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Metamaterials (MTMs) are artificially built materials intended to give its properties from the internal structure, rather than the chemical composition found in natural materials. Electric permittivity (ε) and magnetic permeability (μ) are the two basic parameters which describe the electromagnetic property of a material or medium. Permittivity describes how a material is affected when it is placed in electric field. And permeability describes how a material is affected in presence of magnetic field. Metamaterials may have either negative permittivity or permeability or both may be negative simultaneously. The concept of metamaterials has additionally been utilized to design different kinds of patches with upgraded performance, such as improved gain and enhanced efficiency. Also, it has been utilized for the scaling down of patches. Two parameters are utilized in the collected works for antennas using metamaterials. We can adjust the refractive index of the metamaterial to positive, near-zero or negative values. Utilization of epsilon negative, MNG (μ - Mu negative) or DNG (double negative) are called metamaterial- based antennas and the use of metamaterial unit cell for example complementary split ring resonator, split ring resonator and so on are alluded as metamaterial inspired antennas. The design of complementary split ring resonator and its equivalent circuit will be discussed in this work. CSRR (complementary split ring resonator) provides both isolation enhancement and miniaturization for MIMO antenna.
Vellore Institute of Technology (VIT), Vellore, India
*Address all correspondence to: achristina@vit.ac.in
1. Introduction
Jagadish in 1898 developed the first metamaterial out of artificial chiral components [1]. Lindman, in 1914 made artificial chiral media by installing numerous randomly arranged little wire helices in the host medium [2]. Kock made microwave lenses by inserting metallic strips, wires and disks occasionally so as to tailor the artificial media refractive index [3]. The historical backdrop of left- handed materials can be explained by Veselago’s hypothetical speculation in 1968 [4], in which he showed that the LHMs could give rise to a surprising optical phenomenon as light passes through them. The UCSD (University of California, San Diego) group in 2000, which followed the work by Pendry et al. [5, 6, 7] synthesized the principal left-handed material [8, 9]. As manufacture strategies enhance, the incorporations (artificial structures) inserted in the host medium decrease in size [9].
Electromagnetic waves interact with metamaterials in the host medium, induce electric and magnetic moments, which thus influence the material’s transmission abilities and material parameters, for example, permeability and permittivity. While portraying the permittivity (ε) and permeability (μ) of a metamaterial, one must describe the structure as homogeneous. If one considers a solitary incorporation as a major aspect of a unit cell periodically installed inside the host medium, its size p must be not exactly a fourth of the incident radiation wavelength: p < λ/4 [9]. This homogeneity relation is a standard guideline condition. The relation is normally utilized in recognizing lumped parts from quasi-lumped components, (λ/4 < p < λ/2) and distributed components: p > λ/4 [9]. This condition guarantees that refractive phenomena inborn in homogeneous materials command over scattering and diffusion effects. The electromagnetic radiation is basically uninformed of the lattice structure in the host medium and keeps up field uniformity in the direction of propagation inside the structure.
Metamaterials are designed to make materials with almost zero estimations of permittivity; negative permeability or permittivity. A material with just negative (ε) is called ENG and only negative (μ) is assigned to MNG material. Permittivity describes how a material is affected when it is placed in electric field. And permeability describes how a material is affected in presence of magnetic field. Material with both negative permeability and permittivity is called double negative (DNG). Over the previous decade, various arrangements of metamaterials have been approved which when organized intermittently, showed metamaterial properties for a specific range of frequencies [9]. This left handed material made utilization of an array of conducting, nonmagnetic components, continuous wires like circular shapes etc. to accomplish a negative effective permittivity and negative effective permeability.
Despite the fact that optical characteristics are completely determined by relative parameters ε and μ, the refractive index (n) is frequently utilized. n might be found from Eq. (1) [10],
n=±εμE1
Practically all see-through materials, for example, water or glass, has positive values for both ε and μ [10]. Numerous metals, (for example, gold and silver) has negative ε at observable wavelength [10]. Materials having one or the other ε or μ negative is impervious to EM emission. For the above - mentioned materials, a positive square root is utilized for n by tradition. In any case, some materials having ε < 0 and μ < 0; since their product is positive, n is additionally real. In such conditions, negative square root of n is taken. The prior considerations are simple for materials, having complex values of ε and μ. The real parts of both do not need to be negative [10].
