In addition, the research verifies the great potential of metal vias in low-frequency characteristics through simulation and measurement. On this basis, 36 metal vias were introduced in MA, further reducing the resonant frequency to 1890 MHz [17].

In this paper, a MA structure for the UHF band based on 2.5D is proposed, which can achieve more than 90% absorptance in the range from 500 MHz to 1330 MHz. We established a simplified equivalent circuit model and verified the simulation results experimentally. According to simulation and measurement results, the proposed MA achieves the comprehensive performance of wide-band, miniaturization, low frequency and low profile. On the one hand, it can effectively reduce electromagnetic interference and improve the complex electromagnetic environment. Thus, it can improve stability when applied to UHF-RFID systems. In addition, the proposed MA can also be applied to the field of stealth in the UHF band, absorbing electromagnetic waves reflected in the environment to achieve perfect stealth.

2. Unit Cell Design and Simulation

By combining the methods of bending lines and metal vias, a 2.5D double-layer MA unit was proposed. As shown in Figure 1a, layers composing the unit structure from top to bottom are Metal-Layer I, Dielectric-Layer I, Metal-Layer II, Dielectric-Layer II, Metal-Layer III, Air-Layer and Reflection-Layer. Figure 1b,c show the structures of the three Metal-Layers. The structures of Metal-Layer I and Metal-Layer III are completely the same, and they are orthogonal to Metal-Layer II in the middle. The purple and green patches in Figure 1b are resistors with values R_a = 91 Ω and R_b = 100 Ω. It can be seen that resistors are only designed on the Metal-Layer I and the Metal-Layer III. This is because the Metal-Layer II is located between the double Dielectric-Layers, and it is not suitable to load lumped elements with thickness during the fabrication. Metal-Layers are arranged on the upper and lower surfaces of the Dielectric-Layers and connected by multiple metal vias to form a closed loop in Figure 1d. Unlike 3D structures, the introduction of vias does not increase the profile height of the MA, so it is called a 2.5D structure. Metal holes passing through the Dielectric-Layers connect the upper and lower circuits, and it means that metal patches can be designed as longer loops in the same unit, increasing the level of miniaturization of MA.

Figure 1e shows the multi-layer structure of the MA unit cell. In order to achieve better low-frequency characteristics, the MA is laminated with double FR4 (ε_r1 = 4.4, tanδ = 0.2) Dielectric-Layers, and the thickness of the single Dielectric-Layer is h₁/2 = 2.4 mm. The Air-Layer (ε_r0 = 1.0) with a thickness of h₀ = 40 mm is located between the Dielectric-Layer and the Reflection-Layer, which is conducive to the realization of broadband matching with free space. Due to the symmetry of the MA, we only marked geometry dimensions of one-eighth of the bend line on the top view of Figure 1f. Simulation settings of the MA in HFSS are shown in Figure 1a. The MA is excited by a floquet port, and the sides of the unit are set to the master and slave boundary. The geometric parameters in MA were adjusted to achieve the best broadband characteristics, and the final geometric dimensions are optimized as: a₁ = 8.4 mm, a₂ = 5.6 mm, a₃ = 2.4 mm, a₄ = 6.6 mm, b₁ = 2.4 mm, b₂ = 5.6 mm and b₃ = 4 mm. In addition, the period of the MA is p = 23.8 mm, and the width of the wire is w = 0.5 mm.

Simulation results of the MA are shown in Figure 2. Due to the existence of the Reflection-Layer, the absorptance can be calculated by $A\left(\omega \right)=1-R\left(\omega \right)=1-{\left|S_{11}\right|}^2$. It can be seen that the bandwidth of TE mode is 0.47 GHz to 1.00 GHz, and that of TM mode is 0.47 GHz to 1.06 GHz. The absorption peaks are formed around 550 MHz and 880 MHz in both modes, but trends of reflection coefficient curves are quite different. It is because three Metal-Layers are not completely identical. Generally speaking, such MAs without quadruple rotational symmetry are polarization-sensitive.

Next, we further eliminated the polarization sensitivity of the MA by forming arrays. As shown in Figure 3, we rotated the MA1 along the Z-axis to obtain the orthogonal unit MA2 and stagger them on a 2 × 2 array. MA1 and MA2 have negligible phase differences to plane incident waves under infinite-period boundary conditions. Therefore, the arrayed MAs can produce nearly equal absorption for TE and TM modes when the array scale is large enough.

