# Design of Wideband Absorber Based on Dual-Resistor-Loaded Metallic Strips

Authors: Mingxi Zhang; Binchao Zhang; Xiaochun Liu; Shining Sun; Cheng Jin
Journal: International Journal of Antennas and Propagation
 (2020)

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## Abstract

A method for designing a dual-polarized wideband absorber with low profile by using dual-resistor-loaded metallic strips is proposed in this paper. Each unit cell consists of a resistive sheet with dual-resistor-loaded metallic strips and an underlying conducting plate. Two-dimensional arrays of two unequal metallic strips are printed on the dielectric substrate, and two resistors are embedded in the metallic strips. By properly designing the resonant frequencies of these metallic strips, a wide absorption band with three resonances is obtained. An equivalent circuit model is introduced, and the current distributions are examined to understand the physical mechanism of the proposed absorber. An example of the absorber is fabricated and measured to verify our designed concept. The measured results show that the wideband absorption performance with a fractional bandwidth of 129% under the normal incidence and the stable angular response are achieved. In addition, the proposed absorber has a low profile with 0.08λL, where λL is the wavelength at the lowest operating frequency.


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## Body

## 1. Introduction

Electromagnetic (EM) absorbers have been an intriguing area for their miscellaneous applications, such as improving electromagnetic compatibility of the integrated circuits, eliminating electromagnetic interferences in complicated environments, and being adapted as the chipless radio-frequency indemnification tags [1–3]. Most applications of EM absorbers require wide bandwidth and low profile with more than 10 dB reflection reduction, which limits the extensive usage of classic absorbers, such as Salisbury screens [4] or multilayer Jaumann absorbers [5]. The theoretical minimum thickness for a given absorption performance was depicted in [6], which motivated the development of the frequency selective surface (FSS) pattern used in the lossy layer of the absorber [7].The circuit analog (CA) absorber with a lossy FSS printed on a low-loss substrate backed by a perfect conducting plane is an attractive candidate to approximate the Rozanov limit. In the past, the perception of multiple resonances was employed to widen the absorption bandwidth [8–11]. For the single-layer CA absorber, the design in [12] has achieved a wide absorption bandwidth with three resonances. Similarly, two-layer configuration and loop arrays embedded with chip resistors were utilized to build a wide absorption band [13, 14]. An alternative design, replacing the RLC resonating circuits with low-pass RC circuits, was proposed to design wideband absorbers utilizing multilayer structures with the overall thickness approximating the Rozanov limit [15, 16].Except the aforementioned planar absorber, a new structure named three-dimensional (3D) absorber is another effective approach to obtain wide absorption band [17]. The cavity along the z-direction is utilized to establish the absorption band, and the energy is absorbed by the multiple resonant modes in the air and substrate regions [18]. However, it usually needs a relatively thick profile to accommodate the multiresonant structure, and it also has a complex configuration. In addition, active absorbers provide potentials to break the Rozanov limit [19]. Negative inductors were used for actively matching the equivalent inductance of the thin conductor-backed spacer, and the bandwidth ratio could be larger than 6 : 1 with the thickness of only 0.015λL, where λL is the wavelength at the lowest operating frequency. Unfortunately, the negative inductors are nonnatural devices, and they are difficult to be realized.In this paper, the design of dual-polarized and wideband absorber with two unequal dual-resistor-loaded metallic strips is presented. The lossy layer of the unit cell consists of two orthogonal strips printed on both sides of a dielectric substrate, and two-dimensional arrays of two unequal resistor-loaded metallic strips are printed on each side of the dielectric substrate. By properly designing the resonant frequencies of these two metallic strips, a wide absorption band with three resonances is obtained. An equivalent circuit model is introduced, and the current distributions along the strips are examined to demonstrate the physical mechanism of the proposed absorber with three resonant frequencies. In order to verify our design concept, an example is designed and fabricated, which shows a wideband absorption performance for dual polarizations and stable angular response.


