1. International Journal of Electronics and Communication Engineering & Technology (IJECET),
INTERNATIONAL JOURNAL OF ELECTRONICS AND
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)
ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Special Issue (November, 2013), pp. 279-285
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IJECET
©IAEME
Role of Geometry of Split Ring Resonators in Magnetic
Resonance of Metamaterials
Rajni1, Anupma Marwaha2
1Assoc.
Prof., Deptt. of Electronics and Communication Engg., Shaheed Bhagat Singh State Technical Campus,
Ferozepur, Punjab, India
2Assoc. Prof., Deptt. of Electronics and Communication Engg., Sant Longowal Institute of Engg. And Technology,
Sangrur, Punjab, India
1rajni_c123@yahoo.co.in, 2marwaha_anupma@yahoo.co.in
ABSTRACT: Planar Metamaterials and Many antennas are designed by means of periodic
structures having lattice constants smaller than the wavelength at their resonating frequency.
The basic building blocks of Metamaterials are synthetically fabricated structures of Split Ring
Resonators (SRRs). A magnetic response is attained with this resonator and negative magnetic
permeability values can be achieved which is generally unity for naturally occurring materials.
This paper emphasizes on simulation of a SRR structure of a metal on a substrate inside a
waveguide with Finite Element Method based software ‘High Frequency Structure Simulator’.
The magnetic resonance of Split Ring Resonators has been investigated with variation in
geometrical parameters of SRRs. The results reveal that resonant frequency of Metamaterials
can be controlled by the design of resonators and hence in achieving the bulk metamaterials
with negative permeability.
KEYWORDS: Left-handed Metamaterials (LHM), Metamaterials (MTM), Negative Index
Materials (NIMs), Split Ring Resonators (SRRs), Refraction Index
I.
INTRODUCTION
There has been unprecedented escalation in study of Metamaterials (MMs) with unusual
properties not occurring naturally, in the last decade. The man behind the discovery of the
concept of Metamaterials was Victor Veselago who analyzed incident uniform plane-wave
propagation in a media with both negative permittivity and negative permeability in 1968 [13]. These materials are artificially designed material that gains effective properties from its
structures rather than inheriting them directly from its constituents [4]. The phase velocity and
group velocity in these materials are anti-parallel to each other i.e. the direction of propagation
is reversed with respect to the direction of energy flow. The edifice building blocks of MTM are
synthetically fabricated periodic structures having lattice constants smaller than the
wavelength of the incident radiation. The building blocks of Metamaterials are Thin wires
(TW), Split Ring Resonators (SRRs) and combination of both Thin Wires and Split Ring
International Conference on Communication Systems (ICCS-2013)
B K Birla Institute of Engineering & Technology (BKBIET), Pilani, India
October 18-20, 2013
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2. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
Resonators. So Metamaterial properties can be controlled by the design of their building
blocks. Thin wires and Split Ring Resonators (SRRs) were proposed by Pendry et al. in 1998
and 1999 and then extensively studied by several groups. They demonstrated experimentally
that “Split-Rings” are useful to obtain negative effective permeability (μeff) [3,5]. In year 2000,
Smith et al experimentally confirmed that the use of thin wire arrays in addition to SRR (Split
Ring Resonator) arrays provide negative effective permittivity,(εeff) along with negative
effective permeability (μeff) simultaneously over a common frequency band [6-7]. The
conventional split-ring resonator unit cell was composed of two circular coplanar metallic
rings each with a split displaced by 180 degrees. These rings were patterned on a low-loss
dielectric substrate having the same center and alienated from each other by a short gap
distance. SRRs can be of any shape rectangular, square, triangular etc. These resonators permit
control and manipulation of light on subwavelength length scales for incorporating Optics into
Micro and Nanotechnology. These resonators have a wide range of applications such as
absorbers, frequency selective surfaces, sensors, antenna structures, high frequency
modulators and composite materials. The SRRs have undergone numerous miniaturized
refinements since its inception in order to optimize the resonances supported in the structure
as these resonances hold the solution in tailoring the effective permeability and permittivity of
the MMs [8-10].
In this paper, the magnetic resonance of Square SRRs structure of copper is numerically
investigated to analyze the dependence of the resonance frequency on their parameter designs.
