Semi-analytic slope delay model for CMOS switch-level timing verification

A novel slope delay model for CMOS switch-level timing verification is presented. It differs from conventional methods in being semianalytic in character. The model assumes that all input waveforms are trapezoidal in overall shape, but that they vary in their slope. This simplification is quite reasonable and does not seriously affect precision, but it facilitates rapid solution. The model divides the stages in a switch-level circuit into two types. One corresponds to the logic gates, and the other corresponds to logic gates with pass transistors connected to their outputs. Semianalytic modeling for both cases is discussed.

Switch-level timing verification for CMOS circuits. A semianalytic approach

The paper describes a semianalytic slope delay model for CMOS switch-level timing verification. It is characterised by classification of the effects of the input slope, internal size and load capacitance of a logic gate on delay time, and then the use of a series of carefully chosen analytic functions to estimate delay times under different circumstances. In the field of VLSI analysis, this model achieves improvements in speed and accuracy compared with conventional approaches to transistor-level and switch-level simulation.

Hierarchical approach to timing verification in CMOS VLSI design

This paper describes a novel hierarchical approach to timing verification. Four types of relationship existing among signal paths are distinguished, based on a classification of the degree of interdependency in the circuit. In this way, irrelevant path delays can be excluded through consideration of the interaction between critical paths and others. Furthermore, under suitable conditions, bounded delay values for large hierarchical systems can be deduced using bounded delays determined for their constituent cells. Finally, we discuss the impact on design strategy of the hierarchical delay model presented in this paper.

Jet diameters and velocity profiles in continuous ink-jets

Theoretical predictions of the diameters of continuous ink-jets downstream of long nozzles are generalized to include the important cases of ink-jet fluids and shorter nozzles where the velocity profile at the nozzle exit is undeveloped (non-parabolic). Comparisons of the new predictions with experiments and simulations are made for fairly long nozzles with tapered profiles and short nozzles with conical profiles; experimental and simulated profiles are also compared downstream of the nozzle exit for both industrial and large scale ink-jet print heads. Precise measurements of the un-modulated jet diameters downstream of the nozzle exit can set really useful limits to the possible shapes of the flow profile right at the nozzle exit, and in particular allow some assessment of the axial velocity gradients and fluid shear rates at the nozzle exit where direct speed measurement is usually impractical. Simulations allow further study of the relaxation of the velocity profile downstream of the nozzle exit, and are reported for both un-modulated and modulated CIJ jetting. Implications of this work include speeding up CIJ simulations, absolute calibration of the applied CIJ system modulation, and the likely magnitude of dynamic surface tension effects on observed CIJ satellite speeds.

Forward Smoothing Using Sequential Monte Carlo

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively. Essentially, it is an on-line or "forward only" implementation of a forward filtering backward smoothing SMC algorithm proposed by Doucet, Godsill and Andrieu (2000). Compared to the standard \emph{path space} SMC estimator whose asymptotic variance increases quadratically with time even under favorable mixing assumptions, the non asymptotic variance of the proposed SMC estimator only increases linearly with time. We show how this allows us to perform recursive parameter estimation using an SMC implementation of an on-line version of the Expectation-Maximization algorithm which does not suffer from the particle path degeneracy problem.

A backward particle interpretation of Feynman-Kac formulae

We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals "on-the-fly" as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We provide uniform convergence results with respect to the time horizon parameter as well as functional central limit theorems and exponential concentration estimates. Our results have important consequences for online parameter estimation for non-linear non-Gaussian state-space models. We show how the forward filtering backward smoothing estimates of additive functionals can be computed using a forward only recursion.