We present a numerical modeling and simulation paradigm for multidomain, multiphysics systems with components modeled both in a lumped and distributed manner. The lumped components are modeled with a system of differential-algebraic equations (DAEs), whereas the possibly nonlinear distributed components that may belong to different physical domains are modeled using partial differential equations (PDEs) with associated boundary conditions. We address a comprehensive suite of problems for nonlinear coupled DAE-PDE systems including 1) transient simulation; 2) periodic steady-state (PSS) analysis formulated as a mixed boundary value problem that is solved with a hierarchical spectral collocation technique based on a joint Fourier-Chebyshev representation, for both forced and autonomous systems; 3) Floquet theory and analysis for coupled linear periodically time-varying DAE-PDE systems; 4) phase noise analysis for multidomain oscillators; and 5) efficient parameter sweeps for PSS and noise analyses based on first-order and pseudo-arclength continuation schemes. All of these techniques, implemented in a prototype simulator, are applied to a substantial case study: a multidomain feedback oscillator composed of distributed and lumped components in two physical domains, namely, a nano-mechanical beam resonator operating in the nonlinear regime, an electrical delay line, an electronic amplifier and a sensor-actuator for the transduction between the two physical domains.

Modeling and analysis of low-frequency noise, such as 1/f and burst noise, with time-varying bias conditions is a long-standing open problem in circuit simulation. In this paper, we offer a solution for this problem and present a computational model for low-frequency noise. The merits of our model are twofold. First, it is fully nonstationary. It can represent noise processes with time-varying statistics that are tightly coupled to the circuit variables in a stochastically correct manner. Second, its mathematical structure allows the utilization of well-established, non-Monte Carlo noise analysis techniques which are orders of magnitude faster than their Monte Carlo counterparts. We first provide an overview of our noise model along with the legacy modeling techniques. We verify that, when used with fast non-Monte Carlo analysis methods, our noise model produces results with the same accuracy as computationally laborious Monte Carlo simulations. We then proceed to contrast our nonstationary noise model with the legacy modulated stationary model. As a typical instance, where the results produced by these two models differ significantly due to intricate nonstationary behavior, we analyze the switched biasing technique that was proposed in order to reduce low-frequency noise. As a case study, we examine the 1/f noise behavior in the previously proposed coupled sawtooth oscillator circuit and show that, whereas simulations conducted with the legacy modulated stationary model suggest that no noise reduction is obtainable with switched biasing, our nonstationary noise model predicts the correct amount of noise reduction observed in previously published experimental data.

Stochastic behavior of ion channels, neurotransmitter release mechanisms and synaptic connections in neurons emerge as a source of variability and noise in neuronal circuits, causing uncertainty in the computations performed by the brain. One can gain insight into this important aspect of brain mechanism via computational modeling. Stochastic behavior in neurons is usually modeled with fine-grained, discrete-state, continuous-time Markov Chains (MCs). Although these models are considered as the golden standard, they become computationally prohibitive in analyzing multi-neuron circuits. Thus, several approximate models, where the random behavior is captured by coarse-grained, continuous-state, continuous-time Stochastic Differential Equations (SDEs), were proposed. In this paper, we first present a general, fine-grained modeling framework based on MC models of ion channels and synaptic processes. We then develop a formalism for automatically generating the corresponding SDE models, based on representing generic/abstract MCs as a set of chemical reactions and by utilizing techniques from stochastic chemical kinetics. With this formalism, we can exploit the sparsity and special structure in the MC models and arrive at compact SDE models. We present results obtained by our neuronal circuit simulator based on the proposed methodology in analyzing stochasticity in neurons and neuronal circuits. We employ numerical simulation techniques that were previously developed for noise in electronic circuits. We point to the use of non Monte Carlo noise analysis techniques for large-scale analysis of noise in the nervous system.

Defects or traps in semiconductors and nano devices that randomly capture and emit charge carriers result in low-frequency noise, such as burst and 1/f noise, which are important concerns in the design of both analog and digital circuits. The capture and emission rates of these traps are functions of the time-varying voltages across the device, resulting in nonstationary noise characteristics. Modeling of low-frequency, nonstationary noise in circuit simulators is a long-standing open problem. It has been realized that the low-frequency noise models in circuit simulators were the culprits that produced erroneous noise performance results for circuits under strongly time-varying bias conditions. In this paper, we present two fully nonstationary models for traps, a fine-grained Markov chain model and a coarse-grained Langevin model based on similar models for ion channels in neurons. The nonstationary trap models we present subsume and unify all of the work that has been done recently in the device modeling and circuit design literature on modeling nonstationary trap noise. We provide a detailed explication of these models with regard to their stochastic properties and develop carefully crafted circuit simulation techniques that are stochastically correct. We have implemented the proposed techniques in a MATLAB-based circuit simulator, by expanding the industry standard compact MOSFET model PSP to include a nonstationary description of oxide traps. We present results obtained by this extended model and the proposed simulation techniques for the low-frequency noise characterization of a common source amplifier and the phase jitter of a ring oscillator.

