A New Technique for Analog Integration and Differentiation

A technique is described which enables an approach to ideal analog integration or differentiation by means of passive elements only. A series of RC circuits in a cascade arrangement, uncoupled to each other, provides the first, second, third, etc., integrals or derivatives (according to the connection of the RC circuits) of the input function. The theory establishes that if the outputs of each are fed to an analog summing amplifier, its output becomes arbitrarily close to the ideal integral or derivative of the input function as the number of RC stages is raised indefinitely. A device has been developed according to this idea to perform one of these operations (integration) and to check the results obtained in theory. Mathematical proofs of the theory are given in the paper.