Modeling and Simulation in Science, Engineering and Technology

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2 Modeling and Simulation in Science, Engineering and Technology Series Editor Nicola Bellomo Politecnico di Torino Italy Advisory Editorial Board M. Avellaneda (Modeling in Economics) Courant Institute of Mathematical Sciences New York University 251 Mercer Street New York, NY 10012, USA K.J. Bathe (Solid Mechanics) Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge, MA 02139, USA P. Degond (Semiconductor and Transport Modeling) Mathématiques pour l Industrie et la Physique Université P. Sabatier Toulouse Route de Narbonne Toulouse Cedex, France degond@mip.ups-tlse.fr A. Deutsch (Complex Systems in the Life Sciences) Center for Information Services and High Performance Computing Technische Universität Dresden Dresden, Germany andreas.deutsch@tu-dresden.de M.A. Herrero Garcia (Mathematical Methods) Departamento de Matematica Aplicada Universidad Complutense de Madrid Avenida Complutense s/n Madrid, Spain herrero@sunma4.mat.ucm.es H.G. Othmer (Mathematical Biology) Department of Mathematics University of Minnesota 270A Vincent Hall Minneapolis, MN 55455, USA othmer@math.umn.edu L. Preziosi (Industrial Mathematics) Dipartimento di Matematica Politecnico di Torino Corso Duca degli Abruzzi Torino, Italy luigi.preziosi@polito.it V. Protopopescu (Competitive Systems, Epidemiology) CSMD Oak Ridge National Laboratory Oak Ridge, TN , USA vvp@epmnas.epm.ornl.gov K.R. Rajagopal (Multiphase Flows) Department of Mechanical Engineering Texas A&M University College Station, TX 77843, USA krajagopal@mengr.tamu.edu Y. Sone (Fluid Dynamics in Engineering Sciences) Professor Emeritus Kyoto University Iwakura-Nagatani-cho Sakyo-ku Kyoto , Japan sone@yoshio.mbox.media.kyoto-u.ac.jp W. Kliemann (Stochastic Modeling) Department of Mathematics Iowa State University 400 Carver Hall Ames, IA 50011, USA kliemann@iastate.edu

3 Circuit Simulation with SPICE OPUS Theory and Practice Tadej Tuma Árpád Bűrmen Birkhäuser Boston Basel Berlin

4 Tadej Tuma University of Ljubljana Faculty of Electrical Engineering Tržaška cesta 25 SI-1000 Ljubljana, Slovenia Árpád Bűrmen University of Ljubljana Faculty of Electrical Engineering Tržaška cesta 25 SI-1000 Ljubljana, Slovenia ISBN e-isbn DOI / Library of Congress Control Number: Mathematics Subject Classification (2000): Primary 95Cxx; Secondary 94C05, 94C03 Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkhäuser Boston, c/o Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Birkhäuser Boston is part of Springer Science+Business Media (

5 Contents Abbreviations...xiii About SPICE OPUS and This Book... xv 1 Introduction to Circuit Simulation Signals and Linear Systems Lumped Circuits DC Solutions and the Operating Point of a Circuit Incremental DC Circuit Model Circuit s Response in the Time Domain Fourier Series and Fourier Transformation Incremental Circuit Model in the Time Domain Incremental Circuit Model in the Frequency Domain Noise Signals in LTI Systems Circuit Noise Modeling and Analysis Laplace Transformation and the s-domain Circuit Analysis in the s-domain, DC Solution Stability Short Tutorial Installation Starting SPICE OPUS The Command Window Describing a Circuit Input File Structure Numbers in SPICE A Simple Circuit Operating Point (OP) Analysis Operating Point Sweep (DC), Plotting of Simulation Results Small Signal Analysis (AC and TF) Pole-Zero Analysis (PZ) Small Signal Noise Analysis (NOISE) Time-Domain Analysis (TRAN) v