Modeling and analysis of low frequency noise in circuit simulators with time-varying bias conditions is a long-standing open problem. In this paper, we offer a definite solution for this problem and present a model for low-frequency noise that captures the internal, stochastic dynamics of the individual noise sources via dedicated internal pseudo nodes that are coupled with the rest of the circuit. Our method correctly incorporates the inherent nonstationarity of low-frequency noise into the device model and the circuit simulator. It is based on a probabilistic description of oxide traps in nano-scale devices that individually cause the so-called random telegraph signal (RTS) noise, and, en masse, are believed to be the culprits of other low-frequency noise phenomena, such as 1/f and burst noise. Our model captures the dependence of noise characteristics on the state variables of the circuit. Its simple yet precise mathematical formulation allows the utilization of well-established, non Monte Carlo techniques for nonstationary noise analysis. In one embodiment that we present in this paper, the proposed noise model is used to perform frequency-domain, non Monte Carlo, semi-analytical noise evaluation for circuits under periodic large-signal excitations. For this case, we verify that the computed noise spectral densities match the ones obtained via spectral estimation from timedomain Monte Carlo noise simulation data.

We concentrate on the temporal stochastic behavior of electronic and biological systems due to mainly intrinsic noise and fluctuation phenomena as opposed to extrinsic crosstalk-like interference or statistical variations in system parameters. We provide an overview of modeling and analysis techniques for noise and fluctuation phenomena in biological systems with comparisons to electronic systems. We present several examples where a synergistic cross-fertilization between the two disciplines seems promising. In particular, we discuss the characterization of conformational fluctuations in proteins, the simulation of stochastic behavior in intracellular processes, and the modeling of noise in biological neurons, neuronal networks, nervous system and the brain.

Defects or traps in semiconductors and nano devices that randomly capture and emit charge carriers result in low-frequency noise, such as burst and 1/f noise, that are great concerns in the design of both analog and digital circuits. The capture and emission rates of these traps are functions of the time-varying voltages across the device, resulting in nonstationary noise characteristics. Modeling of low-frequency, nonstationary noise in circuit simulators is a longstanding open problem. It has been realized that the low frequency noise models in circuit simulators were the culprits that produced erroneous noise performance results for circuits under strongly time-varying bias conditions. In this paper, we first identify an almost perfect analogy between trap noise in nano devices and the so-called ion channel noise in biological nerve cells, and propose a new approach to modeling and analysis of low-frequency noise that is founded on this connection. We derive two fully nonstationary models for traps, a fine-grained Markov chain model based on recent previous work and a completely novel coarse-grained Langevin model based on similar models for ion channels in neurons. The nonstationary trap models we derive subsume and unify all of the work that has been done recently in the device modeling and circuit design literature on modeling nonstationary trap noise. We also describe joint noise analysis paradigms for a nonlinear circuit and a number of traps. We have implemented the proposed techniques in a Matlab®based circuit simulator, by expanding the industry standard compact MOSFET model PSP to include a nonstationary description of oxide traps. We present results obtained by this extended model and the proposed simulation techniques for the low frequency noise characterization of a common source amplifier and the phase jitter of a ring oscillator.

With aggressive technology scaling and heightened variability, circuits such as SRAMs and DRAMs have become vulnerable to random telegraph noise (RTN). The bias dependence (i.e., non-stationarity), bi-directional coupling, and high inter-device variability of RTN present significant challenges to understanding its circuit-level effects. In this paper, we present two computer-aided design (CAD) tools, SAMURAI and MUSTARD, for accurately estimating the impact of non-stationary RTN on SRAMs and DRAMs. While traditional (stationary) analysis is often overly pessimistic (e.g., it overestimates RTN-induced SRAM failure rates), the predictions made by SAMURAI and MUSTARD are more reliable by virtue of non-stationary analysis.

