Characterization and Design of Wideband Penta- and Hepta-Resonance SIW Elliptical Cavity-Backed Slot Antennas

Substrate integrated waveguide (SIW) elliptical cavity–backed slot antennas (CBSAs) with either penta- or hepta-resonance are characterized and designed for wideband performance in this paper. First, the resonant behavior of the elliptical cavity is explored. Then the SIW CBSA with penta-resonance is designed by introducing a cross-shaped slot and a pair of unbalanced shorting vias into the cavity to excite two additional odd- and even- half degenerate quasi-TM110 modes, besides other three modes of half quasi-TM010, and odd- and even- quasi-TM110. Further, by adding another pair of unbalanced shorting vias, two extra higher-order modes, i.e., odd- and even- quasi-TM210 modes are successfully introduced to design a hepta-resonance antenna. The corresponding mode analysis and design guidelines are discussed in detail. Two prototypes are fabricated and measured at X-band, exhibiting the measured bandwidths of 21.8% and 22.7%, respectively. Measured results agree well with simulations, thus validating the design concept.


I. INTRODUCTION
Recently, low profile antenna with wideband performance plays a crucial role during the development of high-capacity wireless communication networks. For instance, wireless applications operating at X-band, including marine radar, satellite communication and motion detection, are in great demand for planar wideband antennas [1]- [3]. Substrate integrated waveguide (SIW) cavity-backed slot antennas (CBSAs) have been extensively investigated because they own excellent characteristics of low profile, high efficiency, easy fabrication, low cost, and convenient integration with planar circuits [4]- [27]. However, one evident drawback of conventional SIW CBSA is the narrow operating bandwidth (approximately only 1.7%) due to both the high quality factor and single-mode resonance of the cavity [4].
To alleviate this problem, several methods have been proposed to enhance the bandwidth of SIW CBSAs, which The associate editor coordinating the review of this manuscript and approving it for publication was Yasar Amin .
can be generally categorized into three types. The first type is to use multiple resonant cavity modes jointly to enlarge the bandwidth [5]- [14]. Two hybrid cavity modes are excited through a non-resonant rectangular slot, achieving a relative bandwidth of 6.3% in [5]. In [6], the rectangular slot is replaced with a bow-tie-shaped slot and the bandwidth is enhanced to 9.4%. Using a triangular complementary split-ring slot, the SIW CBSA realizes a bandwidth of 16.7% in [8]. Several broadband SIW CBSAs are represented by using coupled half-mode/quarter-mode/eighth-mode of a split SIW cavity [10]- [12]. In [13] and [14], shorting vias are introduced into the SIW cavity to generate triple-and quad-resonance, and quad-and penta-resonance, achieving bandwidths of 15.2% and 17.5%, 20.0% and 20.8%, respectively. However, the number of used combined cavity modes is no more than five, which limits the bandwidth. The second type is to combine the cavity mode with the radiating slot mode to acquire a wide bandwidth [15]- [17]. Although the antenna in [15] utilizes the higher-order resonant modes (TE 130 , TE 310 , TE 330 ) which yields the wide fractional VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ bandwidth (>26%), it occupies a much larger SIW cavity size. The third type is to load a patch onto the cavity through a slot, combining the cavity mode with additional resonant patch mode [18], [19]. In [18], a cavity mode TE 210 and an additional patch mode are excited to achieve a bandwidth of 15%, which, in fact, is still narrow. Moreover, the published SIW CBSAs are mainly implemented with the ordinary rectangular cavities [4]- [19], circular cavities [20]- [25], triangle cavity [26], and hexagonal cavity [27]. To this end, novel broadband antenna topologies need to be further explored to utilize more cavity modes, aiming to exhibit a wider bandwidth to satisfy the increasing requirement from the modern communication system. In this paper, different from the aforementioned SIW CBSAs based on conventional cavities [4]- [27], a study on exploring and exploiting multiple resonant modes in an SIW elliptical cavity is put forward for wideband SIW CBSAs design. Besides, only the cavity modes are utilized to realize a wide bandwidth, thus possessing design simplicity and convenience. A constructive point of view on the elliptical cavity is that its flexible control ability of resonant modes through the axial ratio k (the ratio between the major and minor axes of the ellipse), providing an extra design freedom [28]. More importantly, the characterization analysis for the eigenmodes in resonant cavity is thoroughly conducted according to the peculiarity of elliptical cavity, which is very essential and insightful for the CBSAs design and implementation. First, a penta-resonance antenna with a bandwidth of 21.8% is obtained with the aid of a cross-shaped slot and two unbalanced shorting vias, successfully generating five resonant modes in the elliptical cavity. Further, by introducing another pair of unbalanced shorting vias, a hepta-resonance antenna is acquired with two additional resonant modes, together with a wider bandwidth of 22.7%. The prototyped antennas are fabricated with conventional single-layer printed circuit board (PCB) process, having features of low cost and mass production.

