Asymptotic Extraction Research Articles

Efficient Computation of the Off-Diagonal Elements of the Vector-Potential Multilayered Periodic Dyadic Green's Function

The authors focus on the efficient computation of the slowly convergent infinite series that lead to the off-diagonal elements of the vector potential multilayered periodic dyadic Green's function. Two different approaches based on Kummer's transformation are applied to the evaluation of these series. The well-known approach that makes use of the generalized pencil of functions (GPoF) and Ewald's method is the fastest approach, but it does not provide accurate results when the distance between the field point and any of the source points is close to zero. To avoid this problem, we present a novel approach based on the GPoF and the spectral Kummer-Poisson's method with higher-order asymptotic extraction. This latter approach is slightly slower than the former one, but it is accurate in the whole range of distances between the field point and the sources.

An Efficient Asymptotic Extraction Approach for the Green's Functions of Conformal Antennas in Multilayered Cylindrical Media

Asymptotic expressions are derived for the dyadic Green's functions of antennas radiating in the presence of a multilayered cylinder, where analytic representation of the asymptotic expansion coefficients eliminates the computational cost of numerical evaluation. As a result, the asymptotic extraction technique has been applied only once for a large summation order. In addition, the Hankel function singularity encountered for source and evaluation points at the same radius has been eliminated using analytical integration.

A Generalized Asymptotic Extraction Solution for Antennas in Multilayered Spherical Media

An efficient model is developed to accelerate the convergence of the dyadic Green's function's (DGF) infinite summation when the source and observation points are placed in different layers of a dielectric sphere, thereby expediting computational analysis. The proposed procedure is based on asymptotic extraction principles in which the quasi-static images are extracted from the spectral domain DGF. The effectiveness of the approach is demonstrated in a method of moment model where a microstrip antenna as well as a conformal dipole array have been studied.

Asymptotic Extraction Approach for Antennas in a Multilayered Spherical Media

An efficient algorithm is introduced to enhance the convergence of dyadic Green's functions (DGF) in a layered spherical media where asymptotic expressions have been developed. The formulated expressions involve an infinite series of spherical eigenmodes that can be reduced to the simple homogenous media Green's function using the addition theorem of spherical Hankel functions. Substantial improvements in the convergence speed have been attained by subtracting the asymptotic series representation from the original DGF. The subtracted components are then added to the solution using the homogenous media Green's function format.

Fast Calculation of the Electromagnetic Field by a Vertical Electric Dipole Over a Lossy Ground and Its Application in Evaluating the Lightning Radiation Field in the Frequency Domain

The evaluation of the electromagnetic field radiated by a lightning stroke is of essential importance for the study of the interaction between lightning electromagnetic fields and power lines, or other sensitive installations. A fast algorithm for calculating the fields generated by a vertical electric dipole over a lossy ground, which can be expressed by the well-known Sommerfeld integrals, is presented in this paper. The integrals are decomposed into two parts. One part can be calculated by a recursive analytical expression, and the other part can be evaluated numerically due to the fact that the extracted integrand damps rapidly with the help of the asymptotic extraction technology. A comparison with some approximate formulas is performed in detail with variable parameters, such as the soil parameters, the geometry, and the excitation frequency of dipole, which shows very good agreement as far as the lightning field is concerned. The technical merit of the proposed approach is its universality, which can be applied for arbitrary parameters, and its computing time is still competitive.

Efficient Analysis of Aperture Antennas on Generally Shaped Convex Multilayered Surfaces Using a Hybrid SD-UTD Method

A novel hybrid method is described for analyzing convex multilayered conformal array antennas. The hybrid method is based on the spectral domain approach in combination with the ray-based uniform theory of diffraction (UTD) method. The analysis is divided in two parts. First, the spectral domain approach is accelerated by using an asymptotic extraction technique where the extracted term of the Green's function is calculated using UTD. It is shown that this new approach results in significant acceleration of the existing spectral domain algorithm without losing accuracy. The modified spectral domain method is then used in the second part where generally shaped convex multilayered surfaces are analyzed by using sets of canonically shaped surfaces (spheres and/or circular cylinders). Their radii are obtained using the UTD formulation, which contains important information such as distance and curvature of the generally shaped surface along each geodesic. The results obtained using the new algorithm are compared to the available results (calculated and measured) for different conformal antennas, showing very good agreement.

An Efficient Algorithm for Calculating the Earth Return Mutual Impedance of Conductors With Asymptotic Extraction Technology

It is very essential to calculate the mutual impedance between overhead and buried conductors for analyzing electromagnetic compatibility problems related to a transmission line system. An efficient algorithm for calculating the Pollaczek integral, whose integrand oscillates rapidly and decays slowly, is proposed in this paper. With the help of the asymptotic extraction technique, the Pollaczek integral can be decomposed into the sum of two parts, one of which is expressed with an exponential integral and the other is the one that has a rapidly damped integrand. A comparison of the numerical results with published data shows very good agreement. The proposed approach is a good candidate for calculating impedances related to the Pollaczek integral.