With aggressive technology scaling and heightened variability, SRAMs and DRAMs have become vulnerable to Random Telegraph Noise (RTN). The bias-dependent, random temporal nature of RTN presents significant challenges to understanding its effects on circuits. In this paper, we propose MUSTARD, a technique and tool for predicting the impact of RTN on SRAMs/DRAMs in the presence of variability. MUSTARD enables accurate, non-stationary, two-way-coupled, discrete stochastic RTN simulation seamlessly integrated with deterministic, continuous circuit simulation. Using MUSTARD, we are able to predict experimentally observed RTN-induced failures in SRAMs, and generate statistical characterisations of bit errors in SRAMs and DRAMs. We also present MUSTARD-generated results showing the effect of RTN on DRAM retention times.

In latest CMOS technologies, Random Telegraph Noise (RTN) has emerged as an important challenge for SRAM design. Due to rapidly shrinking device sizes and heightened variability, analytical approaches are no longer applicable for characterising the circuit-level impact of non-stationary RTN. Accordingly, this paper presents SAMURAI, a computational method for accurate, trap-level, non-stationary analysis of RTN in SRAMs. The core of SAMURAI is a technique called Markov Uniformisation, which extends stochastic simulation ideas from the biological community and applies them to generate realistic traces of non-stationary RTN in SRAM cells. To the best of our knowledge, SAMURAI is the first computational approach that employs detailed trap-level stochastic RTN generation models to obtain accurate traces of non-stationary RTN at the circuit level. We have also developed a methodology that integrates SAMURAI and SPICE to achieve a simulation-driven approach to RTN characterisation in SRAM cells under (a) arbitrary trap populations, and (b) arbitrarily time-varying bias conditions. Our implementation of this methodology demonstrates that SAMURAI is capable of accurately predicting non-stationary RTN effects such as write errors in SRAM cells.

Oscillators have been a research focus for decades in many disciplines such as electronics and biology. The time keeping capability of oscillators is best described by the scalar quantity phase. Phase computations and equations describing phase dynamics have been useful in understanding oscillator behavior and designing oscillators least affected by disturbances such as noise. In this paper, we present a unified theory of phase equations assimilating the work that has been done in electronics and biology for the last seven decades. We first provide a review of isochrons, which forms the basis of a generalized phase notion for oscillators. We present a general framework for phase equations and derive an exact phase equation that is practically unusable but facilitates the derivation of usable ones based on linear (already known) and quadratic (new and more accurate) approximations for isochrons. We discuss the utility of these phase equations in performing (semi) analytical phase computations and also describe simpler and more accurate phase computation schemes. Numerical experiments on several examples are presented comparing the accuracy of the various phase equations and computation schemes described in this paper.

Oscillations and rhythmic activity are seen in natural and man-made systems. Dynamics of oscillators can be compactly described by phase domain models. Phase equations for periodic, single-frequency oscillators have been developed and utilized in analyzing oscillation phenomena that arise in electronic systems, circadian clocks, and the nervous system. We consider quasi-periodic oscillators and present a general phase model theory and numerical techniques for the construction of phase equations for multi-frequency oscillators. We demonstrate the utility of these phase equations in analyzing oscillators experiencing perturbations.

Considerable effort has been expended in the electronic design automation community in trying to cope with the statistical timing problem. Most of this effort has been aimed at generalizing the static timing analyzers to the statistical case. On the other hand, detailed transistor-level simulations of the critical paths in a circuit are usually performed at the final stage of performance verification. We describe a transistor-level Monte Carlo (MC) technique which makes final transistor-level timing verification practically feasible. The MC method is used as a golden reference in assessing the accuracy of other timing yield estimation techniques. However, it is generally believed that it can not be used in practice as it requires too many costly transistor-level simulations. We present a novel approach to constructing an improved MC estimator for timing yield which provides the same accuracy as standard MC but at a cost of much fewer transistor-level simulations. This improved estimator is based on a unique combination of a variance reduction technique, importance sampling, and a cheap but approximate gate delay model. The results we present demonstrate that our improved yield estimator achieves the same accuracy as standard MC at a cost reduction reaching several orders of magnitude.

