A Ka-Band Circular Polarized Waveguide Slot Antenna with a Cross Iris

Featured Application: Segment waveguide slot antenna for a satellite communication and radar. Abstract: A Ka-band circularly polarized (CP) waveguide slot antenna with a cross iris is proposed. To achieve the CP characteristic (LHCP) in the antenna, a hexagonal shaped cavity is used. The impedance matching is improved by adjusting the sizes of the hexagonal cavity and a rectangular matching cavity. To enhance the axial ratio bandwidth, a cross iris is used with two arms of di ﬀ erent lengths. From experimental results, the proposed antenna has a 3 dB axial ratio bandwidth of 6810 MHz (31.72 GHz–38.53 GHz). The − 10 dB reﬂection coe ﬃ cient bandwidth of the proposed antenna ranges from 31.51 GHz to 39.21 GHz (7700 MHz). dB axial ratio is peak gains are 9.08 and at gains of 7.87 dBi and 5.76 dBi are achieved at those two frequencies,


Introduction
Millimeter-wave communication systems support a higher data rate and larger capacity. Millimeter wave frequency has therefore been widely used in various applications such as 5G mobile, radar, satellite, military, and automotive communications [1]. Because mm-wave signals can be easily distorted by atmospheric interference such as fog or dust, waveguide antennas have been considered among the most appropriate for mm-wave applications due to their high power handling, high gain, stable performance and low transmission loss [2,3]. The polarization of antennas is one of the important factors in determining the performance of the communication. For linear polarization antenna, if the polarizations of a transmitter and a receiver do not match each other, communication performance deteriorates. Meanwhile, circular polarization avoids polarization misalignment as the electric field rotates, and it reduces multipath fading with flexibility in orientation the angle between the transmitted receiver [4,5]. Therefore, circular polarized (CP) waveguide antennas in particular are widely used in modern satellite communication systems due to their advantages of enhancing the channel stability and reliability [6,7]. Several techniques have been introduced to realize the waveguide CP horn and aperture antennas such as using a printed circuit board with four printed hook shaped arms [7], loading two metallic arms with a 45 • inclination angle [8], and inserting a meta-surface polarizer or chiral metamaterial transformer [6,9]. However, there are some limitations in applying them to various applications since these antennas are relatively bulky and heavy. In addition, they are not suitable for array systems because a large space is required for polarizers to be installed [10]. Therefore, such antennas are not appropriate for satellite communication systems requiring a high gain array structure with compact size. To overcome these drawbacks of bulk and mass, various types of circular polarized waveguide slot antennas have been studied [11][12][13][14][15][16][17]. Waveguide inclined slot, crossed slot, and v-type slot antennas have been widely used for CP array antennas to generate circularly polarized waves with high gain [13][14][15][16][17]. However, there are few reports on either widening the axial ratio bandwidth of the waveguide slot antenna at the millimeter-wave band region or the design of waveguide slot CP antennas [16,17].
This paper proposes a Ka-band circularly polarized waveguide slot antenna with a cross iris. To achieve a circular polarization characteristic, a hexagonal shaped cavity is used [18]. By mounting a cross iris, the circular polarization performance of the proposed antenna is enhanced. The proposed antenna provides a −10 dB reflection coefficient bandwidth covering from 31.51 GHz to 39.21 GHz. The 3 dB axial ratio bandwidth is 6810 MHz (31.72 GHz-38.53 GHz). The antenna peak gains are 9.08 dBi at 33.5 GHz and 7.33 dBi at 37.6 GHz. The boresight gains of 7.87 dBi and 5.76 dBi are achieved at those two frequencies, respectively. Figure 1 shows the structure of the proposed CP waveguide slot antenna consisting of a rectangular waveguide, an air metal box with hexagonal cavity and matching slot, and a cross iris at the bottom of the rectangular waveguide. The proposed antenna has dimensions of 10.1 mm × 23 mm × 7.06 mm and is made of a copper with a conductivity of 5.8001 × 10 7 S/m. The detailed parameters of the proposed antenna are shown in Figure 1 and the dimensions are given in Table 1. The performances of the proposed antenna were simulated using the commercial electromagnetic simulator, High Frequency Structure Simulator (HFSS) [19]. The antenna is fed from the rectangular waveguide to excite the TE 10 mode for high power handling capability. The dimensions (a = 7.11 mm and b = 3.56 mm) of the feeding waveguide are determined by the cutoff frequency (21.077 GHz) using the following equation with dimensions shown in Figure 2 [20]. As shown in Figure 2, the waveguide has its longest dimension along the x-axis (a).

