Circuits, Matrices and Linear Vector Spaces (Dover Books on Electrical Engineering)

This Dover edition, first published in 2011, is an unabridged republication of the work originally published in 1963 by the McGraw-Hill Book Company, Inc., New York. This high-level undergraduate text explains the mathematics behind basic circuit theory. Its self-contained treatment covers matrix algebra, which provides a general means of formulating the details of a linear system. In addition, the author presents the basic theory of n-dimensional spaces and demonstrates its application to linear systems. A development of the mathematics of matrix algebra and determinants is followed by the application of matrix techniques to a general discussion of circuits. Subsequent topics include the properties of active and passive two-port devices, the basic theory of linear vector spaces, and the natural frequencies of a network. Appendixes cover the indefinite-transfer matrix, gyrators with complex gyration admittance, and network transformations. A wealth of equations and calculation problems appear throughout the text.Reprint of the McGraw-Hill Book Company Inc., New York, 1963 edition. - See more at: http://store.doverpublications.com/048648534x.html#sthash.OdNT98RQ.dpuf Title Page 3 Copyright Page 4 Dedication 5 Preface 6 Contents 8 Chapter 1 Introduction 12 1.1 Circuits and circuit elements 12 1.2 Classifications of circuit elements 12 1.3 Classifications of circuits 13 1.4 Network functions 15 1.5 The use of examples 16 1.6 References for review 17 Chapter 2 Matrices and determinants 19 2.1 Introduction 19 2.2 Matrices 20 2.3 Determinants 21 2.4 Evaluating the determinant 23 2.5 Properties of determinants 26 2.6 Using determinants to solve a set of simultaneous equations 30 2.7 Matrix algebra 33 2.8 Types of matrices and properties of matrices 36 2.9 Theorems on matrices 38 2.10 Matrix partitioning 40 2.11 Matrix equations 41 2.12 Further reading 44 Chapter 3 Circuit-theory applications of matrices 50 3.1 Introduction 50 3.2 The n-port network 52 3.3 Two-port-network parameters 60 3.4 The n-terminal network 73 3.5 The indefinite-admittance matrix 77 3.6 Some applications of the indefinite-admittance matrix 85 3.7 The scattering matrix 88 3.8 Network descriptions 93 Chapter 4 Two-port devices 107 4.1 Introduction 107 4.2 The ideal transformer 110 4.3 The negative-immittance converter 113 4.4 NIC circuits 118 4.5 Synthesis of transfer functions with an NIC 122 4.6 Synthesis of driving-point functions with NICs 124 4.7 The gyrator 129 4.8 Synthesis of n-port networks 137 4.9 Other two-port networks 142 Chapter 5 Linear vector spaces 147 5.1 Introduction 147 5.2 Linear vector spaces 148 5.3 Orthonormal bases 153 5.4 Transformations of basis vectors 158 5.5 Linear transformations 163 5.6 Eigenvalues and eigenvectors 169 5.7 Quadratic forms 176 5.8 Simultaneous diagonalization of two matrices 178 5.9 Reciprocal bases 184 5.10 Further reading 187 Chapter 6 Circuit-theory applications of linear vector spaces 192 6.1 Introduction 192 6.2 RC-network analysis 192 6.3 An example of RC-network analysis 196 6.4 LC-network analysis 202 6.5 Analysis in the frequency domain 206 6.6 Driving functions 209 6.7 A more general method of analysis 213 6.8 The RLC network 219 6.9 Representation using a reciprocal basis 222 Appendix A The indefinite-transfer matrix 229 Appendix B Gyrators and gyration admittance 232 Appendix C Network realization by transformation methods 236 Index 244 Back Cover 254 This high-level text explains the mathematics behind basic circuit theory. It covers matrix algebra, whichprovides a general means of formulating the details of a linear system. In addition, the author presents the basic theory of n -dimensional spaces and demonstrates its application to linear systems. Numerousproblems appear throughout the text. 1963 edition.