Single-Layer Differential-Fed Wideband Metasurface Antenna Using Characteristic Mode Analysis

Huang, Chao; Guo, Chen-Jiang; Yuan, Yi; Ma, Xia; Ding, Jun

doi:https://doi.org/10.1155/2023/5184139

International Journal of Antennas and Propagation

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Abstract Introduction Results and Discussion Conclusion Data Availability Conflicts of Interest References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 5184139 | https://doi.org/10.1155/2023/5184139

Single-Layer Differential-Fed Wideband Metasurface Antenna Using Characteristic Mode Analysis

Chao Huang,¹Chen-Jiang Guo,¹Yi Yuan,¹Xia Ma,¹and Jun Ding¹

Academic Editor: Truong Khang Nguyen

Received08 Jun 2023

Revised17 Aug 2023

Accepted30 Oct 2023

Published11 Nov 2023

Abstract

A single-layer differential-fed (DF) wideband metasurface (MTS) antenna is proposed in this paper. As the prototype, a three-by-three MTS formed by identical rectangular patches is investigated at first. We observe that there are many unwanted higher-order modes (HOMs) resonating near the wanted fundamental mode. Two probes with differential signals feed MTS on its centerline to suppress the majority of HOMs. The remaining HOM can be removed from the discussed frequency range by modifying the prototype MTS to a nonuniform structure. Then, the optimal feeding positions (FPs) are determined by a quantitative prediction of the impendence bandwidth (IBW) without any physical feeds involved. The processes of HOMs suppression and FPs determination are based on characteristic mode analysis with the virtual probes. Moreover, two interdigital capacitor plates are loaded on the probes to improve the impedance matching of the antenna. Finally, the proposed DF MTS antenna is fabricated and measured. The measured −10-dB IBW is 18.4% (4.93 to 5.93 GHz) with broadside radiation, stable high gains, and front-to-back ratios better than 21 dB.

1. Introduction

Differential circuits with the advantages of low noise, harmonic suppression, high linearity, and large dynamic range have been widely applied in radio frequency (RF) integrated circuits and microwave monolithic integrated circuits [1]. To match the differential circuit, various types of differential-fed (DF) antennas, especially DF microstrip patch antennas (MPAs) [2–4], were presented. However, low-profile MPAs usually suffer from narrow impedance bandwidth (IBW) and low gains.

Metasurface (MTS), a two-dimensional form of metamaterial, has rich potential for manipulating electromagnetic waves [5, 6]. As a combination with antennas, MTS antennas have been widely employed to enhance IBW and the gains of MPAs. Compared with MPAs, the resonating modes have a denser distribution for MTS, showing an opportunity in mode combination and a challenge in mode suppression. Therefore, MTS is usually coupled fed by sources with fixed polarization to suppress unwanted orthogonal modes. In [7–9], MTSs are coupled fed by y- or x-polarized slot antennas, and a wider IBW can be achieved by combining a slot mode and MTS modes. However, these antennas usually suffer from lower front-to-back ratios (FBRs) for the bidirectional radiation of slots. To reduce the backward radiation, coupled patches and L-probes are employed to feed MTSs [10–13]. Nevertheless, the configurations of these antennas are always complex. In [14], MTS is fed by an aperture coupling through a short-end coplanar waveguide (CPW). The antenna achieves broadband performance with a simple single-layer structure. Still, it exhibits poor FBRs and distorted radiation patterns. In summary, the above feeding methods cannot simultaneously realize an MTS antenna with broadband, good radiation characteristics, and single-layer configurations.

To investigate the operating mechanism of MTS antennas, various analyzing methods were presented, including the equivalent circuit method [7], reflection coefficients calculation [9], and effective medium theory [15]. Compared with the above methods, the characteristic mode analysis (CMA) shows superiority in characterizing the modal resonant behavior of arbitrarily shaped objects, especially for analyzing nonuniform MTS or small-scale MTS [16, 17].