Antenna Design
When a > b, the cutoff frequency of TE 10 (m = 1, n = 0) mode becomes where µ 0 and ε 0 are the permeability and permittivity of free space, respectively.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 15 reports on either widening the axial ratio bandwidth of the waveguide slot antenna at the millimeterwave band region or the design of waveguide slot CP antennas [16,17]. This paper proposes a Ka-band circularly polarized waveguide slot antenna with a cross iris. To achieve a circular polarization characteristic, a hexagonal shaped cavity is used [18]. By mounting a cross iris, the circular polarization performance of the proposed antenna is enhanced. The proposed antenna provides a −10 dB reflection coefficient bandwidth covering from 31.51 GHz to 39.21 GHz. The 3 dB axial ratio bandwidth is 6810 MHz (31.72 GHz-38.53 GHz). The antenna peak gains are 9.08 dBi at 33.5 GHz and 7.33 dBi at 37.6 GHz. The boresight gains of 7.87 dBi and 5.76 dBi are achieved at those two frequencies, respectively. Figure 1 shows the structure of the proposed CP waveguide slot antenna consisting of a rectangular waveguide, an air metal box with hexagonal cavity and matching slot, and a cross iris at the bottom of the rectangular waveguide. The proposed antenna has dimensions of 10.1 mm × 23 mm × 7.06 mm and is made of a copper with a conductivity of 5.8001 × 10 7 S/m. The detailed parameters of the proposed antenna are shown in Figure 1 and the dimensions are given in Table 1. The performances of the proposed antenna were simulated using the commercial electromagnetic simulator, High Frequency Structure Simulator (HFSS) [19]. The antenna is fed from the rectangular waveguide to excite the TE mode for high power handling capability. The dimensions ( = 7.11 mm and = 3.56 mm) of the feeding waveguide are determined by the cutoff frequency (21.077 GHz) using the following equation with dimensions shown in Figure 2 [20]. As shown in Figure 2, the waveguide has its longest dimension along the x-axis (a).

Antenna Design
When a > b, the cutoff frequency of TE10 (m = 1, n = 0) mode becomes where μ 0 and ε 0 are the permeability and permittivity of free space, respectively.

Antenna Analysis
In the proposed antenna design, the hexagonal shaped cavity with a rectangular waveguide shown in Figure 3 is used as an initial model (first reference antenna) to realize the circular polarization. The hexagonal shape is similar to a corner truncated patch antenna, which can be theoretically analyzed using a cavity model with the magnetic walls resonating in TM (Transverse Magnetic) mode [21]. However, this hexagonal cavity resonates TE mode with electrical side walls [22]. The truncated corners make the hexagonal cavity generate E-fields as two orthogonal modes, which are written in this paper as the E 1 mode and E 2 mode. As shown in Figure 4, because the truncated part (C 1 ) acts as additional capacitive loading, the E 1 mode has slower phase velocity and smaller guided wavelength than does the E 2 mode. As a result, a CP mode is generated by the addition of a lagging (E 1 ) mode and leading (E 2 ) mode.