6 vi Contents 2.11 Interactive Interpreter and Advanced Features Expressions, Vectors, Plots, and Automated Measurements Control Structures, Substitution, and Variables Libraries, Raw Files, and File Output Saving Device Quantities During Analyses Tracing and Interactive Plotting Input File Syntax File Structure Numbers Instances and Nodes Models Instance and Model Parameters Device Syntax Resistor Capacitor Inductor Inductive Coupling Independent Voltage Source Independent Current Source Linear Voltage-Controlled Current Source Linear Voltage-Controlled Voltage Source Linear Current-Controlled Current Source Linear Current-Controlled Voltage Source Nonlinear Controlled Sources Voltage-Controlled Switch Current-Controlled Switch Lossless Transmission Line Lossy Transmission Line Uniformly Distributed RC Line Semiconductor Diode Bipolar Junction Transistor (BJT) Junction Field Effect Transistor (JFET) Metal Semiconductor Field Effect Transistor (MESFET) Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Legacy MOSFET Models (Levels 1 6) BSIM3 and BSIM4 MOSFET Models (Levels 47, 53, and 60) Silicon on Insulator (SOI) MOSFET Models (Levels 55 58) UFET and EKV MOSFET Models (Levels 7 and 44) Binning of MOS Models Including Files in the Netlist Describing Circuits Hierarchically...153

7 Contents vii Defining a Subcircuit, Subcircuit Instantiation Global Nodes Nesting Subcircuits and Understanding the Flat Circuit Parametrization of Subcircuits Initial Operating Point Solution and Initial Conditions Joining Multiple Topologies in a Netlist Simulator Parameters Analyzing the Circuit Operating Point (OP) Analysis Handling of Initial Solutions (Nodesets) Solving Convergence Problems Operating Point Sweep Analysis (DC Analysis) DC Transfer Function Analysis (TF Analysis) Small Signal Analysis (AC Analysis) Pole-Zero (PZ) Analysis Noise (NOISE) Analysis Transient (TRAN) Analysis NUTMEG Scripting Language Input Handling Splitting the Input Line into Words, Escaped Characters History and History Substitution Aliases and Alias Substitution Control Lines and Statements Evaluation of Statements Text Output Plots, Vectors, and Expressions Organization of Numeric Data Plot Management Storing and Restoring Plots in Files Vectors Expressions Operators in NUTMEG Expressions NUTMEG Built-in Functions User-Defined Functions Arithmetic Substitution Variables Variable Basics NUTMEG Control Variables and Simulator Parameters Variable Substitution and Text Input Circuits Circuit and Script Input (source Command) Circuit Management Circuit Listing...206

8 viii Contents Printing Parameter Values of SPICE Primitives Selecting the Topology and Rebuilding the Circuit Changing Nodesets and Initial Conditions Changing Instance, Model, and Subcircuit Parameters Parameter Value Propagation in Subcircuits Changing and Accessing Simulator Parameters for the Current Circuit Accessing Instance, Model, and Subcircuit Parameter Values Simulation Choosing What the Simulator Stores in Vectors (Saving) Tracing Simulation Results During Simulation Plotting Simulation Results During Simulation (Iplotting) Invoking Simulation Analyzing the Results Linearizing the Scale of a Plot Performing Measurements on Vectors Fourier Analysis of Vectors Transforming Vectors to Frequency Domain Plotting the Results The Plot Window Curve Display Styles Plot Window Grids Vector Interpretation Modes The plot Command Examples Control Structures if-elseif-else Block while, dowhile, and repeat Loops Breaking and Continuing a Loop Miscellaneous Directory and File Management Obtaining Statistics from the Simulator The spinit File Mathematical Background Linear Resistive Networks Circuit Tableau Basic Nodal Equations Modified Nodal Equations Solving the Set of Circuit Equations Sparse Matrices LU Decomposition Successful Pivoting Techniques Numerical Error Control...271