Electromagnetics scientists regularly utilize the term LHM, barely, for the materials having negative refractive index. A contrast of refraction in a LHM to a typical material is explained in Figure 1 [11]. The Quadrant 1, of Figure 2 the Electric, magnetic (H) field and the wave ‘k’ structure a right handed system, as given by Maxwell’s equations. The second quadrant of Figure 2 (ε < 0 and μ > 0) shows electric plasmas which bolster evanescent waves. The fourth quadrant (ε > 0 and μ < 0) additionally bolsters evanescent waves. These are both single negative (SNG) quadrants, implying that just a single parameter is negative. The third quadrant (ε < 0 and μ < 0 or double negative (DNG)) contains the left handed materials, which were proposed in 1967 [11]. In LHM, the E, H field and the wave vector k structure a left handed system and these help “in reverse” proliferating waves i.e. negative refraction occurs such that light and other radiation gets bent backwards as it enters the structure [11]. The term reverse refers to the opposite sign of group and phase velocity. The index of refraction n = ±εrμr is negative. A comparison of the materials is shown in Figure 2.
Figure 1.
Refraction in a left-handed metamaterial.
Figure 2.
Comparison of material with different permittivity and permeability, courtesy—http://www.ihf.uni-stuttgart.de.
The light beams would be refracted on a similar side perpendicular when coming inside the material, since n2 is negative. A light source advancing on the way to an eyewitness seems to reduce its frequency, as the doppler shift is reversed. Cherenkov focuses in another way about the radiation delivered by a quick moving molecule as it goes through a media [11]. Phase velocity is antiparallel to the time averaged poynting vector of wave ‘k’. This implies that unlike RHM, the wave fronts are heading backwards to the movement of energy [12]. Plane wave propagation spreading in MTMs, the E, H field and wave propagation abide by a left hand rule, and hence named as left-handed metamaterials [13]. The impact of negative refraction is undifferentiated from wave transmission in a left-handed transmitting line.
MTMs are of main importance in electromagnetics [14]. All together for its physical shape to influence EM waves, a MTM should have physical features small than λ of the EM radiation it connects with. For example, if a MTM is to carry on as a homogenized material precisely depicted by refraction index, the element dimensions need to be a lot littler than the λ. For the visible light having wavelengths of less than one μm commonly, the structures are usually half or not larger than 280 nm in dimensions [14]. The structures need to be of one decimeter [14] for microwave radiation. They are quite often artificial, developed as periodic arrangement of current conducting components, (for example, circles of wire) which have appropriate inductive and capacitive attributes [15].
2.1 Superlens
The materials having negative refractive index, enables to focus near field light (the near-field (or evanescent) light consists of a non-propagating field that exists near the surface of an object at distances less than a single wavelength of light) therefore making an ideal super lens. The first super lens gave resolution three times better than the diffraction limit which was shown at microwave frequencies (1–1000 GHz) at University of Toronto [16].
2.2 Cloaking devices
MTMs are used for constructing cloaking devices as well. These components usually include surrounding the item to be cloaked with a casing which influences the entry of light close to it [17]. A US-British group of researchers made a MTM that made an article undetectable to microwave emission in october 2006 [17]. Since light is simply one more type of EM radiation, this was viewed as the initial move to a cloaking gadget for visible light, however further developed nano systems will be required because of noticeable light small wavelengths. Two engineers from Purdue university declared a hypothetical plan for an optical cloaking gadget dependent on the British idea on April 2, 2007 as explained below. The plan sends a periodic arrangement of minor needles sticking out by a centre rod which will create an object inside the cloak undetectable in a λ of 632.8 nm [18]. Duke University and Imperial College London are as of now looking into this utilization of MTMs and has figured out how to cloak an item in microwave range utilizing exceptional concentrical rings [18]. The microwave frequencies were hardly influenced by the nearness of the cloaked object.
2.3 Agile antennas
Metamaterials are additionally designed for structuring agile antennas [19]. Investigation at National Institute of Standards and Technology in US has shown that slender films created of MTMs can enormously diminish dimensions of resonant circuits which create microwaves, possibly empowering much small mobile phones and other microwave gadgets [19].
