An Overview on Numerical Techniques for Modeling 3-Dimensional Passive Components

Abstract

A number of numerical techniques are described for the analysls of passive components. Fundamental concepts and typical applications are presented and discussed . A list of references is included for representative works reported in literature. INTRODUCTI ONAlthough numerical and analytical, if possible, characterizations and modelings of miniaturized passive components have been exercised by a large number of researchers and engineers for some time; the necessity of such activities are increasingly important in recent years. This is in line with increased research and development in the millimeter-wave circuits and the monolithic integrated circuits. It is no longer economical or, in many cases not even feasible, to tune the circuits once they are built. Therefore, extremely accurate characterization methods are needed to model the structures.Since most structures used in today's printed and planar integrated circuits are not amenable to closed form analytical expressions, the numerical methods needed for characterizations are in fact a necessary evil. The circuit designers would like to use CIO packages which in most cases consist of curve-fitting or empirical formulas. However, these formulas must be backed up by accurate characterizations. In addition, any numerical methods for characterizations need to be as efficient as possible both in CPU time and temporary storage requirement, although recent rapid advances in computers impose less severe restrictions on the efficiency of the method. AMother effort in the development of numerical methods has been the versatility of the method. In reality, however, choice of the numerical methods is the product of trade-off between accuracy, speed, storage requirement, versatility, etc. and is quite structure dependent.Since the advent of microwave integrated circuits, a number of methods have been invented in addition to the somewhat more classical methods refined for these modern structures. SURVEY OF NUMERICAL METHODSWhen a specific structure is analyzed, one has to make a choice of the method best suited for the structure. Obviously, the choice is not unique. Therefore, the user must make a critical assessment for each candidate method. In this paper, we list a number of numerical methods and present geherally accepted appraisals for these methods. It is not possible to make an exhaustive list of all available methods. Rather, most representative ones are reviewed. Although the assessment will be aimed at the characterization of passive components, 3-dimensional structures, many methods are also effective for 2-dimensional problems. Fur-1059 ther, 2-dimensional methods can be used in an integral part of the composite characterization program.(1) Finite difference method [I] This method is well known to be the least analytical. The mathematical preprocessing is minimal and the method can be applied to a wide range of structures. Certain precalutions have to be taken into account when the method is used for an open region problem.(2) Finite element method [2][3][4][5...

Application of the Spectral Domain Approach and the Modal Analysis to Three Dimensional Discontinuity Problems

“…(4p2+w)2U0%er/32) fjzji I =0o (1) 2 d d with VT = a +t 2 dx dy and they have to verify the boundary conditions (periodicity, synumetry, ...etc) and the continuity conditions for their tangential components (zero tangential electric field at the dielectric-conductor interface, and equal electric and magnetic tangential fields at the interface between two different dielectrics). Once the eigen values kn are d%termined, at a given frequencyc,the eigen function Ez i and Hz,i can be determined from Maxwell's equations.…”

“…Many different methods of solution for these discontinuities have been suggested during the past 40 years and an overview on many of these methods are given in [1]. While, in general, some degree of approximation must be made in most of these methods, the Modal Analysis [2,3] provides an exact solution involving straightforward calculations which can easily be applied to a wide variety of structures.…”

Characterization of microstrip antennas using the TLM simulation associated with a Prony‐Pisarenko method

“…The ai yield the absorption coefficients (Yk and the resonant frequency f k in equation (1). zl, z2, .…”

Variational nonquasi-static formulations for the impedance of planar transmission lines

“…Excellent reviews of those methods can be found in [1] and [2]. Many of them explicitly or implicitly use the variational behavior of a parameter or a functional.…”

“…In both cases, the variational form is formulated either in the spatial domain or in the Fourier-transformed domain [8], using for this, the spectral-domain approach presented in [9] and [10]. To the best of our knowledge, and restricting our study to transmission-line parameters, implicit or explicit variational formulations exist only for propagation constants [1], [6], [8] and quasi-TEM inductances [11] or capacitances [12], [13], yielding values for the characteristic impedance under the restrictive quasi-transverse-electromagnetic (TEM) assumption. Such principles are missing for the characteristic impedance of nonquasi-TEM structures.…”