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

a a a 1-Abstract This thesis presents a new CAD simulation method for determining waveform estimates of MOS circuits. The methods are particularly useful in determining the delay times and coupling noise voltages of interconnection networks. Additionally, switching devices are also accurately emulated with a macromodeled equivalent circuit. The moment representation, based on the Laplace Transform, is used as the model for both signals and transfer functions of interconnection networks. A large interconnection network can be modeled by a small number of polynomial terms, making network analysis much simpler, computationally. A new matrix algorithm is developed for solving for the moment representation of almost any linear network. Transistor switching circuits are modeled by macromodeled linear network equivalents. On CMOS test circuits, after several logic stages the moment representation waveforms deviated no more than 10% from SPICE's waveforms, but were computed substantially faster than SPICE. The simulation speed is further improved by "compiling" results, in which an entire switching and interconnection circuit is represented by a macromodeled moment representation approximation. Thesis Supervisor: Jonathan Allen Professor 3 4 IF __ _ _ __ dir 00 Acknowledgments First, I would like to thank Jonathan Allen, my advisor, for his inspiration and encouragement , and for providing the flexibility to define my own work as it progressed. Thanks also to my thesis readers, John Wyatt and Jacob White, for actually reading all 182 pages and for providing good feedback. I thank my friends-particularly Keith Nabors, Andy Ayers and Don Baltus, who expressed occasional interest in this work, and Bob Armstrong, Cyrus Bamji, Barry Thompson and Mark Reichelt, who have been around on the eighth floor through the whole thing. I also thank Dorothy Fleischer. Mostly, I thank my wife, Lynne, for three things: her technical assistance in the form of the work frequently cited in Chapter 6, her emotional support, and her patience as I strived to make this thesis as good as possible. Lastly, I gratefully acknowledge my sponsor, the Joint Services Electronics Program, for supporting this research.

Modeling and simulation of VLSI interconnections with moments

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

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

With the advances of the solid state art and the thin film technique, numerous structures and devices have been developed which essentially are distributed parameter ones. The passive distributed parameter structures possess extremely valuable properties. However, the tools available for analysis and synthesis of these structures are inadequate. A comprehensive review is presented of the modeling attempts made so far.

Modeling of distributed lossless and lossy structures — A review

A new measurement technique for RC delay on distributed RC interconnection lines is presented using step voltage excitation. A circuit for RC delay measurement, called CIRCDEM, is proposed. This circuit can provide the RC product measurement of interconnection lines and the RC time delay to switch a gate connected to the end of the line. The interconnection resistance and the parallel-plate capacitance were also obtained by means of measurements on a cross-bridge sheet-resistor test structure and a field MOS capacitor, respectively. The values of R and C obtained from these structures are in accordance to the RC product obtained by means of CIRCDEM when the correction of the edge effect of the interconnection capacitance is taken into account. >

An experimental measurement technique of interconnection RC delay for integrated circuits using the step voltage response

The impulse response in distributed‐parameter systems results in a spectrum of delta functions in the time domain for LC structures. It is shown that for RC structures the impulse response results in a spectrum of Poisson‐derived functions in the reciprocal time domain. This isomorphism is exploited for the analysis of RC devices to establish a calculus of Poisson‐derived functions and a transform technique which is essentially the Laplace transform. Applications of this technique to thin‐film devices and minority‐carrier devices are examined and lead to the determination of the transient response for one‐ports and two‐ports that are subject to a wide range of terminations. Illustrative examples of excitations include the impulse, the step, and the ramp, as well as signals generated by the distributed parameter devices themselves. Significant advantages accrue from a spectral description of RC devices in the reciprocal time domain: (1) conceptual, by establishing a physical interpretation based on diffusion phenomena; (2) analytical, by developing a systematic approach to transients paralleling the network function approach in the frequency domain; (3) computational, by expressing the response by a rapidly converging spectrum of functions.

W. W. Happ

Papers

Time‐Domain Analysis and Measurement Techniques for Distributed RC Structures. I. Analysis in the Reciprocal Time Domain