Triangular Patch Modeling Research Articles

Design Of Triangular Array Microstrip Patch For Antenna 5g Application

The trend of research on microstrip antennas in the millimeter frequency range has been hotly discussed in recent years. With the aim of increasing the bandwidth, beam gain and return loss in accordance with the standards of 5G needs in a fairly small dimension and low complexity. Previously, several studies of microstrip antennas with conventional patches have been carried out, then followed by a triangular array patch model. The antenna designed using Duroid 5880 substrate with a thickness of 1.575 mm and a dielectric constant value of 2.2 was simulated using Computer Simulation Technology (CST) software. The simulation results work at a frequency of 28 GHz with a return loss value of -26.98 dB, VSWR 1.09, gain 8.8 dB, HPBW value of 25.6° and main lobe of 21.0 dBi. This antenna can work well on millimeter wave range for 5G technology. Compared with previous studies of microstrip antennas, this triangular array patch antenna provides better measurement results.

“Application of boundary integral solution to thermal diffusion problem by edge based basis functions”

In this research paper, heat diffusion problem is solved using the new numerical simulation method called boundary integral equation formulation and boundary element solution method. Three dimensional irregular thermal bodies are addressed by introducing the new edge based basis and weighting functions. The three numerical formulations defined on the edges are Single Layer Formulation (EBSLF), Double Layer Formulation (EBDLF) and Combined Layer Formulation (EBCLF) are presented for higher accuracy of the results for heat dissipation. The triangular patch modeling method is used to divide the arbitrary irregular geometry of the body into triangular patches so that above edge based function are defined on those edge of the patches for numerical solution. Numerically, the solution method is developed by defining the basis functions on the Edge of the triangles, instead of on the nodes as followed in the regular BEM solutions. The temperature diffusion results from the hot surface body are plotted for analysis. Also the convergence study is done to get the result convergence towards the exact solution for the different new numerical formulations. The errors are treated in two different ways. The actual error and the absolute errors are used to determine the best model among all the combinations of numerical formulations and different mesh sizes.

A Straight-Forward Method of Moments Procedure to Solve the Time Domain Integral Equation Applicable to PEC Bodies via Triangular Patch Modeling

In this work, a simple and straight-forward method of moments solution (MOM) procedure is presented to obtain the induced current distribution on an arbitrarily-shaped conducting body illuminated by a Gaussian plane wave directly in the time domain using a patch modeling approach. The method presented in this work, besides being stable, is also capable of handling multiple excitation pulses of varying frequency content incident from different directions in a trivial manner. The method utilizes standard Rao-Wilton-Glisson (RWG) functions and simple triangular functions for the space and time variables, respectively, for both expansion and testing. The method adopts conventional MOM and requires no further manipulation invariably needed in standard time-marching methods. The moment matrix generated via this scheme is a block-wise Toeplitz matrix and, hence, the solution is extremely efficient. The method is validated by comparing the results with the data obtained from the frequency domain solution. Several simple and complex numerical results are presented to validate the procedure.

A face based basis function solutions to thermal conduction problems for 3-D irregular shaped bodies using BEM

Abstract Out of all the numerical methods available to solve the engineering problems using boundary element method, the basis functions which are used to define the unknown quantity in the mathematical formulation, are based on the combination of the shape functions as in a regular finite element procedure. Also, since the BEM is based on defining the source density functions, the kernels in the integral equations become singular, strongly singular and hyper singular for which the traditional BEM does not have a common solution procedure. In this paper, it is proposed to develop boundary element solutions for the thermal conduction problems, for 3-D irregular shaped bodies, using the indirect method i.e. by defining the source density functions. Thermal conduction problem is solved using the boundary integral equation formulation and boundary element solution method. The geometry of the body is divided into triangular patches using triangular patch modeling. A numerical solution is developed effectively by defining the basis functions on the face of the triangles generated in the triangular patch modeling, in contrast to defining it on the nodes as followed in the regular BEM solutions. The temperature distribution from the surface of the hot surface of the cube and sphere is plotted. Also the convergence study is conducted to get the solution convergence towards the exact solution for the case of a sphere and comparison of these two objects for thermal distribution is done.