## 2. Design and Analysis

### 2.1. Configuration of the Unit Cell

As a component of the CA absorber, the lossy layer plays an important role in impedance matching at the interface between the absorber and the air space, and it needs to be carefully designed for wideband performance. Then, the incident EM wave will be absorbed by the resistive component in the lossy layer. In our proposed structure, the lossy layer is implemented by the resistor-loaded frequency selective surface, and its geometry is illustrated in Figure1. In each unit cell, the lossy layer consists of two orthogonal components printed on both sides of a dielectric substrate with a relative dielectric constant εr of 4.4, loss tangent tanδ of 0.02, and thickness t of 0.5 mm to realize a dual-polarized absorber, as shown in Figures 1(a) and 1(b). On each side, there are two shorter dual-resistor-loaded metallic strips with the length l2 of 9.5 mm symmetrically located on either side of a dual-resistor-loaded metallic strip with the length l1 of 27 mm arranged diagonally, and the distance d between these two types of metallic strips is 8 mm. In addition, the width w of the metallic strip is 0.5 mm, the period p of the unit cell is 20 mm, and the thickness h of the air spacer is 8 mm. Moreover, a conducting plate is placed under the lossy layer to keep a good absorption performance.Figure 1
Configuration of the designed absorber. (a) Top surface of the substrate. (b) Bottom surface of the substrate. (c) Side view. (d) 3D view.p=20, h=7.5, l1=27, l2=9.5, d1=1.5, d2=2.5, d=8, w=0.5, and t=0.5 (all dimensions are in mm).
(a)(b)(c)(d)


### 2.2. Operating Principle

In order to intuitively understand the absorption mechanism, the equivalent circuit model of the proposed absorber is given, as shown in Figure2. It is found that the lossy layer is equivalent to a pair of parallel RLC circuits, and it is connected with the ground across a transmission line circuit. Two resistor-loaded metallic strips will result in two series RLC circuits in parallel [20]. In the circuit, R1, L1, and C1 represent the equivalent resistance, inductance, and capacitance of the longer metallic strip, respectively, while R2, L2, and C2 denote those of shorter metallic strips. In addition, the short-circuited transmission line with electric length θ represents the grounded air spacer.Figure 2
Equivalent circuit model of the proposed absorber for normal incidence with TE polarization.Then, the input admittanceYin of the proposed absorber can be expressed as(1)Yin=∑i=121Ri+jωLi−1/ωCi−jY0cotβh,where β=2π/λ is the wavenumber and Y0 is the characteristic admittance of the free space. The initial values of L1, C1, L2, and C2 under normal incidence can be obtained from their geometric relationship, which has been studied in detail [21]:(2)XLZ0=lλlncscπw2p+Gp,w,λ,where Z0 is the characteristic impedance of the free space,l and w are the length and width of the metallic strip, respectively, and Gp,w,λ is the correction term available, which is studied minutely in [22, 23].Therefore, the reflection coefficient of the proposed absorber can be calculated as(3)Γ=Zin−Z0Zin+Z0=ZinRe−Z0+jZinImZinRe+Z0+jZinIm,where Zin=1/Yin is the input impedance and ZinRe and ZinIm are the real and the imaginary part of the input impedance. In order to realize a good absorption performance in a wide frequency band, the reflection coefficient needs to approach zero in the operating frequency band, which can be satisfied when(4)Γ=0⟶ZinRe=Z0,ZinIm=0.The simulated input impedance of the proposed absorber is shown in Figure3. The real part of input impedance oscillates around 377 Ω, and three peaks appear at f1, f2, and f3. In addition, the imaginary part oscillates around zero; thus, the reflection coefficient equals to zero in the operating frequency band according to (4). Then, the incident wave will illuminate the absorber with no reflection and be absorbed by the resistive components finally.Figure 3
Input impedance of the proposed absorber.Figure4 compares the absorption performances of the equivalent circuit model and ANSYS HFSS simulation under the normal incidence, which exhibits a good agreement. Additionally, the cross-polarized reflection coefficient of the absorber is also shown to indicate a negligible cross-polarization response. The dimensions of the proposed absorber are carefully designed to achieve a good absorption performance. The initial values of lumped inductances and capacitances utilized in the equivalent circuit model are obtained using the formulas presented in [21–23] as the following values: L1=19.1 nH, C1=0.017 pF, L2=7.17 nH, and C2=0.081 pF.Figure 4
Simulated and calculated reflection coefficients of the proposed absorber.The simulated result shows that a wide absorption band is obtained from 3.08 to 14.02 GHz, and the absorptivity is greater than 90% in the absorption band. It should be mentioned that the absorptivity is calculated as1−Γ2 because of the existence of the conducting plane. Furthermore, there are three reflection zeros in the absorption band, namely, f1=3.64 GHz, f2=8.32 GHz, and f3=12.96 GHz.The simulated current distributions of the proposed absorber at three reflection zeros are shown in Figure5 to gain physical insight into the existence of three resonances. Without loss of generality, we assume that the incident field is TE-polarized, and its amplitude is 1 V/m. It is found that the resonance at f1 is mainly caused by the fundamental resonant mode of the central longer metallic strip, as shown in Figure 5(a). We can observe that a wave antinode is generated in the center, and the current will pass through the embedded resistors and be consumed finally. The resonant frequency can be calculated by(5)f=c2l∗εr,eff,where l is the length of the metallic strip, c is the velocity of light, and εr,eff is the effective relative permittivity, which was calculated in [13].Figure 5
Simulated current distributions of the proposed absorber at three resonant frequencies of (a)f1 = 3.64 GHz, (b) f2 = 8.32 GHz, and (c) f3 = 12.96 GHz.
(a)(b)(c)In addition, Figures5(b) and 5(c) depict the current distributions at f2 and f3, which are corresponding to the first odd resonant mode with two wave antinodes of the central longer metallic strip and the fundamental mode with one wave antinode of the shorter metallic strip, respectively. We can also observe that slight currents are excited on two shorter metallic strips at the resonant frequency f2, and the same situation happens at the resonant frequency f3, which is caused by the coupling between two metallic strips at these two resonant frequencies.It is well known that the first odd resonance cannot be excited under normal incidence [7] because the symmetric current with opposite directions generated in a receiving dipole-like metallic strip counteracts each other at the resonant frequency. However, our proposed structure can be considered as a superposition of two asymmetrical-dipole-like metallic strips, and two chip resistors are inserted at different feeding ports. The current excited at the first odd resonance is asymmetrical, as shown in Figure 5(b), resulting in a nonzero current [11]. Then, two resistors are loaded on the metallic strip in our proposed structure to realize the excitement of the first odd resonance.