Antenna Analysis
In the proposed antenna design, the hexagonal shaped cavity with a rectangular waveguide shown in Figure 3 is used as an initial model (first reference antenna) to realize the circular polarization. The hexagonal shape is similar to a corner truncated patch antenna, which can be theoretically analyzed using a cavity model with the magnetic walls resonating in TM (Transverse Magnetic) mode [21]. However, this hexagonal cavity resonates TE mode with electrical side walls [22]. The truncated corners make the hexagonal cavity generate E-fields as two orthogonal modes, which are written in this paper as the E1 mode and E2 mode. As shown in Figure 4, because the truncated part (C1) acts as additional capacitive loading, the E1 mode has slower phase velocity and smaller guided wavelength than does the E2 mode. As a result, a CP mode is generated by the addition of a lagging (E1) mode and leading (E2) mode.  In a waveguide antenna, the operating frequency and axial ratio performance are predominantly affected by the dimension and shape of the cavity [17,22]. As the dimension of a hexagonal cavity increases, the operation frequency bandwidth is expected to increase. However, the dimension of the hexagonal cavity is limited to the size of a feeding rectangular waveguide. Under such restriction, the lengths of a set of diagonal edges (C1 and C2) of the cavity are optimized to obtain the best performance. Figure 5 shows the simulated reflection coefficient and axial ratio of the first reference antenna with different values of C1 and C2. As shown in Figure 5, as the dimension of the hexagonal cavity becomes smaller the resonance frequency shifts to the higher side. The circular polarization performance of the first reference antenna is acceptable when C1 = 6.5 mm and C2 = 4.4 mm with the 3 dB axial ratio bandwidth ranging from 30.37 GHz to 31.2 GHz. The first reference antenna has a −6 dB reflection coefficient bandwidth of 3250 MHz (from 30.23 GHz to 33.48 GHz).

Antenna Analysis
In the proposed antenna design, the hexagonal shaped cavity with a rectangular waveguide shown in Figure 3 is used as an initial model (first reference antenna) to realize the circular polarization. The hexagonal shape is similar to a corner truncated patch antenna, which can be theoretically analyzed using a cavity model with the magnetic walls resonating in TM (Transverse Magnetic) mode [21]. However, this hexagonal cavity resonates TE mode with electrical side walls [22]. The truncated corners make the hexagonal cavity generate E-fields as two orthogonal modes, which are written in this paper as the E1 mode and E2 mode. As shown in Figure 4, because the truncated part (C1) acts as additional capacitive loading, the E1 mode has slower phase velocity and smaller guided wavelength than does the E2 mode. As a result, a CP mode is generated by the addition of a lagging (E1) mode and leading (E2) mode.  In a waveguide antenna, the operating frequency and axial ratio performance are predominantly affected by the dimension and shape of the cavity [17,22]. As the dimension of a hexagonal cavity increases, the operation frequency bandwidth is expected to increase. However, the dimension of the hexagonal cavity is limited to the size of a feeding rectangular waveguide. Under such restriction, the lengths of a set of diagonal edges (C1 and C2) of the cavity are optimized to obtain the best performance. Figure 5 shows the simulated reflection coefficient and axial ratio of the first reference antenna with different values of C1 and C2. As shown in Figure 5, as the dimension of the hexagonal cavity becomes smaller the resonance frequency shifts to the higher side. The circular polarization performance of the first reference antenna is acceptable when C1 = 6.5 mm and C2 = 4.4 mm with the 3 dB axial ratio bandwidth ranging from 30.37 GHz to 31.2 GHz. The first reference antenna has a −6 dB reflection coefficient bandwidth of 3250 MHz (from 30.23 GHz to 33.48 GHz). In a waveguide antenna, the operating frequency and axial ratio performance are predominantly affected by the dimension and shape of the cavity [17,22]. As the dimension of a hexagonal cavity increases, the operation frequency bandwidth is expected to increase. However, the dimension of the hexagonal cavity is limited to the size of a feeding rectangular waveguide. Under such restriction, the lengths of a set of diagonal edges (C 1 and C 2 ) of the cavity are optimized to obtain the best performance. Figure 5 shows the simulated reflection coefficient and axial ratio of the first reference antenna with different values of C 1 and C 2 . As shown in Figure 5, as the dimension of the hexagonal cavity becomes smaller the resonance frequency shifts to the higher