Piecewise Sinusoidal Basis Research Articles

An Efficient Method of Moments for Thick-Wire Antennas

Detailed formulation of a simple Galerkin method of moments (MoM) is presented. It is based on compact closed-form expressions of mutual impedance among filamentary sinusoidal monopoles. Using piecewise sinusoidal basis functions, the mutual impedance of thick-wire sections can be computed through an azimuthal integration of the mutual impedance between filamentary dipoles. Each element of impedance matrix is calculated through a rapidly convergent single integral only. This is unlike other MoM techniques, where double or triple integrals are needed to evaluate impedance matrix. In our formulation, it has been assumed that the wire current is uniform in azimuth, and changes along the axial direction only. No approximation on the segment length or radius of the thick-wire is made, and hence our formulation remains efficient for arbitrarily long/thick antennas.

Fast Computation of Electromagnetic Scattering From Dielectric Objects Using Quadrilateral Piecewise Sinusoidal Basis and Characteristic Basis Function Method

A method of moments (MoM)-based procedure is developed to calculate the scattering from homogeneous dielectric bodies. The technique uses quadrilaterals for the approximation of geometry and piecewise sinusoidal (PS) basis functions for the approximation of surface currents. The notable advantage of the PS basis is its radiated fields can be expressed in closed-form. The proposed approach therefore circumvents the need to use Green’s function in formulating the integral equations. Combined with a simple testing procedure, the matrix filling time is reduced and the concern of singularity is removed. To further reduce the computational complexity and enhance the performance, a characteristic basis function method (CBFM) is implemented and embellished with a new characteristic basis function (CBF) generation strategy. Specifically, a cubical surface bounding the entire target is first specified and discretized. A set of auxiliary sources are then defined in a manner similar to that done for a scattering body. These auxiliary sources are defined once and shared by different blocks. In comparison to the traditional plane wave spectrum (PWS) method, the CBFs generated by the new approach are valid not only for plane wave excitations but also for localized excitations. Numerical results are provided to validate the efficacy of the proposed algorithm.

Chiral frequency selective surfaces comprised of multiple conducting strips per unit cell

The periodic structure based on an array of multiple conducting strips per unit cell on a chiral slab is investigated in this letter. Instead of a single strip, a unit cell is constructed by equal and unequal lengths of double or triple strips. In this case, the array is periodic, as opposed to the traditional individual elements. The co-polarised reflectance, co-polarised transmittance and cross-polarised transmittance of new types of frequency selective surfaces (FSS) comprised of perfectly conducting double or triple strips on a chiral slab are analysed theoretically for a plane wave at normal incidence. The analysis is based on the modal expansions and moment methods together with the Floquet theorem. The unknown current coefficients induced on the conducting elements are computed by using the subdomain overlapping piecewise sinusoidal basis functions. By using two or three conducting strips per unit cell, FSS can be operated in different frequency bands. The double and triple strips per unit cell on chiral slab produce double and triple resonances, respectively. The structure can be used in band-stop filter, multiband antenna applications and subreflector systems as well as the polarisation rotator. The computed result of free-standing strip FSS is compatible with the measured and calculated results in literature.

Comments on “Fundamentals of Thin-Wire Integral Equations With the Finite-Gap Generator”

In papers [1], [2], the authors extend the so-called effective current method to the Hallen's and Pocklington's equations with the finite-gap generator (FGG). The indicated method considered earlier in [3] with a reference to [4] is associated with application of the method of auxiliary sources to the analysis of cylindrical dipole antennas [5]-[7]. The purpose of these comments is to draw the authors' and readers' attention to the existence ofpaper [8] where the Pocklington's equation with the FGG is solved for the axial current considered there to be auxiliary. The equation is solved by the Galerkin method using the piecewise sinusoidal basis and testing functions. The auxiliary axial current is used further for calculation of the surface current (which is referred to as the effective current in [1]-[4]), and the surface current itself is used for calculation of the input impedance. So, in some respects papers [1]-[7] just repeat the main idea and technique of paper [8], although of course papers [1]-[7] also contain a lot of their own new, interesting, and useful analytical and numerical results.

