This paper developed a non - split perfectly matched layer (PML) boundary condition (BC) for Finite Difference Time Domain (FDTD) simulation of electromagnetic wave propagation in 2D structure. The
point source for electric field has been exploited for propagation of electromagnetic field through 2D structures to validate developed approach. The identity of resulted field distribution to that obtained for split PML BC have been demonstrated.
MODELING OF PLANAR METAMATERIAL STRUCTURE AND ITS EFFECTIVE PARAMETER EXTRACTIONIAEME Publication
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.
Mutual Coupling Reduction in Antenna Using EBG on Double SubstrateTELKOMNIKA JOURNAL
Malaysia
*Corresponding author, e-mail: raimidewan@gmail.com
Abstract
In this paper, a mutual coupling study is conducted between two-element array
antenna on dual substrate. A single patch antenna is firstly designed on dual substrate layer to
testify appropriate performance at 2.45 GHz. Subsequently, an array of two element patches on
dual substrate are constructed with one of them is incorporated with three EBG unit cell on the
bottom substrate. The radiating patch is on the top substrate, while the EBG unit cell is on the
bottom substrate. With EBGs in separate layers from the antenna array, the antenna elements
are closely separated by a distance of 22 mm with a significant reduced mutual coupling of -
26.61 dB. This corresponds to a distance reduction of 34.68%. The proposed structure
implemented only three EBG unit cells. Apart from that, the study of overlapped case of EBG
with the antenna is also presented.
Numerical simulation of electromagnetic radiation using high-order discontinu...IJECEIAES
In this paper, we propose the simulation of 2-dimensional electromagnetic wave radiation using high-order discontinuous Galerkin time domain method to solve Maxwell's equations. The domains are discretized into unstructured straight-sided triangle elements that allow enhanced flexibility when dealing with complex geometries. The electric and magnetic fields are expanded into a high-order polynomial spectral approximation over each triangle element. The field conservation between the elements is enforced using central difference flux calculation at element interfaces. Perfectly matched layer (PML) boundary condition is used to absorb the waves that leave the domain. The comparison of numerical calculations is performed by the graphical displays and numerical data of radiation phenomenon and presented particularly with the results of the FDTD method. Finally, our simulations show that the proposed method can handle simulation of electromagnetic radiation with complex geometries easily.
Modelling Optical Waveguide Bends by the Method of LinesTELKOMNIKA JOURNAL
A rigorous analytical and semi analytical method of lines has been used to calculate the
transverse-electric field attenuation coefficient of guided mode as it travels in waveguide bends structure.
Both approaches then were compared to get a better understanding on how the attenuation behaves along
single curve waveguides with constant radius of curvature. The Helmholtz Equation in polar coordinate
was transformed into a curvalinier coordinate to simulate the waveguide bends using the method of line
analysis. The simple absorption boundary conditions are used into the method of lines to demonstrate
evanescent field of the guided mode nature as its travels in waveguide bends structures. The results show
that a reasonable agreement between both theoretical approaches.
MODELING OF PLANAR METAMATERIAL STRUCTURE AND ITS EFFECTIVE PARAMETER EXTRACTIONIAEME Publication
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.
Mutual Coupling Reduction in Antenna Using EBG on Double SubstrateTELKOMNIKA JOURNAL
Malaysia
*Corresponding author, e-mail: raimidewan@gmail.com
Abstract
In this paper, a mutual coupling study is conducted between two-element array
antenna on dual substrate. A single patch antenna is firstly designed on dual substrate layer to
testify appropriate performance at 2.45 GHz. Subsequently, an array of two element patches on
dual substrate are constructed with one of them is incorporated with three EBG unit cell on the
bottom substrate. The radiating patch is on the top substrate, while the EBG unit cell is on the
bottom substrate. With EBGs in separate layers from the antenna array, the antenna elements
are closely separated by a distance of 22 mm with a significant reduced mutual coupling of -
26.61 dB. This corresponds to a distance reduction of 34.68%. The proposed structure
implemented only three EBG unit cells. Apart from that, the study of overlapped case of EBG
with the antenna is also presented.
Numerical simulation of electromagnetic radiation using high-order discontinu...IJECEIAES
In this paper, we propose the simulation of 2-dimensional electromagnetic wave radiation using high-order discontinuous Galerkin time domain method to solve Maxwell's equations. The domains are discretized into unstructured straight-sided triangle elements that allow enhanced flexibility when dealing with complex geometries. The electric and magnetic fields are expanded into a high-order polynomial spectral approximation over each triangle element. The field conservation between the elements is enforced using central difference flux calculation at element interfaces. Perfectly matched layer (PML) boundary condition is used to absorb the waves that leave the domain. The comparison of numerical calculations is performed by the graphical displays and numerical data of radiation phenomenon and presented particularly with the results of the FDTD method. Finally, our simulations show that the proposed method can handle simulation of electromagnetic radiation with complex geometries easily.
Modelling Optical Waveguide Bends by the Method of LinesTELKOMNIKA JOURNAL
A rigorous analytical and semi analytical method of lines has been used to calculate the
transverse-electric field attenuation coefficient of guided mode as it travels in waveguide bends structure.
