An overview of standard macromodeling techniques (i.e., employ poles but no phase shifts) for transient simulation of high-speed interconnects is first presented. Then, the limitations of these standard macromodeling techniques (e.g., high model order and slow convergence) are discussed. In order to overcome these limitations, generalized method of characteristics (MoC) techniques include the physical phenomenology of phase shift (time delay) in addition to the system poles, thereby making it possible to model single and coupled transmission lines using far fewer terms than when standard macromodeling techniques are employed. Since MoC techniques incorporate the time delay into the model, causality is also guaranteed. In this paper, the MoC idea is extended by developing a hybrid phase-pole macromodel (HPPM) for the modeling of more complex interconnects with embedded discontinuities. Unlike other generalized MoC techniques that have only been applied to single and coupled transmission lines, the HPPM macromodel can be applied to larger portions of the system that contain multiple cascaded transmission lines and discontinuities. The HPPM parameters can be extracted from either measured or simulated transient data. Comparisons between a standard macromodel and the HPPM show that the HPPM has significant advantages in terms of reduced macromodel orders.

Analytical frequency-domain expressions for single and coupled transmission lines with triangular input waveforms are first developed. The inverse Fourier transform is then used to obtain an expression for the time-domain triangle impulse responses for frequency-independent transmission line parameters. The integral associated with the inverse Fourier transform is solved analytically using a differential-equation-based technique. Closed-form expressions for the triangle impulse responses are given in the form of incomplete Lipschitz-Hankel integrals (ILHI) of the first kind. The ILHI can be efficiently calculated using existing algorithms. Combining these closed-form expressions for the triangle impulse responses with a time-domain convolution method using a triangle impulse as a basis function, provides an accurate and efficient simulation method for very lossy transmission lines embedded within linear and nonlinear circuits.

The authors explore the use of S-parameter-based network techniques for the analysis of coupled, multiconductor, high-speed analog and digital integrated circuit interconnects. S-parameter-based computer-aided design (CAD) techniques, widely used in microwave network analysis, provide a powerful framework for the analysis of analog and digital integrated circuit interconnect systems. The specific additions to the existing S-parameter network analysis framework developed provide for multiport interconnect capabilities and for the use of multiconductor S-parameters derived from three categories of input parameters: (1) lossy quasi-static R,L,C and G; (2) lossy frequency-dependent (dispersive) R,L,C,G; and (3) the propagation constants, characteristic impedance, and conductor eigencurrents, derived from full-wave electromagnetic analysis. Results are compared with computed simulations and experimental measurements.>

A software shell for assisting in VLSI package design is discussed. Called packaging design support environment (PDSE), the shell integrates tools for modeling and simulation of electrical characteristics of VLSI packages. Parameter extractors tools calculate inductance and capacitance for multiconductor, multidielectric, two-dimensional structures with loss dielectrics. The simulation tools compute pulse response characteristics of uniform, multiple, coupled, and lossless transmission lines. The PDSE shell provides facilities for supporting the package design cycle. Such support facilities include an interface to couple PDSE with a CAD design database, model and simulation experiment libraries, simulation management procedures that guide evaluation of alternative design models, and data analysis support tools. Expert systems techniques are being incorporated into PDSE.>

Interpreting uncertain information, a fundamental requirement of many computer vision and pattern recognition systems is commonly supported by models of the uncertainty. Evidence theory, also called Dempster-Shafer theory, is particularly useful for representing and combining uncertain information when a single precise uncertainty model is unavailable. A framework is presented for deriving and transforming evidence-theoretic belief representations of uncertain variables that denote numerical quantities. Belief is derived from probabilistic models using relationships between probability bounds and the support and plausibility functions used in evidence theory. This model-based approach to belief representation is illustrated by an algorithm currently used in a vision system to label anomalous high-intensity pixels in imagery. As the uncertain variables are manipulated to form features and object discriminants, the belief representation of the uncertain variables must be transformed accordingly. Belief transformations, analogous to the transformation of probability-density functions in mappings of random variables, are derived to maintain the same rigorous belief representation for computed quantities. The results demonstrate novel ways to address uncertainty in the use of sensor information, and contribute to understanding of the similarities and distinctions of probability theory and evidence theory.>

A simulation environment for prediction of electrical characteristics of integrated circuit packaging structures is described. The simulation shell, Packaging Design Support Environment (PDSE), integrates tools for modeling and simulation of electrical characteristics in VLSI packages. It also provides facilities for supporting design of VLSI packages. Two simulation tools model inductance and capacitance for multiconductor, multidielectric, two-dimensional structures with lossy dielectrics. Another accepts the L and C matrices and computes pulse response characteristics of uniform multiple, coupled, lossless transmission lines which are terminated at discrete points with R, L, and C elements. The design process in PDSE proceeds in three major phases: modeling, simulation, and evaluation. These processes are interactive and allow the designer to refine a design model, modify simulation experiments, and apply various evaluation processes.>

The authors present techniques for the analysis of signal propagation in the interconnections used in VLSI systems. The propagation is modelled by coupled transmission lines which include losses. For conductors whose thickness is small compared to the skin depth over the principal spectrum of the pulse being propagated, the losses can be treated as frequency-independent; otherwise, the losses must be calculated as a function of frequency. It was observed that the inductance may be approximately treated as constant, but the resistance variations in frequency may be significant. A semi-analytical method for computing the transients in lossy lines serves as the basis for the simulation of nonuniform lines.>