Volume 7, Issue 1, Jan-Feb 2016, pp. 55-62, Article ID: IJECET_07_01_006 Available online at
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MODELING OF PLANAR METAMATERIAL
STRUCTURE AND ITS EFFECTIVE
PARAMETER EXTRACTION
Shilpa KashyapM.sc. Physics, NIT Jalandhar, Punjab, India
ABSTRACT
This paper is about designing a Metamaterial structure and the Scattering Parameter Extraction Method that has become a prime tool for Metamaterial characterization so that there is a better understanding of relation between their configuration and associated properties of these materials in terms of negative permittivity and negative permeability to explore application potential. A 2D planar Metamaterial structure has been designed, fabricated and analyzed. It consists of conducting patches and meander lines on a dielectric substrate. Electromagnetic modeling was carried out using Finite Difference Time Domain method based simulation tool EMPIRE XCcel. The simulated reflection and transmission coefficients for the proposed metamaterial structure indicate the stopband at 5.5 – 12 GHz. The fabricated Metamaterial structure was analyzed using Network Analyzer verifying that material is Doubly Negative in nature.
Key words: Metamaterial, Finite Difference Time Domain, Scattering
Parameters, Network Analyzer.
Cite this Article: Shilpa Kashyap. Modeling of Planar Metamaterial Structure
and Its Effective Parameter Extraction. International Journal of Electronics and Communication Engineering & Technology, 7(1), 2016, pp. 55-62.
http://www.iaeme.com/IJECET/issues.asp?JType=IJECET&VType=7&IType=1
1. INTRODUCTION
Metamaterials (MTM) have the capability to exhibit a state where both permittivity and permeability are negative, resulting in extraordinary index of negative refraction [1,2]. They consist of metal and dielectric substrate. The metamaterial structures have helped to the miniaturization of many electromagnetic devices and have been used to improve the performance of various RF/microwave components such as filters, antennas, transmission lines, etc.[3-5] Although there are different structures of metamaterial existing, now the emphasis is on planar metamaterial configuration. The planar metamaterial structures are classified in two most important categories viz.
uniplanar and non-uniplanar structures. One of the advantages of the uniplanar metamaterial structure is its ease of fabrication, as it is a planar structure without the need for vias. Moreover it can be integrated with the printed circuits board with ease.
2. DESIGN OF PROPOSED STRUCTURE
A 2D planar structure consisting of a conducting patch and a dielectric substrate was studied [6]. After going through its electromagnetic modeling, it was observed that the structure exhibit the modified characteristics if the shape of the conducting pattern is changed.
(a) (b)
Figure 1 (a) Original metamaterial structure and (b) The modified proposed structure
Increasing the length of straight line, can increase the electrical length of the structure within same volume. The resonant frequency of the proposed structure is given by [7]:
(1)
where is the capacitance and is inductance offered by the structure. The capacitances are calculated with the well known formula for parallel plate capacitors for each parallel meander line:
(2)
where is the permittivity in free space and is the relative permittivity of the material in between the capacitor plates, is the area of the plates and is the distance between plates. For the series capacitance , the area = conductor thickness x 0.24 P, where P is the periodicity in mm.
The inductance between cells consists of the self inductance of the straight conductor that connects two cells. In order to increase this inductance, the proposed change of the modification is to alter the geometry from a straight line into a meander. The sections of the meander each have self inductance and also exhibit mutual inductance between sections.
The total inductance is equal to the total self inductance plus the positive mutual inductance and minus the negative mutual inductance :
(3)
The total self inductance is the sum of the self inductances of the conductor segments:
The general equation for the mutual inductance of two parallel conductors of equal length is as follows:
(5)
where is the length in mm and is called the mutual inductance parameter.
3. SIMULATION OF THE ELECTROMAGNETIC STRUCTURE
Finite Difference Time Domain (FDTD) [8] is convenient for dealing with the characteristics of metamaterials over a wide frequency band. An important point to consider when measuring the properties of dielectric materials using plane wave illumination is the distance between the surfaces of the material under test and the measurement planes/ports and/or source of excitation [9]. The EMPIRE XCcel simulation tool is used which is based on the FDTD method. The “Microstrip port” in Empire XCcel® [10] was used to generate the plane waves used in the simulations in this work.
3.1. SIMULATED PLANE WAVE VERIFICATION
In order to verify that the plane wave generation source in the simulation tool give a true Transverse Electromagnetic (TEM) wave, an empty port source is simulated first. The Perfect Electric Conductor (PEC) and Perfect Magnetic Conductor (PMC) boundaries are at ( ) and (y=0, y= ) respectively. The Perfectly Match Layer (PML) boundary conditions are used at each reference plane ( ,
) to minimize reflections from the ports and can be placed in the same position
as the ports, giving a higher accuracy in the S-parameter results. Placing the ports in the same location as the PML boundary is possible as it has been built in to Empire XCcel® when the ports are pre-defined as ‘Absorbing’ ports.
(a) (b)
Figure 2 Simulation window of Empire XCcel® (a) for TEM wave generation and (b) for the structure with microstrip line for reflection and transmission coefficient
measurement.
The ‘P1E’ and ‘P2’ are the measurement and reference planes in the simulations. The ‘E’ in P1E indicates that the port is excited as it is the source. The blue crosses (‘X’) indicate where these ports are, while the dashed lines (---) indicate the measurement/reference planes and in this case coincides with the port positions.
The ‘Dump Box’ is used as a storage box to measure and save the values of the E and H-fields along any path within the box at pre-defined frequencies. Figure (a)
shows the amplitudes of the three cartesian components of each of the fields at 14 GHz. For a plane wave, the E and H fields are in phase and are perpendicular to each other and to the direction of propagation. The wave impedance, ƞ in these regions can be readily obtained by dividing the value of the E field by that of H-filed. This has resulted in the value near to the well-known wave impedance of free space i.e. 376.99 Ω approximately.
