Synthesis and Design of 3-D Microwave Absorber With 70° Angular Stability for C-Band and X-Band

This article presents the synthesis and design of 3-D microwave absorber with 70° angular stability for C-band and X-band. The operating principle is firstly investigated, where the absorber is considered as an energy convertor. With the help of our proposed universal equivalent transmission line (TL) model, the absorptive performance can be accordingly synthesized. Then, a design method for efficient absorption under large angles is presented. By selecting a proper synthesized angle (SA), the angular stability can be effectively improved. After that, the prototype with 70° angular stability is designed as an example with structural realization and practical implementation. Measurements agree well with synthesized and simulated results, successfully verifying the proposed design method. For specific C-band and X-band applications, the measured average absorption ratios (ARs) under normal incidence, 45° incidence, and 70° incidence are 94.2%, 94.0%, and 92.3%. Minimum measured ARs within the operating bandwidth are 88.4%, 81.5%, and 82.0% for normal, 45°, and 70° incidences. Besides, the proposed absorber element owns the advantage of simple structure with only one resistor. Such a class of microwave absorber is a potential candidate for wide coverage electromagnetic absorption.


I. INTRODUCTION
M ICROWAVE absorbers have attracted widespread attention in the research field of electromagnetic scattering, due to their essential role in radar cross section (RCS) reduction, electromagnetic interference (EMI) shielding, and anechoic chambers applications [1].As one of the most significant performances, a larger angular stability is highly preferred for wide coverage of electromagnetic absorption.
During the past few years, great effort has been made to develop wide-angle absorbers.Different resistive or absorptive material-based designs were reported with large angular stability.In [2], octagonal ring-shaped resistive patches were used to obtain a metamaterial absorber with interference theory.The graphene-based structures were utilized in [3] and [4] for large-angle designs.In [5] and [6], the waterbased and biomass-based absorbers were presented with enhanced absorption performance.The indium tin oxide (ITO) film was employed in [7] and [8] to improve the wide-angle performance.In [9], the spatial lossy transmission line was proposed to realize a wide absorption band while maintaining a large oblique incident angle stability.The inkbased resistive layer was used in [10] to cope with the wideband RCS reduction under a planar structure.In [11], polycarbonate substrate was coated with gold films for the broadband absorber with optical transparency.Using ruthenium oxide on a low-temperature co-fired ceramic substrate, an ultrathin single-layer broadband absorber was presented in [12].
In addition to applying resistive materials, lumped loading is also a popular method to design microwave absorber with improved performance.A lump circuit modeling was proposed in [13] to analyze and design a flexible structure for conformal electromagnetic absorbers.In [14], a wideband absorber was presented based on spoof surface plasmon polariton to obtain a high angular stability.By integrating electric resonances and magnetic resonances, a wideband absorber with wide-angle response was reported in [15].In [16], a type of frequency selective surface (FSS) was introduced in the bottom layer to increase the absorption bandwidth.A single-layer impedance-well passive absorber was put forward in [17] with enhanced absorption bandwidth approaching the Rozanov thickness limit for passive absorbers.In [18], a pair of rectangular patches and a rectangular loop embedded with four resistors were utilized to design a broadband microwave absorber operating at an oblique angle of 75 • .A wideband circuit analog absorber was realized in [19] based on the concept of multiple resonances.
More than the above-mentioned methods, structural deformation is able to significantly improve angular stability as well.In [20], the conformal broadband metamaterial was used to put forward a microwave absorber with high angular stability.The wide-angle electromagnetic absorption was addressed in a dynamically controllable manner via a reconfigurable origami-based metamaterial [21].The 3-D origami absorber with four normal vectors provided an effective approach to prevent the deterioration of absorption in a wide-angle range.In [22], the performance under the oblique incidence over wide-angle and wideband was improved by rotating the FSS in 3-D planes through various rotation schemes.However, for these existing works, there is no universal synthetic design method that can provide both predicted wide-angle and wideband performance simultaneously.
In this article, we present the synthesis and design of 3-D microwave absorber with specific performance, such as 70 • angular stability within C-band and X-band.The operating principle is firstly investigated, where the absorber is considered as an energy convertor.Using our established universal equivalent transmission line (TL) model, the absorptive performance can be accordingly synthesized.Then, we propose a design method to realize efficient absorption under large angles.Most importantly, a synthesized angle (SA) is properly selected to effectively improve the angular stability.After that, a prototype is designed for the 70 • angular stability as an example from structural realization to practical implementation.Measurements agree well with synthesized and simulated results, which successfully validates the proposed design method.For given operating frequency in C-band and X-band, the measured average absorption ratios (ARs) under normal incidence, 45 • incidence, and 70 • incidence are 94.2%, 94.0%, and 92.3%.Minimum measured ARs within the operating bandwidth are 88.4%, 81.5%, and 82.0% for normal, 45 • , and 70 • incidences.Additionally, the proposed absorber element possesses the advancement of simple structure which needs only one resistor.Therefore, such a type of microwave absorber is indeed a promising candidate for wide coverage electromagnetic absorption.The main novelties and contributions are summarized as follows: a) Based on the established equivalent TL model, it is easy to synthetic design the Chebyshev absorptive response with different orders and symmetries.b) By employing a synthesized angle of 45 • rather than the traditional 0 • , the angle coverage within operating bands is significantly improved to 70 • with high efficiency.c) The proposed absorber element only applies one piece of substrate and one resistor, avoiding the complex structure caused by multi-layered substrates and multiple resistors.