Square SRR structure on a substrate is investigated with Finite Element Method (FEM) based
software ‘High Frequency Structure Simulator (HFSS)’.
II.
EQUIVALENT CIRCUIT OF SRR
SRRs consist of two metallic rings of metal with a split (gap) introduced in its structure. When
a current circulates in a coil, it produces a magnetic dipole moment. The generated dipole
moment vector is at right angles to the plane of the coil. The coil with a plate capacitor together
gives us an LC circuit and therefore an increased dipole moment at its resonance. The SRR
behaves similar to the LC circuit. The metallic ring does function of an inductance coil (L) and
the split in the ring introduces a parallel plate capacitor (C). The resonance frequency of SRR
with geometrical parameters shown in the Fig. 1 can be derived as follows:
Magnetic resonance frequency ωm =1/√ (LC)
….………(1)
Capacitance, C = ( εo εr Α ) / d = (εo εr w t / d)
………….(2)
Inductance (L) = μo coil area / length (with a single turn in the coil) .......……..(3)
Where,
A is area and d the distance between the plates. εr is relative permittivity of Dielectric present
between the plates.
Fig. 1: Analogy of SRR with LC Circuit [11]
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B K Birla Institute of Engineering & Technology (BKBIET), Pilani, India
October 18-20, 2013
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3. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
Presence of dielectric effects the resonance frequency of SRR which is inversely proportional to
the size of SRR. If there is no split in SRR, then the capacitance will become infinity as d=0 and
there will not be a resonance. So it is imperative to introduce the split in the ring to have a
capacitive effect which can lead to the negative value of magnetic permeability (μ). There are
several parameters that necessitates to be tuned including width and height of the SRRs,
spacing between the rings, size of the Split, Material properties of the rings, thickness of
substrate and surrounding medium in order to get the desired negative permeability property
at certain frequency range.
The Value of Permeability (μ) can be retrieved from Nicolson-Ross-Weir (NRW) approach. This
method is used to attain the permeability from Reflection Coefficient (S11) and Transmission
Coefficient (S21).
V1=S21+S11
V2=S21-S11
............ (4)
............. (5)
k=ω √(εr μr) /c = k0√(εr μr)
............. (6)
Where,
ω=2πf, and k0= ω/c, μr is relative permeability, εr is relative permittivity, c is speed of
light=3*108m/s
μr≈ 2/(j k0d))*(1- V2) / (1+ V2)
................(7)
d is thickness of substrate.
III.
GEOMETRICAL PARAMETERS OF SRR MODEL IN WAVEGUIDE
SRR shown in Fig.2 are considered to be made of Copper. The length (L) and width (W) of
Outer ring is kept as 4mm. The gap of SRR is taken as 0.2mm. The thickness of substrate is kept
as 2mm. The spacing between outer ring and inner ring is 0.2mm. The SRR is patterned on a
Rogers duroid 5880 tm substrate with dielectric constant of 2.2 with Loss tangent 0.0009.
Fig. 2: (i) Geometry of SRR
(ii) Top view of SRR Unit Cell in HFSS
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B K Birla Institute of Engineering & Technology (BKBIET), Pilani, India
October 18-20, 2013
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4. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
IV.
SIMULATION OF MATERIAL UNIT CELL TO DETERMINE VALUE OF PERMEABILITY
In order to obtain the Metamaterial structure that exhibit the left-handed Metamaterial
properties in the desired working frequency region, SRR unit cell with different dimensions is
simulated inside a waveguide and the effect of the geometrical parameters on the resonating
frequency region and the Metamaterial properties is observed. For simulation, the Perfect
Electric Conductor (PEC) boundary conditions were employed on the z-faces of the unit cell.
The Perfect Magnetic Conductor (PMC) boundary conditions were used on the y-faces of the
unit cell so that the negative permeability behavior of SRR would be excited. The two
waveports 1 and 2 are assigned along each of the substrate line on the x-faces. Besides the
effect the variation in dimensions of SRR, spacing and gap, parametric studies on influence of
substrate thickness and the thickness of the SRR are also done.
V.
