A Wideband Slotted Spherical Waveguide Antenna Based on Multi-Mode Concept

: A wideband slotted spherical waveguide antenna based on the multi-mode concept is presented. The proposed design starts from a metallized spherical cavity fed by a rectangular waveguide. Then, two groups of slots are symmetrically cut on the shell. By suitably choosing the slot dimensions and locations, four radiation modes can be excited in a single radiator and merged with each other, resulting in a wideband radiation characteristic. To verify this, a prototype is designed and fabricated using stereolithography apparatus to achieve a light weight. As the measured fractional bandwidth (FBW) of the proposed antenna can be increased to 70.1% while maintaining stable radiation patterns and high gain, a simple and e ﬀ ective design of wideband slotted waveguide antennas with good radiation characteristics can be validated.


Introduction
Due to their desired properties, including high power capacity, low loss, and high radiation gain, slotted waveguide antennas (SWAs) [1,2] have been extensively used in telecommunication systems, i.e., base stations. In recent decades, different SWAs were designed on the basis of cylindrical [3], rectangular [4], and annular [5] waveguides. Although the desirable properties can be realized in the above SWAs, only one radiation mode can be excited. Therefore, they suffer from intrinsically narrow bandwidth, which restricts their applications in high-data-rate wireless communications.
To improve SWA bandwidth, two methods are mostly used: the first one involves a rectangular ridge waveguide [6][7][8][9], and the other is based on a multilayer and corporate-fed structure [10][11][12][13]. Unfortunately, these two methods are only suitable for antenna arrays, which not only need a complex design process and large dimensions, but also expensive fabrication. Furthermore, their corresponding fractional bandwidth (FBW) is relatively small and no more than 36.9%. Such narrow operation bandwidth cannot satisfy the demands of modern telecommunication transceivers. Thus, it is significant to explore new design approaches for further widening SWA bandwidth.
Analogous to the design of wideband filters [14,15], an effective method using the multi-mode concept was proposed [16]. To further demonstrate this method, a new wideband SWA is presented in this paper. The proposed design starts from a metallized spherical cavity with four resonant modes, which is fabricated using stereolithography apparatus (SLA) to achieve light weight, as done in [17][18][19][20]. Then, some symmetrical slots are cut on the shell. With the help of these slots, the energy can be the FBW of the fabricated SWA can be effectively increased to 70.1% from 9.97 to 20.74 GHz, while high gain and stable radiation patterns are maintained. To the best of authors' knowledge, a SWA with such wide bandwidth has never been reported.

Operation Principle and Design
As illustrated in Figure 1, the antenna under study is based on an air-filled metallized spherical cavity with thickness of twall and radius of r, which is fed by a standard WR-90 waveguide segment with a length and height of LF and h, respectively, through a rectangular feeding window with LW × WF. Two groups of slots are symmetrically cut on the metallized cavity shell, which are named Group A and B. In Group A, there are seven slots, which are all symmetrical and parallel with the XOY-plane. The dimensions of slots in Group A are determined by width SA and angle αA, and the spacing between adjacent slots is WA. In Group B, there are two pairs of three slots, which are parallel with the XOZ-plane and symmetrical to the XOY-plane. The length and width of slots in Group B are LB and SB, respectively, and the spacing between adjacent slots is WB.

Resonant Modes
As mentioned in [21], multiple resonant modes exist in an air-filled metallized spherical cavity without any slots, and the frequencies of TM and TE modes can be determined as follows: TEnmp np TEnmp 2 2 where r presents the radius of the air-filled metallized spherical cavity, ωTMnmp and ωTEnmp are the corresponding nature angular frequencies, μ and ε present the permeability and permittivity of the