In this paper, we propose a DF MTS antenna with a single-layer configuration. The design begins with analyzing the intrinsic properties of a uniform three-by-three MTS with rectangular patches, and its higher-order modes (HOMs) with unwanted radiation features are found to resonate near the fundamental broadside mode. By observing the modal E-fields of HOMs, it is possible to suppress most of them by symmetrically arranging two DF probes on the centerline of MTS. The resonating frequency of the remaining HOM can be removed from the discussed range by reducing the length of side patches in MTS. Then, a quantitative prediction of IBW is utilized to determine the optimal feeding positions (FPs). The suppression of HOMs and determination of FPs are all based on source-free CMA with a method of virtual probes, which is easier to understand and more time-saving than the traditional physical port simulation. Moreover, two interdigital capacitor plates (ICPs) are loaded on the DF probes to compensate for the probe inductances and improve IBW. Since no slot modes or HOMs are excited, the proposed antenna exhibits stable broadside radiation with high FBRs in the operating band.

This paper is organized as follows. Section 2 presents the basic theory of CMA and a differential impedance analysis method based on virtual probes, which provides the theoretical basis for the proposed design. Section 3 shows the geometry and working mechanism of the proposed antenna, including the suppression of HOMs, the determination of FPs, and the improvement of IBW. The measured results of the proposed antenna are presented and discussed in Section 4, and we draw the conclusions in Section 5.

2. CMA and Differential Impedance with Virtual Probes

2.1. Theory of CMA

In characteristic mode (CM) theory, the modal resonant behavior of objects in arbitrary shapes can be characterized by their generalized eigenvalue equations as follows [18]:where J_n is the eigenvector, λ_n is the eigenvalue, and subscript n denotes the index number of CMs. The parameters X and R are the real and imaginary parts of the impedance matrix, respectively. The eigenvalue λ_n has a significant physical meaning, whose magnitude can reflect the total stored field energy within a radiation or scattering problem. However, since λ_n has a large value range of , researchers often replace it with the modal significance (MS) as follows [19]:

The value range of MS is [0, 1], which is more convenient for observation. A frequency with MS = 1 is the resonant frequency of a mode, and a mode can be regarded as the dominant mode when its MS ≥ 0.7.

2.2. Differential Impedance with Virtual Probes

Differential impendence Z_dd is an essential parameter for DF antennas, which can be calculated bywhere Z_11/22 and Z_12/21 are the self- and mutual impedances, respectively. For a DF planar antenna shown in Figure 1, referring to the method in [20], its physical probes can be equivalent to two virtual probes in the impedance analysis. The virtual probe is an idealized model that disregards the physical dimensions of the probe and treats it as a uniform current filament. By introducing the concept of “virtual probe,” Z_11/22 and Z_12/21 in (3) can be written as follows [21]:where , , and are the total E-fields, the excitation current densities, and the excitation currents at FPs , respectively. According to the theory of CM, can be expanded using a set of orthogonal modal E-fields as

Assuming the vertical components of are uniform underneath the radiator and substituting (6)–(8) into (4) and (5), the self- and mutual impedances can be simplified as follows [3]:where are the imaginary part of the z-component of . Substituting (9) and (10) into (3), the differential impendence with the virtual probes can be expressed aswhere is the differential impendence of each mode.

However, since (11) is derived based on the virtual probes, it neglects the inductances contributed by the physical probes. Furthermore, to ensure the antenna presents an open circuit at dc, an equivalent dc capacitance C_dc should be introduced [22]. Taking into account of the probe inductances and the dc capacitance, the differential impendence in (11) can be rewritten aswhere L_self and M are the self- and mutual inductances, respectively, expressed as follows [23]:where l is the length, ρ is the radius of the probes, and D is the distance between the two probes. Furthermore, the differential reflection coefficient S_dd of the antenna can also be derived from Z_dd in (12) as follows [24]:where the characteristic impedance Z_c is 100 Ω for the differential port.

In this paper, and λ_n of each mode for MTS can be obtained by source-free CMA simulations performed in FEKO. The values of L_self and M are determined by (13) and (14) with the parameters of the physical probes, and the length of the probes is equal to the height of the substrate h. The dc capacitance C_dc is calculated in Ansys Maxwell using the finite element method.