side. The circular polarization performance of the first reference antenna is acceptable when C 1 = 6.5 mm and C 2 = 4.4 mm with the 3 dB axial ratio bandwidth ranging from 30.37 GHz to 31.2 GHz. The first reference antenna has a −6 dB reflection coefficient bandwidth of 3250 MHz (from 30.23 GHz to 33.48 GHz). To investigate that the circular polarization characteristic is achieved by the hexagonal cavity, the variation of the electric field distributions of the first reference antenna with different phases at 31 GHz are illustrated in Figure 6. As shown in Figure 6, the electric field rotates clockwise as the phase changes from 0° to 270°. Therefore, we conclude that the first reference antenna has a lefthanded circular polarization (LHCP) characteristic. To investigate that the circular polarization characteristic is achieved by the hexagonal cavity, the variation of the electric field distributions of the first reference antenna with different phases at 31 GHz are illustrated in Figure 6. As shown in Figure 6, the electric field rotates clockwise as the phase changes from 0 • to 270 • . Therefore, we conclude that the first reference antenna has a left-handed circular polarization (LHCP) characteristic. Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 15 Although the first reference antenna presents a reasonably good −6 dB reflection coefficient and 3 dB axial ratio bandwidth, additional impedance matching is required because satellite applications generally impose a −10 dB reflection coefficient criteria for communication efficiency [23]. To improve the impedance matching characteristic, we added a rectangular matching cavity located on the hexagonal cavity (second reference antenna). In the equivalent circuit, the long side (S2) of the matching cavity acts as a capacitance while the short side (S1) has an inductive characteristic [24]. Therefore, the impedance matching from the feeding rectangular waveguide to free space is improved through choosing proper values of S1 and S2 for the height (H3) of 0.5 mm. The optimized values of S1 and S2 are 4.3 mm and 4.8 mm, respectively. As shown in Figure 7, the simulated −10 dB impedance bandwidth of the second reference antenna becomes 5690 MHz (30.81-36.50 GHz). Meanwhile, the 3 dB axial ratio bandwidth obtained is 900 MHz (31.79-32.69 GHz). This result indicates that the resonance frequency is moved to the upper frequency side because the dimension of the aperture changes by the addition of the rectangular matching cavity. A similar observation can be made for the axial ratio characteristic. In the second reference antenna, although the −10 dB reflection coefficient bandwidth of 5690 MHz is achieved, most of the bandwidth except for 900 MHz (31.79 GHz-32.69 GHz) does not satisfy the 3 dB axial ratio requirement. This challenge often occurs when designing CP antennas [17,25]. Although the first reference antenna presents a reasonably good −6 dB reflection coefficient and 3 dB axial ratio bandwidth, additional impedance matching is required because satellite applications generally impose a −10 dB reflection coefficient criteria for communication efficiency [23]. To improve the impedance matching characteristic, we added a rectangular matching cavity located on the hexagonal cavity (second reference antenna). In the equivalent circuit, the long side (S 2 ) of the matching cavity acts as a capacitance while the short side (S 1 ) has an inductive characteristic [24]. Therefore, the impedance matching from the feeding rectangular waveguide to free space is improved through choosing proper values of S 1 and S 2 for the height (H 3 ) of 0.5 mm. The optimized values of S 1 and S 2 are 4.3 mm and 4.8 mm, respectively. As shown in Figure 7, the simulated −10 dB impedance bandwidth of the second reference antenna becomes 5690 MHz (30.81-36.50 GHz). Meanwhile, the 3 dB axial ratio bandwidth obtained is 900 MHz (31.79-32.69 GHz). This result indicates that the resonance frequency is moved to the upper frequency side because the dimension of the aperture changes by the addition of the rectangular matching cavity. A similar observation can be made for the axial ratio characteristic. In the second reference antenna, although the −10 dB reflection coefficient bandwidth of 5690 MHz is achieved, most of the bandwidth except for 900 MHz (31.79 GHz-32.69 GHz) does not satisfy the 3 dB axial ratio requirement. This challenge often occurs when designing CP antennas [17,25].  In the proposed antenna, to resolve this problem, a metallic cross iris is mounted on the bottom of the rectangular feeding waveguide to enhance the axial ratio bandwidth which is an important factor for evaluating the CP performance. It can be calculated using the following equation [26].
