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Frequency Response, Filters, and Resonance
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12.1 Frequency Response
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12.2 High-Pass and Low-Pass Networks 12.3 Half-Power Frequencies 12.4 Generalized Two-Port, Two-Element Networks 12.5 The Frequency Response and Network Functions 12.6 Frequency Response from Pole-Zero Location 12.7 Ideal and Practical Filters 12.8 Passive and Active Filters 12.9 Bandpass Filters and Resonance 12.10 Natural Frequency and Damping Ratio 12.11 RLC Series Circuit; Series Resonance 12.12 Quality Factor 12.13 RLC Parallel Circuit; Parallel Resonance 12.14 Practical LC Parallel Circuit 12.15 Series-Parallel Conversions 12.16 Locus Diagrams 12.17 Scaling the Frequency Response of Filters
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Contents
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Two-port Networks
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13.1 Terminals and Ports 13.2 Z-Parameters 13.3 T-Equivalent of Reciprocal Networks 13.4 Y-Parameters 13.5 Pi-Equivalent of Reciprocal Networks 13.6 Application of Terminal Characteristics 13.7 Conversion Between Z- and Y-Parameters 13.8 h-Parameters 13.9 g-Parameters 13.10 Transmission Parameters 13.11 Interconnecting Two-Port Networks 13.12 Choice of Parameter Type 13.13 Summary of Terminal Parameters and Conversion
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Mutual Inductance and Transformers
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14.1 Mutual Inductance 14.2 Coupling Coef cient 14.3 Analysis of Coupled Coils 14.4 Dot Rule 14.5 Energy in a Pair of Coupled Coils 14.6 Conductively Coupled Equivalent Circuits 14.7 Linear Transformer 14.8 Ideal Transformer 14.9 Autotransformer 14.10 Re ected Impedance
334 335 336 338 338 339 340 342 343 344
Circuit Analysis Using Spice and Pspice
15.1 15.2 15.3 15.4 15.5 15.6 15.7 Spice and PSpice Circuit Description Dissecting a Spice Source File Data Statements and DC Analysis Control and Output Statements in DC Analysis Thevenin Equivalent Op Amp Circuits
362 362 363 364 367 370 370
Contents
15.8 AC Steady State and Frequency Response 15.9 Mutual Inductance and Transformers 15.10 Modeling Devices with Varying Parameters 15.11 Time Response and Transient Analysis 15.12 Specifying Other Types of Sources 15.13 Summary
373 375 375 378 379 382
The Laplace Transform Method
16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 Introduction The Laplace Transform Selected Laplace Transforms Convergence of the Integral Initial-Value and Final-Value Theorems Partial-Fractions Expansions Circuits in the s-Domain The Network Function and Laplace Transforms
398 398 399 401 401 402 404 405
Fourier Method of Waveform Analysis
17.1 Introduction 17.2 Trigonometric Fourier Series 17.3 Exponential Fourier Series 17.4 Waveform Symmetry 17.5 Line Spectrum 17.6 Waveform Synthesis 17.7 Effective Values and Power 17.8 Applications in Circuit Analysis 17.9 Fourier Transform of Nonperiodic Waveforms 17.10 Properties of the Fourier Transform 17.11 Continuous Spectrum
420 421 422 423 425 426 427 428 430 432 432
APPENDIX A
Complex Number System
A1 A2 A3 A4 A5 A6 A7 A8 Complex Numbers Complex Plane Vector Operator j Other Representations of Complex Numbers Sum and Difference of Complex Numbers Multiplication of Complex Numbers Division of Complex Numbers Conjugate of a Complex Number
451 451 452 452 452 452 453 453
APPENDIX B
Matrices and Determinants
B1 B2 B3 B4 B5 Simultenaneous Equations and the Characteristic Matrix Type of Matrices Matrix Arithmetic Determinant of a Square Matrix Eigenvalues of a Square Matrix
455 455 456 458 460
INDEX
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Introduction
1.1 ELECTRICAL QUANTITIES AND SI UNITS The International System of Units (SI) will be used throughout this book. Four basic quantities and their SI units are listed in Table 1-1. The other three basic quantities and corresponding SI units, not shown in the table, are temperature in degrees kelvin (K), amount of substance in moles (mol), and luminous intensity in candelas (cd). All other units may be derived from the seven basic units. The electrical quantities and their symbols commonly used in electrical circuit analysis are listed in Table 1-2. Two supplementary quantities are plane angle (also called phase angle in electric circuit analysis) and solid angle. Their corresponding SI units are the radian (rad) and steradian (sr). Degrees are almost universally used for the phase angles in sinusoidal functions, for instance, sin !t 308 . Since !t is in radians, this is a case of mixed units. The decimal multiples or submultiples of SI units should be used whenever possible. The symbols given in Table 1-3 are pre xed to the unit symbols of Tables 1-1 and 1-2. For example, mV is used for millivolt, 10 3 V, and MW for megawatt, 106 W.
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