## Mathematical Aspects of Electrical Network AnalysisHerbert S. Wilf, Frank Harary The volume constitutes the final scientific report for a symposium on Mathematical Aspects of Electrical Network Theory. It contains thirteen papers presented during the April 1969 meeting of the American Mathematical Society. Topics covered include numerical techniques for nonlinear circuit analysis, network models, perturbation theory for nonlinear network synthesis, and graph theoretic applications to electrical network theory. (Author). |

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### Contents

Nonlinear Reciprocal Networks | 1 |

A New Perturbation Theory for the Synthesis of Nonlinear Networks | 17 |

Numerical Techniques for Fast and Accurate Transient Analysis of Nonlinear Circuits | 35 |

Graph Theory and Some of its Applications in Electrical Network Theory | 45 |

Network Models | 65 |

On Global Linearization | 93 |

Successive Secants in the Solution of Nonlinear Network Equations | 103 |

Existence and Uniqueness of Solution to Electrical Network Problem via Homology Sequences | 113 |

Some Properties of a Nonlinear Model of a System for Synchronizing Digital Transmission Networks | 119 |

Equivalent Nonlinear Networks | 141 |

Some Applications in Electrical Network Theory of a Linear Graph Theorem by Berge and GhouilaHouri | 149 |

A Review of Some Recent Developments in the Synthesis of Rational Multivariate PositiveReal Matrices | 161 |

Kirchhoffs Laws and MapColoring Problems | 191 |

### Common terms and phrases

admittance algebraic arbitrary branches capacitors circuit class linearization coloring components connection consider constant convergence Corollary corresponding current graph cut-set defined denote differential equations directed graph driving-point impedance edges electrical network electrical network problem equivalent exists fc-tree flow flowgraph function given graph G graph theory Heawood conjecture hence hermitian hermitian matrix Hurwitz ideal diode inductors infinite number input integration interconnection internal signature matrix joint resistance Kirchhoff's Kirchhoff's current law Kirchhoff's voltage law Lemma Liapunov function linear network linear system linearized equivalent loop multivariable n-vector network theory network-symmetric realization nonlinear networks notation obtained orientation pair passive polynomial ports positive positive-real presumed operating point Proof properties reciprocal resistive n-port resistor result satisfies secant method shown in Figure signature matrix solution stability subgraph successive secant method sup x(f Suppose symmetric synthesis techniques Theorem transformation variables vector vertex vertices voltage weighting pattern zero