Electrical circuit analysis using four dimensional complex numbers, in the form of quaternions

摘要

The paper demonstrates how electrical variables, when formulated as vector quaternions, can be manipulated. Circuit parameters can easily be obtained, for analytical purposes. Quaternions, which were discovered 170 years ago, are the basis for four dimensional vectors. Electrical variables fit into this realm, as some circuit variables are in quadrature with one another when viewed across different circuit components. The manipulation of the variables to obtain power, energy and impedance is shown to be simple and visual when vectors are looked at, in various planes of the four dimensional space. Other applications of quaternions and complex numbers in the general field of electrical engineering are also alluded to in the paper for completeness and in particular the famous and initial application of quaternions in electric field theory analysis by James Clerk Maxwell.