“Development and Application of FBBFBEM Solution for 3-D Complex- Shaped Domain”

In this article, for solving the 3-D thermal conduction problem an effort has been by using the boundary integral equation formulation and BEM. Multidimensional non uniform bodies which are in complex shape are addressed by triangular patch modeling method. The arbitrary geometry of the body is divided into elements which are of triangular patches by triangulation algorithm. A numerical solution is developed by defining the basis functions on the face of the triangles generated in the triangular patch modeling, in contrast to defining it on the nodes as followed in the regular mesh generation technique like BEM, FVM and FEM solutions. The temperature distribution from the surface of the hot body is plotted for understanding the nature of its behaviors. Also the convergence study is conducted to get the solution convergence towards the exact solution for the case of a sphere. Other geometries like cube, cylinder and cone are also treated and analyzed for the field variable.

Measuring Software Test Verification for Complex Workpieces based on Virtual Gear Measuring Instrument

AbstractValidity and correctness test verification of the measuring software has been a thorny issue hindering the development of Gear Measuring Instrument (GMI). The main reason is that the software itself is difficult to separate from the rest of the measurement system for independent evaluation. This paper presents a Virtual Gear Measuring Instrument (VGMI) to independently validate the measuring software. The triangular patch model with accurately controlled precision was taken as the virtual workpiece and a universal collision detection model was established. The whole process simulation of workpiece measurement is implemented by VGMI replacing GMI and the measuring software is tested in the proposed virtual environment. Taking involute profile measurement procedure as an example, the validity of the software is evaluated based on the simulation results; meanwhile, experiments using the same measuring software are carried out on the involute master in a GMI. The experiment results indicate a consistency of tooth profile deviation and calibration results, thus verifying the accuracy of gear measuring system which includes the measurement procedures. It is shown that the VGMI presented can be applied in the validation of measuring software, providing a new ideal platform for testing of complex workpiece-measuring software without calibrated artifacts.

Estimation of Free Space Capacitance and Body Potential of a Spacecraft for Charging Analysis

This paper presents a computation of the absolute free space capacitance and electrostatic body potential of a spacecraft using moment method with triangular patch modeling. Expressions are derived numerically and the moment integral is evaluated. The capacitance of a square plate is computed to validate the approach. Finally, the free space capacitance of a typical spacecraft is computed for various configurations and body potential is evaluated. The derived expressions are simple and suitable for developing the charging analysis tool. As this approach is more general, it can be easily applied to any practical spacecraft configuration.

Constructing curves and triangular patches by Beta functions

A class of new basis functions for curve and triangular patch modeling is constructed by means of Beta functions. Based on these basis functions, a new scheme of generating curves and triangular patches is proposed. First we demonstrate that these basis functions have similar properties as those of the Bernstein–Bézier basis functions, such as non-negativity, partition of unity and others. Thus, these basis functions give rise to curve and triangular patch representations with affine invariance, convex hull, symmetry and endpoint interpolation, as well as an evaluation algorithm, which is similar to the de Casteljau’s algorithm for Bézier curves and surfaces. In addition, these basis functions have a shape parameter. The shape of the curve or triangular patch can be modified by changing the value of the shape parameter under the same control polygon or control net. The modeling examples illustrate the validity of the new methods.

Method of Moments Solution of Electromagnetic Scattering Problems Involving Arbitrarily-Shaped Conducting/Dielectric Bodies Using Triangular Patches and Pulse Basis Functions

We present a new method of moments solution procedure for calculating electromagnetic scattering and radiation from conductor/dielectric composite structures. The solution is obtained using triangular patch modeling and a recently developed pair of mutually orthogonal pulse basis functions to represent the equivalent currents <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> . The pulse basis functions are defined with respect to the edges in the triangulated model and partially spread over the triangles connected to the edge. The orthogonality of the basis functions allows the development of stable solutions for all formulations and configurations investigated. A set of numerical results is presented that illustrates the efficacy of the present approach.