II. OPERATING PRINCIPLE
The operating principle of the proposed absorber is depicted in Fig. 1.The electromagnetic wave in free space flows to the proposed conversion structure, which can be analyzed and designed using microwave circuit theory.Then, the input energy is transformed into thermal energy by the absorption structure (here, a resistor).During this process, the most crucial steps are how to establish a suitable circuit model and how to implement this model under a simple structure.
With regard to the first vital step, a universal equivalent TL model is constructed for the conversion structure, as shown in Fig. 1.A pair of edge-connecting lines are named as TL a and TL d .Two sets of shunt short-ended stubs are denoted as TL b and TL c .Several sections of middle connecting lines are represented as TL 1 , TL 2 , . . ., TL i , . . ., TL n-1 , and TL n .The impedance of spatial wave is Z 0 , the input impedance is Z in , and the loaded resistance is Z R .In this model, all the TLs are of the same length of quarter wavelength at the desired center frequency.Due to the fact that the characteristic impedance of each TL is not limited by any condition, this model can perform as a symmetric or asymmetric model according to the desired response.Moreover, different numbers of middle connecting lines result in circuit property with different orders.Thus, the proposed universal equivalent model owns the capability of converting the input energy under arbitrary order and arbitrary symmetry.
According to our established model, the ABCD matrix of the proposed element is calculated as (1) [23], [24].In this way, the characteristic function can be derived using impedances in this model as [25], [26], [27] Combining the Chebyshev polynomials we can obtain the relationship between characteristic impedances (in the equivalent model) and expected responses (in Chebyshev polynomials).Here, z denotes the normalized characteristic impedance, ε is related to the maximum inband reflection coefficient , p (and q) is a positive integer, and α is determined by the lower cutoff frequency f c .The above synthetic procedure can be summarized as shown in Fig. 2 Since the key elements in our equivalent TL model are characteristic impedance and electrical length, the characteristic impedance for each section of transmission lines can be easily calculated based on the expected performance.
Without loss of generality, we take Z R =Z in , n=2 as an example.Thus, we have All the coefficients of k are given in the appendix.Accordingly, The coefficients of K 1 , K 2 , and K 3 are as follows For ( 4) and ( 5), the following equations must be satisfied After these calculations, each characteristic impedance is determined by the given conversion response.In other words, the desired performance can be theoretically synthesized by conducting the above procedure.
Based on the foregoing analysis, we further present a novel design method for large angular stability.A highly significant parameter of the incident angle θ in is taken into consideration at the very beginning of designing a conversion structure.The incident angle prominently affects the input impedance, which is always overlooked in traditional works.Here, the input impedance of practical incidence is given by [28], [29] For traditional works, the element structure is designed under θ in =0 • (normal incidence).Due to the huge change in input impedance, the impedance mismatching under Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.oblique incidence results in obvious deterioration of element performance compared with that under normal incidence.
On the contrary, in this article, we select a synthesized angle θ s to replace the conventional default of 0 • during the design procedure, where in,TE = Z 0 /cos θ s,TE = Z R,TE , TE − pol.(9) In this way, the expected response will be realized when the actual incident angle is equal to the theoretical synthesized angle, which is θ in = θ s .Therefore, an appropriately selected synthesized angle is of great significance for obtaining the desired angular stability.Herein, considering a TM-polarized example where the fractional bandwidth (FBW) is 110% and = −13dB, the synthesized absorption ratios (ARs) with different θ s are shown in Fig. 3 to Fig. 5.Under normal incidence, when θ s is 0 • , as shown in Fig. 3, the AR shows the highest value as the normalized frequency increases from 0.5 to 1.5.In this case, for θ s = 45 • , the AR results of higher than 85.7% is still obtained.Under 45 • incidence in Fig. 4, all AR curves show high values of larger than 94%.For the most critical 70 • incidence in Fig. 5, when θ s is 45 • , the AR curve attains the highest one with the minimum value of 85.1%.In this case, traditional design with θ s = 0 • only realizes a minimum AR of 73% from ideal calculations.Therefore, the proposed design method can theoretically obtain a stable AR result of higher than 85.1% within the entire desired operating bandwidth.It is worth noting that the above methods and conclusions are also applicable to TE-polarized incident wave absorption.