3. Design of metamaterials (complementary split—ring resonator)
By the parametric investigations and examination of the patch, a design methodology for miniaturizing antenna for variable frequency range utilizing the CSRR technique was created [20, 21, 22, 23, 24]. A CSRR is counter duplicate of split ring resonator, which is made by eliminating the conductor from the outline of SRR within the ground structure. It is a resonant structure utilized broadly in the investigation of MTMs [20]. With recurrent placement of the CSRR, negative ε permittivity can be obtained near its resonant frequency. Its frequency is equivalent to SRR of a similar size and it is demonstrated as a LC circuit [25]. The equivalent LC circuit analysis is discussed in Section 3.5. Distinctive forms of SRR and CSRR are shown to exist in different works, however the dual slit rounded and rectangular split ring resonator are usually considered and utilized due to the ease of creating their structures [25]. The CSRR consist of two concentrical or rectangular rings with an opening in each ring. The procedure is described below in Figure 3.
Figure 3.
A flow chart representation for the design of antenna miniaturization using CSRR.
1. Design the patch antenna utilizing the transmission line model for a frequency double as that of the needed (5 GHz). 2. The patch antenna is simulated using high frequency structure simulator software (HFSS). 3. A CSRR is engraved beneath the patch in such a way that the outward radius of the CSRR is encasing the boundaries of the antenna. 4. Simulate and locate the frequency of the patch. 5. If it is smaller than anticipated, adjust by decreasing the radius ‘r’ or by changing spacing ‘k’ and/or width ‘w’. 6. During fine tuning, if the frequency is beyond as expected, move the feed alongside the antenna element till the resonant frequency is achieved. 7. Amid this procedure, ensure the patch to remain as primary radiating element.
3.1 Design of antenna and its geometry
A circular patch antenna with dimensions 25 × 25 mm2 was at first intended to resonate at 5 GHz utilizing FR4 substrate with a dielectric constant of 4.4 and thickness 1.6 mm [26]. The patch antenna was excited utilizing 50 Ω microstrip line. The geometry of the antenna is shown in Figure 4.
Figure 4.
Single patch antenna structure.
3.2 Parametric analysis of the antenna design
Initially the antenna was designed at a frequency (5 GHz) higher than the desired resonant frequency (2.34 GHz). The radius obtained was 8.39 mm with feed length of 8.25 mm and feed width was 3.05 mm. A parametric analysis was carried out for various radius of the circular patch starting from 7 mm and the optimal radius of 8.39 mm is chosen as shown in Figure 5. It was observed that when the patch radius increases the resonant frequency decreases.
Figure 5.
Reflection co-efficient of the antenna vs. frequency for different patch radius.
Similarly the analyses were carried out for different length of the feed with fixed radius of 8.39 mm and it was seen that as the feed length increases the return loss increases providing better impedance matching as seen in Figure 6. A feed length of λg2 was chosen with 8.25 mm.
Figure 6.
Reflection co-efficient of the for various feed length CSRR.
3.3 Antenna geometry with CSRR
Methodology given in the flow chart, Figure 3, was followed. Parametric analysis is performed using HFSS to determine the dimension of CSRR given in Figure 7. After simulation, if the obtained frequency is greater than the resonant frequency, the CSRR dimensions were altered by expanding the radius of CSRR and diminishing the width of the ring and spacing between the rings. If the frequency is smaller than the resonant frequency, at that point the CSRR is altered by diminishing the radius of CSRR and expanding the width and spacing between the rings. The dimensions of the CSRR were changed to adjust at 2.34 GHz. When the radius of the ring decreased with increase in the width and spacing between the rings, the frequency increased.
Figure 7.
Parametric analysis for design of antenna vs. frequency.
The geometry of the antenna with CSRR at the ground plane is shown in Figure 8 and its dimensions are given in Figure 9. The radius of the inner ring of the CSRR is R1, radius of the outer ring of the CSRR is R2, the width of each ring is ‘w’, the spacing between the rings is ‘g’ and the width of slit in the rings is ‘k’. After including the CSRR, the radius of the patch was optimized to 7.65 mm providing 2.34 GHz resonant frequency.
Figure 8.
Single patch antenna with CSRR structure.
Figure 9.
Dimensions of CSRR.
3.4 Parametric analysis for the position of CSRR
To study the effect of CSRR loading on the patch, parametric study is performed by varying the position of the CSRR. As noted in Figure 10 when the CSRR is shifted away from the feed the resonating frequency is increasing and when it is near to the feed i.e. (c = 0 mm), it provided an impedance matching at 2.34 GHz with return loss of −17 dB.
Figure 10.
CSRR position variation.