II. CHARACTERIZATION OF ELLIPTICAL CAVITY
To characterize the resonant behavior in an elliptical cavity, the first four resonant modes have been simulated and compared with their counterparts in a circular cavity, which are obtained through full wave simulations using the ANSYS High-Frequency Structure Simulator (HFSS). As discussed in [29], conventionally it is difficult to name the resonant modes in an elliptical cavity, and an alternative method proposed in this paper for naming the modes in an elliptical cavity is to compare them with their counterparts in a circular cavity. As shown in Figs. 1(a)-(d), the first four resonant modes in the circular cavity are TM 010 mode, TM 110 mode, degenerate TM 110 mode, and TM 210 mode, respectively. It should be noted that both the circular and elliptical cavities are analyzed with a very small thickness (∼0.016λ) as an SIW cavity usually has, which means there is no variation of E-field along z-axis. When observing the E-field distributions in the elliptical cavity with k = 1.3, as illustrated in Figs. 2(a)-(d),  we find that the resonant modes in the elliptical cavity are quite similar to their counterparts in the circular cavity (a particular elliptical cavity with k = 1). Herein, according to the observed similarities, the first four resonant modes in the elliptical cavity can be named as quasi-TM 010 mode, quasi-TM 110 mode, degenerate quasi-TM 110 mode, and quasi-TM 210 mode, respectively, for convenience. The similarities between the elliptical and the circular cavities can pave the way using elliptical cavity for multi-mode CBSA design, and additionally, these resonant modes can be adjusted flexibly in terms of resonant frequencies, by tuning both the absolute size and the axial ratio k of the elliptical cavity. As displayed in Fig. 3, the normalized resonant frequencies of the first four modes in the elliptical cavity are plotted with k varying from 1.1 to 1.6. It can be seen that k influences obviously the frequency distribution of each resonant mode. If k is smaller than 1.2, the quasi-TM 110 mode and the degenerate quasi-TM 110 mode will be merged to each other and it is difficult to generate the corresponding odd-and even-modes. Besides, the bandwidth is narrow because of the adjacent distance between the degenerate quasi-TM 110 mode and the quasi-TM 210 mode if k is too large, i.e., 1.5 or even larger.
Thereby, choosing k at the approximate range of 1.3-1.4 for the frequency separation and optimal bandwidth. Furthermore, it is worth noticing that here k is served as a relative and independent value of operating frequency, which implies the cavity as well as the corresponding CBSA can be flexibly implemented to operate at any desired frequency band.

III. DESIGH OF SIW ELLIPTICAL CBSAS
A. PENTA-MODE SIW ELLIPTICAL CBSA First, a penta-resonance SIW elliptical CBSA is designed by implementing a cross-shaped slot and a pair of unbalanced   shorting vias into the elliptical cavity to generate the half quasi-TM 010 mode, the odd-and even-modes of quasi-TM 110 , and the odd-and even-modes of half degenerate quasi-TM 110 , which are corresponding to the aforementioned first three resonant modes of the original elliptical cavity. The geometry of the penta-mode antenna is shown in Fig. 4, and its size is determined to operate at X-band with k = 1.3. The SIW elliptical cavity is fulfilled in a substrate by arranging metallic vias along an elliptical curve. The cavity is fed through a 50 − microstrip line printed on the top copper layer, and a cross-shaped slot with different widths is etched on the bottom copper layer of the cavity. Two shorting vias with different radius are placed at the opposite sides referring to the longitude slot (along x-axis). Table 1 exhibits all dimensions of the proposed penta-mode SIW elliptical CBSA.