Resonant Modes
As mentioned in [21], multiple resonant modes exist in an air-filled metallized spherical cavity without any slots, and the frequencies of TM and TE modes can be determined as follows: where r presents the radius of the air-filled metallized spherical cavity, ω TMnmp and ω TEnmp are the corresponding nature angular frequencies, µ and ε present the permeability and permittivity of the dielectric in the cavity, and x np and y np are the roots of the eigenvalue equations, i.e., J n (x) = 0, and J n (y) = 0. Obviously, the resonant frequencies of TM and TE modes are not affected by the thickness of the metallized spherical cavity. Therefore, the thickness of t wall can be preset to 2.0 mm for balancing sufficient mechanical strength and fabrication costs in this design. Considering that the function of the standard 90-WR waveguide segment is to connect the proposed antenna with measuring equipment, its corresponding dimensions also can be predetermined and summarized as h = 5.0 mm, L F = 22.86 mm, and W F = 10.16 mm.
For the modes of TM 101 , TM 211 , TE 101 , and TM 311 , in an air-filled metallized spherical cavity, their corresponding values can be calculated and expressed as 2.774, 3.870, 4.493, and 4.973, respectively. Thus, the resonant frequencies of the four aforementioned modes in free space can be simplified as follows: where the unit of f is Hz while that of r is mm. Figure 2  dielectric in the cavity, and xnp and ynp are the roots of the eigenvalue equations, i.e., Jn′(x) = 0, and Jn′(y) = 0. Obviously, the resonant frequencies of TM and TE modes are not affected by the thickness of the metallized spherical cavity. Therefore, the thickness of twall can be preset to 2.0 mm for balancing sufficient mechanical strength and fabrication costs in this design. Considering that the function of the standard 90-WR waveguide segment is to connect the proposed antenna with measuring equipment, its corresponding dimensions also can be predetermined and summarized as h = 5.0 mm, LF = 22.86 mm, and WF = 10.16 mm.
For the modes of TM101, TM211, TE101, and TM311, in an air-filled metallized spherical cavity, their corresponding values can be calculated and expressed as 2.774, 3.870, 4.493, and 4.973, respectively. Thus, the resonant frequencies of the four aforementioned modes in free space can be simplified as follows:

TE101
2.1438 10 where the unit of f is Hz while that of r is mm. Figure 2

Design Principle of Wideband SWA
No energy can be radiated from an air-filled metallized cavity. To realize low cross-polarization and large radiation efficiency, slots, which are perpendicular to the surface current distributions of the metallized spherical cavity, should be symmetrically cut on the shell [22]. Thus, the first thing is to determine the surface current distributions of the metallized spherical cavity under the resonant modes of TM101, TM211, TE101, and TM311. As shown in Figure 3, the surface current directions of these four modes under study are perpendicular to the XOY-plane in blue dashed area while parallel to the YOZ-plane. Moreover, the surface current distribution of TE101 and TM311 modes also has a large current density in the red dashed area. Hence, the slots should be cut in these areas.

Design Principle of Wideband SWA
No energy can be radiated from an air-filled metallized cavity. To realize low cross-polarization and large radiation efficiency, slots, which are perpendicular to the surface current distributions of the metallized spherical cavity, should be symmetrically cut on the shell [22]. Thus, the first thing is to determine the surface current distributions of the metallized spherical cavity under the resonant modes of TM 101 , TM 211 , TE 101 , and TM 311 . As shown in Figure 3, the surface current directions of these four modes under study are perpendicular to the XOY-plane in blue dashed area while parallel to the YOZ-plane. Moreover, the surface current distribution of TE 101 and TM 311 modes also has a large current density in the red dashed area. Hence, the slots should be cut in these areas.
At first, slots are symmetrically cut in the blue dashed area, which are named Group A and parallel to the XOY-plane. In this case, a wideband SWA with dual resonances can be achieved. Its corresponding Electronics 2020, 9, 1656 4 of 11 performances are simultaneously determined by the slot number of N A and dimensions of W A , S A , and α A . As W A and S A have relatively smaller effects on SWA performance, whose main function is to ensure the sufficient mechanical strength, they can be assumed as 1.0 and 2.0 mm, respectively, to simplify the design procedure. Then, the relationships among the antenna directivity, slot number of N A , and slot angle of α A can be studied, as shown in Figure 4. Apparently, the directivity becomes larger with the increase in N A . As α A increases, the directivity becomes larger at first and then remains almost unaltered, before finally becoming smaller. Thus, the slot number N A should be chosen as 7, while the slot angle should be around 190 • for ensuring the maximum realized gain and radiation efficiency. At first, slots are symmetrically cut in the blue dashed area, which are named Group A and parallel to the XOY-plane. In this case, a wideband SWA with dual resonances can be achieved. Its corresponding performances are simultaneously determined by the slot number of NA and dimensions of WA, SA, and αA. As WA and SA have relatively smaller effects on SWA performance, whose main function is to ensure the sufficient mechanical strength, they can be assumed as 1.0 and 2.0 mm, respectively, to simplify the design procedure. Then, the relationships among the antenna directivity, slot number of NA, and slot angle of αA can be studied, as shown in Figure 4. Apparently, the directivity becomes larger with the increase in NA. As αA increases, the directivity becomes larger at first and then remains almost unaltered, before finally becoming smaller. Thus, the slot number NA should be chosen as 7, while the slot angle should be around 190° for ensuring the maximum realized gain and radiation efficiency.