Both approaches then were compared to get a better understanding on how the attenuation behaves along
single curve waveguides with constant radius of curvature. The Helmholtz Equation in polar coordinate
was transformed into a curvalinier coordinate to simulate the waveguide bends using the method of line
analysis. The simple absorption boundary conditions are used into the method of lines to demonstrate
evanescent field of the guided mode nature as its travels in waveguide bends structures. The results show
that a reasonable agreement between both theoretical approaches.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
Optimization of Surface Impedance for Reducing Surface Waves between AntennasIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
Reduction of Mutual Coupling between Closely Spaced Microstrip Antennas Array...TELKOMNIKA JOURNAL
Reducing mutual coupling is a key research area in design of compact microstrip antennas
arrays. To minimize the overall size of the antennas arrays, the distance between them must be very
small, as a result a strong mutual coupling is appears. Periodic structures can help to design a low profile
of antennas arrays and enable to improve their performances by the suppression of surface waves
propagation in a given frequency range. This paper proposes a novel configuration of mushroom-like
electromagnetic band-gap (2D-EBG) structure created by microstrip technology placed between two
antennas arrays to reduce the mutual coupling more than -33.24dB. When 13×2 EBG structures are used,
the mutual coupling reduces to -59.36dB at the operation frequency 5.8GHz of the antennas arrays. A
26.12dB mutual coupling reduction is achieved, which proves that the surface wave is suppressed. The
proposed configuration is designed, optimized, and miniaturized by using electromagnetic software CST
Microwave Studio. The measured results show that there is a good agreement with the computed results.
PERFORMANCE ANALYSIS OF 2D-EBG UNDER MONOPOLE ANTENNAjantjournal
The artificial properties in two dimensional electromagnetic structures (2D-EBGs), such as PMC and Band Reject Region are investigated for a proposed structure of square shaped mushroom. The radiation characteristics of monopole antenna over this 2D-EBG is tested by considering two cases. During first case monopole antenna is made to operate within band rejection region. Second case monopole antenna made operate outside the band rejection range. The obtained results during first case is showing enhancement in operating band width and smoother radiation pattern. In second case the effect is null and
2D-EBG resembles like conventional plane reflector. The simulated results are presented.
NOVEL BAND-REJECT FILTER DESIGN USING MULTILAYER BRAGG MIRROR AT 1550 NMcscpconf
Novel band-reject filter is proposed using multilayer Bragg mirror structure by computing reflection coefficient at 1550 nm wavelength for optical communication. Dimension of different
layers and material composition are modified to study the effect on rejection bandwidth, and no of layers is also varied for analyzing passband characteristics. GaN/AlxGa1-xN composiiton is taken as the choice for simulation purpose, carried out using propagation matrix method. Refractive indices of the materials are considered as function of bandgap, perating wavelength and material composition following Adachi’s model. One interesting result arises from the computation that band-reject filter may be converted into band-pass one by suitably varying ratio of thicknesses of unit cell, or by varying Al mole fraction. Simulated results can be utilised to design VCSEL mirror as optical transmitter.
A new approach for impedance matching rotman lens using defected ground struc...journalBEEI
Many recent radar applications and smart antenna are based on the electronically steerable beam in order to increase the performance of targeting the desired scan angle with the high performance of gain and directivity. Scanning angle with ±26o based on Microstrip Rotman lens and design frequency 2.45 GHz is presented in this study. Five beam ports provide five output beams directed the beams in five different scanning angles in the azimuth plane is provided. The traditional matching method by tapering the transmission line in order to guarantee a smooth energy transition from the 50 Ω input ports is replaced by Defected Ground Structure to achieve an acceptable return loss with a linear progressive phase for each beam port. The new approach is providing increasing in the scan angle. Besides, the size miniaturization is achieved by removing the tapering length and reduces the total size of the lens length by 23.67 mm. The proposed model is implemented using Computer Simulation Technology (CST) using the FR-4 substrate and the measurements lead to a good validation.
Computational Investigation of Asymmetric Coplanar Waveguides Using Neural Ne...Konstantinos Karamichalis
In order to compute the characteristic impedance and the relative effective dielectric constant of an
asymmetric coplanar waveguide with infinite or finite dielectric thickness, the use of artificial neural networks
is valuable. The method of neural computing presented in this paper uses only one neural model for both
parameters, for this specific waveguide type. The BFGS quasi-Newton back-propagation algorithm was used to
train the developed neural network. Numerical results are given for several configurations along with
comparisons with previously published data.
Initial study and implementation of the convolutional Perfectly Matched Layer...Arthur Weglein
In this report, first steps and results of the implementation of the Convolutional Perfectly
Matched Layer (CPML), for the modeling of the 2D acoustic heterogeneous wave equation
are presented. We also compare the conditions to set to zero, for all angles of incidence, the
reflection coefficient at the interface between two PML media, with the analogous conditions
for the reflection coefficient at an interface between two acoustic media. A side product of the
present work for the M-OSRP is a code to create synthetic data, using Finite-Difference (FD)
methods with PML BCs.
We also provide a short description of the main stages involved in the original Reverse Time
Migration (RTM) algorithm, with focus on the 2D acoustic heterogeneous wave equation. We
include a derivation of the equations of the CPML for the backward propagation of the data,
which is part of the RTM. As far as the authors knowledge, these equations and derivations
have not been reported in the literature. The reason we include the RTM is because the present
report can be considered part of a broader research project whose objective is to compare the
RTM with PML BCs with the Green’s theorem based RTM, developed within the M-OSRP.
Initial study and implementation of the convolutional Perfectly Matched Layer...Arthur Weglein
In this report, first steps and results of the implementation of the Convolutional Perfectly
Matched Layer (CPML), for the modeling of the 2D acoustic heterogeneous wave equation
are presented. We also compare the conditions to set to zero, for all angles of incidence, the
reflection coefficient at the interface between two PML media, with the analogous conditions
for the reflection coefficient at an interface between two acoustic media. A side product of the
present work for the M-OSRP is a code to create synthetic data, using Finite-Difference (FD)
methods with PML BCs.
We also provide a short description of the main stages involved in the original Reverse Time
Migration (RTM) algorithm, with focus on the 2D acoustic heterogeneous wave equation. We
include a derivation of the equations of the CPML for the backward propagation of the data,
which is part of the RTM. As far as the authors knowledge, these equations and derivations
have not been reported in the literature. The reason we include the RTM is because the present
report can be considered part of a broader research project whose objective is to compare the
RTM with PML BCs with the Green’s theorem based RTM, developed within the M-OSRP.