The simulated E-field distributions of the penta-mode antenna are represented in Figs. 5(a)-(e), which are in  Fig. 5 indicate the phases of sub regions divided by the cross-shaped slot, which are helpful to recognize the modes. As can be seen, five resonant modes are successfully generated in the proposed elliptical cavity, comparing with the quad-mode rectangular CBSA [14] in which the even half-TE 120 mode has not been effectively generated.
To further understand the generation of resonant modes, the design procedure is described as follows: 1) Design of the SIW elliptical cavity: including both the absolute size and k. As discussed in above, it can benefit from choosing k at the range of 1.3-1.4 that the resonant frequency of each mode can be separated sufficiently to result in a wide bandwidth; 2) Design of the cross-shaped slot: placing the latitude slot (along y-axis) at the place of the maximum E-field intensity of the quasi-TM 110 mode, which can introduce a discontinuity and excite the odd-and even-quasi-TM 110 modes with the half quasi-TM 010 mode [13]. Then placing the longitude slot at the place of the minimum E-field intensity of the half degenerate quasi-TM 110 mode to assist the generation of its odd-and even-modes with less effect on the original E-field distributions. Fig. 6 (a) depicts the generated conventional tri-mode resonance excited by the cross-shaped slot. The initial length of each slot can be chosen VOLUME 8, 2020 as a half wavelength at the central frequency of the operating band, i.e., 15mm @ 10 GHz, and later both the length and the width are further optimized for impedance matching. Noting that both the latitude and the longitude slots are essentially contributing as radiators simultaneously; 3) Design of the unbalanced shorting vias: similar with the method in [14], the two balanced loaded vias are introduced firstly at the place of the minimum E-field intensity of the odd-and evenquasi-TM 110 modes to keep their E-field distributions almost unchanged and meanwhile shift up the resonant frequency of the half quasi-TM 010 mode as presented in Fig. 6 (b). Second, introducing a relative offset along x-axis between the two shorting vias, as l 0 = l 3 − l 4 , to provide a perturbation for exciting the additional odd-and even-half degenerate quasi-TM 110 modes as shown in Fig. 6 (c). Finally, introducing another relative offset along y-axis between the two shorting vias, as d 0 , and tuning the radius of two shorting vias to adjust the input resistance mainly for the first resonant mode to achieve the best impedance match performance and desired bandwidth, as illustrated in Fig. 6 (d) and (e). To be more concrete, Fig. 7 describes further the generation of the odd-and even-half degenerate quasi-TM 110 modes. It can be observed that the odd-and even-half degenerate quasi-TM 110 modes are generated with the increasing of the offset l 0 along x-axis,  and l 0 = 1.46 is chosen to acquire an optimal resonance. The simulated and measured S-parameter of the proposed penta-mode SIW elliptical CBSA are plotted in Fig. 8, and the measured impedance bandwidth is 21.8% (8.83-10.99 GHz).

B. HEPTA-MODE SIW ELLIPTICAL CBSA
To further improve the operating bandwidth, a heptaresonance SIW elliptical CBSA is developed based on the penta-resonance CBSA, by further introducing another pair of unbalanced shorting vias into the elliptical cavity, as displayed in Fig. 9. The elliptical cavity is set with k = 1.4. Hence, the additional odd-and even-modes of quasi-TM 210 are successfully excited to realize the desired heptaresonance, thus utilizing all the aforementioned four resonant modes in the original elliptical cavity. Table 2    11.20 GHz, even quasi-TM 110 mode at 11.42 GHz, and oddand even-quasi-TM 210 modes at 11.75 and 12.13 GHz, respectively. It is clear that all the seven resonant modes are sufficiently separated from others, without merging into any hybrid mode as reported in [14].