Max
Min At first, slots are symmetrically cut in the blue dashed area, which are named Group A and parallel to the XOY-plane. In this case, a wideband SWA with dual resonances can be achieved. Its corresponding performances are simultaneously determined by the slot number of NA and dimensions of WA, SA, and αA. As WA and SA have relatively smaller effects on SWA performance, whose main function is to ensure the sufficient mechanical strength, they can be assumed as 1.0 and 2.0 mm, respectively, to simplify the design procedure. Then, the relationships among the antenna directivity, slot number of NA, and slot angle of αA can be studied, as shown in Figure 4. Apparently, the directivity becomes larger with the increase in NA. As αA increases, the directivity becomes larger at first and then remains almost unaltered, before finally becoming smaller. Thus, the slot number NA should be chosen as 7, while the slot angle should be around 190° for ensuring the maximum realized gain and radiation efficiency.  After determining W A , S A , and α A , the impedance matching of SWA near the two lower radiation modes of TM 101 and TM 211 is largely affected by the slot number N A , as shown in Figure 5. As the slot number N A increases, the impedance matching near the radiation modes of TM 101 and TM 211 improve, Electronics 2020, 9, 1656 5 of 11 and these two radiation modes are merged with each other when N A = 7, resulting in a wideband SWA with two resonances.
Electronics 2020, 9, x FOR PEER REVIEW 5 of 12 After determining WA, SA, and αA, the impedance matching of SWA near the two lower radiation modes of TM101 and TM211 is largely affected by the slot number NA, as shown in Figure 5. As the slot number NA increases, the impedance matching near the radiation modes of TM101 and TM211 improve, and these two radiation modes are merged with each other when NA = 7, resulting in a wideband SWA with two resonances. From Figure 5, it is apparent that the antenna bandwidth can be further widened if the matching near 16.5 GHz is improved. Hence, other slots named Group B are then introduced in the red area exhibiting a large current density. Similar to the slots in Group A, the width and spacing of slots in Group B can also be assumed as 1.0 and 1.2 mm to simplify the design procedure. In addition, the relationships among the antenna directivity, slot number of NB, and slot length of LB are illustrated in Figure 6. With the increase in NB, the antenna directivity becomes larger. As LB increases, the antenna directivity becomes larger at first, before decreasing. Hence, the slot number NB should be 3 for ensuring the maximum directivity and radiation efficiency.  Under the condition of NB = 3, the matching near the upper two radiation modes of TE101 and TM311 are mainly determined by the slot length of LB, as illustrated in Figure 7. It is apparent that the impedance matching near these two radiation modes improves with the increase in LB, while that near the lower two modes of TM101 and TM211 is not deteriorated. Furthermore, these four modes are merged with each other when LB = 11.0 mm, resulting in a wideband SWA with four resonances. From Figure 5, it is apparent that the antenna bandwidth can be further widened if the matching near 16.5 GHz is improved. Hence, other slots named Group B are then introduced in the red area exhibiting a large current density. Similar to the slots in Group A, the width and spacing of slots in Group B can also be assumed as 1.0 and 1.2 mm to simplify the design procedure. In addition, the relationships among the antenna directivity, slot number of N B , and slot length of L B are illustrated in Figure 6. With the increase in N B , the antenna directivity becomes larger. As L B increases, the antenna directivity becomes larger at first, before decreasing. Hence, the slot number N B should be 3 for ensuring the maximum directivity and radiation efficiency.
Electronics 2020, 9, x FOR PEER REVIEW 5 of 12 After determining WA, SA, and αA, the impedance matching of SWA near the two lower radiation modes of TM101 and TM211 is largely affected by the slot number NA, as shown in Figure 5. As the slot number NA increases, the impedance matching near the radiation modes of TM101 and TM211 improve, and these two radiation modes are merged with each other when NA = 7, resulting in a wideband SWA with two resonances. From Figure 5, it is apparent that the antenna bandwidth can be further widened if the matching near 16.5 GHz is improved. Hence, other slots named Group B are then introduced in the red area exhibiting a large current density. Similar to the slots in Group A, the width and spacing of slots in Group B can also be assumed as 1.0 and 1.2 mm to simplify the design procedure. In addition, the relationships among the antenna directivity, slot number of NB, and slot length of LB are illustrated in Figure 6. With the increase in NB, the antenna directivity becomes larger. As LB increases, the antenna directivity becomes larger at first, before decreasing. Hence, the slot number NB should be 3 for ensuring the maximum directivity and radiation efficiency.  Under the condition of NB = 3, the matching near the upper two radiation modes of TE101 and TM311 are mainly determined by the slot length of LB, as illustrated in Figure 7. It is apparent that the impedance matching near these two radiation modes improves with the increase in LB, while that near the lower two modes of TM101 and TM211 is not deteriorated. Furthermore, these four modes are merged with each other when LB = 11.0 mm, resulting in a wideband SWA with four resonances. Under the condition of N B = 3, the matching near the upper two radiation modes of TE 101 and TM 311 are mainly determined by the slot length of L B , as illustrated in Figure 7. It is apparent that the impedance matching near these two radiation modes improves with the increase in L B , while that near the lower two modes of TM 101 and TM 211 is not deteriorated. Furthermore, these four modes are merged with each other when L B = 11.0 mm, resulting in a wideband SWA with four resonances.
In addition to the above parameters, the impedance matching is also significantly affected by the feeding window length of L W , as shown in Figure 8. It is apparent that the impedance matching near the two lower radiation modes is sensitive to L W , which has little effect on the matching near the two upper radiation modes. In this design, the length of feeding window L W is better chosen as 16.6 mm. In addition to the above parameters, the impedance matching is also significantly affected by the feeding window length of LW, as shown in Figure 8. It is apparent that the impedance matching near the two lower radiation modes is sensitive to LW, which has little effect on the matching near the two upper radiation modes. In this design, the length of feeding window LW is better chosen as 16.6 mm.  On the basis of the above discussion and analysis, a waveguide-fed SWA can be designed, whose simulated frequency responses of refection coefficient are shown in Figure 8 by the blue line. It is clearly observed that four radiation modes can be obtained in the proposed SWA. This indicates that four radiation modes in a single radiator can be successfully excited in a wide operation band.

