Entire-domain Basis Functions Research Articles

Subdomain basis functions from entire domain basis functions for a certain class of problems

Entire domain series expansions used in the method of collocation can give rise to unbalanced system matrices. By studying the asymptotic properties of the expansion functions the numerically ill-behaved part of the functions can be factored out. A well-behaved function can then be obtained by suitable normalization. However, the ill-behaved factor is a function of the coordinates and therefore the normalization factor can be considered constant only over small regions. Hence, the normalization process gives rise to a well-behaved set of subdomain basis functions instead of entire domain functions.

Analysis of coplanar waveguide-fed microstrip antennas

A moment method analysis of a microstrip antenna fed by an open-end coplanar waveguide is presented. The surface electric current on the microstrip antenna is represented by the entire domain basis functions, while the surface magnetic currents in the open-end slot and in the slots of the coplanar waveguide near the open end are expanded by the subsectional roof-top basis functions. Some practical numerical aspects are carefully discussed, and a numerical device is introduced to reduce the computation time for the integrals involving roof-top basis functions and the spectral-domain Green's function. The solution accuracy is thus improved. Computed results for the reflection coefficients and input impedances are given and compared with measured values. Good agreement between theory and experiment is obtained. >

Admittance of a longitudinal waveguide slot radiating into an arbitrary cylindrical structure

In this paper we use a hybrid method to calculate the admittance of a longitudinal slot (of finite length) in a rectangular waveguide, when the slot radiates into a cylindrical outer structure of arbitrary finite cross section. The analysis takes advantage of a Fourier transformation along the cylinder axis, by which the computational effort is drastically reduced. The harmonic spectral currents on the structure are expanded in subsectional triangular basis functions and determined using an electric field integral equation (EFIE) and the moment method. These currents and the corresponding fields are inverse Fourier transformed and matched over the slot to the fields inside the waveguide by an additional moment method approach using entire domain basis functions for the slot field. The calculated slot admittance has good accuracy when compared with measurements on a chosen geometry. >

Efficient solution of the differential form of Maxwell's equations in rectangular regions

One of the problems of the finite element and the finite difference method is that as the dimension of the problem increases, the condition number of the system matrix increases as /spl Theta/(1/h/sup 2/) (of the order of h/sup 2/, where h is the subsection length). Through the use of a suitable basis function tailored for rectangular regions, it is shown that the growth of the condition number can be checked while still retaining the sparsity of the system matrix. This is achieved through a proper choice of entire domain basis functions. Numerical examples have been presented for efficient solution of waveguide problems with rectangular regions utilizing this approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Minimizing the computational cost and memory requirements for the capacitance calculation of 3-D multiconductor systems

A new approach is presented which minimized the computational cost and memory requirements for capacitance calculations of three-dimensional multiconductor systems. The proposed approach, based on the integral equation method (IEM), calculated the capacitance of three-dimensional geometry of ideal conductors in two stages. In the first stage, the integral equation method was used to obtain the charge distribution on each conductor in isolation. In the second stage, the multiple interaction (coupling) among the conductors was included by applying the IEM to the whole structure and considering the charge distribution, obtained in the first stage, as a discretized entire domain basis function. The order of the interaction matrix was thus reduced to the order of conductors in the structure. The proposed method was tested for various geometries and it resulted in tremendous savings in computational time and memory storage; moreover, it gave very good accuracy in comparison with the classical integral equation method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An accurate and efficient entire-domain basis Galerkin's method for the integral equation analysis of integrated rectangular dielectric waveguides

The propagation characteristics of multiple coupled rectangular dielectric waveguides are investigated through an integral equation analysis. In contrast with the widely used subdomain-basis Galerkin's method, in this work a novel set of entire-domain basis functions is introduced. This set consists of plane wave functions that satisfy Maxwell's equations in each guiding region, therefore representing a proper expansion system. The simple form of the basis functions employed enables the accurate numerical evaluation of the spectral integrals, by means of an efficient asymptotic extraction technique. It is found that the computed dispersion curves presented for various single and coupled waveguides compare very favorably to published results of other methods. Finally, leakage effects in lossy waveguides are numerically treated for the first time, in view of mode transitions from leaky to bound regime. The technique presented in this paper is accurate, though conceptually simple, and can deal with a wide variety of integrated circuits and multilayered substrate configurations. It is also demonstrated that its main advantage is superior computational efficiency, since very satisfactory results are obtained with only a few expansion terms.

Full wave analysis of aperture-coupled cylindricalrectangular microstrip antenna

The authors present an original study of an aperture-coupled cylindrical microstrip antenna. The rigorous full wave spectral domain approach uses Green functions for a conducting cylinder with internally or externally coated dielectric substrate to set up integral equations. The Galerkin technique with entire-domain basis functions is applied to solve the integral equations. Results for the rectangular patch are compared with measurements. It is demonstrated that the input impedance is significantly affected by the size of the cylinder.

