DESIGN AND ANALYSIS OF SQUARE SPLIT RING RESONATOR METAMATERIAL FOR MICROWAVE FREQUENCY RANGE

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1 International Journal of Advanced Research in Engineering and Technology (IJARET) Volume 9, Issue 6, November-December 2018, pp , Article ID: IJARET_09_06_021 Available online at ISSN Print: and ISSN Online: IAEME Publication DESIGN AND ANALYSIS OF SQUARE SPLIT RING RESONATOR METAMATERIAL FOR MICROWAVE FREQUENCY RANGE Vani H R Associate Professor, Department of Electronics & Communication Engineering Adichunchanagiri Institute of Technology (AIT), Chikkamagaluru, Karnataka Paramesha Professor, Department of Electronics & Communication Engineering Government Engineering College, Hassan, Karnataka A. Goutham M Professor, Department of Electronics & Communication Engineering, Adichunchanagiri Institute of Technology (AIT), Chikkamagaluru, Karnataka ABSTRACT In this work, Square Split Ring Resonator (SSRR) Metamaterial structure is analyzed at microwave frequencies. The mathematical analysis of the resonator structure is made to estimate the resonant frequency. Transmission characteristics of the resonator structure are extracted using MATLAB tool to demonstrate metamaterial behaviour in the microwave frequency range. Keywords: Frequency Reconfigurable Microstrip; S-Slot Antenna. Cite this Article: T. Subhramaniyan, P. Sankar, P. Paulraj, M. G. Ragunathan and J. Jayanthi, The Prevalence of Causes For Diabetic Retinopathy Using Mathematical Models, International Journal of Advanced Research in Engineering and Technology, 9(6), 2018, pp INTRODUCTION Metamaterials are extensively used in optical and microwave applications due to their ability to their unusual properties. A variety of metamaterials are investigated in [1-8]. In this paper, a single square shaped split ring resonator is designed to operate at 5.5 GHz frequency. The mathematical analysis is made to estimate the resonant frequency. Transmission characteristics of the resonator structure are extracted using MATLAB tool to demonstrate metamaterial behaviour in the microwave frequency range editor@iaeme.com

2 Design and Analysis of Square Split Ring Resonator Metamaterial For Microwave Frequency Range 2. DESIGN AND ANALYSIS Structure and Design of Square Split Ring Resonator Fig. 1 shows the structure of single Square split ring resonator with metallic square ring printed on FR4 epoxy substrate with relative permittivity of 4.4. The resonator structure is designed for 5.5 GHz frequency. The width of the ring is 1mm, the gap width is 1.2mm, and the radius of the outer ring is 6mm. Equivalent circuit model of single split ring resonator is shown in Fig. 2 Fig. 1. Geometry of simulated single SSRR Fig. 2. Equivalent circuit of single SSRR Resonant Frequency Computation of single SSRR The parameters under consideration are the outer radius of the ring, a, the thickness, c, the height, h, and the gap width, g. The metallic ring is modelled by an inductance, L. The gap in the ring corresponds to capacitance, C g which is modelled as a parallel plate capacitor. The charges on the surface are the surface capacitance, C surf. With a magnetic field applied along the z-axis, an electromotive force appears around the single SSRR which makes the structure behaves like an L-C network having resonant frequency expressed as: f = 1 0 2π LC (1) editor@iaeme.com

3 Vani H R, Paramesha and A. Goutham M The inductance can be approximated by that of a closed ring [8] 8am L = µ 0am ln 0. 5 (2) h + c μ 0 is the permeability of free space and a m is the mean radius of the ring, a m = a+w/2. ch 2πh C g = ε 0 + (3) g 2. 4h ln c 2ε h 4a C surf = 0 ln (4) π g 1 C 1 1 = + (5) C g C surf 3. EXTRACTION OF S-PARAMETERS OF SINGLE SSRR To demonstrate the metamaterial behaviour of the designed resonant structure, parameters such as permittivity, permeability and refractive index are extracted. For this purpose, a unit single SSRR is designed using HFSS tool. The periodic boundary conditions using perfect electric and perfect magnetic are shown in Fig. 3a and Fig. 3b respectively. For excitation, waveport is assigned as shown in Fig. 4. Fig. 3a. The simulation model with perfect electric boundary condition editor@iaeme.com

