Teaching Introductory Circuits Using the Theory of Distributions and the Convolution Algebra

Abstract

In this paper we describe what we believe to be an innovation in the teaching of electrical engineering, that is the use of the theory of distributions and the convolution algebra in an introductory circuits course. Teaching the course in this way eliminates the contradiction in the usual defmition of the unit impulse, permits immittance to be defined in the time domain, and facilitates passage from the time domain to the frequency domain. The theory goes far beyond the case of basic circuits and applies to any linear time invariant system. Using distributions, the product of convolution becomes a powerful tool in solving circuit equations; the initial conditions are introduced automatically. It is the authors' belief that in a number of years most linear circuits and systems courses will be taught following the approach presented here.