The notion of isochrons for oscillators, introduced by Winfree and thereon heavily utilized in mathematical biology, were instrumental in introducing a notion of generalized phase and form the basis for oscillator perturbation analyses. Computing isochrons is a hard problem, existing brute-force methods incurring exponential complexity. In this paper, we present a precise and carefully developed theory and numerical techniques for computing local but quadratic approximations for isochrons. Previous work offers the techniques needed for computing only local linear approximations. Our treatment is general and applicable to oscillators with large dimension. We present examples for isochron computations, verify our results against exact calculations in a simple analytically calculable case, test our methods on complex oscillators, and show how quadratic approximations of isochrons can be used in formulating accurate, novel phase computation schemes and finally allude to second-order accurate compact phase macromodels. Oscillator studies seem to have progressed independently in electronics and biology. Even though analyses in electronics did not make use of the notion of isochrons, similar models and methods, expressed in totally different terminologies, have been developed in both disciplines. In this paper, we also reveal the connection between oscillator analysis work in these two seemingly disparate disciplines.

We first review the notion of isochrons for oscillators, which has been developed and heavily utilized in mathematical biology in studying biological oscillations. Isochrons were instrumental in introducing a notion of generalized phase for an oscillation and form the basis for oscillator perturbation analysis formulations. Calculating the isochrons of an oscillator is a very difficult task. Except for some very simple planar oscillators, isochrons can not be calculated analytically and one has to resort to numerical techniques. Previously proposed numerical methods for computing isochrons can be regarded as brute-force, which become totally impractical for non-planar oscillators with dimension more than two. In this paper, we present a precise and carefully developed theory and advanced numerical techniques for computing local but quadratic approximations for isochrons. Previous work offers the theory and the numerical methods needed for computing only linear approximations for isochrons. Our treatment is general and applicable to oscillators with large dimension. We present examples for isochron computations, verify our results against exact calculations in a simple case, and allude to several applications among many where quadratic approximations of isochrons will be of use.

This paper presents a novel stochastic modeling and optimization framework for energy minimization in multicore systems running real-time applications with tolerance to deadline misses. This framework is based on stochastic application models, which capture the variability of and the spatial and temporal correlations among the workloads of concurrent and interdependent tasks that constitute the application. These stochastic models are utilized in novel mathematical formulations to obtain optimal energy management policies. Experimental results on MPEG2 video decoding show that significant energy savings can be achieved, often close to the theoretical upper bound.

Various forms of linearized noise analysis techniques have been extensively used for analyzing the performance of electronic circuits in the presence of undesired disturbances since the early 70's. Practical numerical algorithms based on linearized perturbation formulations have been implemented in public domain and commercial electronic circuit simulators. In this paper, we describe the noise analysis problems in optical fiber communications and discuss their relationships to RF circuit noise analysis. In particular, we recognize that the noise analysis of electronic circuits with time-invariant (time-varying) large signal excitations corresponds to the analysis of noise propagation in optical fibers along with unmodulated (modulated) light carriers. We discuss how linearized perturbation formulations are used for noise analysis in both domains and draw analogies between them by providing a comparative review of the techniques that have been proposed in the literature.

In This work we describe a stochastic integral equation method for computing the mean value and the variance of capacitance of interconnects with random surface roughness. An ensemble average Green's function is combined with a matrix Neumann expansion to compute nominal capacitance and its variance. This method avoids the time-consuming Monte Carlo simulations and the discretization of rough surfaces. Numerical experiments show that the results of the new method agree very well with Monte Carlo simulation results.

The main effort in oscillator phase noise calculation and macromodeling lies in computing a vector function called the perturbation projection vector (PPV). Current techniques for PPV calculation use time-domain numerics to generate the system's monodromy matrix, followed by full or partial eigenanalysis. We present superior methods that find the PPV using only a single linear solution of the oscillator's time- or frequency-domain steady-state Jacobian matrix. The new methods are better suited for implementation in existing tools with harmonic balance or shooting capabilities (especially those incorporating "fast" variants), and can also be more accurate than explicit eigenanalysis. A key advantage is that they dispense with the need to select the correct one eigenfunction from amongst a potentially large set of choices, an issue that explicit eigencalculation-based methods have to face. We illustrate the new methods in detail using LC and ring oscillators.

Wireless transceivers for digital telecommunications are heterogeneous systems that combine digital hardware, software and analog circuitry. The pressure to miniaturization and lower power consumption for these transceivers imposes tight specifications on their analog RF parts. Many aspects of RF circuits cannot be simulated accurately and efficiently with a classical circuit-level SPICE approach. In this paper three important simulation problems for RF circuits are addressed: 1. High-level simulation of analog and RF blocks for the determination of the specifications of the circuits. 2. Accurate circuit-level simulation of nonlinear circuits with time constants that differ largely. 3. Efficient and accurate computation of phase noise in RF oscillators. For each of these problems, solutions are proposed. These solutions illustrate that accurate and efficient simulations of RF communication circuits need a heterogeneous variety of advanced algorithms.

