Non-linear Circuits

The main theme of this text is the analysis of non-linear non-reciprocal resistive circuits. The subject is tackled systematically by a method which is accessible to the intuitive approach of engineers. This is due to the fact that the main method of referring to the connections of the components is to use to orientations of the circuit branches, which are none other than the directions of the currents and voltages in these branches. Thus the topological criteria for the uniqueness of the solution or the possible presence of a finite number of solutions is formulated in terms of the possibility of having certain directions for the currents and voltages in the circuits. The book gives a rigorous description of the classification of non-linear resistive circuits into three groups. The first consists of circuits which are useful for the immediate processing of data. The second consists of those suitable for memorizing data - if the parameters of their components are suitably chosen, they possess several solutions. The third group consists of all those circuits which are inadequate models of devices because they possess either no solutions or an infinite number of solutions.
Purely topological criteria are provided to enable us to determine to which group a given circuit belongs. These criteria can be applied using pencil and paper methods only in the case of circuits consisting of a few elements. Beyond that, a computer must be used. While this book gives a definitive response to the problem of classifying circuits, it also opens up new perspectives in the synthesis of circuits capable of memorizing data. Minimum circuits with several solutions are characterized topologically. These are the elementary modules for circuit synthesis.