I. Introduction
Among the many available next-generation high-gain antennas, studies have identified reconfigurable reflectarray metasurface antennas (RRMAs) to have immense potential [1–3]. Owing to their high gain and beam steering capabilities, RRMAs have been gaining popularity as alternatives to conventional phased array antennas. Furthermore, by adopting an array composed of lumped variable elements, RRMAs without phase shifters offer the advantages of being lightweight, low cost, and bearing a simple control unit, thus exhibiting great promise for use not only in the military but also in civil applications, such as autonomous vehicles and satellite radars.
In this context, the PIN diode-based RRMA has recently been investigated as a simplified example of an RRMA. However, while PIN diodes with switching functions offer fast switching speed, low loss, and a low-cost system [4–7], they have several drawbacks. One such shortcoming is their low aperture efficiency, which is caused by the high quantization loss prevalent in 1-bit control systems with two phase states [8]. Furthermore, a 2-bit control system with four phase states involves complex and difficult design and fabrication processes for the bias circuit. To overcome these issues, a 3-state RRMA—the hybrid reflectarray antenna (HRA)—has been proposed [6]. This RRMA, consisting of a combination of passive and 1-bit unit cells, offers the advantage of higher aperture efficiency while retaining a simple bias circuit, as in 1-bit RRMAs.
In this paper, another pertinent factor—improvement in gain bandwidth—is investigated with regard to the reflection phase of the passive unit cells in previously proposed HRAs. Instead of adopting a wideband structure for the unit cell, passive and 1-bit unit cells characterized by several types of reflection phases are designed and shaped as a square ring patch. Subsequently, based on a theoretical estimation formula for quantization efficiency, the optimal combination of passive and 1-bit unit cells for the gain bandwidth is determined. Ultimately, these estimations establish that the gain bandwidth is closely related to the phase of a passive unit cell. The estimated gain bandwidths are also verified through simulation and experimentation.
II. Design and Analysis
1. Design of Unit Cells
The proposed HRA comprises three phase states (3-states), achieved by combining a passive unit cell and a 1-bit unit cell [6]. Despite utilizing the same control circuit as a 1-bit RRMA, the proposed HRA was able to realize beam switching while maintaining a higher quantization efficiency than the 1-bit control system for specific steering angles. To implement 3-states, the phase difference among the phase states of the unit cell had to satisfy 120°. Notably, as long as the phase difference condition is satisfied, the quantization efficiency will remain the same, notwithstanding the phase value. As a result, HRAs of various phases with a phase difference of 120° were designed.
To calculate the gain bandwidth with regard to changes in the reflection phase, eight phase types of passive and 1-bit unit cells were designed in the shape of a square ring patch, as shown in Fig. 1. The unit cells were patterned on Taconic TLY-5 substrates (ɛr = 2.2, tanδ = 0.0009)—its top and bottom layers measuring 1.575 mm and 0.508 mm, respectively—bearing a periodicity of 10.5 mm (0.35λ0). As shown in Fig. 1, each unit cell consists of a pattern in Layer 1 and a ground in Layer 2. The 1-bit active unit cell features an additional layer (Layer 3) comprising a bias circuit, as well as a PIN diode for on and off switching control that operates with a DC voltage of 1.2 V supplied through bias and shorting vias. For the PIN diode, MA4GP907 of MACOM, which operates in the X-band, was employed.
Finally, eight pairs of passive and 1-bit active unit cells were designed to investigate the gain bandwidth. As shown in Fig. 1, the design dimensions affecting the reflection phase of the unit cells were L1, L2, W1, W2, and pl, whose ranges were considered as follows: 4 mm ≤ L1 or L2 ≤ 10 mm, 0.5 mm ≤ W1 or W2 ≤ 3 mm, and 0.1 mm ≤ pl ≤ 4 mm. Here, L1, L2, and pl are primarily related to the resonant frequency, while W1 and W2 have a significant influence on the slope of the phase with respect to frequency. Considering these characteristics, an optimization procedure was performed by implementing a dimensional sweep based on the frequency-dependent phases extracted from the periodic boundary conditions using Ansys High-Frequency Structure Simulator (HFSS).
As indicated in Table 1, the passive unit cells were designed to provide nearly full phase coverage, maintaining a reflection phase spacing of 45°. Accordingly, the 1-bit unit cells were designed to approximate a phase difference of 120° from the passive unit cells. Notably, the target phase exhibited some errors since it is difficult for 1-bit unit cells of various phases to satisfy a phase difference of 120°. However, these phase errors had only a minor effect on quantization efficiency. Overall, the designed pairs of passive and 1-bit unit cells exhibited similar theoretical gains at an operating frequency of 10.1 GHz.
2. Estimation of Gain Bandwidth
To calculate the gain bandwidth of the designed unit cells, eight types of 12 × 12 HRAs were designed for two beam switching directions. The gain bandwidths of the designed unit cells were then estimated by calculating the theoretical peak gain in terms of the frequency Gcal. (f), which can be expressed as follows:
where Gcal. (f) is the product of the physical peak gain Gmax. and the theoretical aperture efficiency ηap(f). Furthermore, Gmax. can be calculated by accounting for the aperture size S, wavelength λo, and switching angle θ, among which only λo affects the frequency. Meanwhile, ηap.(f) consists of the spillover ηs, taper ηt, element ηe, and quantization efficiencies ηq. The ηs and ηt can be determined by the gain, location, and offset angle of the feed horn, while ηe is related to the loss of the unit cell. Notably, these factors exhibit relatively low sensitivity to frequency. Meanwhile, ηq is related to the reflection phase, showing high sensitivity to frequency. As a result, Gmax. (f) can be approximated as a function of ηq(f). In this study, the values for ηs, ηt, and ηe were considered at the operating frequency of 10.1 GHz, following which ηq was calculated using the following equation:
where AF(θ,φ,f)q. and AF(θ,φ,f)c. indicate the array factors calculated by the quantized and continuous phases of the switching angle (θ,φ) and the frequency f, respectively.
The theoretical peak gain, calculated using Eq. (1), was observed to be proportional to the quantization efficiency, with the highest value achieved at the center frequency f0 of the unit cells. Based on this context, when the frequency of the unit cell deviates from the center frequency, the value of the peak gain will gradually decrease. Based on this characteristic, the theoretical gain bandwidth for x dB of Gain BWx dB can be calculated as follows:
where fH and fL indicate the highest and lowest frequencies at which the peak gain is reduced by x dB from the maximum value, respectively.
Eqs. (1) to (3) were employed to construct HRAs for switching angles of 0° and ±30° in the E-plane. The metasurfaces, as illustrated in Fig. 2, were implemented based on the design algorithm in [9], which represents a method for arranging two types of unit cells such that the phase error can be minimized by applying the least square method. In particular, it is possible to design a metasurface with high quantization efficiency for beam switching in multiple directions. By replacing the two types of unit cells in the design algorithm with passive and 1-bit unit cells, optimal metasurfaces for the switching angles were designed, as shown in Fig. 2. They were designed with an aperture size of 126 mm × 126 mm, along with a feed horn of 11 dBi, an F/D ratio of 0.36, and an offset angle of −25° in the xoz plane. At the center frequency of 10.1 GHz, ηs and ηt of the designed HRAs were found to be 82.1% and 83.5%, respectively, and ηe was observed to be more than 90% for all designed unit cells. Furthermore, the quantization efficiencies for the switching angles of 0° and ±30° were estimated to be 70.6% and 54.0% at 10.1 GHz, respectively, varying significantly with frequency.
Fig. 2 presents the results obtained on calculating the 1-, 2-, and 3-dB gain bandwidths for the reflection phases of the designed passive unit cells. For each designed HRA, the x-axis and y-axis indicate the reflection phase of the passive unit cell and the gain bandwidth, respectively. It is evident that the two types of HRAs show similar behavior in terms of the reflection phase. Furthermore, on fine-tuning the reflection phases of the passive unit cells, it was found that HRAs with the maximum and minimum gain bandwidths occur at reflection phases of 52° and 220°, respectively.
To increase the gain bandwidth of a typical RRMA, a constant phase difference should be maintained over a wide frequency range [10, 11]—a factor that clearly correlates with quantization efficiency. Thus, the ideal condition for achieving a wide gain bandwidth is to satisfy a phase difference of 120° over a wide frequency range. As shown in Fig. 3, the reflection phase differences of the unit cells at the center frequency of 10 GHz are almost 120°. More specifically, it is clearly observed that phase differences of ~120° can be better maintained when the reflection phase of the passive unit cell in Fig. 3(a) is 52° than when the reflection phase of the passive unit cell in Fig. 3(b) is 220°. In other words, a wide gain bandwidth was obtained to design the reflection phase–frequency curve for each phase state (passive, 1-bit on or off) having a similar slope.