Clock and data recovery circuits are essential components in communication systems. They directly influence the bit-error-rate performance of communication links. It is desirable to predict the rate of occasional detection errors and the loss of synchronization due to the non-ideal operation of such circuits. In high-speed data networks, the bit-error-rate specification on the system can be very stringent, i.e., 10/sup -14/. It is not feasible to predict such error rates with straightforward, simulation based, approaches. This work introduces a stochastic model and an efficient, analysis-based, non-Monte-Carlo method for performance evaluation of digital data and clock recovery circuits. The analyzed circuit is modeled as finite state machines with inputs described as functions on a Markov chain state-space. System performance measures, such as probability of bit errors and rate of synchronization loss, can be evaluated through the analysis of a larger resulting Markov system. A dedicated multi-grid method is used to solve the very large associated linear systems. The method is illustrated on a real industrial clock-recovery circuit design.

This paper introduces a novel, discrete optimization based method for the computation of coarsely quantized, oversampled finite-length digital signals. The method, while only suitable for off line computation, is more general than the established sigma-delta encoding technique, due to its capacity to take into account complex specifications and design trade-offs. Signal generation is formulated as a linearly constrained, convex, integer quadratic programming problem which is solved through an application specific branch-and-bound algorithm. The optimization method is illustrated with a fractional-N frequency synthesizer based modulator design example.

In high-speed data networks, the bit-error-rate specification on the system can be very stringent, i.e., 10/sup -4/. At such error rates, it is not feasible to evaluate the performance of a design using straightforward, simulation based, approaches. Nevertheless performance prediction before actual hardware is built is essential for the design process. This work introduces a stochastic model and an analysis-based, nonMonte-Carlo method for performance evaluation of digital data communication circuits. The analyzed circuit is modeled by a number of interacting finite state machines with inputs described as functions on a Markov chain state-space. The composition of these elements results in a typically very large Markov chain. System performance measures, such as probability of bit errors and rate of synchronization loss, can be evaluated by solving linear problems involving the large Markov chain's transition probability matrix. This paper first describes a dedicated multi-grid method used to solve these very large linear problems. The principal bottleneck in such an approach is the size of the Markov chain state-space, which grows exponentially with system complexity. The second part of this paper introduces a novel, graph based, data structure capable of efficiently storing and manipulating transition probability matrices for several million state Markov chains. The methods are illustrated on a real industrial clock-recovery circuit design.

The main effort in oscillator phase noise calculation lies in computing a vector function called the Perturbation Projection Vector (PPV). Current techniques for PAVE calculation use time domain numerics to generate the system's monodromy matrix, followed by full or partial eigenanalysis. We present a superior method that finds the PPV using only a single linear solution of the oscillator's time- or frequency-domain steady-state Jacobian matrix. The new method is better suited for existing tools with fast harmonic balance or shooting capabilities, and also more accurate than explicit eigenanalysis. A key advantage is that it dispenses with the need to select the correct one-eigenfunction from amongst a potentially large set of choices, an issue that explicit eigencalculation based methods have to face.

Introduces a methodology for the evaluation of the interference noise caused by digital switching activity in sensitive circuits of a mixed digital-analog chip. The digital switching activity is modeled stochastically as functions defined on Markov chains. The actual interference signal is obtained through the modulation of this discrete stochastic signal with real current injection patterns stored a priori in a pre-characterized library. The interference noise results from the propagation of these continuous stochastic signals through the linear network that models the chip power grid, substrate and relevant package parasitics. The interference noise power spectral density is computed by linear frequency-domain analysis. The methodology is implemented using advanced numerical techniques that are capable of tackling very large problems.

Phase noise is a topic of theoretical and practical interest in electronic circuits, as well as in other fields such as optics. Although progress has been made in understanding the phenomenon, there still remain significant gaps, both in its fundamental theory and in numerical techniques for its characterisation. In this paper, we develop a solid foundation for phase noise that is valid for any oscillator, regardless of operating mechanism. We establish novel results about the dynamics of stable nonlinear oscillators in the presence of perturbations, both deterministic and random. We obtain an exact, nonlinear equation for phase error, which we solve without approximations for random perturbations. This leads us to a precise characterisation of timing jitter and spectral dispersion, for computing which we develop efficient numerical methods. We demonstrate our techniques on practical electrical oscillators, and obtain good matches with measurements even at frequencies close to the carrier, where previous techniques break down.

