Microstrip patch antenna design using mathematically modeled metamaterial cell

Metamaterial is an artificial material made up of different types of structural designs on a dielectric substrate. In this paper, a broad investigation is being carried out by mathematically modeling and simulating a single negative metamaterial cell comprising a square split ring resonator with two rings. This metamaterial cell has negative permeability values for a particular frequency range. By enhancing properties like bandwidth, reflection loss, and gain in microstrip patch antennae, these metamaterial cells demonstrate unusually remarkable applications in this field. The resonance frequency obtained by simulating the metamaterial cell is compared with the calculated value from the circuit model. The resonance frequency expression is made simple by evaluating the effective permittivity of the substrate after loading the metallic structure on a dielectric substrate. The resonant frequency predicted analytically is found to be extremely close to the frequency obtained by modeling metamaterial structure. A parameter-retrieval method utilising the S parameters is used to determine the curves for the complex permeability of the metamaterial based on its unit element. In order to obtain the S parameters, modeling software is used. This modeled cell is used for designing a rectangular microstrip patch antenna. The parameters such as bandwidth, Gain, return loss, antenna, and metamaterial-based antenna are compared and recorded.


Introduction
Although research on 'synthetic' materials for microwave applications began in 1948 [1].Metamaterial's have only recently emerged as a breakthrough in the realm of electromagnetics.Metamaterials have piqued people's curiosity because of their unusual responses to electromagnetic radiation.These materials are created by structuring precise metallic inclusions onto a host dielectric substrate.The Structural design of metamaterial cells is responsible for the properties of the cell and not the chemical composition of their constituents [2][3][4][5][6].The concept of metamaterials was given by Victor Veselago in 1968 who stated that the Poynting vector of a monochromatic plane wave is anti-parallel to its phase velocity in a medium having dielectric permittivity () and magnetic permeability(), to be negative at the same time [7,8].The materials were named by him as "Left-Handed Materials" (LHM).In 1999, J.B. Pendry proposed the artificial negative permeability medium by an arrangement of an array of small metallic structures called split-ring resonators (SRR).Rectangular rings having equal sides are called square split-ring resonators (SSRR).Through measurements and numerical simulations, Ellstein created analytical circuit models for single-layer and double-layer spiral resonators, proving that these models are superior than earlier circuit 1291 (2023) 012045 IOP Publishing doi:10.1088/1757-899X/1291/1/012045 2 models.[17].The authors noted in [19] that dielectric characteristics affect distributed capacitance associated with the rings of SRR, but inductance is unaffected.We've covered some of the key characteristics of mu negative metamaterials in this article.Mathematical modeling of mu negative metamaterial cells with two rings and structured on Rogers RT/Duroid 5880, Inductance and distributed capacitance of SSRR and hence the resonance frequency are calculated and compared with simulated value.Parameters of mu negative metamaterial cell are extracted using MATLAB script to obtain the curve of complex permeability.Different types of metamaterials are there and they are used for various applications [9][10][11].Using this modeled cell Rectangular microstrip patch antenna (RMPA) has been designed.Its parameters are recorded and judged the advantages of loading SSRR cells on the surface of the patch.

Metamaterials
A metamaterial is a substance that has been artificially constructed and has exceptional electromagnetic properties that are not present in nature or are difficult to achieve.Metamaterials, a fast-expanding interdisciplinary field involving physics, electrical engineering, materials science, optics, and nanoscience, has arisen since the early 2000s.By modifying their internal physical structure, metamaterials can have their attributes precisely tuned.They so differ significantly from natural materials, whose characteristics are primarily governed by their chemical components and bonds.

Double negative or left-handed metamaterials.
The other name for this material is Left-Handed metamaterials.They are artificial materials with negative refractive indexes, permittivity, and permeability.Natural materials don't have these characteristics.The group and phase velocities of electromagnetic waves are opposite to one another because of the negative refractive index, and contrary energy flow is seen.Negative refraction can be achieved when both μ r and ε r are negative, [12][13][14].Equations 1 and 2 are two of Maxwell's equations given to understand metamaterial.
Where є r and μ r are relative permittivity and permeability respectively and Equation 3 is a wave equation derived from the above equation.
If є r and μ r are considered real numbers, then one can observe that the wave equation does not change when signs of Є r and μ r are simultaneously changed.Due to the aforementioned facts, these materials are known as left-handed materials.The Drude-Lorentz model describes the material properties in classical electromagnetic.The effective permittivity and permeability are given in (4) and ( 5) In ( 4) and ( 5), fp and fmp, respectively, stand in for the plasma frequency, the signal frequency, and the resonance frequency, f 0 as well as the damping factor , which is related to material losses.These equations can display a material's properties from the microwave to the optical range.The SSRR presented in figure 1 with some of the rings equal to two is designed on Rogers RT/ Duroid 5880 substrate with a permittivity value equal to 2.2 and thickness equal to 0.25 mm.
is the capacitance per unit length of two parallel strips of width d apart by distance s.The dielectric substrate used in cell affects the distributed capacitance only and is given by equation (8).
Values of K(k) and K(K I ) also can be taken from figure 3. K(k) is called as the complete elliptical integral of the first kind, and K(k I ) is its complex value.It is defined for 0 < k < 1 by (10).Equation (11) presents the average length of the strip.
The dielectric substrate used in SSRR does not affect the inductance.The inductance of SSRR is given by equation ( 12) Where  is the fill ratio of SSRR and is stated as The resonance frequency of the metamaterial cell is given by( 13).