Effect of mesh grid structure in reducing hot carrier effect of nmos device s...ijcsa
This paper presents the critical effect of mesh grid that should be considered during process and device
simulation using modern TCAD tools in order to develop and optimize their accurate electrical
characteristics. Here, the computational modelling process of developing the NMOS device structure is
performed in Athena and Atlas. The effect of Mesh grid on net doping profile, n++, and LDD sheet
resistance that could link to unwanted “Hot Carrier Effect” were investigated by varying the device grid
resolution in both directions. It is found that y-grid give more profound effect in the doping concentration,
the junction depth formation and the value of threshold voltage during simulation. Optimized mesh grid is
obtained and tested for more accurate and faster simulation. Process parameter (such as oxide thicknesses
and Sheet resistance) as well as Device Parameter (such as linear gain “beta” and SPICE level 3 mobility
roll-off parameter “ Theta”) are extracted and investigated for further different applications.
A horn may be considered as a flared out waveguide. In this paper, a powerful electromagnetic simulator, 3D
EM solver WIPL-D software is used to design, analyse and optimize the dimensions of horn antenna which is
based on MOM solution for computations. The standard horn antenna at 10 GHz for 15dB gain is modelled and
the radiation pattern was observed. The horn antenna is optimized to achieve more than 20dB gain using
Genetic Algorithm, radiation patterns of the optimized horn antenna are also presented. Geometry of the horn
can be modelled by exploring the toolbar ‘symmetry’ option in WIPL-D. Design of X band Pyramidal Horn
Antenna is fabricated and measured using Network Analyzer.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
Optimization of Surface Impedance for Reducing Surface Waves between AntennasIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
Reduction of Mutual Coupling between Closely Spaced Microstrip Antennas Array...TELKOMNIKA JOURNAL
Reducing mutual coupling is a key research area in design of compact microstrip antennas
arrays. To minimize the overall size of the antennas arrays, the distance between them must be very
small, as a result a strong mutual coupling is appears. Periodic structures can help to design a low profile
of antennas arrays and enable to improve their performances by the suppression of surface waves
propagation in a given frequency range. This paper proposes a novel configuration of mushroom-like
electromagnetic band-gap (2D-EBG) structure created by microstrip technology placed between two
antennas arrays to reduce the mutual coupling more than -33.24dB. When 13×2 EBG structures are used,
the mutual coupling reduces to -59.36dB at the operation frequency 5.8GHz of the antennas arrays. A
26.12dB mutual coupling reduction is achieved, which proves that the surface wave is suppressed. The
proposed configuration is designed, optimized, and miniaturized by using electromagnetic software CST
Microwave Studio. The measured results show that there is a good agreement with the computed results.
PERFORMANCE ANALYSIS OF 2D-EBG UNDER MONOPOLE ANTENNAjantjournal
The artificial properties in two dimensional electromagnetic structures (2D-EBGs), such as PMC and Band Reject Region are investigated for a proposed structure of square shaped mushroom. The radiation characteristics of monopole antenna over this 2D-EBG is tested by considering two cases. During first case monopole antenna is made to operate within band rejection region. Second case monopole antenna made operate outside the band rejection range. The obtained results during first case is showing enhancement in operating band width and smoother radiation pattern. In second case the effect is null and
2D-EBG resembles like conventional plane reflector. The simulated results are presented.
NOVEL BAND-REJECT FILTER DESIGN USING MULTILAYER BRAGG MIRROR AT 1550 NMcscpconf
Novel band-reject filter is proposed using multilayer Bragg mirror structure by computing reflection coefficient at 1550 nm wavelength for optical communication. Dimension of different
layers and material composition are modified to study the effect on rejection bandwidth, and no of layers is also varied for analyzing passband characteristics. GaN/AlxGa1-xN composiiton is taken as the choice for simulation purpose, carried out using propagation matrix method. Refractive indices of the materials are considered as function of bandgap, perating wavelength and material composition following Adachi’s model. One interesting result arises from the computation that band-reject filter may be converted into band-pass one by suitably varying ratio of thicknesses of unit cell, or by varying Al mole fraction. Simulated results can be utilised to design VCSEL mirror as optical transmitter.
A new approach for impedance matching rotman lens using defected ground struc...journalBEEI
Many recent radar applications and smart antenna are based on the electronically steerable beam in order to increase the performance of targeting the desired scan angle with the high performance of gain and directivity. Scanning angle with ±26o based on Microstrip Rotman lens and design frequency 2.45 GHz is presented in this study. Five beam ports provide five output beams directed the beams in five different scanning angles in the azimuth plane is provided. The traditional matching method by tapering the transmission line in order to guarantee a smooth energy transition from the 50 Ω input ports is replaced by Defected Ground Structure to achieve an acceptable return loss with a linear progressive phase for each beam port. The new approach is providing increasing in the scan angle. Besides, the size miniaturization is achieved by removing the tapering length and reduces the total size of the lens length by 23.67 mm. The proposed model is implemented using Computer Simulation Technology (CST) using the FR-4 substrate and the measurements lead to a good validation.
Computational Investigation of Asymmetric Coplanar Waveguides Using Neural Ne...Konstantinos Karamichalis
In order to compute the characteristic impedance and the relative effective dielectric constant of an
asymmetric coplanar waveguide with infinite or finite dielectric thickness, the use of artificial neural networks
is valuable. The method of neural computing presented in this paper uses only one neural model for both
parameters, for this specific waveguide type. The BFGS quasi-Newton back-propagation algorithm was used to
train the developed neural network. Numerical results are given for several configurations along with
comparisons with previously published data.
Initial study and implementation of the convolutional Perfectly Matched Layer...Arthur Weglein
In this report, first steps and results of the implementation of the Convolutional Perfectly
Matched Layer (CPML), for the modeling of the 2D acoustic heterogeneous wave equation
are presented. We also compare the conditions to set to zero, for all angles of incidence, the
reflection coefficient at the interface between two PML media, with the analogous conditions
for the reflection coefficient at an interface between two acoustic media. A side product of the
present work for the M-OSRP is a code to create synthetic data, using Finite-Difference (FD)
methods with PML BCs.