3. Antenna Design and Operating Mechanism

3.1. Antenna Geometry

The configuration of the proposed DF MTS antenna is shown in Figure 2. From the side view, an MTS and a ground plane are etched on the two sides of an F4B220M substrate (ε_r = 2.2 and tan σ = 0.0009) with a thickness of h, respectively. From the top view, the MTS features a nonuniform structure formed by nine rectangular metallic patches. The dimensions of the middle and the two side patches of MTS are L₁ × W_m and L₂ × W_m, respectively. The distances between adjacent patches are denoted by . In order to excite MTS, two DF probes with a radius of R₁ are symmetrically arranged on its centerline (AA′) at positions of (0 mm, ±18 mm, z). From the enlarged view, two ICPs with an outer radius of R₂ are loaded on the two probes for better impendence matching. The eight fingers with dimensions of L_f × W_f have a gap width of G₁ with ICP.

3.2. Suppression of HOMs

The design starts with a three-by-three MTS with identical rectangular patches (MTS 1) (see Figure 3(a)), and its MSs and corresponding radiation patterns of the dominant modes (J₁–J₈) in the range of 4 to 7 GHz are depicted in Figures 3(b) and 3(c), respectively. As can be seen, modes J₂–J₅, J₇, and J₈ feature radiation nulls at the boresight are unwanted modes that should be suppressed in the design. Although both modes J₁ and J₆ can generate broadside radiation patterns, only J₁ should be excited as J₆ is an x-polarized mode. According to (11), the Z_dd,n of a mode has little contribution to the total differential impendence (Z_dd) when its modal E-fields are identical in magnitude and phase under the two differential ports, i.e., , which also means the mode can be suppressed effectively.

(a)

(b)

(c)

Figure 4 plots the z-component modal E-fields of J₁–J₈ under the centerline (AA′) of MTS 1 at 5.5 GHz. It is found that only J₁ and J₅ in odd-symmetrical E-field distributions can be excited with differential feeds. The other modes in zero-magnitude (J₂, J₄, J₆, and J₇) and even-symmetrical (J₃ and J₈) distributions can be suppressed successfully.

In order to further suppress J₅, the modal currents of J₁ and J₅ are investigated (see Figure 5(a)). Compared with J₁, the modal currents of J₅ mainly distribute on the right and left sides of MTS 1. Therefore, if the length of side patches L₂ is reduced, the resonating frequency of J₅ will move away from the range of 4 to 7 GHz, and the effect of J₅ will be reduced. Figure 5(b) shows MSs of J₅ with different L₂. As L₂ decreases from 13 to 10 mm, J₅ has a remarkable blue shift from 6.35 to 7.8 GHz.

(a)

(b)

To suppress J₅, a modified MTS (MTS 2) with L₂ = 10 mm (see Figure 6(a)) is selected for the following design, and its MSs and corresponding radiation patterns for the dominant modes (J₁’–J₆’) are depicted in Figures 6(b) and 6(c), respectively. Compared with MTS 1, MTS 2 has less unwanted HOMs (J₂’–J₆’). By observing the z-component modal E-fields of MTS 2 in Figure 7, only the wanted mode J₁’ with broadside radiation and odd-symmetrical E-field distributions can be excited when differential probes feed MTS 2. The expression of Z_dd for the MTS 2-based DF antenna can be derived from (12) as

(a)

(b)

(c)

3.3. Determination of FPs

After suppressing all unwanted HOMs of MTS, the FPs need to be further optimized for a wider IBW. According to (6), the bandwidth of each feeding point on the centerline of MTS 2 can be predicted by calculating its S_dd values in the entire operating band. The prediction is based on the method of virtual probes in Section 2, and the corresponding C_dc is estimated as 1.35 pF. The points with y-coordinate values varying from ±2 to ±20 mm (±0.5 mm step) are selected. The IBW values (|S_dd| < −10 dB) of these points calculated with the virtual probes are illustrated in Figure 8(a) (upper bars), and the corresponding results simulated with the physical probes performed in Ansys HFSS (lower bars) are also given for verification. The upper and lower bars have similar trends and values, and both of them illustrate an optimized IBW (about 450 MHz) can be obtained when the probes are fed near the positions of (0 mm, ±18 mm, z). Figure 8(b) shows Z_dd curves of MTS 2 with virtual and physical feeds at (0 mm, ±18 mm, z). The imaginary parts of Z_dd show positive values in the operating band, mainly induced by the self- and mutual inductances of probes.

