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

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 themetallic 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 andmeasured to verify our designed concept. )e 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.


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 radiofrequency indemnification tags [1][2][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]. e 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]. e 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][9][10][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]. e 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 0.015λ L , where λ L 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. e 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.

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. en, 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 Figure 1. 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 ε r of 4.4, loss tangent tan δ 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 l 2 of 9.5 mm symmetrically located on either side of a dual-resistor-loaded metallic strip with the length l 1 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.

Operating Principle.
In order to intuitively understand the absorption mechanism, the equivalent circuit model of the proposed absorber is given, as shown in Figure 2. 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, R 1 , L 1 , and C 1 represent the equivalent resistance, inductance, and capacitance of the longer metallic strip, respectively, while R 2 , L 2 , and C 2 denote those of shorter metallic strips. In addition, the short-circuited transmission line with electric length θ represents the grounded air spacer. en, the input admittance Y in of the proposed absorber can be expressed as where β � 2π/λ is the wavenumber and Y 0 is the characteristic admittance of the free space. e initial values of L 1 , C 1 , L 2 , and C 2 under normal incidence can be obtained from their geometric relationship, which has been studied in detail [21]: where Z 0 is the characteristic impedance of the free space, l and w are the length and width of the metallic strip, respectively, and G(p, w, λ) is the correction term available, which is studied minutely in [22,23]. erefore, the reflection coefficient of the proposed absorber can be calculated as where Z in � 1/Y in is the input impedance and Z Re in and Z Im in 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 e simulated input impedance of the proposed absorber is shown in Figure 3. e real part of input impedance oscillates around 377 Ω, and three peaks appear at f 1 , f 2 , and f 3 . In addition, the imaginary part oscillates around zero; thus, the reflection coefficient equals to zero in the operating frequency band according to (4). en, the incident wave will illuminate the absorber with no reflection and be absorbed by the resistive components finally. Figure 4 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. e dimensions of the proposed absorber are carefully designed to achieve a good absorption performance. e initial values of lumped inductances and capacitances utilized in the equivalent circuit model are obtained using the formulas presented in [21][22][23] as the following values: L 1 � 19.1 nH, C 1 � 0.017 pF, L 2 � 7.17 nH, and C 2 � 0.081 pF. e 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 as 1 − |Γ| 2 because of the existence of the conducting plane. Furthermore, there are three reflection zeros in the absorption band, namely, f 1 � 3.64 GHz, f 2 � 8.32GHz, and f 3 � 12.96 GHz. e simulated current distributions of the proposed absorber at three reflection zeros are shown in Figure 5 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 f 1 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. e resonant frequency can be calculated by Air spacer PEC θ Figure 2: Equivalent circuit model of the proposed absorber for normal incidence with TE polarization.
Metallic strips array Substrate Air spacer Conducting plane where l is the length of the metallic strip, c is the velocity of light, and ε r,eff is the effective relative permittivity, which was calculated in [13]. In addition, Figures 5(b) and 5(c) depict the current distributions at f 2 and f 3 , 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 f 2 , and the same situation happens at the resonant frequency f 3 , 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. e current excited at the first odd resonance is asymmetrical, as shown in Figure 5(b), resulting in a nonzero current [11]. en, two resistors are loaded on the metallic strip in our proposed structure to realize the excitement of the first odd resonance.

Parameter Discussion.
According to the analysis of the operating principle in Section 2.2, four parameters are studied here to reveal their effect on the resonant characteristic of the proposed absorber, which are the lengths l 1 and l 2 of the metallic strips and the resistive values R 1 and R 2 of the embedded chip resistors. e values of loaded dual-chip-resistors should be optimized carefully to achieve a superior absorption performance. Figure 6 shows different frequency responses with various values of the chip resistor. ere 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 R 1 influences the frequency response of the longer metallic strip, and the absorption performance is good when R 1 is set to 120 Ω. On the contrary, the value of R 2 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 7 indicates the variation of the reflection zeros with different values of the length l 1 of the longer strip and l 2 of the shorter strip. e reflection zero of f 1 and f 2 shifts to a lower frequency and f 3 almost unchanged when l 1 increases, as shown in Figure 7(a). Because f 1 and f 2 are the fundamental and the first odd resonant mode of the longer strip, increasing l 1 will enlarge the resonant wavelength. Figure 7(b) illustrates the influence on three reflection zeros when l 2 increases; it is found that f 2 and f 3 move to a lower frequency while f 1 is fixed. Increasing l 2 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.
en, a wideband absorption performance can be obtained with properly designed aforementioned parameters, as shown in Figure 4. 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]: where RL is the Rozanov limit and Γ(λ) 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.

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 Figure 8(b). Additionally, the commercial product of the chip resistors we used in the realized absorber prototype is RF0402-120R-HS and RF0402-69R8-HS. e prototype is measured in an anechoic chamber, which has an arched frame mounted with two horn antennas, as shown in Figure 8(a). en, the measured reflection coefficients for normal and oblique incident waves are obtained by adjusting the angle position of two horn antennas. e measured results show that our designed absorber has a wideband absorption performance and stable angular response, as shown in Figure 9. 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°f or both TE and TM polarizations, as shown in Figure 9. It is seen that the resonant frequencies of f 3 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.   International Journal of Antennas and Propagation e performance of our designed absorber is compared with the state-of-the-art absorbers in the literature, as shown in Table 1. It is shown that our proposed structure realizes an ultrawide absorption band for dual polarization, and its profile is only 0.08λ L . 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]: where λ min and λ max 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.

Conclusion
is paper proposed a methodology for designing a lowprofile wideband absorber, which has the stable angular and polarized responses. e 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.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.