Two approximation methods for wiring delay in MOS LSI are studied. One is analytical and the other is a lumped circuit approximation. The basic model for wiring is a distributed CR line with a drive MOSFET at one end and a capacitive load at the other end. Simple approximated formulas for the delay and the step response of this model are obtained. Approximation of a distributed CR line by lumped Rs and C's combination, which is very useful when incorporated in circuit simulation programs, is also investigated. The widely used L ladder circuit model is found to be a poor approximation, while /spl pi/ and T ladder circuit models give satisfactory results. The simplest circuits that approximate the interconnection line within a given tolerant error are tabulated under various drive and load conditions.

Approximation of wiring delay in MOSFET LSI

The purpose of this paper is to provide an insight into low frequency divergent noises with spectral density |f|?, where ? ? -1, and into their effect on physical measurements, with special reference to 1/|f| noise. This class of noise is widespread in nature, and it presents unique limitations to the measurement accuracy. In an attempt to present a picture of this class of noise with regard to the measurements of observable physical quantities, the questions about generation of noise, its divergence, correlation properties and measurements of variance are discussed. A statistical model for generation of low frequency divergent noises is used to consider the divergence problem in both the frequency and time domain. It is shown that 1/|f| noise is "weakly divergent," and that power limitation presents no reason to impose a low frequency limit within time intervals observable in nature. Correlation properties are discussed in terms of the time-dependent correlation function, using an ideal impulse response which generates low frequency noise from white noise. Two general models for generation of 1/|f| noise are summarized and discussed. Generation of 1/|f| noise from white noise over a limited frequency range by distributed and lumped-parameter filters is described. It is shown that the variance (i.e. mean square noise) is determined by the frequency limits of the observation method.

1/|f| Noise in Physical Measurements

http://www.ecole.ensicaen.fr/~chateign/pdf/TSF515_2943.pdf

Structural properties of cobalt ferrite thin films deposited by pulsed laser deposition: Effect of the reactive atmosphere

The traditional analysis of signal delay in a transmission line begins with a lossless LC representation, which yields a wave equation governing the system response; 2-port parameters are typically derived and the solution is obtained in the transform domain. In this paper, we begin with a distributed RC line model of the interconnect and analytically solve the resulting diffusion equation for the voltage response. A new closed form expression for voltage response is obtained by incorporating appropriate boundary conditions for interconnect delay analysis. Calculations of 50% and 90% delay times for various cases of interest (e.g., open-ended RC line) give substantially different estimates from those commonly cited in the literature, thus suggesting revised delay estimation methodologies and intuitions for the design of VLSI interconnects. The discussion furthermore provides a unifying treatment of the past three decades of RC interconnect delay analyses.

/pdf/delay-analysis-of-vlsi-interconnections-using-the-diffusion-1p2g02r6eq.pdf

Delay Analysis of VLSI Interconnections Using the Diffusion Equation Model

We present a general and, in the limit, exact approach to compute the time-domain response for finite-length RC lines under ramp input, by summing distinct diffusions starting at either end of the line. We also obtain analytical expressions for the finite time-domain voltage response for an open-ended finite RC line and for a finite RC line with capacitive load. Delay estimates using our new method are very close to SPICE-computed delays. Finally, we present a general recursive equation for computing the higher-order diffusion components due to reflections at the source and load ends. Future work extends our method to response computations in general interconnection trees by modeling both reflection and transmission coefficients at discontinuities.

/pdf/analysis-of-rc-interconnections-under-ramp-input-4cck1qpcqj.pdf

Analysis of RC interconnections under ramp input

Transient analysis for uniform RC structures is considered in this paper A method is presented for determining the parameters of such structures The measurements are obtained using impulse excitations in open‐circuit and short‐circuit configurations The theoretical results obtained predict fairly the experimental results

Robert C. Peirson

Papers

Time-Domain Analysis and Measurement Techniques for Distributed RC Structures. II. Impulse Measurement Techniques