(a) (b)
Figure 3 (a) Variation of electric field components and (b) Variation of magnetic
field components with path length
From Figure 3(a), it is observed that and are close to zero while 94 V/m, and from Figure 3(b), and are zero while 0.25 A/m. So the impedance obtained within the simulated environment is nearly equal to that of free space impedance. Similar results are obtained at 12 GHz and 16 GHz. These values show that the wave generated by the port is a true TEM plane.
3.2. SIMULATION OF THE PROPOSED STRUCTURE
Once the simulation setup for the generation of the TEM wave is done successfully, now the simulation for proposed metamaterial structure as presented above is carried out using Empire XCcel® to get the reflection and transmission coefficients. Sufficient distances had to be placed between the structure and the measurement (reference) planes to ensure that any “higher order evanescent modes” that may be present are significantly attenuated before reaching the structure [9]. This principle is analogous to ensuring the material under test is exposed to a plane wave from a source of radiation by placing it in the far-field of the source. The simulation window for the structure with microstrip line that support the TEM in Empire XCcel® is shown in figure 2(b). Depending on the maximum width, or height, of the microstrip line (MSL), whichever is greater, a cut-off frequency point is reached after which spurious resonances occur and any results after this point are not fit for use in the extraction calculations or at worst, completely inaccurate. This frequency is given by:
(6)
where, is the speed of light in free space, ≈ m/s. However, due to the fact that the PEC and PMC boundaries on the z- and y-axes providing a symmetry (mirror) plane reproducing an infinite structure, the cross-section of the MSL can be made as small as necessary to increase the cut-off frequency and so that accurate higher frequency results are possible.
3.3. SIMULATED REFLECTION AND TRANSMISSION COEFFICIENTS
In general the S-parameters are designated by , where m is the receiver port and n is the source port. For example, , is the transmission coefficient for a wave sourced at port 2 and received at port 1. These ratios are complex-valued, and the S-parameter will carry both a magnitude and phase component as a function of frequency. The simulated reflection and transmissions coefficients in the presence of the proposed metamaterial structure are shown in figure 4. The dotted line indicates the transmission coefficient and the solid line indicate the reflection coefficients.
Figure 4 The simulated reflection and transmission coefficients in the presence of the
proposed metamaterial structure
4. EFFECTIVE PARAMETER EXTRACTION OF THE
METAMATERIAL STRUCTURE
A Matlab code available at http://sourceforge.net/projects/effmetamatparam/files/ has been modified to extract the metamaterial parameters. The simulated reflection and transmission coefficients for the proposed metamaterial structure indicating the stopband are shown in figure 5(a). The stopband can be seen at 5.5 – 12 GHz. The EM waves with a frequency inside the forbidden band cannot propagate through the material. The simulated reflection and transmission phase for the proposed metamaterial structure are shown in figure 5(b). The extracted effective permittivity and effective permeability of the proposed metamaterial structure are shown in figure 6(a) and 6(b) respectively. This indicates that the proposed structure exhibits Double Negative (DNG) characteristics.
(c) (d)
Figure 6 (a) Simulated reflection and transmission coefficients, (b) Simulated
reflection and transmission phase, (c) Extracted effective permeability and (d) Extracted effective permittivity for the proposed metamaterial structure.
5. PROTOTYPING WORK
To validate the simulated results, prototyping of the proposed planar structure is done using a CNC machine and experiment is carried out using the vector network analyzer. Computer aided design is created with the help of EMPIRE XCcel software. The layout was exported to the GERBER file format and then imported in the PCAM software to generate the layers of the prototype of the metamaterial’s structure. PCAM software is executed to run the prototyping machine. The fabricated metamaterial structure is shown in figure 7(a) and 7(b). The top view is showing the copper patches and meander lines. The back view is showing the dielectric substrate.
(a) (b) (c)
Figure 7
(a)Top view of the fabricated MTM structure (b)Back view of the fabricated MTM structure
(c) Prototyping machine used to fabricate the metamaterial structure
The Network Analyzer (NA) is used to measure the S-parameters. In practice, a NA will generally measure the incident and reflected waves through a series of couplers or bridges, referred to as directional devices [11]. The directional device is able to separate the incident from reflected waves. Using this measurement practice, the resulting measurements will be quantities that are subject to imperfections of the NA, such as the coupling factor and directivity of the directional devices. Thus, more complicated calculations are needed in order to determine calibrated S-parameters starting from a set of raw quantities. The measured and simulated results are in agreement. The small deviations are due to the limitations of the fixture structure used
to hold the proposed structure. Moreover the extracted parameters from the measured transmission and reflection coefficients are also found to be in fair agreement.
(a) (b)
Figure 8 (a) Experimental set-up for the measurement of S-parameters of proposed
metamaterial structure and (b) Screen shot of the measured transmission and reflection coefficients.
6. CONCLUSION
In recent years, the search for artificial materials i.e. electromagnetic structures, specifically metamaterials has attracted world wide interest from researchers due to their applications in radio frequency/ microwave components. So, designing a meandered line metamaterial structure with negative permittivity and permeability is a good attempt in this field due to ease of fabrication with the printed circuit board. The parameters associated with the proposed metamaterial structure were retrieved from the S-parameters. The S-parameters describe the magnitude and phase relationship between incident and reflected waves and are numbered according to where a wave originates from and where it propagating to.
7. ACKNOWLEDGEMENT
I would like to thank my gratitude to all those who gave me the possibility to complete this project. I would like to take this opportunity to express my sincere thanks to everybody that has helped and encouraged me throughout my project work.
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