We also provide a short description of the main stages involved in the original Reverse Time
Migration (RTM) algorithm, with focus on the 2D acoustic heterogeneous wave equation. We
include a derivation of the equations of the CPML for the backward propagation of the data,
which is part of the RTM. As far as the authors knowledge, these equations and derivations
have not been reported in the literature. The reason we include the RTM is because the present
report can be considered part of a broader research project whose objective is to compare the
RTM with PML BCs with the Green’s theorem based RTM, developed within the M-OSRP.
Initial study and implementation of the convolutional Perfectly Matched Layer...Arthur Weglein
In this report, first steps and results of the implementation of the Convolutional Perfectly
Matched Layer (CPML), for the modeling of the 2D acoustic heterogeneous wave equation
are presented. We also compare the conditions to set to zero, for all angles of incidence, the
reflection coefficient at the interface between two PML media, with the analogous conditions
for the reflection coefficient at an interface between two acoustic media. A side product of the
present work for the M-OSRP is a code to create synthetic data, using Finite-Difference (FD)
methods with PML BCs.
We also provide a short description of the main stages involved in the original Reverse Time
Migration (RTM) algorithm, with focus on the 2D acoustic heterogeneous wave equation. We
include a derivation of the equations of the CPML for the backward propagation of the data,
which is part of the RTM. As far as the authors knowledge, these equations and derivations
have not been reported in the literature. The reason we include the RTM is because the present
report can be considered part of a broader research project whose objective is to compare the
RTM with PML BCs with the Green’s theorem based RTM, developed within the M-OSRP.
Effect of mesh grid structure in reducing hot carrier effect of nmos device s...ijcsa
This paper presents the critical effect of mesh grid that should be considered during process and device
simulation using modern TCAD tools in order to develop and optimize their accurate electrical
characteristics. Here, the computational modelling process of developing the NMOS device structure is
performed in Athena and Atlas. The effect of Mesh grid on net doping profile, n++, and LDD sheet
resistance that could link to unwanted “Hot Carrier Effect” were investigated by varying the device grid
resolution in both directions. It is found that y-grid give more profound effect in the doping concentration,
the junction depth formation and the value of threshold voltage during simulation. Optimized mesh grid is
obtained and tested for more accurate and faster simulation. Process parameter (such as oxide thicknesses
and Sheet resistance) as well as Device Parameter (such as linear gain “beta” and SPICE level 3 mobility
roll-off parameter “ Theta”) are extracted and investigated for further different applications.
A horn may be considered as a flared out waveguide. In this paper, a powerful electromagnetic simulator, 3D
EM solver WIPL-D software is used to design, analyse and optimize the dimensions of horn antenna which is
based on MOM solution for computations. The standard horn antenna at 10 GHz for 15dB gain is modelled and
the radiation pattern was observed. The horn antenna is optimized to achieve more than 20dB gain using
Genetic Algorithm, radiation patterns of the optimized horn antenna are also presented. Geometry of the horn
can be modelled by exploring the toolbar ‘symmetry’ option in WIPL-D. Design of X band Pyramidal Horn
Antenna is fabricated and measured using Network Analyzer.
Comparative Study of Evolutionary Algorithms for the Optimum Design Of Thin B...jmicro
With the increasing levels of Electromagnetic pollution almost exponentially in this modern age of
Electronics reported and highlighted by numerous studies carried out by scientists from all over the world,
inspire engineers to concentrate their research for the optimum design of multilayer microwave absorber
considering various parameters which are inherently conflicting in nature. In this paper we mainly focus
on the comparative study of different Evolutionary algorithms for the optimum design of thin broadband (2-
20GHz) multilayer microwave absorber for oblique incidence (300
) considering arbitrary polarization of
the electromagnetic waves. Different models are presented and synthesized using various Evolutionary
algorithm namely Firefly algorithm (FA), Particle swarm optimization (PSO), Artificial bee colony
optimization (ABC) and the best simulated results are tabulated and compared with each others.
EFFECTIVE PEEC MODELING OF TRANSMISSION LINES STRUCTURES USING A SELECTIVE ME...EEIJ journal
The transmission lines structures are quite common in the system of electromagnetic compatibility (EMC)
analysis. The increasing complexities of physical structures make electromagnetic modeling an
increasingly tough task, and computational efficiency is desirable. In this paper, a novel selective mesh
approach is presented for partial element equivalent circuit (PEEC) modeling where intense coupling parts
are meshed while the remaining parts are eliminated. With the proposed approach, the meshed ground
plane is dependent on the length and height of the above transmission lines. Relevant compact formulae for
determining mesh boundaries are deduced, and a procedure of general mesh generation is also given. A
numerical example is presented, and a validation check is accomplished, showing that the approach leads
to a significant reduction in unknowns and thus computation time and consumed memories, while
preserving the sufficient precision. This approach is especially useful for modeling the electromagnetic
coupling of transmission lines and reference ground, and it may also be beneficial for other equivalent
circuit modeling techniques.
HFSS ANTENNA FOR KU BAND WITH DEFECTED GROUND STRUCTURESAKSHAT GANGWAR
A wide band Microstrip antenna is proposed for Ku band applications with defected groundd structure. A circular shape defect is integrated in the ground plane. A novel equivalent circuit model is proposed for Microstrip patch antenna with defected ground structure. Accurate design equations are presented for the wideband Microstrip antenna and theoretical analysis is done for the proposed structure. The proposed antenna has an impedance bandwidth of 56.67% ranging from 9.8 GHz to 17.55 GHz, which covers Ku-band and partially X-band. The antenna shows good radiation characteristics within the entire band, and has a gain ranging from 5 dBi to 12.08 dBi. Minimum isolation between co-polar and cross-polarization level of 20 dB and 15 dB is achieved in H-plane and E-plane respectively. The simulation of the proposed antenna is done on HFSS v.13, and measured results of fabricated antenna are in good agreement with the theoretical and simulated results
Determination of Surface Currents on Circular Microstrip AntennaswailGodaymi1
This work aims to present a theoretical analysis of the electric and magnetic surface current densities of a circular
microstrip antenna (CMSA) as a body of revolution.