RESULTS AND DISCUSSIONS
NRW method is commonly used technique to determine the value of permeability strength of
the total resonance. The Return Loss or Reflection Coefficient (S11) and Transmission
coefficient (S21) are plotted vs frequency and depicted in Fig. 3. The magnitude and phase of
S11 and S21 are shown in Fig. 4 and Fig. 5. The phase reversal of S21 and S11 confirms the
metamaterial behaviour of SRR. Real and imaginary parts of S11 and S21 are revealed in Fig. 6
and Fig. 7. S21 and S11 values are exported in MATLAB to calculate effective negative
permeability region.
XY Plot 1
Ansoft Corporation
Name
X
m1
0.00
Y
2.2403 m1 -0.0257
m2
5.6223
HFSSDesign2
-0.8301
-0.9637
Curve Info
-10.0541
dB(S(WavePort2,WavePort1))
Setup1 : Sw eep1
-10.00
-10.0000
m2
-10.0000
dB(S(WavePort1,WavePort1))
Setup1 : Sw eep1
Y1
-20.00
-30.00
-40.00
-50.00
-60.00
2.00
3.00
4.00
5.00
Freq [GHz]
6.00
7.00
8.00
MX1: 5.5084
MX2: 5.6228
Fig. 3: Transmission Coefficient (S21) and Reflection Coefficient (S11)
XY Plot 4
SAS IP, Inc.
HFSSDesign2
1.00
0.50
Curve Info
mag(S(WavePort1,WavePort1))
Setup1 : Sw eep1
mag(S(WavePort1,WavePort1))
-0.50
0.60
-1.00
-1.50
0.40
-2.00
0.20
ang_rad(S(WavePort1,WavePort1)) [rad]
0.00
ang_rad(S(WavePort1,WavePort1))
Setup1 : Sw eep1
0.80
-2.50
0.00
-3.00
2.00
3.00
4.00
5.00
Freq [GHz]
6.00
7.00
8.00
Fig. 4: Magnitude and Phase of Reflection Coefficient S11
International Conference on Communication Systems (ICCS-2013)
B K Birla Institute of Engineering & Technology (BKBIET), Pilani, India
October 18-20, 2013
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5. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
XY Plot 5
SAS IP, Inc.
HFSSDesign2
1.00
0.00
Curve Info
mag(S(WavePort2,WavePort1))
Setup1 : Sw eep1
mag(S(WavePort2,WavePort1))
-0.50
0.60
-1.00
0.40
-1.50
0.20
-2.00
0.00
ang_rad(S(WavePort2,WavePort1)) [rad]
ang_rad(S(WavePort2,WavePort1))
Setup1 : Sw eep1
0.80
-2.50
2.00
3.00
4.00
5.00
Freq [GHz]
6.00
7.00
8.00
Fig. 5: Magnitude and Phase of Transmission Coefficient S21
XY Plot 2
Ansoft Corporation
HFSSDesign2
0.80
Curve Info
re(S(WavePort1,WavePort1))
Setup1 : Sw eep1
0.60
im(S(WavePort1,WavePort1))
Setup1 : Sw eep1
0.40
0.20
Y1
0.00
-0.20
-0.40
-0.60
-0.80
-1.00
2.00
3.00
4.00
5.00
Freq [GHz]
6.00
7.00
8.00
Fig. 6: Real and Imaginary part of Reflection Coefficient S11
XY Plot 3
Ansoft Corporation
HFSSDesign2
1.00
Curve Info
re(S(WavePort2,WavePort1))
Setup1 : Sw eep1
im(S(WavePort2,WavePort1))
Setup1 : Sw eep1
Y1
0.50
0.00
-0.50
-1.00
2.00
3.00
4.00
5.00
Freq [GHz]
6.00
7.00
8.00
Fig. 7: Real and Imaginary part of Reflection Coefficient S21
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B K Birla Institute of Engineering & Technology (BKBIET), Pilani, India
October 18-20, 2013
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6. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
Fig. 8: Extracted Real part of Permeability (μr)
S.N.