We describe powerful new techniques for the analysis of RF circuits. Next-generation CAD tools based on such techniques should enable RF designers to obtain a more accurate picture of how their circuits will operate. These new simulation capabilities will be essential in order to reduce the number of design iterations needed to produce complex RF ICs. 1 Introduction Design methodology and superior computer-aided design tools are key to success in the integrated circuit (IC) business. They are particularly important in the case of radio-frequency (RF) IC applications, where the digital IC divide-and-conquerdesign style, based on partitioning by functional blocks and abstraction levels, does not apply. The goal of an RF designer is to get a manufacturable design that meets the specifications with minimum cost, under severe time-to-market constraints. Unlike traditional discretecomponent RF design, prototyping is practically impossible, and the validation of a design can only be done b...

Oscillatorsarekey components of electronic systems.Undesired perturbations, i.e. noise, in practid electronic systems advemelyaffect the specti and timing properties of osdators resrdting in phase noke, which is a key performance firniting factor, Wig a major contributor to bit+rror-rate (BER) of N communicationsystems, and cr-g synchronizationproblems in clockd and sampled-data systems.h this paper, we first present a theory and numerid methodsfor nofllnear perturbationand noiseanalysisof os~ators d~cribed by a systemof dl~erential-ulgebraiceguatiom OW), which extends our re- cent results on perturbation analysis of autonomousordinary dtierentid quations (ODfi).h developing the above theory, we rely on novel results we estabfish for finm periodi~y time-varying LW) systems: Hoquet theory for DAEs.We then use this notdiiear perturbation analysis to derive the stochastic characterization, including the resulting os~ator spectrum, of phase noise in oscillators due to colored (e.g.,,1/f noise), as opposd to white, noise sources.me we of white noise sources has rdr~dy kn Med by us in a ~nt publication.me r=ulfs of the theory develo@ in this work enabled us to implement a rigorous and effective analysis and design tool in a circuit siuudator for low phase noise oscMator design.

Article Estimating noise in RF systems Share on Authors: Jaijeet Roychowdhury Bell Laboratories, Murray Hall, New Jersey Bell Laboratories, Murray Hall, New JerseyView Profile , Alper Demir Bell Laboratories, Murray Hall, New Jersey Bell Laboratories, Murray Hall, New JerseyView Profile Authors Info & Claims ICCAD '98: Proceedings of the 1998 IEEE/ACM international conference on Computer-aided designNovember 1998 Pages 199–202https://doi.org/10.1145/288548.288612Online:01 November 1998Publication History 3citation252DownloadsMetricsTotal Citations3Total Downloads252Last 12 Months2Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

To accelerate the design cycle for analog and mixed-signal systems, we have proposed a top-down, constraint-driven design methodology. The key idea of the proposed methodology is hierarchically propagating constraints from performance specifications to layout. Consequently, it is essential to provide the necessary tools and techniques enabling the efficient constraint propagation. To illustrate the applicability of the proposed methodology to the design of larger systems, we present in this paper the complete design flow for a video driver system. Critical advantages of the methodology illustrated with this design example include avoiding costly low level re-designs and getting working silicon parts from the first run. Following our approach, a jitter constraint is imposed at the system level and then is propagated hierarchically to the circuit blocks and layout, using behavioral modeling and simulation. Experimental results are presented from working fabricated parts.

A time-domain, non-Monte Carlo method for computer simulation of electrical noise in nonlinear dynamic circuits with arbitrary excitations and arbitrary large-signal waveforms is presented. This time-domain noise simulation method is based on results from the theory of stochastic differential equations. The noise simulation method is general in the following sense. Any nonlinear dynamic circuit with any kind of excitation, which can be simulated by the transient analysis routine in a circuit simulator, can be simulated by our noise simulator in time-domain to produce the noise variances and covariances of circuit variables as a function of time, provided that noise models for the devices in the circuit are available. Noise correlations between circuit variables at different time points can also be calculated. Previous work on computer simulation of noise in electronic circuits is reviewed with comparisons to our method. Shot, thermal, and flicker noise models for integrated-circuit devices, in the context of our time-domain noise simulation method, are discussed. The implementation of this noise simulation method in a circuit simulator (SPICE) is described. Two examples of noise simulation (a CMOS inverter and a BJT active mixer) are given.