A novel asymptotic extraction technique for the efficient evaluation of a class of double Sommerfeld integrals

When the Galerkin method of moments (MoM) is used in the numerical analysis of microwave microstrip networks, elements of a network impedance matrix are required. Two dimensional (2D) Sommerfeld (spectral) integrals must be evaluated in such cases. When semi-infinite circuit feed lines are used, certain specific types of Sommerfeld integrals arise whose integrands oscillate rapidly and present serious numerical difficulties for their evaluation. In this paper, a novel, accurate, and much more efficient asymptotic extraction technique (AET) is developed that involves extracting an inner asymptotic angular integral, which is then evaluated analytically before evaluating the outer integral numerically.

Numerical Computation of the Space-Domain Mixed Potential Green's Functions for Planar Layered Structures With Arbitrarily Magnetized Ferrites

This work reports a numerical method to generate the space-domain Green's functions used in the mixed potential integral equation (MPIE) formulation for planar structures when arbitrarily magnetized ferrite slabs are present. The presence of ferrite slabs in planar layered structures has been previously accounted for in the framework of the spectral-domain electric field integral equation (EFIE) formulation of the problem. The proposed numerical approach will allow the MPIE formulation to deal this kind of substrates. Asymptotic extraction and interpolation techniques have been used in order to keep the computational effort within reasonable limits.

Spectral domain analysis of large (M)MIC‐structures using novel quadrature methods

AbstractThe spectral domain approach for the solution of integral equations is especially attractive for planar circuits and antennas in multilayered environments characterized by analytically derived Green's functions. However, for circuits with large lateral dimensions the spectral integrands are strongly oscillatory and accurate evaluation of the integrals is extremely difficult and often time‐consuming. In this paper, we propose higher‐order Legendre quadrature rules optimized for the integration of the oscillating integrands using the Filon principle. The Legendre–Filon quadrature weights are computed for the specific oscillations by solving a small linear system of equations. The method is applied within a spectral domain solution approach evaluating the spectral integrals in cartesian wavenumbers and using asymptotic extraction techniques as well as complex integration path deformation for improved convergence. Since the asymptotic extraction causes a singularity in the origin of the wavenumber domain that is not annihilated by cartesian wavenumber integration, a special procedure for the treatment of this singularity is also introduced. The overall method needs very few sampling points for the numerical evaluation of the spectral integrals but is still applicable to very large structures as compared to the wavelength. Copyright © 2004 John Wiley & Sons, Ltd.

Multilayer Effects on Cavity-Backed Slot Antennas

A hybrid technique of the finite-element method and the method of moments (FEM/ MoM) is used to analyze the effects of multilayered superstrates on cavity-backed slot (CBS) antennas. The spectral-domain approach is used to compute the MoM admittance matrix. An asymptotic extraction technique is applied to improve the computational efficiency of the convolution integrals. Effects on the input impedance, efficiency, gain, and radiation patterns are presented for different antennas. The numerical results are validated with measurements and published data.

Radiation efficiency analysis of submillimeter‐wave receivers based on a modified spectral domain integration technique

Reflector backed submillimeter‐wave slot antennas on substrate lenses are promising candidates for novel astronomical applications in integrated receivers for the far infrared region. Using an adjustable reflector, considerable resonance frequency tuning can be achieved, but with the risk of exciting parasitic parallel plate wave modes. Employing a surface/volume integral equation method and advanced spectral domain integration techniques, a complete radiation efficiency analysis of such kind of receivers is performed. Convenient integration path deformations in complex wavenumber planes allow a very fast evaluation of the spectral domain integrals in combination with efficient database and asymptotic extraction techniques. Saddle point and residue calculation techniques are employed to accurately determine the power of each parallel plate mode and the space wave contributions. The simulations reveal an appropriate set of parameters reducing the radiation loss to less than 10 percent for doubleslot and quadratic slot geometries preserving high tuning capability and optimized radiation patterns as well.

Mutual coupling in aperture-coupled patches on cylindrical reflectors calculated using a spectrum of two-dimensional solutions

The mutual coupling between groundplane slots in aperture-coupled patch antennas on cylindrical structures is calculated using a moment method in the Fourier domain. By separating the three-dimensional (3D) problem into a spectrum of two-dimensional (2D) problems an efficient calculation of the admittance is possible. To increase the accuracy in the mutual admittance calculation, an asymptotic extraction technique is used. Several cases of antenna geometry are investigated and comparison is made to measurements. The method used allows for efficient and accurate analysis of dual polarized aperture-coupled patches placed on general cylindrical structures, as in the case of base-station antenna arrays for mobile communications.

