Int. Journal of Electrical & Electronics Engg.
Vol. 2, Spl. Issue 1 (2015)
e-ISSN: 1694-2310 | p-ISSN: 1694-2426
Investigation on Frequency Analysis of Metamaterial Structure Rajni
Gursharan Kaur, Amanpreet Kaur
Dr. Anupma Marwaha
Associate Professor, Department of ECE SBSSTC, (PTU, Kapurthala)
M.Tech. Research Scholar, Department of ECE SBSSTC, (PTU, Kapurthala)
Associate Professor Department of ECE SLIET (Deemed University), Longowal
rajni_c123@yahoo.co.in,
gursharankaur07@gmail.com, amannatkaur@gmail.com
Abstract - In this work, a Split Ring Resonator (SRR) unit cell is simulated in a waveguide with electromagnetic field solver High Frequency Structure Simulator (HFSS). Analytical calculations of the inductance and capacitance have been also carried out to obtain the resonant frequencies for SRR dimensions. A comparison between calculated and simulated resonance frequencies)) is done. A good correlation between simulated and measured resonance frequencies is achieved. Index Terms – Split Ring Resonator (SRR), Metamaterial, Unit cell, resonant frequency.
I. INTRODUCTION Antennas are gaining attention due to their vital role in today’s world of wireless communication systems. There are a lot of techniques have been used by researchers to to enhance the antenna performance parameters. Use of Metamaterials (structure based materials) in antennas on ground, patch or substrate is one of these techniques. In 1967, Veselago through his theoretical investigation proved the existence of metamaterial [1]. Metamaterials are engineered materials that have unnatural physical properties that are not found in nature. These metamaterial exhibits negative permeability (μ) and negative permittivity (ε) and are defined as double negative materials (DNG). In case of single negative metamaterial, the only permeability (μ) negative materials are known as mu negative (MNG) and only permittivity (ε) negative materials are epsilon negative (ENG) materials. Metamaterial structure is comprised of SRR and thin wire elements that generates negative permeability and negative permittivity respectively. The concept of metamaterial has reversed the Snell's law, Doppler Effect, Cheronkov radiation because of its unconventional properties [2-5]. In 1981 the first ‘split ring resonator’ was invented by Hardy [6]. In 1999 the periodic array of conducting nonmagnetic rings known as SRR was first used to attain negative permeability and proved by Pendry [7] and nowadays has become the popular metamaterial component. There are many structures of different types of SRR are available, such as double split SRR (DS-SRR), broadside couple SRR (BC-SRR), spiral SRR (S-SRR) and edge coupled SRR (EC-SRR). SRR is considered as an important artificial atom for the artificial media’s design and fabrication. However, there are still some parameters of SRR that have scope of an improvement. The idea behind this work is to investigate the performance of nine models of SRR obtained by varying its parameters dimension. In this work, a double split ring structure has been considered as a unit cell and investigation is done on NITTTR, Chandigarh
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marwaha_anupma@yahoo.co.in
SRR instead of an array to simplify analysis and performance calculation. Dimensions of SRR are varied and comparison for calculated and resonating frequency has been carried out for different models. The Ansoft HFSS software is used to analyse various parameters of SRR models. II. SRR UNIT CELL DESIGN The SRR cell consists of concentric rings with cuts (splits) at the opposite ends. Rings have small spacing between them and are made of copper like metals. The magnetic flux will generate the rotating currents in the rings, in response to which rings produce their own flux to intensify the incident field. Presence of splits in the ring leads to resonant wavelengths greater than the diameters of the rings. Figure1 illustrates a dual split ring resonator (SRR), a highly conductive structure having inductance adjusted by the capacitance between the two rings.
Figure 5. Geometry of a Split Ring Resonator with dimensions.
The SRR is placed above the Rogers RT/duroid substrate 5880 of thickness of 3.175 mm, relative permittivity ( ) of 2.2 and loss tangent is 0.0009. The unit cell is enclosed in a waveguide. Perfect electric conductor boundaries are assigned to both faces of the X axis. Perfect magnetic conductor boundary conditions are assigned at top and bottom of the Z-axis. The unit cell is excited by the waveports. Wave penetrates through the two waveguide ports assigned on Y-axis. [8]. Figure 2 presents a structure of SRR inside waveguide.
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Int. Journal of Electrical & Electronics Engg.
Vol. 2, Spl. Issue 1 (2015)
e-ISSN: 1694-2310 | p-ISSN: 1694-2426
In Table 1, Resonant frequency is compared for calculated and simulated value for a variation in spacing s, keeping length a and width t constant. Frequency comparison for different values of SRR width‘t’ is considered in Table 2 and different values of SRR length ‘a’ are considered in Table 3. Different values of SRR parameters are analysed for performance consideration and frequency comparison of measured and simulated frequencies obtained by considering SRR unit cell. TABLE 1: Frequency comparison for the different values of .
Figure 2. Unit cell of SRR
The equivalent circuit of the square split ring resonator can be considered as a parallel LC tank circuit as shown in Figure 3 where metalil corresponds to inductance and the split can be considered to introduce a capacitance.
a (mm)
t (mm)
s (mm)
f simulated (GHz)
f calculated (GHz)
5
0.5
0.1
4.77
4.86
5
0.5
0.2
5.25
5.35
5
0.5
0.3
5.65
5.72
TABLE 2: Frequency comparison for the different values of . a (mm) 5
t (mm) 0.6
s (mm) 0.1
f simulated (GHz) 4.86
f calculated (GHz) 5.43
5
0.65
0.1
4.98
5.52
5
0.7
0.1
5.21
5.72
TABLE 3: Frequency comparison for the different values of . Figure 3. Equivalent LC circuit of SRR [11]
The design equations of SRR are given in [9] [10], the resonance frequency of the metamaterial structure depends on three variables viz. length a, thickness t and spacing s. The equivalent inductance, capacitance and resonance frequency are given by equation (1)-(4). =
(1)
.