Reply to “Comments on ‘Fundamentals of Thin-Wire Integral Equations With the Finite-Gap Generator’”

In papers [1], [2], the authors extend the so-called effective current method to the Hallen's and Pocklington's equations with the finite-gap generator (FGG). The indicated method considered earlier in [3] with a reference to [4] is associated with application of the method of auxiliary sources to the analysis of cylindrical dipole antennas [5]-[7]. The purpose of these comments is to draw the authors' and readers' attention to the existence ofpaper [8] where the Pocklington's equation with the FGG is solved for the axial current considered there to be auxiliary. The equation is solved by the Galerkin method using the piecewise sinusoidal basis and testing functions. The auxiliary axial current is used further for calculation of the surface current (which is referred to as the effective current in [1]-[4]), and the surface current itself is used for calculation of the input impedance. So, in some respects papers [1]-[7] just repeat the main idea and technique of paper [8], although of course papers [1]-[7] also contain a lot of their own new, interesting, and useful analytical and numerical results.

Zigzag metallic conductors as frequency selective surfaces

Reflection and transmission properties of a new type of frequency selective surface (FSS) made of zigzag metallic elements placed periodically on a dielectric substrate are investigated theoretically for arbitrary polarisation. The electric field integral equation technique with the subdomain overlapping piecewise sinusoidal basis functions are employed to compute the unknown current coefficients induced on the metallic elements. The zigzag FSS arrays act as a low-pass filter in S -(1-5 GHz), X -(8-12 GHz) and K u -(12-18 GHz) bands. Owing to multiple resonances the zigzag FSS arrays can be used in multiband frequency applications. Between the resonances there exist transmission windows that allow full energy transfer. By removing the first and third arms, the power reflection coefficient of three-arm zigzag FSS is compared with a freestanding strip FSS, and it is compatible with the measured and calculated results found in the literature.

Frequency Selective Surfaces With Multiple-Strip Group Elements

In this letter, a new group of elements of double and triple strips are proposed. Instead of a single perfectly conducting strip, a group of multiple strips constitutes a unit cell. In this case, the group is periodic, not the individual elements. The fraction of electromagnetic power reflected (reflectance) and transmitted (transmittance) of a new type of freestanding frequency selective surface (FSS), made of the group of elements per periodic cell, is examined theoretically for transverse magnetic (TM) polarization. The electric field integral equation (EFIE) technique with the subdomain overlapping piecewise sinusoidal (PWS) basis functions are employed to compute the unknown current coefficients induced on the metallic elements. It is observed that the spectral characteristic of single-strip FSS is enhanced by using periodic group cells. There exist transmission bands that allow full energy transfer for unequal lengths of double and triple strips. Double and triple resonances appeared in the event of unequal strip lengths. Since it is observed multiple resonances, the structure can be used in multiband antenna applications and subreflector systems. The computed results of strip FSS are compatible with the measured and calculated results in literature.

FSS COMPRISED OF ONE- AND TWO-TURN SQUARE SPIRAL SHAPED CONDUCTORS ON DIELECTRIC SLAB

The scattering of electromagnetic waves from a Frequency Selective Surfaces (FSSs) composed of a new one- and two-turn square spiral shaped periodic structures are investigated by using modal expansion method for a linearly polarized transverse electric (TE) and transverse magnetic (TM) incident waves. The Moment Method (MM) of Galerkin type is employed by expressing the current induced on the metallic surfaces in terms of Piecewise Sinusoidal (PWS) basis functions to determine the FSS structure reflection and transmission coefficients.