Analytical Technique To Evaluate the Asymptotic Part of the Impedance Matrix of Microstrip Dipole On a Uniaxial Substrate - Abstract

The integral transform method with the asymptotic extraction technique is formulated to evaluate a Sommerfeld type integral for the analysis microstrip dipole on a uniaxial substrate. The infinite double integral of the asymptotic part of the impedance matrix with triangular subdomain basis function with edge condition can be reduced to a finite one-dimensional integral. This finite one-dimensional integral can be easily evaluated numerically after the singular part of the integral is treated analytically. It is demonstrated the efficiency and accuracy of the proposed method to evaluate the asymptotic part of impedance matrix.

Analytical Asymptotic Extraction Technique for the Analysis of Bend Discontinuity - Abstract

The purpose of this paper is to use the analytical asymptotic extraction technique to analyze the bend discontinuity. We show that the derived analytical techniques significantly reduce the computational time while improving the accuracy compared to the conventional method. Especially, the advantage of the proposed method can eliminate the truncation error for evaluating the asymptotic part of impedance matrix. The proposed method has applied for solving the bend discontinuity, and verified with measurement results.

Analytical Asymptotic Extraction Technique for the Analysis of Bend Discontinuity

Analytical Asymptotic Extraction Technique for the Analysis of Bend Discontinuity

Surface electric fields of multi-layered medium Green's functions and the calculation of impedance matrix elements of microstrip structures

The electric fields of the spatial Green's functions at the interfaces of a multi-layered medium are calculated by integrating along the Sommerfeld integration path. For the case when both sources and field points are on the same interface of two different dielectrics, convergence of the Sommerfeld integrals can be facilitated by higher-order asymptotic extractions. The results are illustrated for distance ranges from 0.02 free-space wavelengths to 1.5 free-space wavelengths. The tabulated electric fields Green's functions are then used to compute impedance matrix elements of multi-layered microstrip structures in the spatial domain.

Surface electric fields and impedance matrix elements of stratified media

For the various geometrical configurations of waves in stratified media, we consider the important case when both source and field points are located on the same interface separating two different dielectric media. We denote this configuration as surface electric field case. In this paper, the electric fields are calculated numerically without using potentials. For the surface electric field case the integrand of the electric field grows with k/sub /spl rho///sup 3/2/ for large /spl kappa//sub /spl rho// making the Sommerfeld integral singular. To calculate the surface electric fields in the spatial domain, we previously applied a technique of higher order asymptotic extraction. In the higher order asymptotic extraction, the higher order asymptotic parts were calculated analytically. The remainder, which has an integrand decays as /spl kappa//sub /spl rho///sup -3/2/ was calculated numerically along the Sommerfeld contour path of integration. In this paper, we use a different extraction technique, the half-space extraction. After the half-space extraction, the integrand of the Sommerfeld integral of stratified media decays exponentially and the integral is calculated along the Sommerfeld integration path. The half-space extraction part is calculated by numerical integration along the vertical branch cuts. The surface electric fields for stratified media using half-space extraction and higher order asymptotic extraction are in good agreement. To validate the accuracy of the solution, we also compute the impedance matrix elements using surface electric fields, testing, and basis functions all in the spatial domain. The results are then compared with the results of the spectral domain method. The comparisons of the complex impedance matrix elements are tabulated and show that the difference is less than 2%.

Efficient analytical evaluation of the asymptotic part of Sommerfeld type reaction integrals in microstrip/slot structures

An asymptotic extraction technique has been developed for the efficient evaluation of infinite 2D spectral integrals of the method of moments matrix. Analytical, closed form expressions for the asymptotic part of the xx submatrix elements are obtained by evaluating the spectral integrals in the space domain. The xy submatrix is expressed in the form of smooth, 1D finite integrals. These expressions allow fast evaluation with improved accuracy and reliability of the asymptotic contribution for piecewise sinusoidal expansion and test functions. The input impedance of an aperture-coupled microstrip patch antenna is presented, to determine the speed-up factor associated with efficient evaluation of integrals. The technique presented can be used for other expansion functions also if they can be expressed as a polynomial function (e.g. spline functions).

Computation of the capacitance matrix of manhattan geometry planar conductors embedded in multilayered substrates

In this paper we propose an efficient technique for computation of the capacitance matrix of a set of infinitely thin conductor patches embedded in a multilayered medium. The patches present a manhattan-type shape, i.e., they can be subdivided into a finite number of rectangular regions. The generalized biconjugate gradient method (GBGM) in conjunction with FFT algorithms, is adapted to solve the convolution integral equation governing the free-charge density distribution on the conductors. Important computational improvements are achieved by including asymptotic extraction techniques in the determination of the space domain periodic Green's functions. The analysis is also applied to the quasistatic modelling of some microstrip discontinuities. © 1998 John Wiley & Sons, Inc. Int J RF and Microwave CAE 8: 386–397, 1998.