where r is the ratio of magnitudes of orthogonal electric fields, and ∆ is the phase difference between the two orthogonal electric fields at the far zone. In general, it can be said that CP operates well when the value of the axial ratio is less than 3 dB. Accordingly, when r = 1, the phase difference should In the proposed antenna, to resolve this problem, a metallic cross iris is mounted on the bottom of the rectangular feeding waveguide to enhance the axial ratio bandwidth which is an important factor for evaluating the CP performance. It can be calculated using the following equation [26].
AR linear scale = r 2 + 1 2 + r 4 + 1 4 + 2r 2 cos(2∆) 1/2 1/2 r 2 + 1 2 − [r 4 + 1 4 + 2r 2 cos(2∆)] 1/2 1/2 (3) where r is the ratio of magnitudes of orthogonal electric fields, and ∆ is the phase difference between the two orthogonal electric fields at the far zone. In general, it can be said that CP operates well when the value of the axial ratio is less than 3 dB. Accordingly, when r = 1, the phase difference should range from 70 • to 110 • and when ∆ = 90 • , the ratio of magnitudes should satisfy the range of 1 Figure 8 shows the simulated phase differences between the two orthogonal modes (E 1 and E 2 ) of the proposed antenna and the second reference antenna. The phases of the two orthogonal electric fields can be minutely controlled separately because the iris structure consists of two arms with asymmetrical lengths (L 1 and L 2 ). By adjusting the lengths of the cross iris, the improved 90 • phase difference range (70 • to 110 • ) is achieved (31.70 GHz-39.25 GHz). However, the 3 dB axial ratio bandwidth is not the same as the 90 • phase difference range because the ratio of the magnitude of the two orthogonal electric fields should be considered.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 15 Figure 8 shows the simulated phase differences between the two orthogonal modes (E1 and E2) of the proposed antenna and the second reference antenna. The phases of the two orthogonal electric fields can be minutely controlled separately because the iris structure consists of two arms with asymmetrical lengths (L1 and L2). By adjusting the lengths of the cross iris, the improved 90° phase difference range (70° to 110°) is achieved (31.70 GHz-39.25 GHz). However, the 3 dB axial ratio bandwidth is not the same as the 90° phase difference range because the ratio of the magnitude of the two orthogonal electric fields should be considered. To analyze how the cross iris affects the magnitude of the two electric fields, simulated amplitudes of the two orthogonal modes of the proposed antenna and the second reference antenna are presented in Figure 9. In the second reference antenna, the two points where the mode lines cross are located at 30.04 GHz and 31.80 GHz. At these two points, the magnitudes of the two modes are equal. However, as shown in Figure 8, because the 90° phase difference range of the second reference antenna is from 31.7 GHz, it cannot be said that CP is generated at less than 31.7 GHz. Moreover, the difference in amplitude between the two modes from the second point (31.8 GHz) is increasing, which indicates deteriorated CP performance. For the proposed antenna, the magnitudes of the two orthogonal modes are equal at three points (30.75 GHz, 32.32 GHz, and 38.44 GHz). In addition, the amplitudes of the two modes become close to each other over the whole frequency range from (32.32 GHz to 38.44 GHz). It can be said that the proposed antenna has a good equal magnitude characteristic. To analyze how the cross iris affects the magnitude of the two electric fields, simulated amplitudes of the two orthogonal modes of the proposed antenna and the second reference antenna are presented in Figure 9. In the second reference antenna, the two points where the mode lines cross are located at 30.04 GHz and 31.80 