The rigorous analysis of these problems begins with the application of the equivalence principle, which introduces
an unknown electric current density on the conducting surface and both unknown equivalent electric and magnetic
surface current densities on the dielectric surface. These current densities satisfy the integral equations (IEs) obtained
by canceling the tangential components of the electric field on the conducting surface and enforcing the continuity
of the tangential components of the fields across the dielectric surface. The formulation of the radiation problems is
based on the combined field integral equation. This formulation is coupled with the method of moments (MoMs) as
a numerical solution for this equation.
Adjusting primitives for graph : SHORT REPORT / NOTESSubhajit Sahu
Graph algorithms, like PageRank Compressed Sparse Row (CSR) is an adjacency-list based graph representation that is
Multiply with different modes (map)
1. Performance of sequential execution based vs OpenMP based vector multiply.
2. Comparing various launch configs for CUDA based vector multiply.
Sum with different storage types (reduce)
1. Performance of vector element sum using float vs bfloat16 as the storage type.
Sum with different modes (reduce)
1. Performance of sequential execution based vs OpenMP based vector element sum.
2. Performance of memcpy vs in-place based CUDA based vector element sum.
3. Comparing various launch configs for CUDA based vector element sum (memcpy).
4. Comparing various launch configs for CUDA based vector element sum (in-place).
Sum with in-place strategies of CUDA mode (reduce)
1. Comparing various launch configs for CUDA based vector element sum (in-place).
NON-SPLIT PERFECTLY MATCHED LAYER BOUNDARY CONDITIONS FOR NUMERICAL SOLUTION OF 2D MAXWELL EQUATIONS
1. International Journal of Electromagnetics ( IJEL ),Vol 3, No 1
1
NON-SPLIT PERFECTLY MATCHED LAYER
BOUNDARY CONDITIONS FOR NUMERICAL
SOLUTION OF 2D MAXWELL EQUATIONS
Arnold Abramov, Yutao Yue, and Mingming Wang
Institute of Deep Perception Technology, Wuxi, China
ABSTRACT
This paper developed a non - split perfectly matched layer (PML) boundary condition (BC) for Finite
Difference Time Domain (FDTD) simulation of electromagnetic wave propagation in 2D structure. The
point source for electric field has been exploited for propagation of electromagnetic field through 2D
structures to validate developed approach. The identity of resulted field distribution to that obtained for
split PML BC have been demonstrated.
KEYWORDS
Electromagnetic wave, non-split, PML, FDTD,cylinder
1. INTRODUCTION
Electromagnetic field distribution of any system can be known by solving Maxwell’s equations.
There are many numerical techniques allowing to find appropriate solutions. In this paper we will
deal with the finite difference time domain method introduced [1] in 1966 by Kane S. Yee. It has
a number of advantages, such as divergence-free (in contrast to the main methods that require a
condition div B = 0), the grid is very simple and the data is easily for storage). The FDTD
method solves the time-dependent Maxwell’s equations in a spatially finite computation domain.
The electric and magnetic fields are then represented by their discrete values on the each node of
spatial grid, and are extended in time. Without any boundary conditions, Yee’s algorithm
assumes that the domain is surrounded by a perfect electric conductor (PEC) layer. The presence
of the boundaries in the model can affect significantly the simulation results, due to spurious
reflection from the boundaries of electromagnetic waves incident on them. To obtain physically
reasonable solutions, the calculation area should be interrupted at the edges via special boundary
conditions that extend the definite area to infinity, representing it as unbounded volume. Such a
boundary condition could be obtained by a reflectionless absorbing layer that surrounds the
calculation area and absorbs all incident waves, regardless of the angle of incidence and
wavelength. Thus, in the implementation of FDTD, we set the layers of a hypothetical material
along the boundaries of computational area specially designed in such a way to completely
absorb the radiation incident on it. Such a layers have been called perfectly matching layer
(PML) and were first introduced by J. P. Berenger [2]. The PML conditions have a low reflection
coefficient, as well as practical independence from the angle of incidence of the wave.
Unfortunately, there is still a reflection: from the first layer of PML; between layers of PML,
because to save computing resources, losses increase from layer to layer; after the last layer of
PML, since there is a PEC border. Reflection from the first PML layer and between the PML
layers is caused by finite-difference discretization errors, and, first of all, by the fact that the
vectors E and H do not coincide in space. To reduce reflection within the PML, it is necessary to
2. International Journal of Electromagnetics ( IJEL ),Vol 3, No 1
2
strict the growth rate of losses to some reasonable limit. Reflection from the PEC boundary after
the last PML layer occurs usually for already much attenuated wave. The reflected wave
continues to weaken on the way back. But if there are few layers (usually less than 5), then the
reflected wave can be significant. To reduce the reflection from the first layer, the value of
conductivity σ1 is specially chosen to be small. To reduce the reflection between the layers, the
loss profile is selected in such a way to have a limited growth rate of loss. In order to reduce the
effect of waves reflected from the PEC boundary, the number of PML layers should be increased.