3.5 Analysis of permittivity for complementary split - ring resonator (CSRR)
Metamaterials (MTM) are utilized for isolation improvement between nearby components because of the presence of a band gap in their frequency response [27]. A significant decrease in patch antenna size was additionally seen by CSRR stacking on a patch antenna [28]. The two most generally utilized metamaterial structures for isolation enhancement between neighboring components are the utilization of split ring resonators (SRR) and complementary split ring resonator (CSRR) [27].
The resonant frequency of a SRR is equivalent to that of a CSRR of a similar measurement. CSRRs are the opposite image of SRRs (Babinet’s standard), and an axial time changing E field is important to energize the rings that make a feasible negative ε medium and hinder signal transmission at resonance. CSRRs are used as a negative permittivity bandstop filter. Band stop filter blocks and rejects frequencies that lie between its two cut-off frequency point’s passes all those frequencies either side of this range. CSRR is a resonant structure which acts as an LC circuit [29]. It interacts with the axial E field and displays negative permittivity close to the resonant frequency. The unit cell of CSRR is shown in Figure 11. Antenna miniaturization by loading CSRR is studied through unit cell analysis and equivalent circuit analysis. Unit cell CSRR was simulated with HFSS.
Figure 11.
Unit cell complementary Split - ring resonator.
Relative permittivity is to comprehend the behavioral attributes of CSRR. The equations given by Nicolson, Ross and Weir (NRW) empower the calculation of the complex permittivity and permeability of a material from the measured S-parameters. S-parameters describe the input-output relationship between ports (or terminals) in an electrical system. NRW had shown the extraction of relative permittivity utilizing S parameters [25, 30, 31, 32] and is given by,
V1=S11+S21E2
V2=S21−S11E3
εr=2c1−V1ωdi1+V1E4
μr=2c1−V2ωdi1+V2E5
Where ω is the frequency in radian, c is the velocity of light in m/s, d is the thickness of the substrate, i correspond to imaginary part and V1 is the voltage maxima in volts and V2 is the voltage minima in volts. From the S parameters, relative permittivity was plotted with Eqs. (2)–(5). The negative estimation of relative permittivity was acquired at the ideal resonant frequency of 2.34 GHz plainly displaying that CSRR goes about as a band stop filter as in Figure 12.
Figure 12.
Relative permittivity vs. frequency for a unit cell CSRR for LTE band 40.
3.6 Equivalent circuit analysis for CSRR
The equivalent circuit analysis for the unit cell CSRR for the proposed work is discussed. The lumped element equivalent model of the unit cell CSRR is modeled in AWR microwave office software as shown in Figure 13 [32] and the simulation results of unit cell in HFSS mentioned in Figure 11 are compared and its results are given in Figure 14. Both the results are in good agreement. The transmission line is represented by the MLIN in AWR software, parallel LC circuit (C2, L3) represents the resonant circuit, the current flowing through the rings representing the inductance (L1, L2) and capacitor (C1) indicates the electric coupling between the transmission line and CSRR (Figure 13).
Figure 13.
Equivalent circuit for a unit cell CSRR for band 40.
Figure 14.
S parameter for the equivalent unit cell CSRR circuit for band 40.
The unit cell CSRR was analyzed using NRW method to check for the negative permittivity of CSRR. Its lumped element equivalent circuit model of the CSRR was analyzed in AWR and verified with the HFSS results.
To minimize the dimensions of the antenna, a CSRR was etched out beneath the patch in the ground plane. The antenna with CSRR resonates at 2.34 GHz and without CSRR resonates at 4.8 GHz as shown in Figure 15 covering a band of 2.3 to 2.374 GHz occupying the LTE band long term evolution (2.3-2.4) GHz. If the antenna is designed for 2.34 GHz, the radius of the patch would be 17 mm. But by introducing CSRR, the antenna designed for 5 GHz has radius 7.621 mm with a shift in the resonant frequency to 2.34 GHz providing a size reduction of 55.17%.
Figure 15.
Comparison of reflection co-efficient with and without CSRR for single patch antenna.
4.1 MIMO antenna geometry
The simulation was extended for MIMO configuration by designing two circular patch antennae with dimensions (50 × 25 × 1.6 mm3) shown in Figure 16.
Figure 16.
2 × 1 MIMO antenna structure.
The front and back view of the photograph of the fabricated antenna is shown in Figure 17a and b, respectively.
