A unified theory of lumped circuits and differential systems based on Heaviside operators and causality

摘要

The paper demonstrates that a coherent and logical foundation for circuits and systems can, in an entirely elementary manner, be based upon the Heaviside operational calculus and causality. It is commonly believed that the operational calculus is both difficult and nonrigorous; in fact, it is neither. Further, it is more general than the Laplace transform in that it involves integration over only a finite interval and thus introduces no convergence questions as does the latter. Since it analyzes circuits and systems directly in the time domain, the Heaviside method is more intuitive and direct to apply. Furthermore, it provides a theme, a motif, linking all of the major concepts of circuits and systems. It is argued here that circuit analysis and system theory are currently taught as disparate disciplines, both being presented as a collection of isolated topics. The Heaviside theory, on the other hand, permits the two to be taught in an integrated fashion-with circuits providing concrete examples and system theory the abstract and general mathematical methodology.