3×3 subarray design

The proposed 3×3 subarray is shown in Fig. 1. The subarray consists of one substrate layer and two metallic layers. The monolayer substrate is Rogers 5880 with a thickness of 1.575 mm. The asymmetric orthogonal slots with a length, width, and offset of 3 mm, 1.2 mm, and 0.25 mm are etched at the upper metal layer. The high-order mode TE₃₃₀ in the square SIW cavity is excited by the coaxial feeding. The resonant frequency of the mode is given as follows:

(1)\begin{equation} f_{\text{mnp}} =\frac{c}{2\pi\sqrt{\mu\varepsilon}} \sqrt{(\frac{m\pi}{L_{\text{eff}}})^{2}+(\frac{n\pi}{W_{\text{eff}}})^{2}+(\frac{pm\pi}{h})^{2}}, \end{equation}

(2)\begin{equation} \begin{aligned} L_{\text{eff}}=L-\frac{d^{2}}{0.95p},\\ W_{\text{eff}}=W-\frac{d^{2}}{0.95p}, \end{aligned} \end{equation}

Figure 1.

Subarray antenna: (a) over view, (b) top view, and (c) bottom view.

where W, L, and h are the width, length, and height of the SIW cavity (SIWC) and d and p are the diameter and spacing of the SIW vias, respectively. The TE₃₃₀ mode inside SIWCmeans $\textit{m}=3$, $\textit{n}=3$, and $\textit{p}=0$. The permeability and permittivity of the substrate µ and ɛ are 1 and 2.2, respectively. The electric field is determined by (3), where E ₀ and ϕ are the amplitude and phase of the waves [Reference Pozar20],

(3)\begin{equation} E_{\text{Z, TE}_{330}} = E_{0}\sin\frac{3\pi x}{L_{\text{eff}}}\sin\frac{3\pi y}{W_{\text{eff}}}\cos(\omega t+\phi). \end{equation}

The 45° linear polarization is achieved by introducing asymmetric orthogonal slot radiation into the copper layer, which is on the top layer of the HOM cavity. To better explain the principle of the slot position by HOM cavity, the distribution diagram of electric and magnetic fields of the TE₃₃₀ mode is shown in Fig. 2. The 3×3 standingwave electric peaks are evenly distributed inside the SIWC. The signs “+” and “−” represent the direction of the electric field. The closed curves indicate the magnetic vector, and its arrow direction is the vector direction. The offset transverse and the longitudinal slots with the same size are etched in each segment along the horizontal and vertical directions of the magnetic field vector. The electric field distributions at the radiation slots in this paper have the same phase. Due to the same size of the horizontal and vertical slots, the orthogonal components in the horizontal and vertical directions are of equal amplitude. A sum magnetic field vector can be formed, resulting in the radiation of 45 ° linearly polarized electromagnetic waves.

Figure 2.

Electric field and magnetic vector of TE₃₃₀ mode.

Note that the directions of the electric field in adjacent subsections are out of phase, and the directions of rotation of the magnetic field vector are opposite. Therefore, radiation in the same phase and same polarization requires etching a pair of orthogonal slots at positions with the same vector direction in each subsection. In the same way, −45° linear polarization can also be achieved in this way, and the diverse linear polarizations can be realized by designing this pair of the orthogonal slots into different size. Figure 3 illustrates the electric field distribution before and after etching the slots for the purpose of the effect of the asymmetric cross slots on the antenna radiation.

Figure 3.

Electric field distribution at 39 GHz: (a) before etching slots and (b) after etching slots.