Parameter to be varied
1
Length of outer ring of
SRR(mm)
2
Gap (split)of Rings)
3
Spacing between
and inner ring
4
Thickness of substrate
5
Thickness of Split ring
outer
Value in
(mm)
5
4
3
0.2
0.3
0.4
0.2
0.4
0.6
1
2
3
0.05
0.1
Range of negative
Permeability
3.96 GHz -- 4.15GHz
5.46 GHz – 5.8 GHz
8.14 GHz – 8.4 GHz
5.35 GHz – 5.75 GHz
5.55 GHz – 5.8 GHz
5.62 GHz – 5.95 GHz
5.28 GHz – 5.7 GHz
6.3 GHz – 6.7 GHz
6.75 GHz – 7.45 GHz
5.03 GHz – 5.3 GHz
5.33 GHz – 5.8 GHz
5.48 GHz -- 5. 9 GHz
5.46 GHz – 5.8 GHz
5.33GHz – 5.6 GHz
Table 1: The effect of Split Ring Resonators dimensions on magnetic resonance
VI.
CONCLUSION
It can be summarized that for a small gap and spacing, the resonance will appear in the low
frequency domain and shift to higher frequencies with increasing size of split or spacing. This
behavior is accredited to a decrease in capacitance for larger gap widths and spacing, resulting
in increase in the resonance frequency. Increase in length of SRR legs leads to an increase in
SRR inductance and hence resonant frequency get decreased. Increase in thickness of SRR will
shift the resonating frequency and negative permeability region to lower frequency. With the
reduction of thickness of the substrate, the strength of the magnetic resonance will enhance.
This will increase the negative value of the effective permeability. Thus reducing the thickness
of the substrate allows the behaviour of the structure to make transition from conventional
material to Metamaterial behaviour. Thus resonant frequency of Metamaterials can be
controlled by the design of resonators and hence negative permeability region.
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B K Birla Institute of Engineering & Technology (BKBIET), Pilani, India
October 18-20, 2013
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7. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
REFERENCES
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[4] J.B. Pendry, Metamaterials and the Control of Electromagnetic Fields, The Blackett Lab,
Imperial College London.
[5] J.B. Pendry, A. J. Holden, D. J. Robins, and W. J. Stewart, Magnetism from conductors and
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[6] R. A. Shelby, D. R. Smith, S. Schultz, Experimental Verification of a Negative Index of
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[7] D. Smith, W. Padilla, D. Vier, S. Nemat-Nasser, and S. Schultz, Composite medium with
simultaneously negative permeability and permittivity,” Physical Review Letters, 84, 2000,
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[8] Jiangfeng Zhou1, Thomas Koschny and Costas M. Soukoulis, Magnetic and electric
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[9] Ranjan Singh, Ibraheem A. I. Al-Naib, Martin Koch, and Weili Zhang, Asymmetric planar
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[10] Miguel Durán-Sindreu Jordi Naqui, Ferran Paredes, Jordi Bonache and Ferran Martín ,
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[11] Rajni, Anupma Marwaha, Analysis of Magnetic Resonance in Metamaterial Structure,
Excerpt from the proceedings of the 2011 COMSOL Conference in Bangalore, Oct. 2011
BIOGRAPHY
Rajni is currently Associate professor at SBS State Technical Campus,
Ferozepur, India. She has completed her M.E. from NITTTR, Chandigarh,
B.Tech from NIT, Kurukshetra. At present, She is persuing her Ph.D. from
SLIET, Longowal, Punjab. She has fifteen years of academic experience. She
has authored a number of research papers in international journals, National
and International conferences. Her areas of interest include Wireless
communication and Antenna design.
Dr. Anupma Marwaha is currently Associate Professor at Sant Longowal
Institute of Engg. & Tech, Logowal (Sangrur). She has done her Ph. D from
GNDU, Amritsar, M.Tech from REC Kurukshetra (Now NIT, Kurukshetra), B.E.
from Punjab University, Chandigarh. She has 20 years of academic experience.
She has authored 25 research papers in International and National journals
and 50 research papers in National and International conferences. She has
supervised 02 Ph.D thesis and 10 M.Tech thesis and 04 are under progress. Her areas of
interest include Electromagnetics, Microwave Comm., Wireless communication and Antenna
design.
International Conference on Communication Systems (ICCS-2013)
B K Birla Institute of Engineering & Technology (BKBIET), Pilani, India
October 18-20, 2013
Page 285