ACCURACY AND COMPLEXITY ASSESSMENT OF SUB-DOMAIN MOMENT METHODS FOR ARRAYS OF THIN-WIRE LOOPS

A direct sub-domain moment-method formulation is presented for the analysis of arrays of thin-wire loops. Curved piecewise sinusoidal basis functions are used for the description of the currents on the loops, while both point matching and reaction matching are examined as testing schemes. Numerical results are provided for representative array structures with the intention to delve into the behavior of the solutions as the number of basis/testing functions grows, but also for the purpose of comparison with well-documented results. Finally, the complexity of the developed codes is estimated and general guidelines are provided for the efficient and accurate analysis of multi-element arrays.

Frequency selective surfaces comprised of periodic arrays of two-turn square spiral shaped conductors

The scattering of electromagnetic waves from a frequency selective surfaces (FSSs) composed of a new two-turn square spiral shaped periodic structures are investigated by using modal expansion method. The moment method of Galerkin type is employed by expressing the current induced on the metallic surfaces in terms of Piecewise Sinusoidal (PWS) basis functions to determine the FSS structure reflection and transmission coefficients.

ANALYSIS OF CIRCULARLY POLARIZED DIELECTRIC RESONATOR ANTENNA EXCITED BY A SPIRAL SLOT

The hemispherical dielectric resonator antenna (DRA) excited by a single-arm spiral slot is studied theoretically in this paper. The Green’s function technique is employed to formulate an integral equation for the spiral slot current. The moment method with piecewise sinusoidal (PWS) basis and testing functions is used to convert the integral equation into a matrix equation by using a deltagap exciting source. The input impedance, return loss, axial ratio and radiation pattern are calculated. Numerical results demonstrate that the analysis is efficient.

An application of wavelet bases in the spectral domain analysis of transmission line discontinuities

The local support and vanishing moment property of wavelet bases have been recently used to obtain a sparse matrix representation of integral equations in the spatial domain. In this paper, an application of the cubic spline and the corresponding semi-orthogonal wavelets in the spectral domain is proposed for the evaluation of the reflection coefficient for open/short transmission lines. Because of the nearly optimal time (space)–frequency (wavenumber)–window product of the cubic spline and wavelet, the double spectral integrals appearing in the formulation can be computed more efficiently than with the commonly used piecewise sinusoidal (PWS) or triangular basis functions. It is shown that the time–frequency-window product of the triangular and PWS function are close to each other, whereas those of the cubic spline/wavelet are close to 0·5, the lowest possible value corresponding to functions of Gaussian class. Both the PWS and wavelet bases are applied to microstrip and coplanar waveguides with isotropic and anisotropic substrates, and the results are compared with published theoretical and experimental data. It is observed that even though the number of splines/wavelets required for an accurate representation of the current distribution in the transmission line is almost twice as high as the number of PWS functions, the overall computation time decreases significantly in the former case. © 1998 John Wiley & Sons, Ltd.

Moment-method analysis of printed wire spirals using curved piecewise sinusoidal subdomain basis and testing functions

Archimedian and logarithmic printed wire spirals are analyzed using a moment-method incorporating curved piecewise sinusoidal subdomain basis and testing functions. Results for spiral parameters including input impedance and current distribution are presented and are shown to have good agreement with published results for the same antennas obtained using linear segmentation. Since the curved basis functions exactly follow the spiral contour, significantly fewer curved segments are, therefore, required for accurate analysis compared with linear segmentation.

Moment method analysis of printed single-arm wire spiral antennas using curved segments

Single-arm wire spirals printed on grounded dielectric substrates are analysed using a moment method algorithm which uses piecewise sinusoidal subdomain basis and test functions on curved segments, which follow exactly the spiral curvature. Results are compared with those obtained from measurements and with published results using linear segmentation, and it is shown that the curved segment model is accurate and significantly more computationally efficient.