From the simulation results in Figure 4, the bandwidth of the proposed structure meeting the requirements of the absorptance above 90% is 500 MHz to 1330 MHz, and the relative bandwidth is 90.7%. The MA unit cell is miniaturized through wire bending. The unit cell size is 23.8 mm × 23.8 mm, and the profile height is 44.8 mm. Two absorption peaks of the arrayed MA are formed at F_L = 0.59 GHz and F_H = 1.13 GHz with reflection coefficients of −19.6 dB and −22.7 dB and absorptance of 98.9% and 99.5%. It is due to the blocking effect of resistors with different resistance values, which cuts the closed-loop into current paths of different lengths, which can further adjust the position of F_L and F_H to realize broadband absorption at low frequency. It can be seen that the curves at different polarizations basically coincide, and the arrayed MAs achieve polarization insensitivity.

Figure 5 shows the simulated absorptance curves of TE and TM polarizations at different oblique incident angles. As shown in Figure 5a, with the increase in oblique incident angle, the position of F_L in TE polarization basically does not change, while F_H gradually moves slightly to a high frequency. In addition, the absorptance gradually decreased within the bandwidth, and the depression between F_L and F_H gradually deepened. Different from TE polarization, the absorption curve of TM polarization has a more obvious blue shift under oblique incidence, and the low-frequency characteristics are gradually lost. In general, the 2.5D structure maintains more than 80% of the absorptance under the incident angle of 40° and has good oblique incidence stability.

3. Absorption Mechanism

We proposed a simplified equivalent circuit model based on transmission-line theory. As shown in Figure 6, the bent metal wire is composed of two parallel resonant loops in series. The Dielectric-Layer and Air-Layer are equivalent to uniform transmission lines, and the Reflection-Layer is represented by a short-circuit line.

Section A in Figure 6 represents the transmission line in free space, which characteristic impedance is Z₀ = 377 Ω, and the electromagnetic wave of normal incidence enters the surface of the MA through A. Section B is the Metal-Layers in MA. LP1 and LP2 loops generate low and high-frequency resonance points, respectively, whose admittances are represented by Y_LP1 and Y_LP2. The coupling effect of metalized vias between adjacent units is represented by the supplementary capacitance C_via. Sections C and D are equivalently modeling the Dielectric-Layer and Air-Layer. Sections C simulates a transmission line with characteristic impedance Z1 and length h₁. Sections D simulates a transmission line with characteristic impedance Z₀ and length h₀.

The admittances of LP1, LP2 loops and C_via are expressed as follows.

$$Y_{LP1}=\frac{1}{R_1+jw{L}_1}+j\omega C_1$$

(1)

$$Y_{LP2}=\frac{1}{R_2+jw{L}_2}+j\omega C_2$$

(2)

$$Y_{via}=j\omega C_{via}$$

(3)

so

$$Y_{LP}=\frac{1}{\frac{1}{Y_{LP1}}+\frac{1}{Y_{LP2}}+\frac{1}{Y_{via}}}=G_{LP}+j{B}_{LP}$$

(4)

According to transmission-line theory, Y_d is expressed as

$$\begin{array}{c}{Y}_d=Y_1\cdot \frac{\left(-j{Y}_0\cdot \cot \left({\beta }_0\cdot h_0\right)\right)+j{Y}_1\cdot \tan \left({\beta }_1\cdot h_1\right)}{Y_1+j\left(-j{Y}_0\cdot \cot \left({\beta }_0\cdot h_0\right)\right)\cdot \tan \left({\beta }_1\cdot h_1\right)}\\ =j\frac{Y_1\left(Y_1\cdot \tan \left({\beta }_1\cdot h_1\right)-Y_0\cdot \cot \left({\beta }_0\cdot h_0\right)\right)}{Y_1+Y_0\cdot \cot \left({\beta }_0\cdot h_0\right)\cdot \tan \left({\beta }_1\cdot h_1\right)}=j{B}_d\end{array}$$

(5)

Y₀ and Y₁ are the admittance forms corresponding to the characteristic impedances Z₀ and Z₁. The admittance corresponding to the input impedance Z_in of the MA can be expressed as.

$$Y_{\mathrm{in}}=\frac{1}{Z_{\mathrm{in}}}=\frac{1}{Z_d}+\frac{1}{Z_{LP}}=Y_d+Y_{Lp}=G_{LP}+j\left(B_d+B_{LP}\right)$$

(6)

where, $Y_i=Y_0\cdot \sqrt{{\epsilon }_{r_i}}, {\beta }_i=2\pi \sqrt{{\epsilon }_{ri}}/\lambda$, $i=0,1,w=2\pi f$, $Y_0=1/Z_0=1/377S$. According to the transmission-line theory mentioned above, the reflection coefficients of the model at discrete points are calculated in ADS, and the simulation results of each discrete point are fitted into a smooth reflection coefficient curve. Then, the parameter values of the lumped elements in the circuit model are optimized to achieve the minimum error between the circuit and the full-wave simulations. The circuit component values in the model are optimized as follows: R₁ = 85 Ω, C₁ = 0.85 pF, L₁ = 18 nH, R₂ = 60 Ω, C₁ = 0.20 pF, L₁ = 3.6 nH and C_via = 1.20 pF. To verify the accuracy of the model, we compare the results of ADS circuit simulation and HFSS full-wave simulation in Figure 7. The results show that the variation trend of the absorption curve in bandwidth is consistent with the full-wave simulation. The working bandwidth of the circuit simulation is 515 MHz to 1310 MHz, and the positions of the two absorption peaks basically coincide.

