Analysis of the Resonator Element in Different Positions in the Circular Patch Microstrip Antenna

— In this article, a circular patch microstrip antenna with a metamaterial resonator for 4G applications is proposed. For the design of the circular antenna patch, an approximate calculation was performed. The circular resonator is inserted into the patch for some antennas, in different positions for a parametric study. When incorporating the resonator, the performance of the antenna is improved and analyzed through some parameters, when compared with the antenna without the resonator. To verify the influence of the resonator and validate its performance, simulated results were performed with the ANSYS HFSS ® software and compared with the experimental results, through prototypes, in which they showed a good agreement .

In addition, some works report antenna designs with resonant MTM geometries immersed in the microstrip antenna patch, as in [4], who investigated an MTM based on Hilbert's fractal geometry, manufactured with printing of conductive material on the substrate. Increased bandwidth on two frequencies and increased gain. For [6], who proposed an MTM CSRR resonator for a UWB antenna that wishes to reject a frequency band. According to [7], an active MTM CSRR ring structure, based on varicap diodes, obtaining multibands. In [8], an X band antenna with circular SRR slots to achieve narrow bandwidth was designed. For [12], it was designed an antenna with a CSRR resonator and proposed two techniques. The first is made up of a split ring resonator cell. In the second, an arrangement of split periodic resonators was integrated. In both techniques, the resonators had variable positions and angles in order to find the best results. In [13], an antenna with a CSRR resonator is designed and used as a sensor, which can be applied to characterize different types of dielectric materials, in addition to being used to determine the percentage of water contained in different types of soil. In [14], it was proposed a Rectangular MTM Complementary Split Ring Resonator (RCSRR), contributing to the antenna miniaturization, good impedance matching, gain and bandwidth. For [15], split SRR square rings were used next to the antenna patch with PIN diodes.
Control in the direction of the beam was investigated, obtaining a better gain and bandwidth for a frequency. In [16], an antenna with an MTM matrix in Hexagonal Complementary Split Ring Resonators (CSRRs) was used to evaluate the frequency response and radiation performance of the antenna. Another article developed a circular CSRR for broadband applications with reduced antenna size [17]. Finally, a design of a compact Multiple Split Ring Resonator (MSRR) obtained a better frequency, compact antenna for wireless local area network (WLAN) and radio frequency identification (RFID) applications [18].
Thus, in this work an MTM CSRR resonator for 2.6 GHz is proposed and analyzed in different positions in microstrip patch antenna. In addition, an approximate calculation for the size of the circular patch is applied. Electromagnetic simulations were performed using the ANSYS HFSS ® software. The simulated and experimental results were investigated through the parameters of return loss (RL), bandwidth (BW), radiation diagram, gain, Smith chart graphic and current distribution.

II. CSRR DESIGN
The MTM structure called Complementary Split Ring Resonator (CSRR) was proposed by Pendry based on SRR geometry, these two geometries being the most explored by researchers, since they have resonant elements and provide a high quality factor in the frequencies of microwaves and millimeter waves [6], [19] - [20]. With the advancement of SRR and CSRR, other forms of geometries have emerged, such as square and triangular. The geometries are formed by two concentric rings with divisions in their opposite in the inner and outer rings, having behavior characteristics such as, stop band device, electric dipole and negative effective permeability [6], [21].
CSRR is produced by etching ring-shaped grooves on the metallic part of the upper or lower surface of microstrip antena substrate, and its electrical and magnetic properties are exchanged in relation to the SRR. In addition, it can be excited by a time-varying axial electric field and exhibit negative values of dielectric permittivity [21]. Fig. 1a shows the comparison between an SRR and CSSR geometry, while Fig. 1b shows the CSRR equivalent circuit [21]. As the geometry works according to an equivalent circuit, the resonance frequency can be determined by (1) [6], [19] - [20].
where 0 is the resonance frequency, L is the inductance per length, C is the total capacitance of the CSRR and r is the average radius of two annular slots.
Based on the MTM CSRR geometry presented in the literature, the resonator for this work was designed and defined empirically by means of computer simulations, until obtaining a good agreement with the microstrip antenna patch design. Thus, the geometry was shown in Fig. 2. The dimensions were called r0 = 1.6 mm, r1 = 2.8 mm, r2 = 4 mm and r3 = 5.2 mm. III. ANTENNA DESIGNS AND RESONATOR POSITIONS The antennas were designed for 4G applications with 2.6 GHz, considered an input impedance of 50 Ω and excited from a power line with a quarter of the wavelength. The material adopted in the patch, transmission line and ground plane, was copper laminate with a thickness of 0.05 mm. For the dielectric substrate, FR4 (Fiberglass) with a thickness of 1.58 mm was adopted, which is normally applied to wireless devices and has a dielectric constant εr = 4.4 with a loss tangent (δ) equal to 0.02.

A. Antenna without Resonator
In the antenna without resonator, its design was considered the use of inset fed for better power transfer and impedance matching. To determine the dimensions of the microstrip antenna, normally the literature presents studies with the rectangular patch [1], [22]. It is worth mentioning that the most used method for calculating the values of Wg and Lg, is the method of the transmission line [1]. In this work, an approximation calculation to determine the dimensions of the circular antenna patch (Fig. 3), was considered by equation (2) [23]. The antenna dimensions are shown in Table I.    Table II.

IV. RESULTS AND DISCUSSIONS
In this section, we present the results of the simulations and measurements from the prototypes of For the antenna without resonator (Fig. 5a), a frequency of 2.62 GHz and RL of -15.5 dB (Fig. 6) are observed in the simulated result. For the measured result, it presents the frequencies of 2.25 GHz, 2.75 GHz and RL of -12.5 dB, -22.5 dB. Fig. 7 shows the plane E and H of the radiation diagram and the gain. For the antenna with resonator in position A (Fig. 5b), Fig. 8 Fig. 9 shows the plane E and H of the radiation diagram and the gain.   For the antenna with resonator in position B (Fig. 5c), Fig. 10 Fig. 11 shows the plane E and H of the radiation diagram and the gain. For the antenna with resonator in position C (Fig. 5d), Fig. 12 13 shows the E and H plane of the radiation diagram and the gain. For the antenna with resonator in position D (Fig. 5e), Fig. 14 Fig. 15 shows the E and H plane of the radiation diagram and the gain.   To validate the performance of the resonator and its positions in the antenna patch,   V. CONCLUSION In this article, a simple and easy to manufacture resonator geometry was proposed to be applied to the patch of a circular antenna, in different positions. Parametric analyzes were performed using the ANSYS HFSS ® software, then prototypes were manufactured and measured to validate the results.
Therefore, it was observed that the antenna designs met equation (2) for an approximate calculation of the circular patch, as well as the Federal Communication Commission (FCC) for the return loss below -10 dB, which can be produced commercially.
In addition, the antenna with resonator in position A and aligned in the direction ± with the power line, showed a better performance, that is, depending on the position of the CSRR in the patch, it can considerably increase the gain, change the width of band, but also to change the operating frequency and radiation of the antenna. It was also found that the use of the resonator resulted in better gains when compared to the antenna without resonator.
Thus, this work showed that the results proved the simplicity of the resonator and the application of an approximation calculation for the circular antenna patch, made possible a good agreement between the results.