### 2.3. Parameter Discussion

According to the analysis of the operating principle in Section2.2, four parameters are studied here to reveal their effect on the resonant characteristic of the proposed absorber, which are the lengths l1 and l2 of the metallic strips and the resistive values R1 and R2 of the embedded chip resistors.The values of loaded dual-chip-resistors should be optimized carefully to achieve a superior absorption performance. Figure6 shows different frequency responses with various values of the chip resistor. There are two degrees of freedom that one of the two chip resistors is tuned when another is fixed. Figure 6(a) exhibits that the value of R1 influences the frequency response of the longer metallic strip, and the absorption performance is good when R1 is set to 120 Ω. On the contrary, the value of R2 can impact the frequency response of shorter metallic strips, as shown in Figure 6(b), and it is chosen to 70 Ω to get a wider absorption band and good absorption performance.Figure 6
Different frequency responses of the proposed absorber with various values of chip resistors. (a) Different values ofR1. (b) Different values of R2.
(a)(b)Figure7 indicates the variation of the reflection zeros with different values of the length l1 of the longer strip and l2 of the shorter strip. The reflection zero of f1 and f2 shifts to a lower frequency and f3 almost unchanged when l1 increases, as shown in Figure 7(a). Because f1 and f2 are the fundamental and the first odd resonant mode of the longer strip, increasing l1 will enlarge the resonant wavelength. Figure 7(b) illustrates the influence on three reflection zeros when l2 increases; it is found that f2 and f3 move to a lower frequency while f1 is fixed. Increasing l2 will result in a large resonant wavelength of the shorter strip, and it will also increase the resonant wavelength of the longer strip because of the coupling between these two strips.Figure 7
Variations of the reflection zero frequencies in the absorption band with respect to (a) the lengthl1 of the longer strip and (b) the length l2 of the shorter strip.
(a)(b)Then, a wideband absorption performance can be obtained with properly designed aforementioned parameters, as shown in Figure4. For the certain performance of absorption, including the bandwidth and absorptivity, there is a physical boundary for the thickness of the nonmagnetic absorber, defined as Rozanov limit [6]:(6)RL≥∫0∞lnΓλdλ2π2,where RL is the Rozanov limit and Γλ is the reflection coefficient of the wavelength response. In this paper, our designed absorber has the Rozanov limit of 7.36 mm calculated by (6). Compared with the realized thickness of the absorber, there is only 8% thicker than the Rozanov limit.