Fabrication and Results
For verification, a wideband SWA was designed and measured. The proposed SWA was fabricated using SLA and electroless copper technologies, whose advantages and fabrication processes were exhaustively explained in [19]. In order to minimize the SWA weight, a low-density ceramic-filled photosensitive resin was used as the printing material. After printing the resin structure, the surface metallization was performed with the help of a 10 μm thick conductive layer of copper. Figure 9 shows the photographs of the proposed antenna before and after metallization, which was fed by a WR  In addition to the above parameters, the impedance matching is also significantly affected by the feeding window length of LW, as shown in Figure 8. It is apparent that the impedance matching near the two lower radiation modes is sensitive to LW, which has little effect on the matching near the two upper radiation modes. In this design, the length of feeding window LW is better chosen as 16.6 mm. On the basis of the above discussion and analysis, a waveguide-fed SWA can be designed, whose simulated frequency responses of refection coefficient are shown in Figure 8 by the blue line. It is clearly observed that four radiation modes can be obtained in the proposed SWA. This indicates that four radiation modes in a single radiator can be successfully excited in a wide operation band.

Fabrication and Results
For verification, a wideband SWA was designed and measured. The proposed SWA was fabricated using SLA and electroless copper technologies, whose advantages and fabrication processes were exhaustively explained in [19]. In order to minimize the SWA weight, a low-density ceramic-filled photosensitive resin was used as the printing material. After printing the resin structure, the surface metallization was performed with the help of a 10 μm thick conductive layer of copper. Figure 9 shows the photographs of the proposed antenna before and after metallization On the basis of the above discussion and analysis, a waveguide-fed SWA can be designed, whose simulated frequency responses of refection coefficient are shown in Figure 8 by the blue line. It is clearly observed that four radiation modes can be obtained in the proposed SWA. This indicates that four radiation modes in a single radiator can be successfully excited in a wide operation band.

Fabrication and Results
For verification, a wideband SWA was designed and measured. The proposed SWA was fabricated using SLA and electroless copper technologies, whose advantages and fabrication processes were exhaustively explained in [19]. In order to minimize the SWA weight, a low-density ceramic-filled photosensitive resin was used as the printing material. After printing the resin structure, the surface metallization was performed with the help of a 10 µm thick conductive layer of copper. Figure 9 shows the photographs of the proposed antenna before and after metallization, which was fed by a WR-90 waveguide. The final dimensions of the proposed antenna were concluded as folows: r = 12. The reflection coefficient and radiation patterns were measured using a Keysight N5224A vector network analyzer and anechoic chamber, respectively. When measured at the X band, the antenna was connected with a WR-90 adaptor. When measured at other bands, the antenna was mated to a WR-62 waveguide-to-coax adapter through an X-to-other-band waveguide taper. In Figure 10, the measured set-ups in the anechoic chamber are illustrated. In Figure 11, the measured and simulated reflection coefficients are compared with each other. Obviously, they are in good agreement with each other, and four measured radiation modes can be clearly observed at 10.81, 12.48, 16.37, and 18.69 GHz, respectively. Moreover, the impedance matching is better than −10.0 dB over a wide frequency range from 9.97 to 20.74 GHz. Hence, the FBW of the proposed SWA is 70.1%, while the center frequency (CF) is 15.36 GHz. The reflection coefficient and radiation patterns were measured using a Keysight N5224A vector network analyzer and anechoic chamber, respectively. When measured at the X band, the antenna was connected with a WR-90 adaptor. When measured at other bands, the antenna was mated to a WR-62 waveguide-to-coax