Chaper 1 Introduction

Abstract

This chapter introduces the methods for studying the properties of electrical networks, which are independent of the device characteristic. Only topological constraints are used—namely, Krichoff's current law (KCL) and Kirchoff's voltage law (KVL). These methods are also called “network topological.” The chapter presents applications to circuit simulation and circuit partitioning and establishes the relations between the optimization problems that arise naturally, while using these methods, to the central problems in the theory of submodular functions. There are more immediate applications possible. The most popular general purpose simulator currently running—SPICE—uses the modified nodal analysis approach. In this approach, the devices are divided into two classes, generalized admittance type whose currents can be written in terms of voltages appearing somewhere in the circuit, and the remaining devices. The final variables in terms of which the solution is carried out is the set of all nodal voltages and current variables. The resulting coefficient matrix is very sparse but suffers from several defects.