In order to achieve better antenna performance, it is necessary to determine the size of the cavity in the antenna and the mode excited within it. Figure 4 shows different antenna design and performance comparison using TE₃₃₀ mode and TE₃₄₀ mode. The antenna subarrays are arranged in two ways, 3×3 and 3×4. The size of the resonant cavity is calculated using (1), (2), and (3), as shown in Fig. 4. The offset of the feeding position, the size of the etching gap, and the offset value are kept consistent. From the simulation gain results of the E-plane (Phi = 45°) in Fig. 5, it can be seen that the antenna excited by TE₃₃₀ mode has more advantages in XPD than the antenna excited by TE₃₄₀ mode. In conclusion, for the 45° linearly polarized antenna in this paper, the cavity size has a significant impact on XPD. A square cavity can better form the 45° linearly polarized wave due to the consistent size of the metal walls, while the shape of a rectangular cavity can reduce the XPD. It is worth mentioning that when using an HOM cavity to achieve a compact design, we aim to use a single feed port to excite as many radiation slots as possible. On the other hand, we want to maintain a wide bandwidth. However, as the mode order increases, the bandwidth of the antenna decreases. This is because higher-order modes are more sensitive to the cavity size. Therefore, there is a trade-off between mode order and bandwidth.

Figure 4.

Subarray structures: (a) 3×3 and (b) 3×4.

Figure 5.

Radiation performance of the subarray of different resonant modes.

In addition, W4 is the offset dimension between the center of the transverse slot and the center of the longitudinal slot. As depicted in Fig. 6, when W4 varies between 0.1 mm, 0.2 mm, 0.25 mm, and 0.3 mm, it is evident that both the antenna matching bandwidth and the gain increase with increasing W4. To ensure the impedance bandwidth ($|S_{11}|\le$ −10 dB) of the antenna, the value of W4 is chosen as 0.25mm.

Figure 6.

The influence of the slots offset of W4 on subarray performance: (a) S-parameter and (b) gain.

R2 is the size of concentric circle etching on the outer side of the probe in the metal layer. It can be seen from Fig. 7 that when the antenna presents an upper metal electrical contact, R2 = R1 = 0.2 mm, it can be seen that the matching situation of the antenna is much worse than that without an electrical contact. In summary, electrical contact can cause impedance matching to deteriorate, and as the R2 increases, impedance matching will deteriorate, resulting in an increase in low-frequency bandwidth. Therefore, selecting an appropriate etching size can effectively improve the working bandwidth of the antenna. So the value of R2 is chosen to be 0.4 mm.

Figure 7.

The influence of the R2 on subarray performance: (a) S-parameter and (b) gain.

The detailed parameters are shown in Table 1 with values in millimeters. The simulated results of the proposed 45° subarray are given in Fig. 8. As shown in Fig. 8, the subarray can achieve an impedance bandwidth of 27.8% (34.4–45.53 GHz) and a 3-dB gain bandwidth of 17.1% (36.88–43.76 GHz). The maximum gain is 13.5 dBi.

Figure 8.

The S-parameter and peak gains in the broadside direction of the subarray antenna.

Table 1.

Dimensions of the subarray in millimeters.

6×6 array design

Array design

Based on the structure of the proposed subarray, an exploded view of a 6×6 antenna array is shown in Fig. 9. Two PCB layers are used for array construction. The upper layer consists of 2×2 subarrays, with a spacing of 13.2 mm between each two subarrays. Figure 10(a) shows the feed network of the proposed antenna for TE₃₃₀ mode excitation. The feed network is fed by a WR-22 waveguide, and a conversion to the probe (shown in Fig. 10(b)) is used at the end to feed the subarray. The substrate of the feeding network layer is Rogers 5880 with a thickness of 0.787 mm. As shown in Fig. 10(c), the simulated −15 dB $|S_{11}|$ bandwidths of the feed network and the transition structure cover 36–43.5 GHz. The transmission loss of the feednetwork is 0.16 dB, and the maximum difference among $|S_{12}|$, $|S_{13}|$, $|S_{14}|$, and $|S_{15}|$ is below 0.44 dB within the operation bandwidth.

Figure 9.

3D exploded view of the proposed antenna array ( $\textit{h1}$ = 1.515 mm, $\textit{h2}$ = 0.787 mm).

Figure 10.