Figure 17.
Fabricated antenna (a) front view (b) back view.
A stub was introduced between the two patches. The parametric analysis for the width and length of the stub was carried out using HFSS as shown in Table 1. Without stub the S11 parameter is 2.30 to 2.37 and S22 is 2.33 to 2.40 GHz and with the stub the S11 parameter is 2.30 to 2.37 and S22 is 2.31 to 2.38 GHz.
S. no
Stub length (ls) (mm)
Slub width (ws) (mm)
S11 (Imp BW)
S22 (Imp BW)
Inference
1
17
3
2.36–2.43
2.38–2.45
Both S11 and S22 are shifted beyond 2.3 to 2.4 GHz range
2
17
2
2.3–2.38
2.34–2.47
S11 shifted from 2.30 to 2.31 GHz and S22 shifted from 2.33 to 2.34 GHz
3
15
3
2.40–2.48
2.40–2.48
Both S11 and S22 are shifted to high frequency range beyond 2.40 GHz
4
12
2
2.28–2.35
2.34–2.41
S11 shifted from 2.30 to 2.28 GHz and S22 shifted from 2.33 to 2.34 GHz
5
9.8
3
2.30–2.371
2.31–2.388
S22shifted from 2.33 to 2.31 GHz low frequency range
Table 1.
Parametric analysis of stub length and width.
With the introduction of the stub, there is a shift in frequency for S22. When the length of the stub is decreased, keeping width constant S22 is shifted towards left (lower frequency range - i.e. frequency reduced with increased physical length of the stub). When the width of the stub is decreased, S11 is shifted towards left (lower frequency range).
4.2 Return loss, bandwidth, and isolation characteristics
The simulation result for the return loss and isolation were observed to be −30 dB and − 35.51 dB at the resonant frequency of 2.34 GHz and the measured results for the return loss and isolation were − 27 dB and − 33.5 dB, respectively, at the resonant frequency of 2.3 GHz as shown in Figures 18 and 19. The designed antenna covered a bandwidth of 2.3–2.372 GHz using simulation whereas 2.26–2.34 GHz for the measurement.
Figure 18.
Comparison of measured and simulated reflection co-efficient characteristics for MIMO antenna.
Figure 19.
Comparison of measured and simulated isolation characteristics for MIMO antenna.
It was observed that there was a shift in resonating frequency of second patch and hence a stub was inserted between two patches. The purpose of stub between the two antenna elements is in increasing the electrical length between the two elements thereby there is a shift in the resonant frequency of second patch in the lower side i.e. (2.354 GHz). S11 occurs at 2.34 GHz and S22 occurs at 2.367 GHz. By introducing the stub between the patches, there is an increase in the current path which shifts the frequency for S22 from 2.367 to 2.354 GHz. Also, the isolation between the two elements is increased from −33 dB to −35 dB with the introduction of the stub as shown in Figure 20.
Figure 20.
Comparison of reflection co-efficient and isolation for MIMO antenna with stub and without stub.
The simulated results for the return loss without stub was observed to be −27.35 dB and with stub is −30 dB at the resonant frequency of 2.34 GHz with an isolation of −33.3 dB without stub covering a bandwidth of 2.3–2.373 GHz and the comparative plot for both with and without stub is shown in Figure 20.
Using CSRR, a size reduction of 55.17% was achieved. The antenna designed covered a bandwidth of 2.3–2.374 GHz with a maximum return loss of −27 dB at 2.34 GHz and isolation of −33.5 dB amid the ports. The antenna performance is suitable for LTE band 40 operation. Here the analysis of CSRR with respect to the permittivity was discussed and its equivalent circuit was analyzed. Also the antenna miniaturization was discussed by incorporating the CSRR. The antenna resonated at a frequency of 4.8 GHz. With the introduction of CSRR beneath the patch in the ground plane the antenna resonated at a frequency of 2.34 GHz providing a size reduction of 55.17%. If the antenna was designed for 2.34 GHz, the dimension of the patch would be 17 mm but by introducing CSRR, the antenna designed for 5 GHz of dimension 7.621 mm there is a shift in the resonant frequency to 2.34 GHz providing a size reduction of 55.17%.
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Written By
Andrews Christina Josephine Malathi
Submitted: 08 May 2022Reviewed: 30 June 2022Published: 17 August 2022
Open access peer-reviewed chapter