adapter through an X-to-other-band waveguide taper. In Figure 10, the measured set-ups in the anechoic chamber are illustrated. The reflection coefficient and radiation patterns were measured using a Keysight N5224A vector network analyzer and anechoic chamber, respectively. When measured at the X band, the antenna was connected with a WR-90 adaptor. When measured at other bands, the antenna was mated to a WR-62 waveguide-to-coax adapter through an X-to-other-band waveguide taper. In Figure 10, the measured set-ups in the anechoic chamber are illustrated. In Figure 11, the measured and simulated reflection coefficients are compared with each other. Obviously, they are in good agreement with each other, and four measured radiation modes can be clearly observed at 10.81, 12.48, 16.37, and 18.69 GHz, respectively. Moreover, the impedance matching is better than −10.0 dB over a wide frequency range from 9.97 to 20.74 GHz. Hence, the FBW of the proposed SWA is 70.1%, while the center frequency (CF) is 15.36 GHz. In Figure 11, the measured and simulated reflection coefficients are compared with each other. Obviously, they are in good agreement with each other, and four measured radiation modes can be clearly observed at 10.81, 12.48, 16.37, and 18.69 GHz, respectively. Moreover, the impedance matching is better than −10.0 dB over a wide frequency range from 9.97 to 20.74 GHz. Hence, the FBW of the proposed SWA is 70.1%, while the center frequency (CF) is 15.36 GHz. In Figure 12, the normalized radiation patterns of the proposed antenna at 11.0, 16.15, and 20.0 GHz are illustrated. It is apparent that the measured and simulated results agree well with each other. Within the impedance bandwidth, the sidelobes at the H plane were effectively suppressed, and the stable directional radiation patterns were maintained, while peak gain was absolutely located in the direction of θ = 90° and φ = 90°. Additionally, two sidelobes were found at the E plane,  In Figure 12, the normalized radiation patterns of the proposed antenna at 11.0, 16.15, and 20.0 GHz are illustrated. It is apparent that the measured and simulated results agree well with each other. Within the impedance bandwidth, the sidelobes at the H plane were effectively suppressed, and the stable directional radiation patterns were maintained, while peak gain was absolutely located in the direction of θ = 90 • and ϕ = 90 • . Additionally, two sidelobes were found at the E plane, which became larger with the increase in operation frequency. This is because, with the increase in operation frequency, the surface currents in the red areas become larger, as shown in Figure 2. Hence, there will be energy radiated from these areas when the currents are disturbed by slots in Group B, and more energy will be radiated as the operation frequency increases. In Figure 13, the simulated and measured peak gains are presented with the radiation efficiency. Apparently, the measured peak gain is varied from 9.32 to 13.89 dBi within the operation bandwidth, while the average peak gain is 11.38 dBi. Furthermore, the radiation efficiency is above 91%. In Figure 12, the normalized radiation patterns of the proposed antenna at 11.0, 16.15, and 20.0 GHz are illustrated. It is apparent that the measured and simulated results agree well with each other. Within the impedance bandwidth, the sidelobes at the H plane were effectively suppressed, and the stable directional radiation patterns were maintained, while peak gain was absolutely located in the direction of θ = 90° and φ = 90°. Additionally, two sidelobes were found at the E plane, which became larger with the increase in operation frequency. This is because, with the increase in operation frequency, the surface currents in the red areas become larger, as shown in Figure 2. Hence, there will be energy radiated from these areas when the currents are disturbed by slots in Group B, and more energy will be radiated as the operation frequency increases. In Figure 13, the simulated and measured peak gains are presented with the radiation efficiency. Apparently, the measured peak gain is varied from 9.32 to 13.89 dBi within the operation bandwidth, while the average peak gain is 11.38 dBi. Furthermore, the radiation efficiency is above 91%.