(a) Structure of the feed network for TE₃₃₀ mode. (b) Transition structure from SIW to probe. (c) Their properties in simulations ($\textit{d1}$ = 5.5 mm, $\textit{d2}$ = 3.83 mm, $\textit{d3}$ = 1.7 mm, $\textit{d4}$ = $\textit{d5}$ = 1.8 mm, $\textit{d6}$ = 0.2 mm).

In the M2 layer, a larger concentric circle at the location of the probe is etched for better impedance matching. The part outside the cavity is loaded with through holes for mounting screws, in order to reduce the performance deteriation caused by the air gap between two PCBs. The feeding network design parameters and values are shown in Fig. 10.

Results and discussion

Figure 11 shows the images of the 6×6 antenna array prototype and the array in the test environment. The antenna was fabricated using standard PCB technology. The antenna array has the dimensions of 53 mm×30 mm×2.432 mm and the aperture area of 21.6 mm×21.6 mm surrounded by screw holes for assembly. In Fig. 12(a), the simulated and measured S-parameters of the 6×6 antenna array for $|S_{11}|\le$ −10 dB are 15.3% (36.89–43 GHz) and 13.9% (36.98–42.52 GHz), respectively.

Figure 11.

(a) The image of the fabricated prototype. (b) Measurement environment of the antenna.

Figure 12.

Measured and simulated results of the antenna array. (a) $|S_{11}|$ and (b) gain and radiation efficiency.

The antenna was measured using a spherical near-field measurement system. In Fig. 12(b), the simulated and measured peak gain is 19.06 dBi and 19.3 dBi, respectively. The simulated 3-dB gain bandwidth is 16.02% (36.85–43.31 GHz), and the measured one is 13.6% (37–42.4 GHz). The measured aperture efficiency is 88.1% at 38.5 GHz, and the average measured aperture efficiency is 66.9%. The simulated radiation efficiencies are above 86.5% within the impedance bandwidth, and the maximum radiation efficiency can reach 91.7% at 39 GHz. The average measured radiation efficiency is 75%. The discrepancies in the measured results are due to the fact that the antenna test environment is not ideal, in which the placement and the test accuracy need to be improved.

The simulated and measured radiation patterns in −90° $ \lt $ θ $ \lt $ 90° are given in Fig. 13. The XPD levels in the maximum radiation direction are higher than 30 dB at 38, 40, and 42 GHz, indicating good 45° linear polarization characteristic.

Figure 13.

Simulated and measured radiation patterns in E-plane (ϕ = 45°) and H-plane (ϕ = 135°): (a) 38 GHz, (b) 40 GHz, and (c) 42 GHz.

There are many papers that aimed at the 45° linear polarized antenna, and a comparison is made in Table 2. Compared to other SIW technology-based 45° linearly polarized antennas, the proposed antenna etching asymmetric cross slots on the top layer of HOM cavity is more dominant in terms of bandwidth and XDP level, which is better than that in [Reference Abdallah, Wang, Abdel-Wahab and Safavi-Naeini15, Reference Chen, Wu, Wong and Chen19, Reference Yu, Hong, Jiang and Zhang21] and is comparable to that in [Reference Guntupalli and Wu22]. However, [Reference Guntupalli and Wu22] has a wide impedance bandwidth at the expense of the profile. Meanwhile, [Reference Zhou, Lu, You, Wang and Huang23] and [Reference You, Lu, Skaik, Wang and Huang24] are slot array antennas fed by hollow-waveguide, which have wide impedance bandwidths and high XPD levels, but the profiles are higher than the proposed antenna. What is more, the radiation efficiency is higher than that in [Reference You, Lu, Skaik, Wang and Huang24].

Table 2.

Comparision with other 45° LP antennas

IBW: relative impedance bandwidth; RE: radiation efficiency; AE: aperture efficiency; XPD: cross-polarization discrimination level at θ = 0°; HW: hollow-waveguide; DR: dielectric resonator;

* : simulated results; N.A.: not apply; CS: cavity size; #:Average value within the working band