Electromagnetic Scattering From Arbitrarily Shaped Dielectric Bodies Using Paired Pulse Vector Basis Functions and Method of Moments

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A pair of orthogonal pulse vector basis functions is demonstrated for the calculation of electromagnetic scattering from arbitrarily-shaped material bodies. The basis functions are intended for use with triangular surface patch modeling applied to a method of moments (MoM) solution. For modeling the behavior of dielectric materials, several authors have used the same set of basis functions to represent equivalent electric and magnetic surface currents. This practice can result in zero-valued or very small diagonal terms in the moment matrix and an unstable numerical solution. To provide a more stable solution, we have developed orthogonally placed, pulse basis vectors: one for the electric surface current and one for the magnetic surface current. This combination ensures strongly diagonal moment matrices. The basis functions are suitable for electric field integral equation (EFIE), magnetic field integral equation (HFIE), and combined field formulations. In this work, we describe the implementations for EFIE and HFIE formulations and show example results for canonical figures. </para>

Node based Method of Moments Solution to Combined Layer Formulation of Acoustic Scattering

In this work, a novel numerical technique, based on method of moments Solution, Is presented to solve the Combined layer formulation (CLF) to insure unique Solution to the exterior acoustic scattering problem Lit all frequencies. A new set of basis functions, narnely, Node based basis functions are used to represent the Source distribution Oil the Surface of rigid body and the same functions are used as testing, functions as well. Combined layer formulation (CLF) is defined by linearly combining the Single layer formulation (SLF) and Double layer formulation (DLF) with complex coupling parameter The matrix equations for the SLF and DLF are derived and same equations are oxtencled to the CLE The surface of the body is modeled by triangular patch modeling. Results of numerical technique presented in this paper, using node based basis functions, are compared with the exact Solutions wherever available. Also, condition numbers of the impedance matrices of SLF, DLF and CLF are plotted, for some objects of canonical shapes, to show that only CLF is free from resonance problem.

FAST COMPUTATIONAL ALGORITM FOR EFIE APPLIED TO ARBITRARILY-SHAPED CONDUCTING SURFACES

This work presents a fast computational algorithm that can be used as an alternative to the conventional surface-integral evaluation method included in the electric field integral equation (EFIE) technique when applied to a triangular-patch model for conducting surfaces of arbitrary-shape. Instead of evaluating the integrals by transformation to normalized area coordinates, they are evaluated directly in the Cartesien coordinates by dividing each triangular patch to a finite number of small triangles. In this way, a large number of double integrals is replaced by a smaller number of finite summations, which considerably reduces the time required to get the current distribution on the conducting surface without affecting the accuracy of the results. The proposed method is applied to flat and curved surfaces of different categories including open surfaces possessing edges, closed surfaces enclosing cavities and cavity-backed apertures. The accuracy of the proposed computations is realized in all of the above cases when the obtained results are compared with those obtained using the area coordinates method as well as when compared with some published results.

Acoustic scattering from rigid bodies of arbitrary shape—Double layer formulation

In this work, a numerical method is presented, based on the well-known method of moments (MoM), to calculate the acoustic fields scattered by a three-dimensional, arbitrarily shaped, acoustically rigid body subjected to a plane wave incidence. The mathematical formulation is based on the potential theory and, in this work, the numerical method is applicable to the so-called double layer formulation (DLF). The scattering body is approximated by planar triangular patches. For the MoM solution using triangular patch modeling, edge-based basis functions are utilized to approximate the source distribution efficiently. These basis functions along with an appropriate testing procedure generates a simple numerical algorithm that is versatile enough to be applicable to closed, as well as open bodies. Finally, the present solution method is validated with several representative examples.

Nanosecond Rise Time Generator for Electro-Magnetic Pulse

We have developed an electro-magnetic pulse simulator for the radiated susceptibility tests that can generate three kinds of electro-magnetic pulses including nanosecond rise time and high electric field pulse. This paper describes simulated and measured results for the fastest rise time voltage generator of this simulator. A new circuit of the voltage generator has developed to stabilize the output voltage waveform and the effect of the connection geometry between the generator and an antenna is estimated by using transient electro-magnetic analysis program based on method of moment by triangular patch modeling.

