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This book was initially conceived as a revision of Linear Network Analysis by Sundaram Seshu and Norman Balabanian in the summer of 1965. Before the work of revision had actually started, however, Seshu died tragically in an automobile accident. Since then the conceived revision evolved and was modified to such a great extent that it took on the character of a new book and is being presented as such. We (especially Norman Balabanian) wish, nevertheless, to acknowledge a debt to Seshu for his direct and indirect contributions to this book.

The set of notes from which this book has grown has been used in a beginning graduate course at Syracuse University and at the Berkeley campus of the University of California. Its level would also permit the use of selected parts of the book in a senior course. In the study of electrical systems it is sometimes appropriate to deal with the internal structure and composition of the system. In such cases topology becomes an important tool in the analysis. At other times only the external characteristics are of interest.

Then " systems " considerations come into play. In this book we are concerned with both internal composition and system, or port, characteristics.

The mathematical tools of most importance are matrix analysis, linear graphs, functions of a complex variable, and Laplace transforms. The first two are developed within the text, whereas the last two are treated in appendices. Also treated in an appendix, to undergird the use of impulse functions in Chapter 5, is the subject of generalized functions. Each of the appendices constitutes a relatively detailed and careful development of the subject treated. In this book we have attempted a careful development of the fundamentals of network theory. Frequency and time response are considered, as are analysis and synthesis.

Active and nonreciprocal components (such as controlled sources, gyrators, and negative converters) are treated sideby-side with passive, reciprocal components. Although most of the book is limited to linear, time-invariant networks, there is an extensive chapter concerned with time-varying and nonlinear networks. Matrix analysis is not treated all in one place but some of it is introduced at the time it is required. Thus introductory considerations are discussed in Chapter 1 but functions of a matrix are introduced in Chapter 4 in which a solution of the vector state equation is sought. Similarly, equivalence, canonic forms of a matrix, and quadratic forms are discussed in Chapter 7, preparatory to the development of analytic properties of network functions.

The analysis of networks starts in Chapter 2 with a precise formulation of the fundamental relationships of Kirchhoff, developed through the application of graph theory. The classical methods of loop, node, nodepair, and mixed-variable equations are presented on a topological base. In Chapter 3 the port description and the terminal description of multiterminal networks are discussed. The usual two-port parameters are introduced, but also discussed are multiport networks. The indefinite admittance and indefinite impedance matrices and their properties make their appearance here. The chapter ends with a discussion of formulas for the calculation of network functions by topological concepts.

The state formulation of network equations is introduced in Chapter 4. Procedures for writing the state equations for passive and active and reciprocal and nonreciprocal networks include an approach that requires calculation of multiport parameters of only a resistive network (which may be active and nonreciprocal).

An extensive discussion of the timedomain solution of the vector state equation is provided. Chapter 5 deals with integral methods of solution, which include the convolution integral and superposition integrals. Numerical methods of evaluating the transition matrix, as well as the problem of errors in numerical solutions, are discussed.

The set of notes from which this book has grown has been used in a beginning graduate course at Syracuse University and at the Berkeley campus of the University of California. Its level would also permit the use of selected parts of the book in a senior course. In the study of electrical systems it is sometimes appropriate to deal with the internal structure and composition of the system. In such cases topology becomes an important tool in the analysis. At other times only the external characteristics are of interest.

Then " systems " considerations come into play. In this book we are concerned with both internal composition and system, or port, characteristics.

The mathematical tools of most importance are matrix analysis, linear graphs, functions of a complex variable, and Laplace transforms. The first two are developed within the text, whereas the last two are treated in appendices. Also treated in an appendix, to undergird the use of impulse functions in Chapter 5, is the subject of generalized functions. Each of the appendices constitutes a relatively detailed and careful development of the subject treated. In this book we have attempted a careful development of the fundamentals of network theory. Frequency and time response are considered, as are analysis and synthesis.

Active and nonreciprocal components (such as controlled sources, gyrators, and negative converters) are treated sideby-side with passive, reciprocal components. Although most of the book is limited to linear, time-invariant networks, there is an extensive chapter concerned with time-varying and nonlinear networks. Matrix analysis is not treated all in one place but some of it is introduced at the time it is required. Thus introductory considerations are discussed in Chapter 1 but functions of a matrix are introduced in Chapter 4 in which a solution of the vector state equation is sought. Similarly, equivalence, canonic forms of a matrix, and quadratic forms are discussed in Chapter 7, preparatory to the development of analytic properties of network functions.

The analysis of networks starts in Chapter 2 with a precise formulation of the fundamental relationships of Kirchhoff, developed through the application of graph theory. The classical methods of loop, node, nodepair, and mixed-variable equations are presented on a topological base. In Chapter 3 the port description and the terminal description of multiterminal networks are discussed. The usual two-port parameters are introduced, but also discussed are multiport networks. The indefinite admittance and indefinite impedance matrices and their properties make their appearance here. The chapter ends with a discussion of formulas for the calculation of network functions by topological concepts.

The state formulation of network equations is introduced in Chapter 4. Procedures for writing the state equations for passive and active and reciprocal and nonreciprocal networks include an approach that requires calculation of multiport parameters of only a resistive network (which may be active and nonreciprocal).

An extensive discussion of the timedomain solution of the vector state equation is provided. Chapter 5 deals with integral methods of solution, which include the convolution integral and superposition integrals. Numerical methods of evaluating the transition matrix, as well as the problem of errors in numerical solutions, are discussed.