III. ABSORBER DESIGN AND IMPLEMENTATION
To verify the proposed method in Section II, a prototype is practically designed and implemented in this section.In order to provide a clear illustration of the design process, Fig. 6 shows the design flow and design example of the proposed method.The complete design flow can be divided into five steps: a) Assume a set of desired absorption performance according to the given target requirements; b) Calculate the characteristic impedances of all the TLs using the synthetic design method in Section II; c) Choose the appropriate types of TL, taking into account both impedance and structure features; d) Connect all the TLs corresponding with the equivalent TL model.Transitions need to be designed between different types of TLs; e) If necessary, optimize the entire structure to ultimately obtain the expected performance.
Following the above design flow, a design example is practically implemented: a) In order to realize the 70 • coverage for C-band and X-band, we set the performance to FBW = 110%, = −13dB, Z 0 = 377Ohm, and θ s = 45 • ; Here, the reasons for using different types of transmission lines can be explained from two aspects: 1) slotlines are employed to achieve efficient energy conversion from spatial waves in free space to guided waves in transmission lines, and 2) microstrip lines are used to realize the absorptive circuit where a resistive load is connected in series at the end of the last transmission line.
The element configuration of the proposed absorber design is shown in Fig. 7. From the overall view in Fig. 7(a), the single-layered structure is surrounded by the periodic boundary condition.Two sections of slotlines (TL a and TL b ) are etched on the backside ground, while four sections of microstrip lines (TL 1 , TL 2 , TL c , and TL d ) are printed on the front side.The loaded resistor is made by the resistive film from Ohmega (50Ohm/square) and connected to the backside ground via a shorting pin.In order to realize a good structural strength under effective cost, the FR4 substrate (relative permittivity of 4.4, loss tangent of 0.0166) is employed in this work.Fig. 7(b) shows the detailed view for microstrip lines and resistive film, where the bent transmission lines are for a compact element size.
To clearer display the absorption performance, Fig. 8 shows electric field distribution of the proposed absorber element under different incidences.As seen in Fig. 8(a), for out-of-band frequencies (2GHz on the left and 14GHz on the right), the incident wave is reflected back to the upper free  space.Meanwhile, the incidence within operating bandwidth (4GHz, 8GHz, and 12GHz in the middle) is absorbed by the proposed structure.The conversion and absorption can be well defined from the electric field distribution.In this way, the energy vacuum can be realized in the free space below the proposed element.Regarding oblique incidences in Fig. 8(b) and Fig. 8(c), similar phenomena occur as well, which further validates the wide-angle performance.
This designed absorber is fabricated and tested, as shown in Fig. 9.In order to guarantee the proper element distances and attain a durable prototype, a supporting frame is made of photosensitive resin and applied for the actual absorber with 25×25 elements, as shown in Fig. 9(a).Then, 25 pieces of substrate strip are inserted into the supporting frame.In Fig. 9(b), the bow-shaped reflectivity testing system is used to obtain the accurate reflection coefficients.The transmitting and receiving horns (Tx and Rx) are located on two swinging arms, and gradual rotation on the same radius arc trajectory to realize reflectivity testing at different incident angles.In addition, a simple transmission testing system is set up and used as shown in Fig. 9(c).Two horn antennas are placed opposite to each other, with a rotatable absorption screen in the middle.By obtaining the transmission coefficient between two horns, the electromagnetic properties of the fabricated prototype can be gained.the measurement, the far-field condition in [30] and calibration method in [31] are taken into account for better measurement accuracy.
The comparisons between synthetizations, simulations, and measurements are shown in Fig. 10 Fig. 12. Acceptable agreement can be observed in these results.The main reasons for result deviation can be attributed to discontinuities between different TLs, additional losses from manufacturing, and measurement errors.For normal incidence in Fig. 10, the synthesized, simulated, and measured bandwidths (absorption ratio larger than 80%) are 116.25%(from 3.35 to 12.65GHz), 114.11% (from 3.5 to 12.8GHz), and 128.83% (from 2.9 to 13.4GHz).Herein, ratio (AR) can be derived as [23].The average in-band ARs are 92.1%,91.0, and 93.5%, respectively.The undesired reflections (|S  1.From these results, the proposed design method can be indeed utilized to obtain the microwave absorber with 70 • angular stability.
In order to further demonstrate the advantages of our work in terms of important performance, Table 2 shows the detailed comparisons between the proposed design and Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
other published absorber works for wide-angle applications.
Compared with [5], [9], [14], [15], and [22], the proposed structure realizes a predictable higher absorption ratio under a large angle.The structure in [18] achieves high efficiencies under large angles, however, the usable angle and fractional bandwidth are narrower than our design.In addition, our work is synthesized and obtained with a single-layered substrate and a single resistor.According to the above comparison, it is clear that the proposed absorber design in this article accomplishes a predictable and stable high efficiency within a large angle range under a simple structure.