9 Contents ix 6.3 Introducing Nonlinear Devices Fixed Point Iteration Newton Raphson Algorithm Convergence Detection Automatic Convergence Helpers Specifying the Initial Point for the Newton Raphson Algorithm Dynamic Devices and Frequency-Domain Analysis Small Signal Response (AC) Analysis Poles and Zeros of the Small Signal Transfer Function (PZ) Small Signal Noise Analysis (NOISE) Frequency-Domain Model of an Inductor in SPICE OPUS Transient (Time-Domain) Analysis (TRAN) Backward Euler Integration Trapezoidal Integration General Linear Multistep Numerical Integration Local Truncation Error (LTE) Inductors in SPICE OPUS Time-Domain Analysis Initial Conditions Predictor-Corrector Integration Choosing the Integration Algorithm Integration Time-Step Control Examples Parametrized Attenuator and Transmission Lines Modeling a Nonlinear Transformer Analyzing a CMOS Differential Amplifier Using Corner Models Local Variations (Mismatch) and Monte-Carlo Analysis Drawing Histograms, Yield Analysis Logic Gates Flip-Flops Counters and Frequency Dividers Phase Frequency Detector Voltage-Controlled Oscillator Phase-Locked Loop References Index...391

10 For Prof. Franc Bratkovič, our dear mentor And all amid them stood the Tree of Life, High eminent, blooming Ambrosial Fruit Of vegetable Gold; and next to Life Our Death the Tree of Knowledge grew fast by, Knowledge of Good bought dear by knowing ill. John Milton, Paradise Lost (4,218) xi

11 Abbreviations ASCII BDF BJT BSIM CMOS EKV FET FM IC IGFET Inf JFET KCL KVL LTE LTI MESFET MN MOSFET NaN NR ODE PFD PLL PSRR RMS SOI SPICE STAGSOI THD TM UFSOI VCO American standard code for information interchange Backward differentiation formula Bipolar junction transistor Berkeley short-channel IGFET model Complementary metal oxide semiconductor Enz Krummenacher Vittoz Field effect transistor Frequency modulation Integrated circuit Insulated gate field effect transistor Infinity Junction field effect transistor Kirchhoff current law Kirchhoff voltage law Local truncation error Linear time-invariant Metal semiconductor field effect transistor Modified nodal Metal oxide semiconductor field effect transistor Not a number Newton Raphson Ordinary differential equation Phase frequency detector Phase-locked loop Power supply rejection ratio Root mean square Silicon on insulator Simulation Program with Integrated Circuit Emphasis Southampton Thermal Analogue silicon on insulator Total harmonic distortion Typical mean University of Florida silicon on insulator Voltage-controlled oscillator xiii

12 xiv Abbreviations WO WP WS WZ Worst one Worst power Worst speed Worst zero

13 About SPICE OPUS and This Book To most people who are new to SPICE, it may be interesting to note that the circuit simulation program and the topic of the following 400+ pages was created as a tool for analyzing integrated circuits (ICs). As a matter of fact, in the 1960s and 1970s the IC industry was a rising star on the high-tech horizon. It quickly became obvious that designing ICs by trial and error was just too tedious and expensive. Prediction of circuit behavior using mathematical models of circuit components and digital computers seemed to be a far better approach. In 1967 William Howard, at the time a recent post-graduate student of Donald Pederson, created a computer program for the analysis of the DC operating point of an integrated circuit and named it BIAS. This research at the University of California, Berkeley continued and the next result was a program named SLIC (Simulator for Linear Integrated Circuits). It was capable of solving the operating point of a circuit and then simulating the corresponding linearized circuit in the frequency domain. CANCER (Computer Analysis of Nonlinear Circuits, Excluding Radiation) was developed in parallel with SLIC and appeared in It is considered the predecessor of the Simulation Program with Integrated Circuit Emphasis (SPICE). The proprietary nature of CANCER s code was the reason that triggered the development of SPICE. Lawrence Nagel, a graduate student at UC Berkeley, created SPICE1 as a result of his graduate study. The program was first released in Dr. Nagel continued his work on SPICE until version SPICE2A. SPICE2 [33] was first released in 1975, and the development eventually led to version 2G6 released in 1983, which is the basis of many commercial simulators. Among other features, SPICE2 introduced dynamic memory management, which makes it possible for the program to be scalable with respect to circuit size. The clumsy FORTRAN source code of SPICE2 was rewritten in the C programming language, which became the de facto standard for software development. The rewrite was done in the 1980s by Thomas Quarles, and his efforts resulted in SPICE3 [36] (released in 1985). SPICE3 had many improvements in device models and analysis techniques, albeit it also contained many bugs and memory leaks which made it useless when the analysis and the postprocessing commands were run in a loop with several thousand iterations. The last released version of SPICE3 was 3F5. More on the history of SPICE can be found in [34, 35, 39, 50]. xv