GHz. At these two points, the magnitudes of the two modes are equal. However, as shown in Figure 8, because the 90 • phase difference range of the second reference antenna is from 31.7 GHz, it cannot be said that CP is generated at less than 31.7 GHz. Moreover, the difference in amplitude between the two modes from the second point (31.8 GHz) is increasing, which indicates deteriorated CP performance. For the proposed antenna, the magnitudes of the two orthogonal modes are equal at three points (30.75 GHz, 32.32 GHz, and 38.44 GHz). In addition, the amplitudes of the two modes become close to each other over the whole frequency range from (32.32 GHz to 38.44 GHz). It can be said that the proposed antenna has a good equal magnitude characteristic. 31.7 GHz, it cannot be said that CP is generated at less than 31.7 GHz. Moreover, the difference in amplitude between the two modes from the second point (31.8 GHz) is increasing, which indicates deteriorated CP performance. For the proposed antenna, the magnitudes of the two orthogonal modes are equal at three points (30.75 GHz, 32.32 GHz, and 38.44 GHz). In addition, the amplitudes of the two modes become close to each other over the whole frequency range from (32.32 GHz to 38.44 GHz). It can be said that the proposed antenna has a good equal magnitude characteristic.  Figure 10 depicts the simulated amplitudes of E1 and E2 modes for various values of two different lengths (L1 and L2) of the cross iris. The long side of (L1) of the cross iris has a more dominant effect on the amplitude of mode than on E1 mode. The E1 mode changes more with the variation in the length of short side (L2). Therefore, we can conclude that the amplitude of E2 mode increases as L1 increases and that the amplitude of E1 mode increases as L2 increases. When L1 = 6 mm and L2 = 5 mm, a good magnitude match occurs between the two modes with a wide 90° phase difference range, leading to the wide axial ratio bandwidth. Additionally, because the cross iris has a height of 1.2 mm, it acts as a step between the rectangular waveguide and the radiation slot resulting in gradual change in the impedance so that the matching condition is improved [27].  Figure 10 depicts the simulated amplitudes of E 1 and E 2 modes for various values of two different lengths (L 1 and L 2 ) of the cross iris. The long side of (L 1 ) of the cross iris has a more dominant effect on the amplitude of E 2 mode than on E 1 mode. The E 1 mode changes more with the variation in the length of short side (L 2 ). Therefore, we can conclude that the amplitude of E 2 mode increases as L 1 increases and that the amplitude of E 1 mode increases as L 2 increases. When L 1 = 6 mm and L 2 = 5 mm, a good magnitude match occurs between the two modes with a wide 90 • phase difference range, leading to the wide axial ratio bandwidth. Additionally, because the cross iris has a height of 1.2 mm, it acts as a step between the rectangular waveguide and the radiation slot resulting in gradual change in the impedance so that the matching condition is improved [27]. Figure 11 shows the simulated reflection coefficients when the height of the cross iris (H 4 ) varies from 0.8 mm to 1.2 mm. When H 4 equals 1.2 mm, an enhanced impedance bandwidth is obtained. As a result, as shown in Figure 7 length of short side (L2). Therefore, we can conclude that the amplitude of E2 mode increases as L1 increases and that the amplitude of E1 mode increases as L2 increases. When L1 = 6 mm and L2 = 5 mm, a good magnitude match occurs between the two modes with a wide 90° phase difference range, leading to the wide axial ratio bandwidth. Additionally, because the cross iris has a height of 1.2 mm, it acts as a step between the rectangular waveguide and the radiation slot resulting in gradual change in the impedance so that the matching condition is improved [27].