## 2.1. Configuration of the Unit Cell

As a component of the CA absorber, the lossy layer plays an important role in impedance matching at the interface between the absorber and the air space, and it needs to be carefully designed for wideband performance. Then, the incident EM wave will be absorbed by the resistive component in the lossy layer. In our proposed structure, the lossy layer is implemented by the resistor-loaded frequency selective surface, and its geometry is illustrated in Figure1. In each unit cell, the lossy layer consists of two orthogonal components printed on both sides of a dielectric substrate with a relative dielectric constant εr of 4.4, loss tangent tanδ of 0.02, and thickness t of 0.5 mm to realize a dual-polarized absorber, as shown in Figures 1(a) and 1(b). On each side, there are two shorter dual-resistor-loaded metallic strips with the length l2 of 9.5 mm symmetrically located on either side of a dual-resistor-loaded metallic strip with the length l1 of 27 mm arranged diagonally, and the distance d between these two types of metallic strips is 8 mm. In addition, the width w of the metallic strip is 0.5 mm, the period p of the unit cell is 20 mm, and the thickness h of the air spacer is 8 mm. Moreover, a conducting plate is placed under the lossy layer to keep a good absorption performance.Figure 1
Configuration of the designed absorber. (a) Top surface of the substrate. (b) Bottom surface of the substrate. (c) Side view. (d) 3D view.p=20, h=7.5, l1=27, l2=9.5, d1=1.5, d2=2.5, d=8, w=0.5, and t=0.5 (all dimensions are in mm).
(a)(b)(c)(d)


