Analysis of the Propagation in High-Speed Interconnects for MIMICs by Means of the Method of Analytical Preconditioning: A New Highly Efficient Evaluation of the Coefficient Matrix

Mario Lucido

doi:10.3390/app11030933

Abstract

The method of analytical preconditioning combines the discretization and the analytical regularization of a singular integral equation in a single step. In a recent paper by the author, such a method has been applied to a spectral domain integral equation formulation devised to analyze the propagation in polygonal cross-section microstrip lines, which are widely used as high-speed interconnects in monolithic microwave and millimeter waves integrated circuits. By choosing analytically Fourier transformable expansion functions reconstructing the behavior of the fields on the wedges, fast convergence is achieved, and the convolution integrals are expressed in closed form. However, the coefficient matrix elements are one-dimensional improper integrals of oscillating and, in the worst cases, slowly decaying functions. In this paper, a novel technique for the efficient evaluation of such kind of integrals is proposed. By means of a procedure based on Cauchy integral theorem, the general coefficient matrix element is written as a linear combination of fast converging integrals. As shown in the numerical results section, the proposed technique always outperforms the analytical asymptotic acceleration technique, especially when highly accurate solutions are required.

Highlights

The latest advances in the development of integrated circuit technology have increased the attractivity of microstrip transmission lines for the realization of high-speed interconnects in monolithic microwave and millimeter waves integrated circuits (MIMICs)
In order to search for the solution of an integral equation which cannot be expressed in a closed form, a discretization scheme has to be provided
Denotes the wavenumber in medium l, where k0 = ω ε 0 μ0 = 2π/λ0 is the free-space wavenumber in vacuum, ω is the angular frequency, ε 0 and μ0 are the dielectric permittivity and the magnetic permeability of vacuum, respectively, and λ0 is the wavelength in vacuum

Summary

Introduction

The latest advances in the development of integrated circuit technology have increased the attractivity of microstrip transmission lines for the realization of high-speed interconnects in monolithic microwave and millimeter waves integrated circuits (MIMICs). A classical way to overcome this problem is the extraction of suitable asymptotic contributions from the integrands, such that the integrals of the extracted contributions can be expressed in closed form [33,34,35] Such a technique leads to accelerated integrands with a faster but still algebraic decay, and it does not modify the asymptotic oscillating behavior of the integrands themselves. Following the same line of reasoning, in this paper, a new fast-converging expression for the improper integrals of oscillating and slowly decaying functions, arising from the analysis of the propagation in polygonal cross-section microstrip lines when an EFIE formulation in the spectral domain is discretized by means of MAP, is provided. The comparisons between the presented technique and the analytical asymptotic acceleration technique (adopted in Ref. [16]) provided in Section 4 clearly state that the technique proposed in this paper always outperforms the analytical asymptotic acceleration technique, especially when highly accurate results are required

Background

Fast Evaluation of the Matrix Coefficients

Discussion

5.5.Conclusions