CIRCUITS, SYSTEMS, AND SIGNALS FOR BIOENGINEERS: A MATLAB-BASED INTRODUCTION

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1 CIRCUITS, SYSTEMS, AND SIGNALS FOR BIOENGINEERS: A MATLAB-BASED INTRODUCTION John L. Semmlow ELSEVIER ACAUEMIC PRFSS AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO

2 CONTENTS 1 BIOENGINEERING SIGNALS AND SYSTEMS Biological Systems Biosignals Signal Encoding Linear Signal Analysis: Overview Analysis of Linear Systems Analog Analysis and Analog Models Systems Analysis and Systems Models Systems and Analog Analysis: Summary Noise and Variability Electronic Noise Signal-to-Noise Ratio Summary 27 Problems 29 BASIC SIGNAL PROCESSING Basic Signals: The Sinusoidal Waveform Sinusoidal Arithmetic Complex Representation Signal Properties: Basic Measurements Decibels Advanced Measurements: Correlations and Covariances Standard Correlation and Covariance Autocorrelation and Cross-Correlation MATLAB Implementation Mean, Variance, and Standard Deviation Ensemble Averaging Covariance and Correlation 58

3 X CONTENTS Autocorrelation and Cross-Correlation Summary 65 Problems 66 FREQUENCY TRANSFORMATIONS Useful Properties of the Sinusoidal Signal Fourier Series Analysis Symmetry Frequency Representation Compiex Representation The Continuous Fourier Transform Discrete Data: The Discrete Fourier Transform Data Sampling: Sampling Theorem Amplitude Slicing: Quantization (Optional) Data Length: Truncation Power Spectrum Spectral Averaging Signal Bandwidth MATLAB Implementation Summary 115 Problems 116 CIRCUIT AND ANALOG ANALYSIS IN SINUSOIDAL STEADY STATE Circuits and Analog Systems System Variables and Elements Electrical Variables Electrical Elements Active Elements The Fluid Analogy Phasor Analysis Phasor Representation: Electrical Elements Mechanical Elements Passive Elements Elasticity Sources Summary 157 Problems 158

4 6 ANALYSIS OF ANALOG MODELS AND PROCESSES Conservation Laws: Kirchhoff's Voltage Law Mesh Analysis: Single Loops Mesh Analysis: Multiple Loops Mesh Analysis: MATLAB Implementation Conservation Laws: Kirchhoff's Current Law Nodal Analysis Conservation Laws: Newton's Law Mechanical Systems Summary 186 Problems 187 FREQUENCY CHARACTERISTICS OF CIRCUITS AND ANALOG PROCESSES: THE TRANSFER FUNCTION The Circuit or Mechanical System as a Process Superposition The Transfer Function Transfer Function Characteristics Transfer Function Frequency Plots: The Bode Plot Frequency Characteristics of Bode Plot Primitives Filters Filter Types Filter Bandwidth Filter Order Filter Initial Sharpness Evaluating Filter Frequency Characteristics Filter Design MATLAB Implementation Transfer Function System Identification The Transfer Function and Fourier Series Decomposition Summary 234 Problems 234 RELATIONSH1PS BETWEEN ANALOG ELEMENTS System Simplifications: Passive Network Reduction Series Electrica! Elements Parallel Elements Network Reduction: Passive Networks Ideal and Real Sources The Voltage-Current or v-i Plot 252

5 xii CONTENTS Real Voltage Sources: The Thevenin Source Real Current Sources: The Norton Source Thevenin and Norton Circuit Conversion Thevenin and Norton Theorems: Network Reduction with Sources Measurement Loading Jdeal and Real Measurement Devices Maximum Power Transfer Mechanical Systems Multiple Sources: Revisited Summary 283 Problems 283 THE ANALYSIS OF TRANSIENTS: THE LAPLACE TRANSFORM The Laplace Transform Definition of the Laplace Transform Laplace Representation of Elements: Calculus Operations in the Laplace Domain Initial Conditions Voltage-Current and Force-Velocity Relationships in the Laplace Domain Sources: Common Signals in the Laplace Domain Converting the Laplace Transform to the Frequency Domain The Time-Delay Element The Inversc Laplace Transform Laplace Analysis: The Laplace Transfer Function First-Order Processes Second-Order Processes Nonzero Initial Conditions Initial and Final Value Theorems The Laplace Domain and the Frequency Domain Summary 330 Problems 330 SYSTEM MODELS AND BEHAVIOR The System Model Feedback The Convolution Integral M.ATLAB Implementation Resonance Resonant Frequency Resonant Bandwidth, Q 355

6 CONTENTS xiii 9.4 Summary 365 Problems BASIC ANALOG ELECTRONICS: OPERATIONAL AMPLIFIERS The Amplifier The Operational Amplifier The Noninverting Amplifier The Inverting Amplifier Practical Operational Amplifiers Limitations in Transfer Characteristics of Real Operational Amplifiers Input Characteristics Output Characteristics Power Supply Operational Amplifier Circuits, or 101 Things to Do with an Operational Amplifier The Differential Amplifier The Adder The Buffer Amplifier The Transconductance Amplifier Analog Filters Instrumentation Amplifier Summary 411 Problems 411 APPENDIX A 415 A.l Derivation of Euler's Formula 415 A.2 Confirmation of the Fourier Series 416 A.3 Derivation of the Transfer Function of a Second-Order Op Amp Filter 417 A.4 Derivation of the Transfer Function of an Instrumentation Amplifier 41? APPENDIX B Laplace Transforms 421 APPENDIX C Trigonometrie and Other Formulas 423

7 xiv CONTENTS APPENDIX D Units 425 APPENDIX E Complex Arithmetic 429 E.l.l Addition and Subtraction 430 E.1.2 Multiplication and Division 430 APPENDIX F LF 356 Specifications 433 APPENDIX G Determinants and Cramer's Ruie 435 BIBLIOCRAPHY 437 INDEX 439

Signals and Systems Using MATLAB

Signals and Systems Using MATLAB Second Edition Luis F. Chaparro Department of Electrical and Computer Engineering University of Pittsburgh Pittsburgh, PA, USA AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK