Antenna Gain-Bandwidth Enhancements Using CRLH Hilbert Fractal-based Structure

performance; a dual-bandwidth was achieved extended from (3.72 to 3.79) GHz and (6.99 to 8.55) GHz with maximum antenna gain equal to (5.28, 7.66) dBi, respectively. The antenna is characterized by its small size and high efficiency, making it suitable for Long-Term Evolution LTE, 5G, and satellite applications.


Introduction
With the development of communication systems and the increase of subscribers, finding antennas of small size, low cost, high efficiency, and scan capability was necessary. Therefore, these requirements have become an important area for researchers to find the latest techniques that provide solutions to these requirements [1][2][3][4].
Metamaterials (MTM) are considered technologies that have received particular attention in this field to control and manipulate electromagnetic waves to develop features and characteristics that are not available in nature, thus improving the overall performance [5,6]. Negative constitutive parameters characterize the MTM, therefore called left-handed materials, as they generate a left-handed triad when spreading, which contrasts with the normal spread of other materials. Left -handed (LH) materials are not feasible due to the parasitic effects generated by the right-handed component [7].
A new type of MTM [CRLH-MTM] which combines the properties of LH-and right-handed (RH) materials, has been proposed by CALOZ [8]; it is used in many applications to provide high bandwidth and low loss in communication systems [9,10]. The CRLH MTM consists of a series interdigital capacitor (IDC) and a shunt stub inductor (SI), as shown in Figure 1.
CRLH is used in many different radio applications and microwave systems. In this section, a summary of the latest research findings was discussed. [11] This work analyzed and fabricated a reactive impedance surface (RIS)-MTM antenna. The antenna offers triple-band covering (1.66-1.72 GHz), (1.94-2.20 GHz), and (3.68-3.87 GHz) with gains equal to 1.6 dBi, 4.74 dBi, and 3.28 dBi, respectively. Dual-band circular polarization was obtained by combining the patch antenna with split -ring resonator (SLR) based RIS-MTM. The antenna can be used for different WiMAX, LTE, and satellite applications. [12]. Synthetic material is designed to achieve negative constitutive parameters over the operating frequency range. The material was tested for both gap 2 and gap-less transitions. The material showed double negative parameters at low frequencies, and at high frequencies, the material showed double-positive parameters. As a result, the transition occurs at the same resonant frequency, thus providing a balanced CRLH. [13] CMOS technology-based 2D-CRLH was used to construct an antenna with a double polyimide layer of 500 μm thickness. A high bandwidth was achieved, ranging from 0.350-0.385 THz with a gain equal to 8.15dBi. This paper proposes a new MTM antenna array to provide a good gain with a considerable spectrum across the operated bands. The proposed structure consists of a T-uniform CRLH and a 3 rd -order Hilbert curve.
The dual-band antenna array operates from (3.72 to 3.79) GHz and (6.99 to 8.55) GHz, with maximum antenna gain equal to (5.2 and 7.66) dB, respectively. The S11 <= -20 dB along the operated bands.
Antenna geometrical details are discussed in the second section, where the design procedure and methodology used to arrive at the proposed design are presented. Results and simulation are discussed in section three, and a comparison between the proposed antenna and the latest research is dis cussed in the fourth section. In contrast, the design significance and originality are discussed in the fifth section, and finally, the conclusion is discussed in the last section.

Antenna Geometrical Details
The proposed antenna is implemented from two main parts based on the CRLH structure and Hilbert curve structure. Therefore, we denote the proposed design based on the following: Figure 2 shows a T-symmetric CRLH TL, represented by interdigital capacitors and stub inductors. The periodical separation between the CRLH unit cells provides significant enhancements to the proposed antenna gain -bandwidth product by suppressing the generated Skew waves from the edges of the substrates [14]. The interdigital capacitor is centered on the stub structure to realize a T-network of two impedance branches with 2CL and LR/2 values. The admittance branch with LL and CR values. The parameters of the CRLH unit cell are given in Table 1. The proposed T-network is represented by the equivalent circuit shown in Figure 2. The IDC and SI define left-handed parameters, while the RH parameters are formed due to the parasitic effects caused by the passage of current through the circuit. As the current pass through the IDC, a magnetic field is present, and a shunt inductor is generated, while the voltage gradient between the trace and ground plane causes the series capacitance.

Third-order Hilbert curve structure details
A Hilbert curve line is a continuous curve that fills a two -dimensional space with one-dimensional line segments. It is characterized by its simplicity and similarity [15]. The following equation gives Hilbert c urve length:- The length increases exponentially with n even though the total curve fills a square area of size one. The Hilbert curve configuration process is shown in Figure 3. at zero-order, the Hilbert curve is characterized by a U shape. This shape is repeated indefinitely for higher orders while maintaining the exact dimensions. In other words, the previous order curve replaces the higher vertices. In contrast, the lower vertices experience a rotation where the left vertex rotates 90° clockwise, and the right rotates 90° counterclockwise. For example, see Figure 3; at n=1, the fractal consists of four U shapes filling one area; at n=2, four 1 st -order curves represent the fractal.

Figure 3: Hilbert configuration process
The proposed structure is constructed as a 3rd-order Hilbert shape fractal. The conducted Hilbert design is arranged as a 3×1 array placed in front of the CRLH-MTM unit cell to occupy an area of 13.69* 13.73 mm2, as seen in Figure 3.
There is a direct proportion between area inductance and wire length. By increasing the wire length, the inductance can be improved, increasing the bandwidth while maintaining the miniaturization of the antenna [16]. Fractal structures are used in various applications to increase the operated band and create multiple resonances [17]. The dimension of the Hilbert unit cell is shown in Figure 4.