IV. CONCLUSION
In this article, the synthesis and design of 3-D microwave absorber with large angular stability for specific C-band and X-band have been presented.The operating principle is investigated based on our proposed universal equivalent TL model.The wide-angle performance is successfully improved by selecting a proper synthesized angle.A prototype with 70 • angular stability is implemented from theoretical analysis and element design.Within C-band and X-band, the measured average ARs under different incidences are higher than 92.3%.Minimum ARs within the operating bandwidth are larger than 81.5%.In addition to the single-layered structure with only one resistor in each element, this type of absorber can be viewed as a promising candidate for wide-angle absorption applications.

FIGURE 1 .FIGURE 2 .
FIGURE 1. Operating principle and universal equivalent transmission line model of the proposed 3-D absorber element.
: a) Construct an equivalent TL model and calculate the entire ABCD matrix to obtain the characteristic function.Here, the elements in the ABCD matrix include the characteristic impedance of each transmission line; b) Properly select and expand the Chebyshev function according to the characteristic function, where the Chebyshev function contains information about the S-parameters; c) By equating the characteristic function with the Chebyshev function, the relationship between the equivalent TL model and S-parameters (expected performance) can be obtained.

FIGURE 3 .
FIGURE 3. Absorption ratios with different synthesized angles under normal incidence.

FIGURE 6 .
FIGURE 6. Design flow and design example of the proposed method.

FIGURE 7 .
FIGURE 7. Element configuration of the proposed 3-D absorber.(a) Overall view with periodic boundary condition.(b) Front-side metal and resistive film.(c) Back-side metal.(d) Side view.

FIGURE 12 .
FIGURE 12. Synthetizations, simulations, and measurements of S-parameters and absorption ratios for the proposed design under 70 • incidence.

k 5 =
− z 1 2 z c +z b z 1 z c +(z 2 +z c )z b z 2 z d +z b z 2 2 z c z a 2 z d + z R z in z 2 2 −z 1 2 z d 2 z a z b z c +[z 1 z d +((z 1 +z 2 )z 2 )]z R z in z b z 1 z c 2 √ z R z in z a z b z 1 z 2 z c z d k 6 = z R z a 2 z 2 2 −z in z 1 2 z c 2 z b z c 2 √ z R z in z a z b z 1 z 2 z c z d (A-1)

TABLE 2 . Comparisons between our proposed design and other published absorber works for wide-angle applications.
11,co.| and |S 11,cro.and transmissions (|S 21,co.| and |S |) lower than −7dB, leading to high in-band ARs with low energy leakage and polarization conversion.With regard to 45 • oblique incidence, operating bandwidths of 113.75% (average AR of 97.2%), 114.81% (average AR of 95.0%), and 120% AR of 92.9%) are realized synthetizations, simulations, and measurements.As to the larger incident angle of 70 • ,