Method to find various parameters of SSRR metamaterial cell.
Numerical simulations can reveal the SSRR's practical parameters.MATLAB code was used to create the artificial SSRR.This produces a metal surface, as seen in figure 1.The tank circuit capacitance, as shown in the diagram, is assumed to be the parallel equivalent of the capacitances in each pair of adjacent loops.negative µ near resonance frequency is produced by the SSRR.The magnetic field which is perpendicular to the SSRR was the only magnetic field that the metamaterial allowed to propagate backward waves.In order to confirm a cell's mu negativity, we have demonstrated the recovery of parameters from a metamaterial cell using MATLAB.Through a MATLAB script, the CST platform is invoked using an inherent feature of CST.[20][21][22].The effective impedance of cell and refractive index has been shown in equation 14 and 15 respectively.
where d is the substrate thickness, k 0 represents wave vector in vacuum, defined as k 0 =2π/ ω o , and m is an integer.We can find z eff and n eff from the given equation.The metamaterial are passive media with this consideration, That is a real impedance is positive and imaginary part of refractive index is negative.Further є r,eff and μ r,eff can be obtained according to ,є r,eff = n eff /z eff and μ r,eff = n eff z eff .After simulation, It is observed that the metamaterial cell resonates at 28 GHz frequency.The graph of S11 and S21 v/s frequency is shown in figure 4. The resonating frequency thus observed which is 28 GHz is shown in the figure.It is also observed from figure 5 that the permeability of the cell is negative at 28 GHz frequency.Also, inductance, capacitance, and resonance frequency of SSRR are shown in Table 1.The value of inductance and distributed capacitance is calculated using the equations shown above.

Application of modeled metamaterial in designing rectangular shape microstrip patch antenna. (RMPA).
The design of antennas is done with SNG or DNG Metamaterial cells.Which are used to increase the performance of the system.These cells could significantly boost an antenna's gain and output power.These antennas can also enhance performance in terms of efficiency and bandwidth.For wireless communication, 4G and 5G applications, etc., a variety of metamaterial-based antennas can be used.[23][24][25].A rectangular shape microstrip patch antenna (RMPA) at resonance frequency 28 GHz as used in 5G communication was designed on an RT Duroid substrate and tested using the FEKO software.Equation ( 16) gives the width of RMPA.In equations ( 17) and ( 18), the effective permittivity and delta L fringing length are correspondingly displayed. ) Effective length and actual length are given in eq 19 and 20.

conventional rectangular shape microstrip patch antenna (RMPA) design at 28 GHz resonating frequency.
Figure 6.shows the top view and design of conventional edge-fed RMPA on RT duroid 5880 substrates.Figure 7 depicts the frequency v/s reflection coefficient graph of RMPA.These parameters determine the ratios of the amplitudes in the transmitted and reflected wave when a plane wave incident on the dielectric DNG medium.When a split-ring resonator is put onto the microstrip patch antenna, these factors improve its performance.The antenna radiates its greatest power at the resonance frequency because the return loss is relatively low (-50dB).At the resonance frequency, It is observed that the return loss is very low,Antenna radiates maximum power when return loss of antenna is very low.The BW, Gain, return loss, and VSWR are depicted in Table 4.Return loss Of the antenna depends on its impedance matching.Return loss is expected to be very low for the perfectly matched antenna.That is perfectly matched with source impedance.2.17     Figure 11 and Figure 12 shows the top view RMPA and the bottom view of RMPA respectively.Figure 12 depicts the metamaterial cells on the bottom of the substrate.Frequency v/s reflection coefficient graph of metamaterial loaded RMPA is depicted in Figure 13.An antenna can emit its maximum power when very low return loss (-45 dB) at the resonance frequency.The frequency v/s reflection coefficient graph of metamaterial loaded RMPA is depicted in figure 13, The reflection coefficient recorded from graph is -45 and bandwidth recorded is equal to 2.19 GHz.   Figure 16.VSWR of RMPA with metamaterial.
Figure 15 shows the impedance matching of metamaterial loaded RMPA at 28 GHz.The impedance is almost 50 ohms at 28 GHz and the reactive impedance observed is close to zero, which matches the source impedance.Figure 16 presents VSWR, and it is equal to 1.00 which signifies perfect matching of source impedance of 50 ohms with an antenna.Figure 17 presents the far-field of RMPA with metamaterials at 28 GHz resonance frequency respectively Total gain has been depicted in the figure.The radiation performance in the antenna indicates the efficiency of the radiation measured in terms of percentage and is obtained by calculating the value of the ratio of the amount of power fed to the antenna to that of the power emitted (radiated) from an antenna.This radiation efficiency boosts the performance of the antenna useful for 5G wireless technology and its applications.The author's proposed antenna has higher radiation efficiency of 89.5% at 28 GHz.
In the one of the research paper metamaterial based antenna was designed with resonance frequency 28 GHz, The(-10 dB) band width obtained was equal to 1.7 Ghz [27].In the second paper (-3 dB) bandwidth of metamaterial loaded patch antenna with resonance frequency 26 GHz was equal to 5.36 GHz [28].In the third paper the patch antenna loaded with metamaterial resonates at 28.89 Ghz and the gain of the antenna was 7.7 dBi. [29]