Berenger’s PML is typically referred to as a split field PML because the field components in
PML regions are split into two unphysical field components to obtain additional degrees of
freedom. This modification allows the creation of a reflectionless interface between a dielectric
medium and the PML layer. But extra splitting variables that are introduced in Berenger’s PML
BC increase computational memory time burden in implementation. In addition, it leads also to
the difficulties of numerical implementation. In order to avoid those issues scholars have done a
lot of researches on developing of versions of PML absorbing boundary condition for non
splitting fields: unsplit-field and material independent PML formulations are obtained in [3]
incorporating the auxiliary differential equation method into the PML formulations. The non split
PML BC has been used in seismic wave modeling introducing auxiliary variables [4]. A use of
non-split PML boundary condition for second -order elastic wave FETD forward modeling with
high calculation accuracy and great improvement in calculation efficiency have been
demonstrated in [5]. Nonsplit PML BC formulation developed previously [3] for one dimensional
case adopted in the present paper for 2D Maxwell’s equations. Another feature of the presented
formulations (except nonsplit PML BC) is that the use of the electric displacement field instead
of the electric field. This allows the PML to be independent of the material of the FDTD
computational domain.
2. BASIC EQUATIONS
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2.1. General Format, Page Layout and Margins
The starting point for the construction of an FDTD algorithm is Maxwell’s time-domain
equations.
E
t
H
E
t
0
0
1
D
H
D
(1)
where E
is the electric field strength vector in volts per meter, D
is the electric displacement
vector in coulombs per square meter, H
is the magnetic field strength vector, 0 and 0 –
dielectric and magnetic constant respectively, is the permittivity of the material. Using new
expressions for the fields
3. International Journal of Electromagnetics ( IJEL ),Vol 3, No 1
3
D
1
D
0
0
0
0
E
E
(2)
leads to
E
t
H
E
c
t
c
D
H
D
(3)
where we used the speed of light in free space.
For specifics, we further consider the case of TE polarizations for which electric field (along z
axis) is orthogonal to the plane (x,y) of electromagnetic field propagation. Thus the field has next
nonzero components: Ez, Hx, Hy.
x
E
t
H
y
E
t
H
E
D
y
H
x
H
c
t
D
z
y
z
x
z
x
y
c
c
z
z
(4)
In order to implement the FDTD method and calculate the field at all points of the computational
domain we have to replace the derivatives by finite-difference approximations and set the field
values at the boundaries of the computational domain. But before we will modify these equations
assuming the presence of an additional region around the computational domain where the field
will be absorbed, excluding its reflection to the back into computational area. For this purpose,
we introduce fictitious values that will be selected in such a way as not to affect the field inside
the computational domain, and to ensure its absorption outside it. We first write down the system
(4) for the case of continuous, time-harmonic fields (i.e. time dependence are described by factor
exp(it)):
x
E
H
i
y
E
H
i
E
y
H
x
H
c
i
z
y
z
z
x
y
c
c
)
(
)
(
D
D
x
z
z
(5)
0
0
/
1
c
4. International Journal of Electromagnetics ( IJEL ),Vol 3, No 1
4
3. NON-SPLIT PML BOUNDARY CONDITIONS
In order to implement PML we input fictitious constants x
*
, y
*
, x
*
, y
*
:
x
E
H
i
y
E
H
i
E
y
H
x
H
c
i
z
y
x
y
z
y
x
z
x
y
y
x
c
c
D
D
*
*
*
*
x
z
*
*
z
(6)
These fictitious parameters should be chosen so both that there are no changes in the medium
parameters within the main computational domain and ensure the absorption of the field in the
PML domain. By preserving the electric displacement field Dz in the equations (6), we obtain
that all dimensional parameters, as well as all the detailed information about the structure of the
computational domain, are enclosed on the input of the dielectric constant. It also allows the PML
to be independent of the material in the FDTD computing area. In [6] it was shown that in order
to ensure absorption in the PML layers, the expressions for the *
and *
should be as follows
0
m
*
0
m
*
i
i
Hm
m
Dm
m
(7)
m=x,y, with following selection of parameters
0
0
0
m
m 1
Hm
Dm
(8)
Theoretically, if the condition σi / ε0 = σi
*
/ μ0 is satisfied, then the average velocity of the
electromagnetic waves does not change at the interface and the reflection is equal to zero. At the
same time, because σi, σi
*
0 the absorption of electromagnetic waves takes place within the
PML. PML parameters used in this work will be described below.
Substituting (7-8) into (6) we get:
x
E
H
i
y
i
x
i
y
E
H
i
y
i
x
i
E
y
H
x
H
c
i
y
i
x
i
z
y
z
z
x
y
c
)
(
1
)
(
1
c
)
(
1
)
(
1
D
D
)
(
1
)
(
1
1
0
0
x
0
1
0
z
z
0
0
(9)
5. International Journal of Electromagnetics ( IJEL ),Vol 3, No 1
5
We can rewrite these equations as follows
x
E
i
y
x
E
H
x
i
y
E
i
x
y
E
H
y
i
E
D
y
H
x
H
c
D
y
x
i
i
y
x
i
z
z
z
z
z
x
y
0
y
0
0
x
0
z
z
2
0
0
)
(
c
)
(
)
(
c
)
(
)
(
)
(
1
)
(
)
(
(10)
To go back to time dependence, we will perform a formal replacement i → d/dt. Then instead
of (10) we have:
n
z
z
n
z
z
z
x
y
n
t
x
E
y
x
E
H
x
t
H
t
y
E
x
y
E
H
y
t
H
E
D
y
H
x
H
c
t
D
y
x
D
y
x
t
D
0
y
0
y
0
x
0
x
z
z
2
0
z
0
z
)
(
c
)
(
)
(
c
)
(
)
(
)
(
)
(
)
(
(11)
Now we replace the derivatives with their finite-difference approximations and we finally get the
PML-modified FDTD equations:
)
2
/
1
,
(
)
2
/
1
,
(
)
,
2
/
1
(
)
,
2
/
1
(
)
,
(
)
(
)
(
)
(
)
,
(
2
)
(
)
(
1
)
,
(
)
(
)
(
)
(
2
)
(
)
(
1
n
x
n
x
n
y
n
y
1/2
n
z
2
2
0
1/2
-
n
z
0
1/2
n
z
2
2
0
0
j
i
H
j
i
H
j
i
H
j
i
H
x
t
c
j
i
D
t
y
x
j
i
D
t
y
x
j
i
D
t
y
x
t
y
x
n
n
t
y
E
x
x
j
i
E
j
i
E
t
c
j
i
H
t
y
j
i
H
t
y
z
0
1/2
n
z
1/2
n
z
n
x
0
1
n
x
0
)
(
)
,
(
)
1
,
(
)
2
/
1
,
(
2
)
(
1
)
2
/
1
,
(
2
)
(
1
n
t
x
E
y
x
j
i
E
j
i
E
t
c
j
i
H
t
x
j
i
H
t
x
z
0
1/2
n
z
1/2
n
z
n
y
0
1
n
y
0
)
(
)
,
(
)
,
1
(
)
,
2
/
1
(
2
)
(
1
)
,
2
/
1
(
2
)
(
1
The selection of the fictitious parameters can be determined by the following expressions
introduced in Ref. [6]:
6. International Journal of Electromagnetics ( IJEL ),Vol 3, No 1
6
y
x
m
p
t
m
m ,
,
2
)
(
0
with pm=0.333(i/NPML)3
, i=1.. NPML, NPML – number of PML.
