INVITED PAPER Fundamentals of Fast Simulation Algorithms for RF Circuits The newest generation of circuit simulators perform periodic steady-state analysis of RF circuits containing thousands of devices using a variety of matrix-implicit techniques which share a common analytical framework. By Ognen Nastov , Rircardo Telichevesky, Member IEEE, Ken Kundert, and Jacob White, Member IEEE ABSTRACT | 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 exten- sions, 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 re- searcher 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. KEYWORDS | Circuit simulation; computer-aided analysis; design automation; frequency-domain analysis; numerical analysis I. INTRODUCTION The intensifying demand for very high performance portable communication systems has greatly expanded the need for simulation algorithms that can be used to efficiently and accurately analyze frequency response, distortion, and noise of RF communication circuits such as mixers, switched-capacitor filters, and amplifiers. Al- though methods like multitone harmonic balance, linear time-varying, and mixed frequency-time techniques [4], [6]–[8], [26], [37] can perform these analyses, the computation cost of the earliest implementations of these techniques grew so rapidly with increasing circuit size that they were too computationally expensive to use for more complicated circuits. Over the past decade, algorithmic developments based on preconditioned matrix-implicit Krylov-subspace iterative methods have dramatically changed the situation, and there are now tools which can easily analyze circuits with thousands of devices. Precondi- tioned iterative techniques have been used to accelerate periodic steady-state analysis based on harmonic balance methods [5], [11], [30], time-domain shooting methods [13], and basis-collocation schemes [41]. Additional results for more general analyses appear constantly. Though there are numerous excellent surveys on analysis technques for RF circuits [23], [35], [36], [42], the literature analyzing the fundmentals of fast methods is limited [40], making it difficult for novice researchers to contribute to the field. In this paper, we try to provide a comprehensive yet approachable presentation of fast Manuscript received May 23, 2006; revised August 27, 2006. This work was originally supported by the DARPA MAFET program, and subsequently supported by grants from the National Science Foundation, in part by the MARCO Interconnect Focus Center, and in part by the Semiconductor Research Center. O. Nastov is with Agilent Technologies, Inc., Westlake Village, CA 91362 USA (e-mail: ognen_nastov@agilent.com). R. Telichevesky is with Kineret Design Automation, Inc., Santa Clara, CA 95054 USA (e-mail: ricardo@teli.org). K. Kundert is with Designer’s Guide Consulting, Inc., Los Altos, CA 94022 USA (e-mail: ken@designers-guide.com). J. White is with the Research Laboratory of Electronics and Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e-mail: white@mit.edu). Digital Object Identifier: 10.1109/JPROC.2006.889366 600 Proceedings of the IEEE | Vol. 95, No. 3, March 2007 0018-9219/$25.00 Ó2007 IEEE