Simulation results
The metamaterial cell comprising of SSRR is designed and simulated using the software.A metamaterial cell with only SSRR shows negative permeability to state it as a single or mu-negative metamaterial cell.The parameter comparison of RMPA and metamaterial-based RMPA with the same resonance frequency is listed in Table 4. Rectangular microstrip patch antenna for 5G wireless Network technology is effectively and efficiently designed, implemented, and compared for better performance at a 28 GHz resonance frequency.Conventional RMPA and RMPA loaded with metamaterial on the bottom or ground plane of substrate are simulated at a frequency of 28 GHz using FEKO software, When compared to conventional RMPA, it has been found that patch antenna bandwidth significantly outperforms RMPA in terms of both gain and bandwidth.The gain of RMPA without metamaterial is 6.31 dBi and with metamaterial cells is found to be equal 7.64 dBi.This results in a 1.36 GHz increase in bandwidth.Simulated findings have shown that the RMPA's bandwidth has increased.The VSWR of the conventional antenna is 1.01 and that of the metamaterial-equipped antenna is 1.00, indicating that the source impedance of 50 ohms and the antenna impedance are exactly matched.

Conclusion
A rectangular shape microstrip patch antenna is shown in this study both with and without metamaterial.
By loading metamaterial on it, the bandwidth has increased significantly, according to design and simulation results.whereas a minor component has been added to the antenna's gain.The simulated outcome depicts the antenna and source being matched for impedance at 50 ohms at a frequency of 28 GHz.RMPA for 5G wireless Network technology is effectively and efficiently designed, implemented, and compared for better performance at a 28 GHz resonance frequency.Simulation and review of the proposed design are done using FEKO software.Table 4 highlights the substantial improvement in the proposed antenna design and shows better performance with an immense bandwidth for real-time smart device communication and other various applications of 5 G-enabled smart devices, improved return loss for good impedance matching, maximum power energy transfer with high radiation efficiency and good antenna gain for strong signal strength at long-range wireless communication.
In future metamaterial inspired microstrip patch antenna or MIMO antenna on flexible substrate for specific applications like 5G communication can be implemented.Phased array with metamaterial structure can be designed for electronically controlled beam steering function.

Figure 1 .
Figure 1.Square split-ring resonators (SSRR) metamaterial cell with two square split rings on top of the substrate.

Figure 4 .
Figure 4.The graph of S11 and S21 v/s frequency of SSRR with Roger RT Duroid 5880 substrate.

Figure 5 .
Figure 5.The graph of Permeability V/s frequency of SSRR with Roger RT Duroid 5880 substrate.

Figure 8
Figure 8 depicts a far-field radiating pattern in UN and VN planes at 28 GHz frequency.The antenna gain is 6.31 dBi at 0 degrees.

Figure 8 .
Figure 8. Far-field radiating pattern and total gain of RMPA at 28 GHz without metamaterial.

Figure 9
Figure 9 presents the smith chart which depicts the impedance matching at 28 GHz of RMPA .The impedance is approximately 50 ohms at 28 GHz.VSWR is at 28 GHz is 1.02.Very important parameter of antenna is the gain of an antenna.Figure10 shows the far-field of RMPA and total surface current distribution at 28 GHz.The variation of current is shown in figure.

Figure 14 .
Figure 14.Far-field radiating pattern and total gain at 28 GHz of metamaterial-based RMPA.
Design of mu Negative Metamaterial Cell on RT/Duroid 5880 Substrate.

Table 1 .
Comparison of calculated and simulated resonance frequencies of SSRR.

Table 4 .
Parameters of RMPA.Conventional RMPA bandwidth and returns loss is 0.826 GHz and -50 dB respectively.Whereas metamaterial-based RMPA the values of bandwidth and return loss are 2.19 GHz &-45 dB respectively.