Cover; Title Page; Copyright Page; Foreword; Preface; Table of Contents; Chapter 1: Introductory Topics in Circuit Simulation; 1.1 Main concepts; 1.1.1 Systems, models, circuits, equations and responses; 1.1.2 Direct current, transient and alternating current responses; 1.2 Principles of circuit characterization; 1.2.1 Circuit branches; 1.2.2 Circuit topology; 1.2.3 Canonical equations and structural identity; 1.3 Circuit equations; 1.3.1 Transformation of circuit variables; 1.3.2 Transformation of canonical circuit equations; 1.3.3 Nodal equations; 1.3.4 Modified nodal equations; References
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3.1.2 Ill-conditioned systems3.2 Finite methods of solving linear algebraic equations; 3.2.1 Gaussian elimination; 3.2.2 LU factorization methods; 3.2.3 Numerical difficulties in the LU method; 3.3 Sparse matrix technique; 3.3.1 Introductory notes on sparse matrix techniques; 3.3.2 Data-structures for sparse matrix techniques; 3.3.3 A problem of fill-ins and reordering; 3.3.4 Initial nonsymmetrical reordering; 3.3.5 Implementation of the solution procedure; 3.3.6 The sparse-matrix technique dedicated to the tableau equations; References; Chapter 4: D.c. Analysis of Nonlinear Circuits
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4.1 Introduction to d.c. analysis4.1.1 Importance of d.c. analysis; 4.1.2 Substitute d.c. nonlinear circuits; 4.1.3 Outline of iterative methods used in practical simulators; 4.2 A basic Newton-Raphson method; 4.2.1 The case of a single nonlinear equation; 4.2.2 NR method for a system of algebraic equations; 4.2.3 Methods for automatic formulation of iterative equations; 4.2.4 Realization of the basic d.c. analysis algorithm; 4.3: Practical quasi-Newton-Raphson algorithms; 4.3.1 Numerical problems with the basic NR algorithm; 4.3.2 Technique of NR step limiting on nonlinear elements
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4.3.3 Other improvements and extensions of the NR method4.4 Continuation methods; 4.4.1 Homotopies and their applications; 4.4.2 Efficient algorithms for solving homotopies; References; Chapter 5: Time-domain Analysis of Nonlinear Circuits; 5.1 Introduction to integrating circuit equations; 5.1.1 Basic polynomial methods; 5.1.2 Realization of an algorithm for integrating OADE; 5.1.3 BDF based on Newton's interpolation; 5.2 Formulation of circuit equations for time-domain transient analysis; 5.2.1 The companion circuit method; 5.2.2 Numerical problems due to selection of state variables
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Chapter 2: Numerical Analysis of Linear Circuits2.1 Formulation of algebraical circuit equations; 2.1.1 General characterization of linear circuits; 2.1.2 Nodal Equations; 2.1.3 Modified nodal equations; 2.1.4 Two-graph modified nodal equations; 2.1.5 Tableau equations; 2.2 Frequency domain a.c. circuit analysis; 2.2.1 A.c. analysis of linear circuits; 2.2.2 Small-signal frequency analysis of nonlinear circuits; References; Chapter 3: Numerical Solution of Linear Algebraic Equations; 3.1 Introduction to simultaneous linear algebraic equations; 3.1.1 Solvability of sets of linear equations