4 Design and Analysis of Square Split Ring Resonator Metamaterial For Microwave Frequency Range Fig. 3b. The simulation model with perfect magnetic boundary condition Fig. 4. The unit element excitation: Waveport After defining the boundary conditions and excitations, solution frequency is set to 5.5GHz and the structure is simulated. The S-parameters graph thus obtained are shown in Fig. 5. Fig. 5. Simulated S-parameter plot of single SSRR As seen from Fig. 5, the simulated resonant frequency is 5.5GHz. S(2,1) and S(1,1) crosses each other at 4.8GHz and 6.1GHz which depicts the bandwidth of the resonant structure. The theoretical resonant frequency obtained from (1) is 5.56GHz and is in good agreement with simulation. The S-parameters so obtained are substituted in the equation given in [5]

5 0 ink [{ [ ( )] } [ ( )] ] '' ' 0d ink0 ln e + 2m i ln e 1 d n = π (6) k d n ε = (7) z µ = nz (8) Vani H R, Paramesha and A. Goutham M Where k o is the wave vector. Permittivity, permeability and refractive index obtained using MATLAB tool are shown in Fig. 7, Fig. 8 and Fig.9 respectively. Fig. 7. Real and imaginary values of permittivity Fig. 8. Real and imaginary values of permeability editor@iaeme.com

6 Design and Analysis of Square Split Ring Resonator Metamaterial For Microwave Frequency Range Fig. 9. Real and imaginary values of refractive index As seen from Fig. 7, Fig. 8, and Fig. 9 the values of permittivity, permeability and refractive index are negative in the desired frequency range. The results obtained establish the metamaterial behaviour of the single SSRR. 4. CONCLUSION A single square shaped split ring resonator is demonstrated and mathematical analysis to estimate resonant frequency is presented. Theoretical resonant frequency is in good agreement with the simulation. The transmission characteristics such as permittivity, permeability and refractive index extracted through S-parameter obtained from HFSS simulation shows negative values in the desired frequency range which establish metamaterial behaviour. REFERENCES [1] V.G. Veselago, The electrodynamics of substances with simultaneously negative values of and?." Soviet Physics Uspekhi, Vol.10, No.4, Pp.509, [2] C.T. Jun, D.R. Smith and R. Liu, Metamaterials: Theory, Design, and Applications, Springer, New York, [3] C. Saha, J. Y. Siddiqui, Y.M.M. Antar, Theoretical investigation of the square split ring resonator, Proceedings of URSI NA Radio Science Meet, [4] C. Saha, J.Y. Siddiqui, Estimation of the resonance frequency of conventional & rotational circular split ring resonators, IEEE Applied Electro magnetics Conference (AEMC), Kolkata, [5] M.R. Vidyalakshmi and Dr.S. Raghavan, A CAD Model of Triangular Split Ring Resonator Based on Equivalent Circuit Approach, IEEE Applied Electromagnetics Conference (AEMC), Kolkata, Pp.1-4, [6] V. Sharma, S.S. Pattnaik, T. Garg and S. Devi, A microstrip metamaterial split ring resonator, International Journal of Physical Sciences, Vol.6, No.4, Pp , [7] R. Marquez, F. Mesa, J. Martel, F. Medina, Comparative analysis of edge- and broadside-coupled split ring resonators formetamaterial design-theory and experiments, IEEE Transactions on Antennas Propagation, Vol.51, No.10, pp , [8] V.J. Bashenoff, Abbreviated methods for calculating the inductance of irregular plane polygons of round wire, Proceedings ofinstitute of Radio Engineers, Vol.15, No.12, Pp , [9] Q. Li and A.P. Feresidis, Reduction of mutual coupling between compact MIMO antennas arrays, In Antennas and Propagation Conference (LAPC), 2010 Lough borough, Pp , [10] M. Jagadish, A.S. Pradeep, Design of Hexagonal Shaped Split Ring Resonator for Multi-Resonant Behaviour, onfring International Journal of Research in Communication Engineering, Vol., Special Issue, November editor@iaeme.com