14 xvi About SPICE OPUS and This Book The need for a stable and memory leak-free simulator was the trigger for the development of SPICE OPUS [51], which began in the 1990s. These features were a prerequisite for implementing optimization algorithms in the simulator. The name SPICE OPUS is an acronym for SPICE engine for OPtimization UtilitieS. Until 2000 there were several releases that supported only the Windows operating system. In 2000 SPICE OPUS 2.0 was released with a completely redesigned graphical front-end. Version 2.0 was also available for the Linux operating system. SPICE OPUS has over 10,000 users worldwide in the areas of research, education, and industry. Due to its public domain licensing, SPICE spread like wildfire. The source code of SPICE2 and SPICE3 was used as a basis or model for many commercial simulators like PSPICE [42], ISSPICE [25], HSPICE [22], SPECTRE [49], and many others. This book is intended for a very wide audience ranging from undergraduate students to IC designers and simulator developers. Not all chapters are intended for all readers. Some readers might find a certain chapter irrelevant to their work, while others may find in the same chapter just what they are looking for. The first chapter deals with the formulation of the circuit equations and basic mathematical notions required to understand circuit modeling and simulation. This chapter is intended mostly for students and simulator developers. The second chapter is a kind of tutorial for SPICE OPUS. Everyone who wants to make a quick start in circuit simulation with SPICE OPUS should read this chapter first. It provides an overview of the features SPICE OPUS offers and also contains brief installation instructions. The third, fourth, and fifth chapters constitute a manual for SPICE OPUS. They describe all features of SPICE OPUS, starting with the input file syntax, followed by circuit analysis methods offered by SPICE OPUS, and finally the built-in scripting language (NUTMEG). These chapters are intended for users of SPICE OPUS primarily as a reference. The sixth chapter returns to the theory that makes SPICE tick. It is less general than the first chapter and focuses mostly on the simulation techniques used by SPICE. The material is described in a more gradual way, starting with linear resistive circuits and ending with dynamic circuits and numerical integration algorithms. The target audience is undergraduate students and simulator developers. For the latter, the second half of the chapter will be more interesting because it describes the inner workings of SPICE, ranging from tricks that make operating point analysis possible to algorithms for time-step control. The seventh and final chapter is a collection of examples. The examples cover the simulation of various circuits and systems, ranging from simple serially connected transmission lines to a complete phase-locked loop. Some of the most common uses of SPICE OPUS are presented, with an emphasis on the built-in scripting language (NUTMEG). Chapter 7 is intended primarily for SPICE OPUS users. Ljubljana, Slovenia June 2009 Tadej Tuma Árpád Bűrmen

Circuit Simulation with SPICE OPUS

Circuit Simulation with SPICE OPUS Theory and Practice Tadej Tuma Arpäd Bürmen Birkhäuser Boston Basel Berlin Contents Abbreviations About SPICE OPUS and This Book xiii xv 1 Introduction to Circuit Simulation