In order to further understand the generation mechanism of the double resonance point, we studied the real and imaginary parts of Y_in in the equivalent circuit. According to Equations (4) to (6), we plotted the curves of G_LP, B_d, B_LP and B_d plus B_LP in Figure 8. It can be seen in Figure 8a that the sum of B_d and B_LP is 0 at f₁ = 600 MHz, f₂ = 762 MHz and f₃ = 1089 MHz, which means that the imaginary part of Y_in is 0. In general, the real part of the impedance that can generate resonance should match Z₀, and the conductance range corresponding to (377 ± 50) Ω is marked in the gray part shown in Figure 8b. The conductance of f₁ and f₃ are within the matching range of the free space, which is basically consistent with F_L and F_H in full-wave simulation. However, the G_LP at f₂ is about 0.005, corresponding to a characteristic impedance of about 200 Ω. It is quite different from the characteristic impedance of free space, resulting in a mismatch, so there is no absorption peak at f₂.

4. Experiment Results and Discussions

As shown in Figure 9a,b, the MA is fabricated with a dimension of 400 mm × 400 mm (16 cells × 16 cells), and Teflon nuts and bolts are used to control the thickness of the air gap. The measurement system of the fabricated absorber is shown in Figure 9d, and the reflection coefficient of the sample in free space was measured with a log-periodic antenna operating from 0.4 GHz to 3 GHz.

Calibrate the environment with a metal aluminum plate of the same scale, and the difference between it and the fabricated MA is the true reflection coefficient of the sample. As shown in Figure 10, the measured reflection coefficient less than −10 dB under normal incidence is from 535 MHz to 1310 MHz. Compared with simulation results, it can be seen that the bandwidth and the position of the F_L and F_H in experimental results are basically accurate. However, the absorptance of the experiment results is generally lower. It is because the copper adsorbed on the surface of the through-hole during fabrication is not uniform enough, which leads to the poor conduction effect of some circuits, thus causing errors during the experiment.

5. Conclusions

In this paper, a miniaturized structure of a low-frequency broadband MA was proposed. The structure connects the upper and lower surface circuits of the double-layer dielectric layer through metal holes. The size of the unit cell is 23.8 × 23.8 mm², realizing the miniaturization of the MA. The absorption band of the MA is from 0.50 GHz to 1.33 GHz, and the unit cell forms two absorption peaks at F_L and F_H and the corresponding absorptance is 98.9% and 99.5%, respectively. With the help of the simplified equivalent circuit model, the study further analyzed the generation of double absorption peaks and physically validated the sample by the free space method.

Table 1. Comparison of the proposed MA with few published MAs.

Ref.	MA Unit Structure			MA Unit Performance
	Design Dimension	Lumped Element	Bending Wires	Absorption Band	Relative Bandwidth	Unit Size	Profile Height
[5]	2.5D	Yes (C)	No	102 MHz	/	0.012 λL × 0.012 λL	0.001 λL
[7]	2D	Yes (L)	No	2400 MHz	/	0.027 λL × 0.027 λL	0.043 λL
[8]	2D	No	Yes	377 MHz	/	0.056 λL × 0.045 λL	0.014 λL
[9]	2D	No	Yes	395 MHz	/	0.014 λL × 0.014 λL	0.011 λL
[10]	2D	Yes (R)	Yes	840–990 MHz	16.3%	0.056 λL × 0.056 λL	0.060 λL
[11]	2D	Yes (R)	Yes	800–2700 MHz	108.5%	0.053 λL × 0.053 λL	0.071 λL
[18]	2D	Yes (R)	Yes	1350–3500 MHz	88.7%	0.090 λL × 0.090 λL	0.097 λL
[19]	2.5D	Yes (R)	No	1100–2000 MHz	58.1%	0.257 λL × 0.257 λL	0.088 λL
our work	2.5D	Yes (R)	Yes	500–1330 MHz	90.7%	0.040 λL × 0.040 λL	0.075 λL

λ_L is the wavelength corresponding to the lowest frequency. C stands for capacitor, L stands for inductor and R stands for resistor.

compares the performance of the MA with other related research results. It can be seen that although the structure proposed in reference [9] achieves a larger absorption bandwidth, our work achieves absorption at a lower frequency band and successfully reduces the low-frequency response by 300 MHz, which is extremely challenging in the UHF band. Therefore, the proposed MA combines the advantages of low-frequency, miniaturization and broadband. It is expected to be widely used in the field of UHF stealth technology.