(a)

(b)

3.4. Improvement of Impedance Matching

In order to compensate for the probe inductances, two circular capacitor plates (CCPs) are loaded on the probes at first for IBW improvement. The CCP (see Figure 9(a)) has been widely applied to enhance the IBW of probe-fed patch antennas with a thick substrate because it can introduce a series radial capacitor C_s [25]. The radius of CCP is set to 2 mm (slightly less than h) for larger C_s while weakening the effect of its TEM mode [26]. From Figure 8(b), the imaginary part of Z_dd is j85 Ω at 5.35 GHz for the physical probe simulation, and the required value of C_s is 0.7 pF. Then, the corresponding radial gap width G_p can be calculated using the equations in [26] as 0.03 mm, which is narrow and sensitive to the dimensional errors in fabrication. Because the interdigital capacitor has a greater capacitance than the gap capacitor in the same size, the final design adjusts the CCPs to ICPs with an interdigital gap width (G₁) of 0.1 mm. Figure 9(b) shows the simulated Z_dd results of MTS 2 fed by the nonloaded, the CCP-loaded, and the proposed ICP-loaded probes at (0 mm, ±18 mm, z). This figure illustrates ICP with G₁ = 0.1 mm has a similar effect as CCP with G_p = 0.03 mm in compensating for the imaginary part. Moreover, the real part with ICP loading is closer to 100 Ω at the resonant frequency, showing a better match with Z_c (100 Ω) than CCP loading.

(a)

(b)

4. Results and Discussion

The proposed DF antenna with the parameters in the caption of Figure 2 was fabricated, and its |S_dd| results are calculated based on S-parameters measured by the vector network analyzer [27]. In order to facilitate far-field testing, the fabricated antenna is integrated with a wideband balun (see Figure 10). The balun referenced in [28] is etched on a 0.5-mm thick F4B220M substrate and shares the same ground plane with the proposed DF antenna. Figure 11(a) shows the photographs of the proposed antenna, and its measured and simulated |S_dd| and gains are plotted in Figure 11(b). The measured results agree with the simulated ones, indicating that the proposed antenna can cover 4.93 to 5.93 GHz (18.4%) with reflection coefficients less than −10 dB and broadside gains varying from 8.17 to 8.96 dBi. Figure 12 shows the simulated and measured normalized radiation patterns of the proposed antenna at 5.35 GHz, showing broadside radiation with good polarization purity and a front-to-back ratio (FBR) better than 21 dB in both the xoz- and yoz planes.

(a)

(b)

Comparisons of the proposed antenna with the other reported wideband MTS antennas are tabulated in Table 1. With approaching IBW and FBR performances, the proposed antenna achieved a simpler structure than the works in [11, 12], making fabrication easier. Although antennas in [8, 14] exhibit a much broader IBW than our work, the introduction of slots and HOMs render them worse than the proposed antenna in the backward radiation and the pattern stability.

5. Conclusion

In this paper, a single-layer DF wideband MTS antenna with broadside radiation is proposed and discussed. The suppression of HOMs is achieved by adding differential feeds and reshaping the geometry of MTS. Unlike other reported designs with time-consuming full-wave simulations, the optimization of FPs in this study is based on an IBW prediction, which is more efficient. All the above processes use CMA with virtual rather than physical feeds. Moreover, the conventional CCP loading for the thick substrate is modified to the novel ICP loading, which can compensate for the probe inductances of the proposed antenna printed on a thin substrate. The proposed antenna has a simple structure and a low profile, which is easy to fabricate. Its measured results show an 18.4% IBW with an FBR greater than 21 dB. In addition, the proposed MTS antenna also presents stabilities in gains and radiation patterns in the entire operating band. Compared with other reported wideband MTS antennas, the proposed antenna can achieve broadband, good radiation characteristics, and single-layer configurations simultaneously, ensuring its potential applications in balanced RF systems.

Data Availability

All data, models, and code used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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Copyright © 2023 Chao Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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