A broadband Fabry–Perot resonator antenna using partially reflecting surface with positive reflection phase gradient

The Fabry–Perot resonator antenna (FPRA) has received significant attention due to its compact size and ease of achieving high gain without using complex feed networks.^1–3 Usually, the FPRA is mainly composed of a ground plane, a feed source, and a partially reflective surface (PRS). Electromagnetic (EM) waves radiated from the feed antenna experience multiple reflections between the ground plane and the PRS. When the height of the cavity satisfies the resonant condition, the EM waves transmitted through the PRS can achieve an in-phase superposition, thus improving the antenna gain. However, since both the reflection phase of the PRS and the resonant cavity height are extremely sensitive to the operating frequency, the traditional FPRA suffers from the disadvantage of narrow bandwidth, which strictly restrains its application in many fields.⁴ Therefore, the current FPRA research mainly focuses on increasing the working bandwidth.

In recent years, several methods were proposed to broaden the operational bandwidth of the FPRA with remarkable results. One popular approach is to employ the array antenna as the feed source of the FPRA. For instance, in Ref. 5, Lian et al. used slot-coupled patch arrays as the primary source to excite the resonant cavity. Compared with the performance of the FPRA with a one feed patch, the proposed antenna with a two-element patch array as the primary source achieves good impedance matching over a wider frequency band. This is mainly because the current intensity excited by the patch array source on the PRS is stronger in a larger area, which makes the electric field distribution in the resonant cavity much more uniform. While the impedance bandwidth is improved, the patch array feed antenna introduces a complicated feeding network and makes the antenna design more difficult. Another approach is to provide multiple resonances by using a multilayer PRS. The EM waves transmitted out of the PRS can achieve in-phase superposition in a wider frequency band so that the 3 dB gain bandwidth can be further improved.^6–9 In Ref. 10, the 3 dB gain bandwidth is improved to 15% and the maximum gain of the antenna reaches up to 20 dBi at 14.5 GHz by using a three-layer PRS. Although the bandwidth is obviously improved, the use of a multi-layer PRS will greatly increase the profile of the FPRA, which is not conducive to the miniaturization of the FPRA.

In this paper, a wideband FPRA employing a novel single-layer PRS with a positive reflection phase gradient is proposed. The proposed PRS unit cell consists of a circular ring and a circular patch, which are printed on the bottom and top surfaces of the single substrate, respectively. In addition, a wideband aperture-coupled microstrip antenna (ACMA) is used as its excitation source. The measured results demonstrate that the proposed antenna achieves broadband and high gain characteristics. The −10 dB impedance bandwidth is about 64.4% (from 8.68 to 15.12 GHz), and the 3 dB gain bandwidth is 31.9% (from 8.61 to 11.80 GHz). In addition, a maximum gain of 14.2 dBi has been achieved.

According to the ray-tracing theory of the FPRA in Ref. 11, the maximum directivity of the FPRA occurs at the broadside when the following equation is satisfied:

where φ_PRS and φ_ground are the reflection phases of the PRS and the ground plane, respectively; H is the cavity height; c is the speed of light in vacuum; and f is the operating frequency. When the cavity height of the FPRA H is fixed for a certain operating frequency and the reflection phase (φ_ground = π for an electric conducting ground plane) of the ground plane is fixed, the reflection phase of the PRS φ_PRS and resonance frequency f can be controlled. Therefore, if the FPRA is designed to operate over a wide frequency band, the reflection phase φ_PRS of the PRS should change continuously vs frequency f. By transforming FPRA resonance conditional formula (1), the relationship between the reflection phase φ_PRS of the PRS and the resonance frequency f can be written as follows:

It can be clearly seen that the reflection phase φ_PRS of the PRS should increase linearly with the frequency f to ensure the FPRA satisfies the resonance condition over the working frequency band (i.e., the reflection phase φ_PRS meets the positive gradient relation with respect to frequency f). Therefore, to broaden the bandwidth of the FPRA, a PRS with a positive reflection phase gradient slope is essential.¹² 

The proposed PRS unit design is shown in Fig. 1(a). A circular ring and a circular patch are printed on opposite sides of a PTFE substrate, with the thickness h₃ = 3 mm and the relative dielectric constant ɛ_r = 2.65, respectively. Figure 1(b) shows that the equivalent circuit qualitatively describes the electromagnetic response of the PRS unit. The gap between the two circular rings at the bottom of the substrate acts as a capacitor C_s. L₁ corresponds to the circumference of the circular ring, and C₁ is in parallel with the inductor L₁, which represents the inner space of the circular ring. Z_R represents the characteristic impedance of the substrate. The gap between the two circular patches at the top of the substrate acts as a capacitor C₂, and the circular patch itself also provides a low-value inductor L₂ in series with the capacitor C₂. When the radiated EM waves are incident normal to the PRS unit cell, it can be equivalent to a parallel connection of a circular ring, patch, and substrate.

