Asymptotic Extraction Technique Research Articles

Dispersion characteristics of open microstrip lines using closed-form asymptotic extraction

A full-wave spectral-domain method with an asymptotic extraction technique is formulated for multilayer microstrip lines. This formulation provides a simple closed-form representation of the asymptotic part of the impedance matrix by using Chebyshev polynomial basis functions with the square-root edge condition and the asymptotic behaviour of the Green's function. The formulation is applied to open microstrip lines. Numerical results, in the form of the effective dielectric constants, are presented for the dominant mode. It is shown that the proposed method significantly reduces the computational time and improves the accuracy over the conventional spectral-domain approach (SDA).

Ultra‐wideband electromagnetic pulse propagation in a homogeneous, cold plasma

In this paper, we investigate the propagation of an ultra‐wideband electromagnetic pulse in a homogeneous, cold plasma which is used to represent a simplified model of the atmosphere. The standard procedure for the computation of the corresponding transient field involves the application of a fast Fourier transform (FFT) to a well‐known, analytical, frequency‐domain solution. However, because of the long tails in both the time and frequency domains, a large number of sample points are required to compute the transient response using this FFT approach. In this paper, we introduce a new asymptotic extraction technique which dramatically reduces the number of sample points required by the FFT. First, we review the recently derived closed‐form expression for a double‐exponential pulse propagating in a homogeneous, collisionless, cold plasma. Since the high‐frequency behavior does not depend on the electron collision frequency, an analytical frequency‐domain expression, which is similar in form to the one encountered for the collisionless, cold plasma and encompasses this high‐frequency behavior, can be subtracted from the exact expression for the plasma with a nonzero collision frequency. The extracted term is evaluated analytically. The remaining expression, which can be transformed to the time domain with a FFT, requires only a modest number of sample points. This dramatically improves the numerical efficiency of the approach. We find that the extracted analytical term provides a very good approximation for the early‐time behavior of the transient pulse.

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.

Quasi‐tem analysis of thick multistrip lines using an efficient iterative method

AbstractAn efficient iterative technique—the generalized biconjugate gradient method (GBGM)—is extended to the quasi‐TEM treatment of multi‐conductor multilayered thick‐strip MIC and MMIC transmission lines. A new simple model is proposed to account for finite thickness metallizations having rectangular and trapezoidal cross sections. The convergence of the model is analyzed. Asymptotic extraction techniques are introduced to work out the spatial Green's function. © 1992 John Wiley & Sons, Inc.

An improved iterative technique for the quasi-TEM analysis of generalized planar lines

The generalized bioconjugate gradient method (GBGM) and fast Fourier transform (FFT) algorithm are used for the quasi-transverse electromagnetic (TEM) analysis of generalized multistrip lines embedded in multilayered lossless/lossy, iso/anisotropic dielectric and/or magnetic media. Important computational improvement is achieved by including asymptotic extraction techniques in the determination of the spatial Green's function matrix. Comparisons with other iterative procedures are presented. Several practical structures are analyzed and numerical results are compared with previously published data. >

Numerical computation of 2D sommerfeld integrals— A novel asymptotic extraction technique

The accurate and efficient computation of the elements in the impedance matrix is a crucial step in the application of Galerkin's method to the analysis of planar structures. As was demonstrated in a previous paper, it is possible to decompose the angular integral, in the polar representation for the 2D Sommerfeld integrals, in terms of incomplete Lipschitz-Hankel integrals (ILHIs) when piecewise sinusoidal basis functions are employed. Since Bessel series expansions can be used to compute these ILHIs, a numerical integration of the inner angular integral is not required. This technique provides an efficient method for the computation of the inner angular integral; however, the outer semi-infinite integral still converges very slowly when a real axis integration is applied. Therefore, it is very difficult to compute the impedance elements accurately and efficiently. In this paper, it is shown that this problem can be overcome by using the ILHI representation for the angular integral to develop a novel asymptotic extraction technique for the outer semi-infinite integral. The usefulness of this asymptotic extraction technique is demonstrated by applying it to the analysis of a printed strip dipole antenna in a layered medium.

Numerical computation of 2D sommerfeld integrals— Deccomposition of the angular integral

Spectral domain techniques are frequently used in conjunction with Galerkin's method to obtain the current distribution on planar structures. When this technique is employed, a large percentage of the computation time is spent filling the impedance matrix. Therefore, it is important to develop accurate and efficient numerical techniques for the computation of the impedance elements, which can be written as two-dimensional (2D) Sommerfeld integrals. Once the current distribution has been found, then the near-zone electric field distribution can be obtained by computing another set of 2D Sommerfeld integrals. The computational efficiency of the 2D Sommerfeld integrals can be improved in two ways. The first method, which is discussed in this paper, involves finding a new way to compute the inner angular integral in the polar representation of these integrals. It turns out that the angular integral can be decomposed into a finite number of incomplete Lipschitz-Hankel integrals, which in turn can be calculated using series expansions. Therefore, the angular integral can be computed by summing a series instead of applying a standard numerical integration algorithm. This new technique is found to be more accurate and efficient when piecewise-sinusoidal basis functions are used to analyze a printed strip dipole antenna in a layered medium. The incomplete Lipschitz-Hankel integral representation for the angular integral is then used in another paper to develop a novel asymptotic extraction technique for the outer semi-infinite integral.

Numerical computation of 2D Sommerfeld integrals—A novel asymptotic extraction technique

Numerical computation of 2D Sommerfeld integrals—A novel asymptotic extraction technique

Quasi-TEM analysis of the generalized microstrip line by using FFT and iterative methods

A quasi-TEM analysis of a generic microstrip line is carried out by the combined use of iterative methods and FFT. Asymptotic extraction techniques are used in the determination of the Green's function, allowing reduction of memory storage requirements and CPU time. Several iterative algorithms are compared for solving the final system of convolution linear equations. Numerical results are presented and compared with published data.

A new method for computing the reaction between two rooftop basis functions in a planar structure

Accurate and efficient techniques are developed for computing spectral domain reaction integrals involving rooftop basis functions. Representing the angular integral in terms of special functions not only reduces the two-dimensional integration by one dimension, but it also leads to the development of a novel asymptotic extraction technique.