## 2.2. Operating Principle

In order to intuitively understand the absorption mechanism, the equivalent circuit model of the proposed absorber is given, as shown in Figure2. It is found that the lossy layer is equivalent to a pair of parallel RLC circuits, and it is connected with the ground across a transmission line circuit. Two resistor-loaded metallic strips will result in two series RLC circuits in parallel [20]. In the circuit, R1, L1, and C1 represent the equivalent resistance, inductance, and capacitance of the longer metallic strip, respectively, while R2, L2, and C2 denote those of shorter metallic strips. In addition, the short-circuited transmission line with electric length θ represents the grounded air spacer.Figure 2
Equivalent circuit model of the proposed absorber for normal incidence with TE polarization.Then, the input admittanceYin of the proposed absorber can be expressed as(1)Yin=∑i=121Ri+jωLi−1/ωCi−jY0cotβh,where β=2π/λ is the wavenumber and Y0 is the characteristic admittance of the free space. The initial values of L1, C1, L2, and C2 under normal incidence can be obtained from their geometric relationship, which has been studied in detail [21]:(2)XLZ0=lλlncscπw2p+Gp,w,λ,where Z0 is the characteristic impedance of the free space,l and w are the length and width of the metallic strip, respectively, and Gp,w,λ is the correction term available, which is studied minutely in [22, 23].Therefore, the reflection coefficient of the proposed absorber can be calculated as(3)Γ=Zin−Z0Zin+Z0=ZinRe−Z0+jZinImZinRe+Z0+jZinIm,where Zin=1/Yin is the input impedance and ZinRe and ZinIm are the real and the imaginary part of the input impedance. In order to realize a good absorption performance in a wide frequency band, the reflection coefficient needs to approach zero in the operating frequency band, which can be satisfied when(4)Γ=0⟶ZinRe=Z0,ZinIm=0.The simulated input impedance of the proposed absorber is shown in Figure3. The real part of input impedance oscillates around 377 Ω, and three peaks appear at f1, f2, and f3. In addition, the imaginary part oscillates around zero; thus, the reflection coefficient equals to zero in the operating frequency band according to (4). Then, the incident wave will illuminate the absorber with no reflection and be absorbed by the resistive components finally.Figure 3
Input impedance of the proposed absorber.Figure4 compares the absorption performances of the equivalent circuit model and ANSYS HFSS simulation under the normal incidence, which exhibits a good agreement. Additionally, the cross-polarized reflection coefficient of the absorber is also shown to indicate a negligible cross-polarization response. The dimensions of the proposed absorber are carefully designed to achieve a good absorption performance. The initial values of lumped inductances and capacitances utilized in the equivalent circuit model are obtained using the formulas presented in [21–23] as the following values: L1=19.1 nH, C1=0.017 pF, L2=7.17 nH, and C2=0.081 pF.Figure 4
Simulated and calculated reflection coefficients of the proposed absorber.The simulated result shows that a wide absorption band is obtained from 3.08 to 14.02 GHz, and the absorptivity is greater than 90% in the absorption band. It should be mentioned that the absorptivity is calculated as1−Γ2 because of the existence of the conducting plane. Furthermore, there are three reflection zeros in the absorption band, namely, f1=3.64 GHz, f2=8.32 GHz, and f3=12.96 GHz.The simulated current distributions of the proposed absorber at three reflection zeros are shown in Figure5 to gain physical insight into the existence of three resonances. Without loss of generality, we assume that the incident field is TE-polarized, and its amplitude is 1 V/m. It is found that the resonance at f1 is mainly caused by the fundamental resonant mode of the central longer metallic strip, as shown in Figure 5(a). We can observe that a wave antinode is generated in the center, and the current will pass through the embedded resistors and be consumed finally. The resonant frequency can be calculated by(5)f=c2l∗εr,eff,where l is the length of the metallic strip, c is the velocity of light, and εr,eff is the effective relative permittivity, which was calculated in [13].Figure 5
Simulated current distributions of the proposed absorber at three resonant frequencies of (a)f1 = 3.64 GHz, (b) f2 = 8.32 GHz, and (c) f3 = 12.96 GHz.
(a)(b)(c)In addition, Figures5(b) and 5(c) depict the current distributions at f2 and f3, which are corresponding to the first odd resonant mode with two wave antinodes of the central longer metallic strip and the fundamental mode with one wave antinode of the shorter metallic strip, respectively. We can also observe that slight currents are excited on two shorter metallic strips at the resonant frequency f2, and the same situation happens at the resonant frequency f3, which is caused by the coupling between two metallic strips at these two resonant frequencies.It is well known that the first odd resonance cannot be excited under normal incidence [7] because the symmetric current with opposite directions generated in a receiving dipole-like metallic strip counteracts each other at the resonant frequency. However, our proposed structure can be considered as a superposition of two asymmetrical-dipole-like metallic strips, and two chip resistors are inserted at different feeding ports. The current excited at the first odd resonance is asymmetrical, as shown in Figure 5(b), resulting in a nonzero current [11]. Then, two resistors are loaded on the metallic strip in our proposed structure to realize the excitement of the first odd resonance.


## 2.3. Parameter Discussion

According to the analysis of the operating principle in Section2.2, four parameters are studied here to reveal their effect on the resonant characteristic of the proposed absorber, which are the lengths l1 and l2 of the metallic strips and the resistive values R1 and R2 of the embedded chip resistors.The values of loaded dual-chip-resistors should be optimized carefully to achieve a superior absorption performance. Figure6 shows different frequency responses with various values of the chip resistor. There are two degrees of freedom that one of the two chip resistors is tuned when another is fixed. Figure 6(a) exhibits that the value of R1 influences the frequency response of the longer metallic strip, and the absorption performance is good when R1 is set to 120 Ω. On the contrary, the value of R2 can impact the frequency response of shorter metallic strips, as shown in Figure 6(b), and it is chosen to 70 Ω to get a wider absorption band and good absorption performance.Figure 6
Different frequency responses of the proposed absorber with various values of chip resistors. (a) Different values ofR1. (b) Different values of R2.
(a)(b)Figure7 indicates the variation of the reflection zeros with different values of the length l1 of the longer strip and l2 of the shorter strip. The reflection zero of f1 and f2 shifts to a lower frequency and f3 almost unchanged when l1 increases, as shown in Figure 7(a). Because f1 and f2 are the fundamental and the first odd resonant mode of the longer strip, increasing l1 will enlarge the resonant wavelength. Figure 7(b) illustrates the influence on three reflection zeros when l2 increases; it is found that f2 and f3 move to a lower frequency while f1 is fixed. Increasing l2 will result in a large resonant wavelength of the shorter strip, and it will also increase the resonant wavelength of the longer strip because of the coupling between these two strips.Figure 7
Variations of the reflection zero frequencies in the absorption band with respect to (a) the lengthl1 of the longer strip and (b) the length l2 of the shorter strip.
(a)(b)Then, a wideband absorption performance can be obtained with properly designed aforementioned parameters, as shown in Figure4. For the certain performance of absorption, including the bandwidth and absorptivity, there is a physical boundary for the thickness of the nonmagnetic absorber, defined as Rozanov limit [6]:(6)RL≥∫0∞lnΓλdλ2π2,where RL is the Rozanov limit and Γλ is the reflection coefficient of the wavelength response. In this paper, our designed absorber has the Rozanov limit of 7.36 mm calculated by (6). Compared with the realized thickness of the absorber, there is only 8% thicker than the Rozanov limit.