Experimental Results
Photographs of the fabricated antenna are shown in Figure 12. The manufactured antenna is assembled in two parts: an upper cavity and a rectangular waveguide with a cross iris. To minimize manufacturing errors, the electroforming process was used. For measuring the reflection coefficient and the radiation pattern with the axial ratio, an Agilent N5247A vector network analyzer with Agilent R11644A calibration kit with a WR-28 coaxial to waveguide adapter were used. They were measured inside the millimeter-wave anechoic chamber equipped with MTG operating software. Figure 13 shows the simulated and measured reflection coefficients and axial ratio of the proposed antenna. The measured -10 dB reflection coefficient bandwidth is 7700 MHz (31.51 GHz-39.21 GHz) and the fractional bandwidth is about 21.7%. The measured 3 dB axial ratio bandwidth is 6810 MHz (31.72 GHz-38.53 GHz) and the fractional bandwidth is about 19.38%. There are slight discrepancies between the simulation and measurement results. The discrepancies are due to the differences in the cross iris dimensions of simulation and those of the manufactured antenna.

Experimental Results
Photographs of the fabricated antenna are shown in Figure 12. The manufactured antenna is assembled in two parts: an upper cavity and a rectangular waveguide with a cross iris. To minimize manufacturing errors, the electroforming process was used. For measuring the reflection coefficient and the radiation pattern with the axial ratio, an Agilent N5247A vector network analyzer with Agilent R11644A calibration kit with a WR-28 coaxial to waveguide adapter were used. They were measured inside the millimeter-wave anechoic chamber equipped with MTG operating software. Figure 13 shows the simulated and measured reflection coefficients and axial ratio of the proposed antenna. The measured -10 dB reflection coefficient bandwidth is 7700 MHz (31.51 GHz-39.21 GHz) and the fractional bandwidth is about 21.7%. The measured 3 dB axial ratio bandwidth is 6810 MHz (31.72 GHz-38.53 GHz) and the fractional bandwidth is about 19.38%. There are slight discrepancies between the simulation and measurement results. The discrepancies are due to the differences in the cross iris dimensions of simulation and those of the manufactured antenna.

Experimental Results
Photographs of the fabricated antenna are shown in Figure 12. The manufactured antenna is assembled in two parts: an upper cavity and a rectangular waveguide with a cross iris. To minimize manufacturing errors, the electroforming process was used. For measuring the reflection coefficient and the radiation pattern with the axial ratio, an Agilent N5247A vector network analyzer with Agilent R11644A calibration kit with a WR-28 coaxial to waveguide adapter were used. They were measured inside the millimeter-wave anechoic chamber equipped with MTG operating software. Figure 13 shows the simulated and measured reflection coefficients and axial ratio of the proposed antenna. The measured -10 dB reflection coefficient bandwidth is 7700 MHz (31.51 GHz-39.21 GHz) and the fractional bandwidth is about 21.7%. The measured 3 dB axial ratio bandwidth is 6810 MHz (31.72 GHz-38.53 GHz) and the fractional bandwidth is about 19.38%. There are slight discrepancies between the simulation and measurement results. The discrepancies are due to the differences in the cross iris dimensions of simulation and those of the manufactured antenna.    Figure 14 shows the simulated and measured radiation patterns of the proposed antenna in the xz-plane (∅ = 0 • ) and yz-plane (∅ = 90 • ) at 33.5 GHz and 37.6 GHz. The simulated and measured radiation patterns agree well in both the xz and yz planes. It can be observed that the antenna has directional patterns with the inclined maximum gains due to the effect of a hexagonal shaped cavity. The simulated bore-sight gains are 8.27 dBi and 6.13 dBi, and those measured are 7.87 dBi and 5.76 dBi at 33.5 GHz and 37.6 GHz, respectively. At 33.5 GHz, the maximum gain of 9.08 dBi is achieved at 18 • in the xz-plane. At 37.6 GHz, the peak gain of 7.33 dBi is obtained at 24 • in the xz-plane.