Figure 2 plots the influences of four parameters p, M, N, and r₁ on the simulated reflection phase. As can be seen from Fig. 2(a), the reflection phase curve shifts to higher frequencies as p increases due to the decrease in C_s and C₂. As shown in Fig. 2(b), when M decreases, the phase curve moves to higher frequencies due to the decrease in C_s and L₁. Conversely, as shown in Fig. 2(c), with the increase in N, the phase curve moves to lower frequencies, which is due to the increase in L₁. As shown in Fig. 2(d), when r₁ increases, the phase curve moves to a lower frequency due to the increase in C₂ and L₂. Therefore, to achieve a larger positive phase gradient, the final unit cell size is determined as p = 8 mm, M = 3.8 mm, N = 1.5 mm, and r₁ = 3.2 mm.

The unit cell structure is simulated by CST with a periodic boundary. Figure 3 plots the reflection amplitude and phase of the PRS unit cell as a function of frequency. In the frequency range of 9–11 GHz, the reflection phase shows an increasing trend with the increase in frequency, which realizes the positive phase gradient required by Eq. (2). In addition, the reflection phase at the central frequency of 10 GHz is −157.7°. Moreover, the amplitude of the reflection coefficient reaches above 0.52.

Figure 4 shows the configuration of the air-loaded ACMA (i.e., an air spacer is inserted between the patch and the ground plane to suppress the generation of surface waves), which is selected as the primary source for the proposed FPRA. The attractive feature of the aperture coupled antenna is its broadband radiation. The feed antenna is composed of double-layer dielectric substrates with thicknesses of h₁ = 1.6 mm and h₂ = 0.8 mm, respectively. In addition, the thickness of the air spacer is h_c1 = 3.5 mm. Both dielectric substrates are made of the same material—PTFE—with a dielectric constant ɛ_r = 2.65. The parasitic circular patch with a radius r = 4.5 mm is printed on the bottom surface of the upper-layer dielectric substrate. The microstrip feeding line is located at the lowest layer with an impedance characteristic of 50 $Ω$⁠, which can ensure good impedance matching. In this design, the electromagnetic wave is coupled from the feeding line and then through a cross-shaped slot on the ground plate. The driven circular patch is located right on the cross-shaped slot. Therefore, multiple resonances can be generated, and effective radiation is realized. Thus, a wide impedance bandwidth is obtained. The final size of the feeding antenna is shown as follows: L = 70 mm, X = 10.4 mm, Y = 3 mm, F₁ = 36.3 mm, and F_w = 2.4 mm.

The feeding antenna was designed and simulated by the CST microwave studio. Figure 5 shows the measured and simulated reflection coefficients and gain variations of the feeding antenna. As can be seen from Fig. 5(a), the antenna achieves an impedance bandwidth (|S₁₁| < −10 dB) of 40.3%, ranging from 8.59 to 12.62 GHz. Due to the coupling between the radiation patch and the cross slot, three resonant frequencies are generated. The low frequency matches well, while the high frequency matches poorly due to the influence of joint loss, plate thickness, and machining accuracy. However, the relatively wide bandwidth indicates that this antenna is very suitable to be the feed of the proposed FPRA. From Fig. 5(b), it can be seen that the measured gain is slightly lower than the simulation results and they have the same trend. Moreover, the antenna provides a stable gain of 6.43 ± 0.18 dBi over the entire operating band.

Based on the previously designed PRS unit cell and ACMA feeding antenna, a broadband FPRA operating at 10 GHz is constructed. The schematic view of the proposed FPRA is shown in Fig. 6. The PRS consists of 6 × 6 unit cells with an aperture size of 70 × 70 mm². The reflection phase of the ground plane is generally a fixed value π, and the reflection phase φ_PRS of the PRS is equal to −157.7°. According to Eq. (1) in Sec. II, the initial height of the antenna cavity is 15.9 mm, which is ∼0.5λ₀. To obtain better radiation performance, the cavity height and other key parameters need to be analyzed.

First, the air layer height h_c1 of the feed source has a great influence on the antenna performance. Figure 7 shows the variation curves of S₁₁ and the gain with the change in h_c1 within the operating band. When h_c1 increases, both the 3 dB gain bandwidth and the peak gain decrease. The antenna has the best impedance matching and a higher peak gain when h_c1 = 3.5 mm. Therefore, h_c1 is chosen to be 3.5 mm.