## 3. Measurement Verification

A prototype is fabricated with an array of 15 × 15 unit cells to verify the absorption performance of the designed absorber, and the total size of the prototype is 300 mm × 300 mm. Both chip resistors and metallic strips are printed on the FR4 substrate, and the plastic screws are used to separate the lossy layer and metallic ground with a certain distance of 7.5 mm, as shown in Figure8(b). Additionally, the commercial product of the chip resistors we used in the realized absorber prototype is RF0402-120R-HS and RF0402-69R8-HS. The prototype is measured in an anechoic chamber, which has an arched frame mounted with two horn antennas, as shown in Figure 8(a). Then, the measured reflection coefficients for normal and oblique incident waves are obtained by adjusting the angle position of two horn antennas.Figure 8
(a) Reflection measurement setup and (b) photograph of the prototype.The measured results show that our designed absorber has a wideband absorption performance and stable angular response, as shown in Figure9. It is found that the absorption band is from 3.1 to 14.2 GHz with a fractional bandwidth of 129% under the normal incidence. In addition, the absorption performances of the designed absorber are relatively stable when the incidence angle increases up to 30° for both TE and TM polarizations, as shown in Figure 9. It is seen that the resonant frequencies of f3 shift to a lower frequency, and the width of the absorption band becomes narrower when the incident angle increases, which is caused by the nonnegligible parasitic capacitance and inductance of the used chip resistors in the high frequency.Figure 9
Simulated and measured results of the proposed absorber under oblique incidences for (a) TE polarization and (b) TM polarization.
(a)(b)The performance of our designed absorber is compared with the state-of-the-art absorbers in the literature, as shown in Table1. It is shown that our proposed structure realizes an ultrawide absorption band for dual polarization, and its profile is only 0.08λL. In addition, the ratio of wavelength difference to thickness in the operating band is utilized to intuitively evaluate the performance advantage, which can be expressed as the figure of merit P [26]:(7)P=λmax−λmind,where λmin and λmax are the minimum and maximum wavelengths in the operating band, respectively. Compared with other structures, our designed absorber has relatively better performance, considering bandwidth and thickness comprehensively.Table 1
Performance comparison.
Ref.Thickness (λmax)FBW (%)λmax−λmin/dObliquePolarized[1]0.07770.76.6730°Dual[10]0.07192.28.8530°Dual[11]0.08127.99.730°Dual[12]0.088126.88.6330°Dual[17]0.11127.1730°Single[18]0.1011488.4545°Dual[24]0.1041126.9530°Dual[25]0.081209.1530°DualThis work0.081299.4630°Dual


## 4. Conclusion

This paper proposed a methodology for designing a low-profile wideband absorber, which has the stable angular and polarized responses. The proposed absorber is made up of a lossy layer with two orthogonal strips printed on both sides of a substrate and a metallic ground under the lossy layer. Arrays of two unequal metallic strips are printed on the substrate, and each strip is loaded with two resistors. By properly designing the resonant frequencies of these metallic strips, a wide absorption band with three resonances can be obtained. An example of the designed absorber is fabricated, and the measured results attest that it achieves an attractive wide absorption band for dual polarization and a stable angular response with a low-profile configuration.



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