Likewise, Fig. 11 shows the design procedure for the generation of the seven resonant modes by using the variation of the input resistance curves. The concrete design process of hepta-mode antenna is similarly summarized as follows: 1) repeating the design process of SIW elliptical cavity and the cross-shaped slot to generate the conventional tri-mode resonance as used in penta-mode CBSA; 2) Design of the unbalanced shorting vias: first, putting two pairs of balanced shorting vias into the elliptical cavity to shift upward the resonant frequencies of the half quasi-TM 010 mode and the odd-and even-quasi-TM 110 modes, and meanwhile introduce the even quasi-TM 210 mode as plotted in Fig. 11 (a). Second, offsetting the upper two vias along x-axis with the parameter l 0 = l 3 − −l 4 to excite the odd quasi-TM 210 mode as shown in Fig. 11 (b). Third, setting another offset between the upper two shorting vias along the y-axis with the parameter d 0 and movement s 1 to provide a further perturbation for exciting the even-and odd-half degenerate quasi-TM 110 modes, respectively, as observed in Fig. 11 (c) and (d). So far, the required seven resonant modes have been excited completely. The location and radius of the lower two shorting vias can be tuned as needed to achieve the best impedance match performance. The simulated and measured S-parameters of the proposed hepta-mode antenna are presented in Fig. 12, and the measured impedance bandwidth is 22.7% (9.75-12.25 GHz). Fig. 13 illustrates two prototypes of the penta-and the heptaresonance antennas, which are fabricated on a single-layer Taconic TLY substrate (ε r = 2.2, and tan δ = 0.0009) with thickness of h = 1 mm. The measured impedance bandwidth is 21.8% and 22.7%, respectively, as shown in Figs. 8 and 12. Fig. 14 displays the measured and simulated radiation patterns of these two types of antennas. The slight differences between the measured and simulated reflection coefficients   are attributed to the fabrication tolerance and the coaxial connecter, and the parasitic radiation from the connector further contributes to ripples appearing in the radiation patterns measured in the xoz-plane. The radiation efficiency and gain of the antennas are depicted in Fig. 15. The simulated radiation efficiency has a peak value of 97.2% and 95.6%, and the measured peak gain is 7.0 dBi and 7.4 dBi, respectively, both of which have a maximum gain variation within 2 dB. The gain fluctuation at high frequency is due to the alternating variation of in-and out-phase, which results in the small concaves on the gain and radiation efficiency curves. Table 3 gives a comparison among the proposed penta-and hepta-resonance SIW elliptical CBSAs with other previously reported SIW rectangular CBSAs. As can be seen that these two types of proposed SIW elliptical CBSAs occupy the prominent bandwidths as well as a high radiation efficiency. Moreover, it is worth pointing out that the introduced both five and seven resonant modes in the elliptical cavity are generated completely, and neither hybrid modes nor mode merging appears when comparing previous works which use the rectangular cavity in [14]. The successful generation of five and seven modes contributes to a wider operating bandwidth as expected. In addition, although prototypes are fabricated and measured at X-band, the presented design guidelines are independent of operating frequency, which is that the shape of the elliptical cavity is only determined by its axial ratio k, and the placement of cross-shape slot and shorting vias are mainly associated with E-field distributions of the resonant modes. Therefore, the proposed SIW CBSAs, by tuning their absolute geometrical size, can be theoretically implemented at any targeted frequency band, including millimeter-wave band, which will be studied in future work.

V. CONCLUSION
For X-band wideband wireless applications, two types of SIW elliptical CBSAs have been designed. The proposed penta-and hepta-resonance CBSAs exhibit a low profile of 0.03λ 0 , flexible tuning ability, and wide impedance bandwidth. For the penta-mode antenna, a wide bandwidth is obtained with the assistance of a cross-shaped slot and a pair of unbalanced shorting vias. As for the hepta-mode antenna, a wider bandwidth is accomplished through adding another pair of unbalanced shorting vias. To verify the design principles, prototypes of these SIW elliptical CBSAs have been fabricated and measured. Measured results show that the penta-and hepta-resonance antennas possess broad impedance bandwidths of 21.8% and 22.7%, respectively.