Second, Fig. 8 shows the effect of height h_c2 on the S₁₁ curve and gain response. It is found from the figure that h_c2 has little effect on the antenna impedance matching. However, it has a significant impact on antenna gain. With the increase in h_c2, the 3 dB gain bandwidth is reduced and shifts downward. Meanwhile, the peak gain is weakened. Finally, h_c2 = 12.8 mm is chosen.

In addition, the influence of the period of the unit cell p is also investigated. As shown in Fig. 9, when p decreases to 7.6 mm, the gain within the operating band decreases sharply while the impedance matching is barely affected. When p increases to 8.4 mm, the impedance matching still changes slightly but the gain is reduced to some extent, especially at higher frequencies. Therefore, the period of the unit cell p is finally selected as 8 mm.

Based on the previous analysis, it can be found that h_c1 = 3.5 mm and h_c2 = 12.8 mm. Therefore, the overall cavity height of the designed FPRA is finally determined to be H = h_c1 + h_c2 = 16.3 mm, which compares well with the theoretical value of 15.9 mm. The slight discrepancy is attributed to two factors. First, there is a reflection phase error of the PRS unit cell. Second, there are undesirable effects of edge diffraction. The small discrepancy obtained validates our proposed design.

In order to verify the performance of the proposed FPRA, a prototype antenna was fabricated and measured, as shown in Fig. 10. To ensure accurate assembly, four nylon screws with nuts are used to fix the PRS and to maintain the thickness of the air layer. The prototype antenna was tested in a microwave anechoic chamber, and the reflection coefficient of the antenna was measured using an Agliente326B vector network analyzer. Figure 11 shows the measured and simulated reflection coefficient and gain variation against frequency. It can be seen from Fig. 11(a) that the measured impedance bandwidth is about 64.4% in the frequency range of 8.68–15.12 GHz. Generally, the proposed FPRA measured results consistent with the simulated results. The small discrepancy is mainly owing to the following reasons: One is the assembling tolerance as the four nylon columns make height error between the PRS and the AMCA feed source. The other one is that the SMA connector connected to the feeding line used in the measurement introduces higher losses at frequencies higher than 8 GHz.

The measured and simulated gain vs frequency is shown in Fig. 11(b). The maximum gain of the proposed FPRA reaches up to 14.2 dBi at 9.5 GHz. The measured gain curve follows a similar trend to the simulation and with a difference of less than 1 dB. The measured 3 dB gain bandwidth is 3.19 GHz (8.61–11.80 GHz), and the relative bandwidth is 31.9%. The gain improvement is found to be >7.6 dB all over the band in comparison with the primary feeding antenna.

Figure 12 depicts the measured and simulated radiation patterns at 9.5, 10, and 10.5 GHz in both the E-plane and H-plane. All measured results are consistent with the simulated ones. It can be seen that the measured simulated radiation patterns are consistent with the simulated ones. Besides, the antenna also achieves low sidelobe levels (less than −10.75 dB) and cross-polarization levels (less than −20.56 dB). Table I lists the comparison of the proposed FPRA and some recently published designs. It can be observed that although it has the smallest aperture size, the proposed design exhibits the widest 10 dB impedance bandwidth and 3 dB gain bandwidth. A maximum peak gain is provided in Ref. 13, but the proposed design has a larger plane size (80 × 80 mm²). The gain of the FPRA in Ref. 14 is reduced by 2.7 dB at nearly the same plane size. Compared with the designs in Refs. 15 and 16, our proposed design has a higher gain and the smallest aperture. In addition, this antenna has a simple structure and a compact size of 70 × 70 mm², which meets the requirement of modern wireless communications.

An FPRA with wideband characteristics (impedance bandwidth and gain bandwidth) in the X-band is presented. A wide-band feed antenna, ACMA, is selected as a primary radiator to ensure the wideband operation of the FPRA. A substrate consisting of a circular ring and a circular patch constitutes the PRS unit cell. Using the proposed unit cell, a positive reflection phase with a positive gradient is obtained. A PRS consisting of 6 × 6 unit cells is employed to construct the resonant cavity. The measured experimental results show that the impedance bandwidth is up to 64.4% (8.68–15.12 GHz). The 3 dB gain bandwidth is 31.9% from 8.61 to 11.80 GHz with a peak gain of 14.2 dBi at 9.5 GHz. Within the working frequency band, the sidelobe and cross-polarization levels are less than −10.75 and −20.56 dB, respectively. Compared with the recently published designs, the proposed FPRA provides excellent bandwidth performance with a compact size.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 62071282 and 12174232) and the China-Belarus Belt and Road Joint Laboratory on Electromagnetic Environment Effect (Grant No. ZBKF2022020102).

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.