Discussion
In general, the proposed method is more attractive in the design of high-gain and wideband SWAs. As the frequencies of multiple modes are only controlled by the inner radius of the spherical cavity, and the radiation modes can be merged with each other by suitably cutting some slots on the shell, some parameters, including the thickness of spherical cavity, spacing between adjacent slots, slot width, and dimensions of standard WR-90 waveguide segment, have relatively smaller effects on the antenna responses. To reduce the design complicity, these parameters can be preset by balancing sufficient mechanical strength and fabrication costs. Moreover, after knowing SWA center frequency and bandwidth, the inner radius and employed radiation modes can be decided. By investigating the surface current density under the employed radiation modes, the slot locations can be ascertained, and the slot number and length can be initially determined. For obtaining the best performance, the relationships among SWA responses, slot number, and length are studied. Of course, the feeding window affects the match near the two lower radiation modes, which also need to be investigated. After finishing the above steps, the final parameters of SWA with desired center frequency and bandwidth can be determined. Thus, this antenna is designed using an engineering design process, not a cut-and-try method.
On the other hand, there were some discrepancies among the simulated and measured results. These may have been caused by the fabrication precision, discontinuity effects, and so on. To highlight the merits of the proposed SWA, comparisons between this work and other high-power designs are listed in Table 1. Apparently, as the proposed SWA is a unit antenna fabricated by three-dimensional (3D) printing technology, it is light weight with a simple design process. Furthermore, the proposed SWA owns the widest operation bandwidth compared with other high-power antennas.

Conclusions
In this paper, a novel wideband waveguide-fed SWA with excellent radiation characteristics was presented. The proposed design was based on 3D printing and multi-mode technologies. By suitably introducing some symmetrical slots on the shell of a metallized spherical cavity, four radiation modes could be excited and merged with each other, resulting in a wide radiation characteristic. The measured results showed that the proposed antenna had the widest operation bandwidth and excellent radiation patterns. It can be anticipated that the proposed SWA will be extensively used in modern high-data-rate telecommunication systems.