Where,
( − − )
+ 1.84
= length of the SRR = thickness of SRR =spacing between the rings
= (2) = (3)
.
,
is fill ratio
− 1.5( + )
a (mm) 5
t (mm) 0.5
s (mm) 0.1
f simulated (GHz) 4.52
f calculated (GHz) 4.86
5.1
0.5
0.1
4.21
4.82
5.2
0.5
0.1
4.21
4.68
III. RESULTS AND DISCUSSION The transmission coefficient for nine models of SRR is obtained by varying spacing, width and length of SRR. Transmission minimum of different square SRR models is plotted. A. Effect of variation in spacing between rings The spacing (s) between the double split ring resonators is changed by keeping the other parameters unchanged (t and a). A shift to the higher values of resonant frequency is observed in Figure 4 as the spacing between the rings is increased. Increasing the SRR spacing shifts the LC resonance towards higher frequencies due to a reduced capacitance [12].
where is capacitance per unit length between the rings. The resonant frequency of SRR structure from its equivalent circuit is evaluated from the following equation as:
(4)
167
=
√
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EDIT-2015
Int. Journal of Electrical & Electronics Engg.
Vol. 2, Spl. Issue 1 (2015)
e-ISSN: 1694-2310 | p-ISSN: 1694-2426
IV. CONCLUSION
Figure 4. Transmission coefficient of unit cell for s = 0.1, 0.2, 0.3 mm and a= 5mm, t= 0.5mm.
B. Effect of variation in width of rings The SRR width t is changed by keeping the other parameters unchanged (s and a) and the corresponding results are shown in Figure 5. It is observed that the resonant frequency increases as we increase the width of the SRR due to the decrease in capacitance between the rings.
Figure 5. Transmission coefficient of unit cell for t = 0.6, 0.65, 0.7 mm and a=5mm, s=0.1 mm.
C. Effect of variation in length of Outer ring The double split ring resonator length “a” is changed by keeping the other parameters unchanged (s and t). The results are shown in Figure 6. On dependence of various parameters, the resonance associated with the LC-circuit changes its frequency. Increasing the SRR length leads to an increase in the SRR inductance and hence resonant frequency get decreased.
In this paper, the investigation is done on double ring structure of square SRR. Nine models are being analysed and frequency comparison is done for calculated and simulated resonant frequency by varying the geometry dimensions of SRR. The simulated and measured frequencies are in very good agreement with each other for every case when variable a, w and d is varied. Results reveal that there is a regular shift in the resonant frequency when various parameters of SRR are varied. Hence it is concluded that desired values of frequencies can be obtained according to particular application by simply varying the SRR parameters. REFERENCES 1) V G Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Physics USPEKHI, Vol. 10, pp. 509-14, 1968. 2) R W Ziolkowski and A Erentok, “A path to an efficient electrically small antenna: A dipole enclosed in a double negative (DNG) or a single-negative (SNG) metamaterial spherical shell,” Proceedings of ISAP, Seoul, Korea, pp. 499-502, 2005. 3) D R Smith, D C Vier, T H Koschny and C M Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials, ” Physical Review, E71, pp. 036617-1-10, 2005. 4) R W Ziolkowski, “Design, fabrication, and testing of double negative metamaterials,” IEEE Transactions on Antennas and Propagation, Vol. 51, No.7, pp. 1516-29, Jul. 2003. 5) Marques, R., F. Mesa, J. Martel, and F. Medina, “Comparative analysis of edge and broad-side coupled split ring resonator for metamaterial design-theory and experimentation,” IEEE Transactions on Antennas and Propagation, Vol. 51, No. 10, 25722581, Oct. 2003. 6) W. H. Hardy and L. A. Whitehead, “Split-ring resonator for use in magnetic resonance from 20-2000 MH,” Review of Scientific Instruments, vol. 52, pp. 213-216, Feb. 1981. 7) J B Pendry, A J Holden, D J Robbins and W J Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Transactions on Microwave Theory and Techniques; Vol. 47, No. 11, pp. 2075-84, Nov. 1999. 8) Baena, J. D., J. Bonche, F. Martin, R. M. Sirello, F. Falcone, T. Lopetegi, M. A. G. Laso, J. Garcia Garcia, and I. Gill, “Equivalent circuit models for split ring resonators and complementary split ring resonators coupled to planar transmission lines,” IEEE Microwave Theory and Techniques, Vol. 53, No. 4, Apr. 2005. 9) B.-I. Wu, W. Wang, J. Pacheco, X. Chen, T. Grzegorczyk, and J. A. Kong, “A study of using metamaterials as antenna substrate to enhance gain, ” Progress In Electromagnetics Research, vol. 51, pp. 295-328, 2005. 10) Vidyalakshmi, M. R. and S. Raghavan, “Comparison of optimization techniques for square split ring resonator,” International Journal of Microwave and Optical Technology, ” Vol. 5, No. 5, Sep. 2010. 11) S. Raghavan1 and Anoop Jayaram, “Metamaterial Loaded Wideband Patch Antenna, ” PIERS Proceedings, Taipei, March 2528, 2013. 12) Rajni and Anupma Marwaha, “Analysis of magnetic resonance in Metamaterial structure,” COMSOL conference,Bangalore,2011.
Figure 6. Transmission coefficient of unit cell for a = 5, 5.1, 5.2 mm and s=0.1mm, t=0.5mm.
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