Analysis of wide inclined slot coupled narrow wall coupler between dissimilar rectangular waveguides

Analysis of a waveguide coupler coupled through a wide inclined slot in the common narrow wall of a rectangular waveguide for high power applications is presented. A simplified technique to find the internal scattered magnetic field due to this wide inclined slot has been used. Both variational method and method of moments using entire domain basis functions and Galerkin's technique have been used in finding out the S parameters of the four port coupler. The experimental results have shown good agreement with the corresponding theoretical results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Comparison between two sets of basis functions for the current modeling in the Galerkin spectral domain solution for microstrips

A frequently used technique for the numerical full wave analysis of planar microwave passive structures is the method of moments (MoM). A very important determinant for the accuracy and efficiency of this technique is the choice of the basis functions used in the approximation of the unknown current components. The application of several types of entire and subsectional domain basis functions has been proposed in the literature. However, little comparison has been made between different types of basis functions. In this paper, a comparison is presented between two sets of frequently used subsectional domain basis functions for the canonical case of the microstrip transmission line. The emphasis in this paper is on the relative accuracy, the convergence and the computational efficiency of both sets of basis functions. The intent of the paper is primarily to be an eye opener for the implications of the choice of the basis functions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A method for treating junctions between bodies of revolution and arbitrary surfaces

A method to treat junctions between bodies of revolution (BOR) and arbitrary surfaces is presented. The method is applicable to formulations employing the method of moments to solve surface integral equations for structures consisting of combined BOR and arbitrary surfaces. Harmonic entire domain basis functions are used on the bodies of revolution and triangular surface patches are used on the arbitrary surfaces. A junction is formed by creating a spatially coincident region between a body of revolution and an arbitrary surface. The geometry of the junction region is determined by the arrangement of the triangular surface patches used to form the junction. It determines the accuracy with which the junction currents are modeled. Numerical results are presented to demonstrate the accuracy of the junction models for both radiation pattern and input impedance predictions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Scattering from a conductive rectangular plate covered by a thick dielectric layer and excited from a dipole source or a plane wave

The scattering of electromagnetic radiation from a conductive rectangular plate of infinitesimal thickness covered by a dielectric parallelepiped of arbitrary size is analyzed. An integral equation formulation is employed in terms of the electric field inside the dielectric layer and the surface current density on the conductive plate, and is solved approximately by using entire domain Galerkin technique. The electric field inside the dielectric layer is described in terms of a superposition of exponential waves while, in describing the surface current density on the conductive plate, two types of entire domain basis functions are utilized: either Fourier-exponential series or Chebyshev series type finite-term expansions are employed alternatively. Numerical results are computed and presented for several scatterer sizes and excitation types.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Identification of propagation regimes on integrated microstrip transmission lines

There has been a resurgence of interest in the propagation characteristics of open integrated microstrip transmission lines. This is due in part to the discovery of diverse propagation regimes for higher-order modes on open lines. In contrast to the dominant EH/sub 0/ mode, three distinct propagation regimes exist for higher-order modes on microstrip transmission lines. In this paper, a rigorous spectral-domain integral equation formulation is used to analyze propagation in all three regimes. This formulation provides a clear physical picture of the different propagation regimes based on the mathematical location of poles and branch points in the complex spectral-variable plane. As an illustration, the formulation is applied to the case of an isolated uniform microstrip transmission line. The integral equation is discretized via the method of moments, and entire-domain basis functions incorporating suitable edge behavior are utilized to provide convergence with relatively few terms. The results obtained are compared to the results of other workers, and good agreement is observed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Entire-domain galerkin method for analysis of metallic antennas and scatterers

The paper presents the general theory of an entire-domain Galerkin method for the analysis of metallic (i.e. perfectly conducting) antennas and scatterers. The antenna and scatterer surfaces are approximated by generalised quadrangles (i.e. curved curvilinear quadrangles defined by means of parametric equations, whose edges coincide with local coordinate lines). Surface currents are expanded in such local coordinate systems and the general form of the corresponding electric field integral equation is derived. A procedure is decribed for obtaining entire-domain basis functions which satisfy automatically the continuity equation along the surface element interconnections and free edges, and the expressions are derived for the impedance matrix elements in this case. Starting from the general theory, two new particular methods are presented. The first is intended for the analysis of general structures, and is based on application of truncated cones and bilinear surfaces for the approximation of geometry. The second is aimed for the analysis of spherical scatterer, and is based on the application of generalised rectangular elements which follow the sphere shape. Both methods use polynomials for approximation of currents. Very good agreement of the results obtained by the proposed method with available experimental and numerical results is achieved by using small number of unknowns per wavelength squared (about ten for large surfaces of simple form).