Moment-method analysis of printed circular wire-loop antenna using curved piecewise sinusoidal subdomain basis and test functions

A computationally efficient method for analyzing printed wire-loop antennas on grounded dielectric substrates which uses curved piecewise sinusoidal subdomain current basis and test functions spanning two segments in a moment-method solution to Pocklington's equation is presented. Results for loop-input impedances are convergent, and these, together with efficiencies, compare favorably with computations using entire domain and linear subdomain basis and test functions.

Characterization of cylindrical microstrip gap discontinuities

AbstractA rigorous full‐wave analysis of microstrip gap discontinuities on cylindrical surfaces is presented. Numerical results for the frequency‐dependent reflection and transmission coefficients and the gap capacitance and conductance are calculated using a moment‐method calculation, in which a combination of entire‐domain sinusoidal and piecewise sinusoidal basis functions is used to represent the currents on the microstrip line. The characteristics of cylindrical microstrip gap discontinuities for various curvatures and gap spacings are analyzed. © 1995 John Wiley & Sons, Inc.

Numerical and experimental studies of current distributions on thin metallic posts inside rectangular waveguides

A fast converging and stable moment method solution for the current distribution on arbitrary size rectangular obstacles mounted transversely inside the rectangular waveguide has been developed. A special arrangement of piecewise sinusoidal and pulse basis functions has been utilized to determine the transverse current distributions on the obstacles and their scatterings in the waveguide. The method has been compared well with the Marcuvitz's results for the inductive and capacitive posts and the experimental data of an arbitrary size rectangular obstacle.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Electromagnetic characteristics of superquadric wire loop antennas

The analysis of antenna configurations in the form of a generalized superquadric loop, which includes circular, elliptical and rectangular loop geometries, is presented in this paper. Use of a Galerkin form of the moment method with piecewise sinusoidal subsectional basis and testing functions provides rapid numerical convergence and accurate representation of the antenna current. A convenient parametric representation for the superquadric curve is developed to allow a subsectional formulation using curved wire segments, rather than the commonly employed piecewise linear segments, to construct the geometry. Both magnetic frill and delta gap source models are implemented to allow a detailed study of input impedance, directivity, radiation pattern and current distribution as a function of various geometrical parameters. The results are shown to compare well with previous results for the special case of a circular loop antenna. Some useful curves are presented to aid in the design of practical superquadric loop antennas.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Characterisation of electromagnetically coupled superquadric loop antennas for mobile communications applications

Analysis of two mutually coupled loop antennas with arbitrary relative orientation and position and possibly different geometries is presented. The antennas are represented by generalised superquadric curves, which include circular, elliptical, and rectangular loop geometries, and they may be located either in a homogeneous region or next to an infinite ground plane. A Galerkin-type moment method with piecewise sinusoidal subsectional basis and weighting functions is used. Special consideration is given to implement the solution using curved wire segments instead of the commonly employed linear segments to improve computational efficiency. This very general computational tool is used to investigate the behaviour of coupled loops in configurations suitable for personal communications applications. A discussion of the use of antenna diversity to increase the received signal-to-noise ratio for communications equipment used in a multipath fading environment is also presented. Computational examples show that antenna diversity can provide significant improvements even for closely spaced loop antennas used in mobile communications applications.

Moment method analysis of linearly tapered slot antennas

AbstractAn accurate Method of Moments (MoM) model is developed and implemented for the analysis of the linearly tapered slot antenna (LTSA). The model employs an unequal size reactangular sectioning for conducting parts of the antenna. Piecewise sinusoidal basis functions are used for the expansion of conductor current. The effect of the dielectric is incorporated in the model by using equivalent volume polarization current density and solving the equivalent problem in free space. The feed section of the antenna including the micro‐stripline is handled rigorously in the MoM model by including slotline short‐circuit and microstripline currents among the unknowns. Comparison with measurements is made to demonstrate the validity of the model for both the air case and the dielectric case. Numerical results for the effect of the dielectric permittivity are presented.