Numerical Initial Value Problems in Ordinary Differential Equations

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 characterization. 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 characterization of timing jitter and spectral dispersion, for computing of which we have developed efficient numerical methods. We demonstrate our techniques on a variety of practical electrical oscillators and obtain good matches with measurements, even at frequencies close to the carrier, where previous techniques break down. Our methods are more than three orders of magnitude faster than the brute-force Monte Carlo approach, which is the only previously available technique that can predict phase noise correctly.

Phase noise in oscillators: a unifying theory and numerical methods for characterization

Chapter 8 establishes the relationship between the input and output power spectral densities of a linear system. Limitations on results are carefully detailed and the case of oscillator noise is considered. The theory is extended to multiple input-multiple output systems.

Linear System Theory

Flicker noise in the mixer of a zero- or low-intermediate frequency (IF) wireless receiver can compromise overall receiver sensitivity. A qualitative physical model has been developed to explain the mechanisms responsible for flicker noise in mixers. The model simply explains how frequency translations take place within a mixer. Although developed to explain flicker noise, the model predicts white noise as well. Simple equations are derived to estimate the flicker and white noise at the output of a switching active mixer. Measurements and simulations validate the accuracy of the predictions, and the dependence of mixer noise on local oscillator (LO) amplitude and other circuit parameters.

Noise in RF-CMOS mixers: a simple physical model

This survey presents an overview of recent advances in the state of the art for computer-aided design (CAD) tools for analog and mixed-signal integrated circuits (ICs). Analog blocks typically constitute only a small fraction of the components on mixed-signal ICs and emerging systems-on-a-chip (SoC) designs. But due to the increasing levels of integration available in silicon technology and the growing requirement for digital systems to communicate with the continuous-valued external world, there is a growing need for CAD tools that increase the design productivity and improve the quality of analog integrated circuits. This paper describes the motivation and evolution of these tools and outlines progress on the various design problems involved: simulation and modeling, symbolic analysis, synthesis and optimization, layout generation, yield analysis and design centering, and test. This paper summarizes the problems for which viable solutions are emerging and those which are still unsolved.

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Computer-aided design of analog and mixed-signal integrated circuits

Gaussian-elimination based shooting-Newton methods, a commonly used approach for computing steady-state solutions, grow in computational complexity like N/sup 3/, where N is the number of circuit equations. Just using iterative methods to solve the shooting-Newton equations results in an algorithm which is still order N/sup 2/ because of the cost of calculating the dense sensitivity matrix. Below, a matrix-free Krylov-subspace approach is presented, and the method is shown to reduce shooting-Newton computational complexity to that of ordinary transient analysis. Results from several examples are given to demonstrate that the matrix-free approach is more than ten times faster than using iterative methods alone for circuits with as few as 400 equations.

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Efficient Steady-State Analysis Based on Matrix-Free Krylov-Subspace Methods

In this paper we present a preconditioned recycled Krylov-subspace method to accelerate a recently developed approach for ac and noise analysis of linear periodically-varying communication circuits. Examples are given to show that the combined method can be used to analyse switching filter frequency response, mixer 1/f noise frequency translation, and amplifier intermodulation distortion. In addition, it is shown that for large circuits the preconditioned recycled Krylov-subspace method is up to forty times faster than the standard optimized direct methods.

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Efficient AC and noise analysis of two-tone RF circuits

RF integrated circuit designers make extensive use of simulation tools which perform nonlinear periodic steady-state analysis and its extensions. However, the computational costs of these simulation tools have restricted users from examining the detailed behavior of complete RF subsystems. Recent algorithmic developments, based on matrix-implicit iterative methods, is rapidly changing this situation and providing new faster tools which can easily analyze circuits with hundreds of devices. In this paper we present these new methods by describing how they can be used to accelerate finite-difference, shooting-Newton, and harmonic-balance based algorithms for periodic steady-state analysis.

Fast simulation algorithms for RF circuits

Designers of RF circuits such as power amplifiers, mixers, and filters make extensive use of simulation tools which perform periodic steady-state analysis and its extensions, but until the mid 1990s, the computational costs of these simulation tools restricted designers from simulating the behavior of complete RF subsystems. The introduction of fast matrix-implicit iterative algorithms completely changed this situation, and extensions of these fast methods are providing tools which can perform periodic, quasi-periodic, and periodic noise analysis of circuits with thousands of devices. Even though there are a number of research groups continuing to develop extensions of matrix-implicit methods, there is still no compact characterization which introduces the novice researcher to the fundamental issues. In this paper, we examine the basic periodic steady-state problem and provide both examples and linear algebra abstractions to demonstrate connections between seemingly dissimilar methods and to try to provide a more general framework for fast methods than the standard time-versus-frequency domain characterization of finite-difference, basis-collocation, and shooting methods

Fundamentals of Fast Simulation Algorithms for RF Circuits

Periodic small-signal analysis is a recently developed approach for AC and noise analysis of linear periodically-varying circuits. This paper presents several new approaches to characterizing the transfer functions, noise, and distortion of communication circuits using this new technique. A receiver is used as an example, but the techniques presented are applicable to a wide variety of circuits, including mixers, samplers, sample-and-holds, chopper-stabilized amplifiers, multipliers and switched-capacitor filters.

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Ricardo Telichevesky

Papers

Efficient Steady-State Analysis Based on Matrix-Free Krylov-Subspace Methods

Efficient AC and noise analysis of two-tone RF circuits

Fast simulation algorithms for RF circuits

Fundamentals of Fast Simulation Algorithms for RF Circuits

Receiver characterization using periodic small-signal analysis