Electromagnetic Scattering from Aperiodic Strip Gratings

In this paper, a comparison between electromagnetic scattering from periodic and aperiodic gratings is made. The effects of strip grating truncation are included for both cases. A Galerkin formulation with entire domain basis functions is utilized to solve for the induced currents on the strips for both TE and TM polarizations. Current densities and bistatic scattering results are presented for both periodic and aperiodic profiles. Moreover, the focusing capability of aperiodic gratings is also presented.

Entire-domain basis MOM analysis of coupled microstrip transmission lines

A full-wave spectral-domain integral equation formulation is used to analyze coupled open-boundary microstrip transmission lines. A general rigorous formulation is specialized to the case of two identical uniform lines and a method of moments (MOM) solution is implemented. In contrast with earlier subdomain basis MOM solutions, entire-domain basis functions which incorporate appropriate edge conditions for transverse and longitudinal current components are utilized. This allows closed-form evaluation of relevant spatial integrals and results in improved accuracy using far fewer terms. Numerical results in the form of propagation constants and current distributions are presented for the dominant and first two higher-order coupled modes, and compare favorably to results of other techniques. >

Electromagnetic transmission through inhomogeneously filled slots in a thick conducting plane-arbitrary incidence

The penetration of an arbitrarily incident electromagnetic wave through a slot filled with inhomogeneous material in a thick conducting plane is analyzed. The solution is obtained via a combined finite-element method/method of moments algorithm based on the generalized network formulation. The discretization of the generalized network formulation is performed via the method of moments. The finite-element method is then used to compute the fields within the inhomogeneous interior cavity region, leading to the construction of the interior aperture admittance matrix. It is shown that with the use of entire domain basis functions, the construction of the aperture admittance matrices is computationally efficient. Furthermore, this method is attractive since it preserves the sparsity of the finite-element method matrix, reducing computational memory requirements. Some examples of the penetration of inhomogeneously filled slots of various cross sections are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Numerical field modelling of objects with edges and corners using a conformal mapping

A numerical method is developed to study electromagnetic scattering from three-dimensional geometries, which is an extension of the method previously used for bodies of revolutions. On the object's surface two orthogonal tangent vectors are defined. Along one, surface currents are represented by discrete triangular functions and along the other by a finite set of entire domain basis functions. To enable the latter expansion the object's cross-section is conformally transformed onto a circle, and Fourier type basis functions are selected in the new space. The technique is then applied to study the scattering from prismatic geometries, such as cubic boxes and plates. The behavior of the solutions with the number of modes is investigated to determine the coupling of the entire domain modes. The formulation is applicable to other geometries, but it needs the transformation function to be useful.

Coplanar waveguide‐fed microstrip antennas

AbstractA microstrip antenna fed by a coplanar waveguide is investigated using a full‐wave analysis based on the method of moments in the spectral domain. The surface current density on the microstrip antenna and the field distribution in the slots of the coplanar waveguide are represented by entire domain and subsectional basis functions. The reflection coefficient referenced on the coplanar waveguide is calculated and compared to the experimental results.

Numerical solution of integral equations for dielectric objects of prismatic shapes

A numerical method to investigate scattering from dielectric geometries of prismatic shapes has been developed. The surface integral equations are formulated by Schelkunoff's equivalence principle in terms of equivalent surface electric and magnetic currents. To solve these integral equations for the unknown currents, the object's cross-section is mapped onto a circle. In the transformed space, Fourier type entire-domain basis functions are used in the cross section and triangular subdomain basis functions are selected along the generating curve to represent the currents. A moment method is then used to reduce the integral equations to a matrix equation to compute the current coefficients. It is found that the transformation of the object's surface to a circular shape improves the convergence of the current mode in the cross-section. However, the current modes are coupled on the surface and the matrix equation includes all the modes. >

Moment-method analysis of large, axially symmetric reflector antennas using entire-domain functions

The moment-method technique utilizing entire domain basis functions is applied to the analysis of large, axially symmetric reflector antennas. The electric surface current is modeled as a finite series of sinusoids whose domain consists of the entire generating curve. This expansion results in a matrix size of less than 5% of that produced with subdomain basis functions. Only a slight increase in the CPU requirements occurs from this analysis. The results from this technique show good agreement when compared to both physical optics and a subdomain-based moment-method formulation on small, axially fed paraboloidal and hyperboloidal reflector antennas. Extension to a large 100- lambda paraboloidal reflector with f/D=0.4 produces results comparable to that obtained using physical optics. Convergence is obtained with as few as two expansion terms per wavelength. Discretization of the generating curve with four points per wavelength leads to results which agree within 0.5 dB over data from a more densely defined curve. >