Based on this design, the calculated maximum and minimum 3-dB gain bandwidths were found to be 3,600 MHz (36%) and 870 MHz (8%) for the switching angle of 0° and 3,200 MHz (32%) and 730 MHz (7%) for switching angles of ±30°, respectively.
III. Simulation and Experimental Verification
Simulations and measurements were performed for the HRAs related to the maximum and minimum gain bandwidths for structures radiating at switching angles of ±30° in the E-plane. The 12 × 12 metasurfaces for the maximum and minimum gain bandwidths were fabricated for reflection phases of 52° and 220° of the fine-tuned passive unit cells, respectively, as shown in Fig. 4.
In particular, the fabricated dimensions were L1 = 7.2 mm, W1 = 2.6 mm, L2 = 7.2 mm, W2 = 1.2 mm, and pl = 2.0 mm for the HRA with the maximum gain bandwidth, and L1 = 6.8 mm, W1 = 0.6 mm, L2 = 5.6 mm, W2 = 0.5 mm, and pl = 1.1 mm for the HRA with the minimum gain bandwidth. Fullwave simulations were performed using HFSS. Meanwhile, the measurements were conducted in an anechoic chamber containing Keysight’s E8362B network analyzer, with the receiving antenna positioned 7 m away from the fabricated HRA.
As shown in Fig. 5, the measured radiation patterns are in good agreement with the simulation results. However, the operating frequency of the HRA with the minimum gain bandwidth shifted upward by 0.3 GHz, possibly due to an error in fabrication. Furthermore, the measured aperture efficiencies of the HRAs with the maximum and minimum gain bandwidths were 25.8% and 26.5% for the switching angle of −30°, and 26.8% and 25.6% for the switching angle of 30°, respectively. Moreover, Fig. 5 confirms that the peak gain in terms of frequency maintains a similar tendency across calculations, simulations, and measurements. As for the measured results, the maximum and minimum 3-dB gain bandwidths were 2,860 MHz (28.3%) and 630 MHz (6.2%) for the switching angle of −30°, and 3,210 MHz (31.8%) and 690 MHz (6.8%) for the switching angle of 30°, respectively. In other words, compared to the minimum gain bandwidths, the maximum gain bandwidths for the switching angles of −30° and 30° increased by 4.6 and 4.7 times, respectively. Overall, these results verify that the relationship between the reflection phase and frequency has a significant influence on the gain bandwidth.
Table 2 compares the 3-dB gain bandwidths achieved in the current study with those reported in previous research on HRA. By optimizing the reflection phase, the proposed design enhanced the gain bandwidth by 2 times compared to other designs using the same unit cell, such as in [6]. Therefore, the proposed design method can be considered a potent tool for achieving a wide gain bandwidth without any additional costs.
As summarized in Table 3, the gain bandwidth of the designed HRA is similar to that of other wideband RRMAs. Notably, [10] and [11] proposed structures that extend the gain bandwidth using stacked and bowtie patches, which inherently feature a broader bandwidth than ring patch structures. In contrast, the proposed design achieved a wide gain bandwidth by adjusting the reflection phase without the need for specific structural modifications. Additionally, it is noteworthy that the thickness of the substrate employed in the current study is thinner than that used in other wideband structures. Therefore, if the proposed method were applied to the RRMAs in [10] and [11], they would achieve a wider gain bandwidth.
IV. Conclusion
In this paper, a novel method is presented for increasing the gain bandwidth of RRMAs by adjusting the reflection phase of passive unit cells in the HRA. Unit cells characterized by various reflection phases were designed, and the resulting gain bandwidths were investigated. Based on the formula for peak gain pertaining to quantization efficiency, the phases of the passive unit cells that achieved the maximum and minimum gain bandwidths were identified. Subsequently, the maximum and minimum 3-dB gain bandwidths were measured to be 2,860 MHz (28.3%) and 630 MHz (6.2%) for the beam switching angle of −30°, and 3,210 MHz (31.8%) and 690 MHz (6.8%) for the beam switching angle of 30°, respectively. Overall, this work offers robust guidelines for achieving a wide gain bandwidth HRA without any additional costs.
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