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The vector-fitting algorithm has been used as the main macromodeling tool for approximating frequency domain responses of complex interconnects and electrical packages [Gustavsen and Semlyen, 1999]. In this paper, a new methodology is proposed to fit transfer functions of frequency response data obtained from numerical electromagnetic simulation or measured frequency-domain or time-domain response...
The paper is concerned with the simulation of signal propagation on low-loss highly inductive interconnect. The analytical solution of the output voltage signal is derived by solving the transmission line model of interconnect with multiple scales perturbation method of differential equation solving. The usefulness and limitations of the method are considered and some practical examples are presented.
The impact of data-pattern variation on timing for on-chip interconnect timing is investigated for typical local, global, and clock wiring. The validity of the methodology to combine noise and timing engines is benchmarked against accurate non-linear simulations with R(f)L(f)C circuit representation and recommendations for CAD tool development are given.
With the advent of nanoscale technologies, even RTL and system designers must consider interconnect analysis to provide predictable performance, reliability and meet power budgets. However, system-wide modeling of high-speed interconnects using conventional circuit simulators such as SPICE can become prohibitively CPU expensive. We propose to formulate analytical interconnect macromodels capturing...
In previous papers we presented MOR (model order reduction) methods based on the construction of a Gram matrix subsequent to a decomposition in Laguerre series. In this paper we propose an alternative solution using Kautz series, more adequate for modeling poorly damped systems.
This paper introduces a new approach for rational macromodeling of multiport devices that ensures high accuracy with arbitrary terminal conditions. This is achieved by reformulating the vector fitting technique to focus on eigenpairs rather than matrix elements. By choosing the least squares weighting equal to the inverse of the eigenvalue magnitude is achieved that the eigenvalues are fitted with...
Introduction of different low-K to ultra low-K dielectric material in the spacing between neighbour copper interconnects localised on the same level of metallization is analyzed. It is done to evaluate signal integrity such as crosstalk, propagation delay and rise time on a set of several unintentionally coupled Cu lines of micron and nanometer sizes. A full wave analysis based on tangential vector...
Vector fitting is a rational approximation technique, which is frequently used to calculate accurate macromodels of electrical and electronical structures. The robustness of the technique is obtained by combining the use of a weighted iterative least squares scheme and a well-chosen partial fraction basis. It was discussed in that numerical problems may occur if poles of higher-order multiplicities...
This paper addresses the problem of scaling interconnects to nanometric dimensions in future VLSI applications. Traditional copper interconnects are compared to innovative ones made by bundles of metallic carbon nanotubes. A new model is presented to describe propagation along CNT bundles, in the framework of the classical transmission line theory. A possible future scaled CNT bundle microstrip is...
Practical methods of making use of measured twinax cable S-parameters for transient circuit simulations are discussed and compared. Due to extremely long delay of the cable, most available tools fail or give inaccurate simulation results if we use the measured S-Parameters directly. Careful verification is absolutely necessary for any tool. For complex tasks like the worst-case eye diagram with nonlinear...
The use of current methods of length matching in differential microstrip transmission lines when used with data-rates up to 15 GHz is explored. It is shown that using current methods of length matching could make worse mode conversion and EM loss than with no length matching at all. A new method is suggested whereby interconnect geometry can be engineered to match the length of a pair at a specific...
Passivity must be enforced on rational macromodels in order to ensure a stable time domain simulation. This paper investigates procedures for enforcing passivity for transmission line models based on the method of characteristics. Adding a conductive correction term externally to the line terminals is shown to be a robust and simple procedure for ensuring a passive model. The perturbation of the line...
The paper deals with methodology to analyze electromagnetic (EM) leakages from connectors shielding due to the presence of apertures and slots. Some experimental and numerical results will be proposed to evaluate the electromagnetic coupling between connector apertures and a PCB trace line in terms of current and voltage induced on the line.
Voids on reference planes are commonly seen in organic chip packages and printed circuit boards. In this paper, the effects of these voids on the signal integrity of a high-density data bus will be studied. A generic FCPBGA chip package is used to illustrate the signal integrity concerns and perform sensitivity analysis on the key mechanisms including void size, adjacent plane interactions, and adjacent...
For accurate RLCG-parameter extraction the measured S-parameter matrix needs to be converted to the Z-matrix. However, there exist three different definitions of S-parameters and consequently three different formulas of converting S-matrix into Z-matrix. In this article, we present an overview of existing S-parameters definitions and examine the uncertainties associated with the S-matrix to Z-matrix...
Special test vehicles have been built for first and low loss second level packages including product related test line structures. The characteristic transmission line parameters were measured in the time and in the frequency domain in a wide frequency range. Advantages and limitations of the different methods are discussed by comparing the obtained results.
SEM photographs of a typical copper conductors prepared by the PCB industry exhibit a 3-D "snowball" structure of copper surface distortions. We have developed an analytical basis for the electromagnetic scattering by the copper "snowballs" to predict additional power losses to those presented by the propagating medium that compare well with the observed measurements for a set...
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