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 15 Figure 14 shows the simulated and measured radiation patterns of the proposed antenna in the xz-plane (∅ = 0°) and yz-plane (∅ = 90°) at 33.5 GHz and 37.6 GHz. The simulated and measured radiation patterns agree well in both the xz and yz planes. It can be observed that the antenna has directional patterns with the inclined maximum gains due to the effect of a hexagonal shaped cavity. The simulated bore-sight gains are 8.27 dBi and 6.13 dBi, and those measured are 7.87 dBi and 5.76 dBi at 33.5 GHz and 37.6 GHz, respectively. At 33.5 GHz, the maximum gain of 9.08 dBi is achieved at 18° in the xz-plane. At 37.6 GHz, the peak gain of 7.33 dBi is obtained at 24° in the xz-plane.  Table 2 compares the dimensions, 3-dB axial ratio bandwidth, and −10 dB reflection coefficient bandwidth values from the literature with those of the proposed antenna. The fractional 3-dB axial ratio bandwidth of the proposed antenna is much wider than the others with a broad overlapping bandwidth (88%) over which both the 3 dB axial ratio and −10 dB reflection coefficient requirements are satisfied. Even though some antennas [11,12] have a shorter length, their overlapping bandwidths (40.5% and 50%) are much smaller than that of the proposed antenna. The antenna in [17] has a very narrow 3 dB axial ratio and −10 dB reflection coefficient bandwidth even with the size comparable to the proposed antenna. Therefore, the proposed antenna has several advantages over other waveguide CP antennas such as a good CP characteristic with a wide operating frequency and a low profile.   Table 2 compares the dimensions, 3-dB axial ratio bandwidth, and −10 dB reflection coefficient bandwidth values from the literature with those of the proposed antenna. The fractional 3-dB axial ratio bandwidth of the proposed antenna is much wider than the others with a broad overlapping bandwidth (88%) over which both the 3 dB axial ratio and −10 dB reflection coefficient requirements are satisfied. Even though some antennas [11,12] have a shorter length, their overlapping bandwidths (40.5% and 50%) are much smaller than that of the proposed antenna. The antenna in [17] has a very narrow 3 dB axial ratio and −10 dB reflection coefficient bandwidth even with the size comparable to the proposed antenna. Therefore, the proposed antenna has several advantages over other waveguide CP antennas such as a good CP characteristic with a wide operating frequency and a low profile.

Conclusions
In this paper, a Ka-band circularly polarized waveguide slot antenna with a cross iris is proposed. By using a hexagonal shape cavity, the proposed antenna achieves a circular polarization characteristic (LHCP) by generating two orthogonal modes. Improved impedance matching is realized by applying a rectangular matching slot, which acts as capacitance and inductance in the equivalent circuit. In addition, widening the axial ratio bandwidth is introduced by using a cross iris. Through adjusting the two different lengths of the cross iris, equal amplitude and 90 • phase difference between two orthogonal electric field modes are realized over the wide −10 dB reflection coefficient bandwidth. From the experimental results, a 21.7% (31.51 GHz-39.21 GHz) fractional impedance bandwidth for -10 dB reflection coefficient is obtained. The measured 3 dB axial ratio bandwidth is 6810 MHz (31.72 GHz-38.53 GHz) and the fractional bandwidth is about 19.38%. Because the overlap between the 3 dB axial ratio bandwidth and −10 dB reflection coefficient bandwidth is greater than 88%, we can conclude that the proposed antenna is well suited for the design goal. Along with the wide operating frequency bandwidth, the proposed antenna has a high gain with a directional pattern showing relatively good agreement between the simulated and measured results. Furthermore, since the proposed antenna is made of all metal and is compact in size, it can be a good candidate for tough operating environments such as radar, spacecraft, and satellite communication.