Results and Discussion
This section discusses the design process based on a numerical parametric study applied to arrive at the proposed antenna design. Therefore, a numerical simulation-based CST software tool package based on the finite integral technique [18] is invoked as follows:

CRLH unit cell performance
A parametric study on the geometrical construction is performed to realize the effect of cell details. As seen in Figure 5, t he proposed CRLH Model can be defragmented into three parts: a transmission line only, an interdigital capacitor with five finge rs each, and a T-stub inductor to represent a capacitive tuner. Therefore, the S11 is computed individually for each part, as shown in Figure 6. In such a study, the design is exciting with a 75Ω port.   Figure 7 (a) shows the resulting antenna array with CRLH after arriving at the optimum unit cell dimensions. The antenna performance in terms of S11 spectra and radiation patterns is presented in Figures 7(b) and 7(c). We found that the proposed antenna provides a triple bandwidth from (7 to 7.9) GHz, (8.2 to 8.6) GHz, and (9.2 to 9.3) GHz. the maximum antenna gain is equal to (7.13, 4.44, 1.35) dBi respectively.
The antenna radiation pattern at the resonance frequencies (7.6, 8.4, and 9.2) is given in Figure 7 (c). The current is concentrated in the middle; this is clear from the surface current flowing along the structure's surface as the current exp eriences the most negligible attenuation along with the interdigital capacitor, see Figure 8. The design procedures and basic paramete rs that significantly increase the gain and spectrum are briefly described in Figure 9.

Antenna interdigital capacitor parametric study
A detailed parametric study was conducted on the number of fingers concerning the antenna transmission line. The fingers were changed from 1 to 5; antenna performance was calculated in each case for realized gain and S11, see Figure 10. With the increase in finger numbers, the losses within the structure are reduced, resulting in better current distribution and, thus, greater gain and S11. To clarify the slots' role in the design and their importance in crystallizing the results in their final form. A study was conducted on the array with and without slots, s 11, and realized gains were calculated in each case. It significantly obtains a wide bandwidth extending from 7 to 9.2 GHz and achieves high gain in th e forward direction, in contrast to the band and gain achieved without slots; see Figure 11. Figure 11: Periodic slots parametric study (a) S11 parameter (b) radiation pattern for the array without periodic slots

Stub inductor parametric study
In this section, the effect of the stub inductor on the array performance was studied, the stub dimensions were changed from 8 to 12 mm, and the gain and impedance bandwidth was calculated in each case, see Figure 12. The introduction of the stub creates a second resonance frequency at 6 GHz, where the voltage gradient between the ground and the copper develops a parasitic effect that produces a second resonance. As the length of the stub increases, this parasitic effect increases, redu cing the matching and gain at some level, so dimension 12 is selected, giving the best result when combined with the Hilbert curve structure.

After the introduction of the Hilbert curve structure
This section studied the effect of the MTM Hilbert curve structure. The introduction of the proposed unit cell realizes several advantages: reducing the overall losses and enhancing performance without introducing extra size and complexity. Furthermore, the Hilbert curve structure can introduce multiple resonance frequencies as it acts as a second radiator that allows the current to flow with tremendous energy. Moreover, each cell is considered balanced to the stub length where the capacitive effect is equ al 8 on both sides. Finally, the antenna inductance is increased due to the introduction of the Hilbert structure, thus compensating for the capacitance effect and expanding the operating frequency range.
The unit cell dimensions were modified and selected to be 13.7 * 13.7 to increase t he effective electrical length of the unit cell. The T stub inductor and the Hilbert structure create resonance at 3.7 GHz with good matching. In addition, the Hilbert cell represents a shading area in self-power wireless devices. The current activates the cell, and the energy is coupled to the cell through SI. Figure 13 shows the s11 and gain after introducing the Hilbert structure . Figure 13: Hilbert curve parametric study (a) S11 parameter (b) radiation pattern

Comparisons With the Latest Publications
The following Table2 gives insight and compares with the relative research findings in this field:-It was found that the proposed antenna provides high gain with excellent impedance -matched bandwidth in the first and second bands, respectively. These characteristics make the antenna a good candidate for applications such as radar, mobile phones, commercial wireless LANs, and the 5G sub-6 GHz network.

Discussion of the Significance and Novelty of The Proposed Structure
The novelty of the design is a nine-cell MTM -array design that achieves a gain equal to 29-cells of the original design. The VIA that causes high losses has been replaced with a fractal that achieves high gain using an inexpensive substrate  compared to the expensive substrate [Roger substrate] design . The periodic slots resulted in a wideband extended from 6.9 to 8.55 GHz with S11 less than -20 dB. As far as we know, it was not previously used in the design of CRLH MTM. Furthermore, 9 The study evidence shows that such antenna gain-bandwidth enhancement is improved by: reducing the influence of via losses, the capacitive losses caused by the ground metallization, and the suppression of surface waves by the Hilbert curve.
The importance of design lies in designing a compact, low-complexity, broadband, high-gain antenna suitable for wireless applications. In addition, the design represents the beginning of creating antennas with various developing performances such as beamforming through different technologies such as electronic, mechanical, or any other technology.

Conclusion
This paper presents a detailed study on designing a new MTM antenna array. First, a regular microstrip line was generated, and left-handed components were added to form a CRLH-MTM structure. Finally, the Hilbert curve has been added to compensate for the VIA. As a result, The antenna Operates in dual-bands with good gain and s 11, which is characterized by its simplicity, making it suitable for wireless devices.

Author contribution
All authors contributed equally to this work.

Funding
This research received no specific grant from any funding agency in the public, commercial, or not -for-profit sectors.

Data availability statement
The data that support the findings of this study are available on request from the corresponding author.

Conflicts of Interest
The authors declare no conflict of interest.