Finally the FDTD equations are as follow:
)
2
/
1
,
(
)
2
/
1
,
(
)
,
2
/
1
(
)
,
2
/
1
(
4
1
1
1
4
)
,
(
4
1
1
)
(
1
)
,
(
n
x
n
x
n
y
n
y
1
1/2
-
n
z
1/2
n
z
j
i
H
j
i
H
j
i
H
j
i
H
x
t
c
p
p
p
p
I
p
p
j
i
D
p
p
p
p
p
p
j
i
D
y
x
y
x
y
x
y
x
y
x
y
x
2
/
1
2
/
1
1
2
/
1
1 I
I
n
z
n
n
D
2
1/2
n
z
1/2
n
z
n
x
1
n
x 2
)
,
(
)
1
,
(
)
1
(
)
2
/
1
,
(
1
1
)
2
/
1
,
( I
p
j
i
E
j
i
E
x
p
t
c
j
i
H
p
p
j
i
H x
y
y
y
)
,
(
)
1
,
( 1/2
-
n
z
1/2
-
n
z
2
/
1
2
2
/
1
2 j
i
E
j
i
E
I
I n
n
3
1/2
n
z
1/2
n
z
n
y
1
n
y 2
)
,
(
)
,
1
(
)
1
(
)
,
2
/
1
(
1
1
)
,
2
/
1
( I
p
j
i
E
j
i
E
x
p
t
c
j
i
H
p
p
j
i
H y
x
x
x
)
,
(
)
,
1
( 1/2
-
n
z
1/2
-
n
z
2
/
1
3
2
/
1
3 j
i
E
j
i
E
I
I n
n
4. RESULTS
The model we used consists of rectangular area of size 200x200 unit cells. The size of the unit
cell x was chosen in such a way that one wavelength is equal to integer number N of unit
cells: =Nx. Point source generating electric field was defined offset 30 cells from the left edge
of the problem space along x axis. Number of PML layers NPML =10. As mentioned above a
propagation of TE-polarized wave in 2D plane was simulating via solution of Maxwell’s
equations (1) by FDTD method. The direction of wave propagation is along the x-axis (Fig.1).
Fig.1 Computational domain of the two dimensional problem spaces:
1 – PML; 2 – area of real space parameters; 3 – infinite cylinder (top view)
7. International Journal of Electromagnetics ( IJEL ),Vol 3, No 1
7
The origin of the coordinates corresponds to the centre of the computational domain. Three cases
were considered: 2D homogeneous space (Fig.1a) and two kinds of structures placed into centre
of 2D computational area: single cylinder (Fig.1b); group of 9 cylinders (Fig.1 c). We choose
cylinder as main figure in our simulation due to since it is the study of scattering on the cylinder
that led to the discovery of photonic nanojet [7] and a further increase in researchers' attention to
scattering effects on cylindrical objects [8-13].
Refraction index of each cylinder are nA=1.59. All results below are presented after 1200 time
step simulations. Each time step was equal t=Sc*x/c, where Sc =0.5 is Courant stability factor.
Polynomial [12] and power dependence [6] models for medium parameters have been choused
for split and non-split PML BC respectively. Effectiveness of those models demonstrates Fig.2:
projections of the calculated field distribution E(x,y) on the plane of two variables (E,x) and (E,y)
have been drawn. Field absorption occurs within PML layers (x,y=0-10 and x,y=190-200). A
maximal value on the dependencies corresponds to position of the point source, where a field
magnitude is kept constant
The difference between two approaches (non-split and split PML BC) was estimated by
expression
R=(Ens-Es)/Es
where Ens and Es are absolute value of calculated electric field for the cases of non-split and split
BC respectively. The Fig.3 demonstrates change of R along and across field propagation for the
cases of (0, 1) and 9 cylinders inside a computational area. As it is seen the relative difference is
less than 4%. The cases of 0 (empty computational domain, i.e. free propagation of
electromagnetic wave) and 1 cylinder are represented by 1 line because the difference in R for
Fig.2 Projections of the field distribution E(x,y) inside 2D area (Fig.1a) on the plane of two variables (E,x)
(a) and (E,y) (b).
solid line – split PML BC; dashed line – non-split PML BC
them occurred less than 1%. A point where R=0 corresponds to position of point source. In fact,
all the lines on Fig.3 are oscillating and short vertical lines shows an amplitude of those
8. International Journal of Electromagnetics ( IJEL ),Vol 3, No 1
8
Fig.3 Relative difference between simulation results for nonsplit and split PML BC along x (dashed line)
and y (solid line) axis’s for one (a) and nine (b) cylinders in computational area.
oscillations while main lines itself represent average positions for R dependencies. More
complex structure clearly leads to a greater error and oscillations. However, overall these changes
are minor, within 4 %, those demonstrating efficiency of approximation efficiency and
applicability of non-split BC for FDTD method.