Comments on "AC impedance of an isolated flat conductor"

For original paper see Z. Zhihua and M. Weiming, IEEE Trans. Electromagn. Compat., vol.44, pp.482-486, (2002). Employing the moments method, and a triangular patch modeling technique, this paper gives an analysis of the AC impedance of an isolated flat conductor, taking into consideration capacitive effects. It is observed that, for the flat conductor under consideration, the capacitance has a significant effect on the impedance beyond a frequency of about 20 MHz. Thus, it can be concluded that the capacitive effects should also be considered in evaluating the AC impedance of an isolated conducting strip.

Numerical solution of time domain integral equations for arbitrarily shaped conductor/dielectric composite bodies

In this work, we present a numerical solution of the coupled time domain integral equations to obtain induced currents and scattered far fields on a three-dimensional, arbitrary shaped conducting/dielectric composite body illuminated by a Gaussian electromagnetic plane wave pulse. The coupled integral equations are derived utilizing the equivalence principle. The solution method is based on the method of moments and involves the triangular patch modeling of the composite body, in conjunction with the patch basis functions. Detailed mathematical steps along with several numerical results are presented to illustrate the efficacy of this approach.

Using the T-Matrix Method for Light Scattering Computations by Non-axisymmetric Particles: Superellipsoids and Realistically Shaped Particles

Light scattering by non-axisymmetric particles is commonly needed in particle characterization and other fields. After much work devoted to volume discretization methods to compute scattering by such particles, there is renewed interest in the T-matrix method. We extended the null-field method with discrete sources for T-matrix computation and implemented the superellipsoid shape using an implicit equation. Additionally, a triangular surface patch model of a realistically shaped particle can be used for scattering computations. In this paper some exemplary results of scattering by nonaxisymmetric particles are presented.

Radiation through Waveguide-backed Apertures of Arbitrary Shape in a Conducting Screen

A moment-method analysis of waveguide-backed apertures of arbitrary shape is presented. The “generalized network formulation” for aperture problems[1] has been used for formulating the problem in terms of an operator equation. Triangular patch modeling, with suitably defined basis functions, is utilized for the solution of the operator equation. Representative aperture shapes considered include rectangular, circular, elliptic, diamond, and H. Numerical results are presented for equivalent surface magnetic current, equivalent aperture admittance and antenna power gain patterns.

Modeling of Complex Geometries for Electromagnetic Simulation

In this work, we discuss the surface patch modeling techniques to describe a complex geometry to the computer to asses the electromagnetic field interaction from a given source. The most popular technique to model complex geometries is the triangular patch modeling method. Here, we present this technique in detail to model complex bodies such as an aircraft. Lastly, we discuss the topic of modeling Induced error in the numerical solution and means to reduce it.

Application of a new MPIE formulation to the analysis of a dielectric resonator embedded in a multilayered medium coupled to a microstrip circuit

A new mixed-potential integral-equation (MPIE) formulation is developed for the analysis of electromagnetic problems due to conducting or dielectric objects of arbitrary shape embedded in a planarly stratified medium. In the new MPIE formulation, the dyadic kernel of the vector potential is kept in the simple form originally developed by Sommerfeld. The scalar potential, which is related to the vector potential via the Lorenz gauge, is then represented by a double dot product of a dyadic kernel with a dyadic charge density. An extra line integral term, which is well behaved and nonsingular, will appear when the object penetrates an interface. The numerical implementation of the double dot product is found to be trivial if one takes advantage of the well-established basis functions in which the unknown current density is expressed. The new MPIE formulation is employed in conjunction with the triangular patch model to treat the problem of a dielectric resonator (DR) excited by microstrip circuit. A matched-load simulation procedure has been used to extract the network S-parameters of a DR microstrip circuit. The diameters of the Q circles have been measured to determine the coupling coefficients and the Q factors of the DR excited by a microstrip circuit. The validity of the new MPIE formulation and the numerical procedure have been verified by comparing the obtained S-parameters, with available measurement data.