5. CONCLUSIONS
The FDTD method to solve 2D Maxwell’s equations has been described. Non-split PML BC has
been used. This approach allows to avoid electromagnetic field splitting which does not follow
from Maxwell's equations, and thus it can lead to the save of the computational time. As result of
used approach, all dimensional parameters, as well as all the detailed information about the
structure of the computational domain, are enclosed on the input of the dielectric constant. It is
because of using the electric displacement field instead of the electric field. This allows also the
PML to be independent of the material of the FDTD computational domain. The developed
calculation scheme verified by comparison of final results to those obtained for ordinary (split)
version of BC. Calculated field distributions for different parameters of computational domain
examined for both cases and are in the good agreement.
REFERENCES
[1] Yee, K. S., (1966) “Numerical solution of initial boundary value problems involving Maxwell’s
equations in isotropic media”, IEEE Trans. Antenn. Propag., Vol. 17, pp585 – 589.
[2] Berenger, Jean-Pierre, (1994) “A Perfectly Matched Layer for the Absorption of Electromagnetic
Waves”, Journal of Computational Physics, Vol. 114, pp185-200.
[3] Ramadan, O., (2003) “Auxiliary Differential Equation Formulation: An Efficient Implementation of
the Perfectly Matched Layer”, IEEE Microwave and Wireless Components Lett., Vol. 13, No. 2,
pp69-71.
[4] Zhang, C., Sun, B., Yang, H., Ma, J., (2016) “A non-split perfectly matched layer absorbing boundary
condition for the second-order wave equation modelling”, Journal of Seismic Exploration, Vol.25,
pp1-9.
[5] Basu, U., Chopra, A.K., (2004) “Perfectly Matched Layers for Transient Elastodynamics of
Unbounded Domains”, International Journal for Numerical Methods in Engineering, Vol.59, pp1039
-1074.
[6] Sullivan, Dennis, “Electromagnetic simulation using the FDTD method”, New York IEEE Press,
2000.
9. International Journal of Electromagnetics ( IJEL ),Vol 3, No 1
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[7] Chen, Z.A., Taflove, A., Backman, V., (2004) “Photonic Nanojet Enhancement of Backscattering of
Light by Nanoparticles: A Potential Novel Visible-Light Ultramicroscopy Technique”, Opt. Express,
Vol.12, pp1214 -1220.
[8] Zhishen, Z., Yin, H., Yuanhua, F., Yuecheng, S., Zhaohui, L., (2019) “An ultranarrow photonic
nanojet formed by an engineered two-layer microcylinder of high refractive-index materials”, Opt.
Express,Vol. 27, No. 6, pp9178-9188.
[9] Liu, C.Y., (2013) “Photonic nanojet enhancement of dielectric microcylinders with metallic coating”,
J Optoelectron Adv Mater., Vol.15, pp150–154.
[10] Schaefer, J., Lee, S.-C., Kienle, A., (2012) “Calculation of the near fields for the scattering of
electromagnetic waves by multiple infinite cylinders at perpendicular incidence”, J. Quant.
Spectrosc. Radiat. Transf., Vol.113, pp2113–2123.
[11] Abramov, A., Ji, C., Liu, R., Kostikov, A., (2016) “Enhancement of the Electromagnetic Waves
Intensity by Scattering on Multiple Infinite Cylinders”, Journal of Photonic Materials and
Technology, Vol. 2, No. 1, pp1-5.
[12] Abramov A., Kostikov A., (2017) “Formation of whispering gallery modes by scattering of an
electromagnetic plane wave by two cylinders”, Phys. Lett. A, Vol. 381, No 12, pp1107-1110.
[13] Abramov, A., Kostikov, A., Liu, R., Ji, C., Li, X., Zhou, J. and Chen, Z., (2017) “Formation of the
high electromagnetic waves intensity areas by multiple cylinders scattering: whispering gallery
modes and photonic nanojet”, Journal of Electromagn. Waves and Applications, Vol.31, No8, pp820-
827.
[14] Taflove A. and Hagness S. Computational Electrodynamics: The Finite-Difference Time-Domain
Method, 3 ed. Artech House, Boston, MA, 2005.
AUTHORS
Arnold Abramov is a Deputy Director of Artificial Intelligence Innovation Centre,
Institute of Deep Perception Tecnnology, China. He received the Ph.D. in Dоnetsk
Institute for Physics and Engineering of the National Academy of Sciences, Ukraine,
(2003). His current research interests include development of prototype radar devices,
electromagnetics and photonics.
Yutao Yue received his B.S. degree of applied physics from University of Science and
Technology of China in 2004, Ph.D. degree of computational physics from Purdue
University in 2010. He then served as senior scientist of Kuang-Chi Institute, team
leader of Guangdong “Zhujiang Plan” Introduced Innovation Scientific Research Team,
and associate professor of Southern University of Science and Technology of China,
etc. He has authored 17 papers and over 300 patents, and advised 13 postdoc
researchers. He also serves as the “Industrial Professor” of Jiangsu Province, advisory
panel member of SAIIA, technical review expert of Guangdong, Jiangsu, Shenzhen,
and Wuxi. He is now the founder and director of Institute of Deep Perception Technology (IDPT), Jiangsu
Industrial Technology Research Institute (JITRI). His research interests include modeling and optimization,
computational electromagnetics, radar perception, artificial intelligence theories.
Mingming Wang was born in Liaoning province, China in 1980. He received the M.S.
degree in microelectronics and solid state electronics from Shandong University in
2006, and received the Ph.D. degree in integrated circuit design from the Institute of
Microelectronics of the Chinese Academy of Sciences, Beijing, in 2009. His research
interests include microwave/millimeter-wave IC design, circuits and systems.