A New Representation of Distorted Wave Forms

A new method for representing distorted wave forms is investigated. The method suggested by us is a modified vector symbolic method. It has been hitherto thought that the vector symbolic method cannot be applied to the distorted waves, because the rotating speeds of each harmonic vector are not identical. Representing the argument of the n-th harmonic vector by l/n times as large as the phase angle of the harmonic component, the relative positions of respective harmonic vectors are invariable wherever the standard vector is put, and the wave shape can be deduced from the vector diagram. We found various correspondences between the wave forms and the vector diagrams. Therefore, the wave shape can be estimated from the vector diagram, and the mutual relationships between two wave forms can also be known. In electric or magnetic circuits, the causes of distorted wave forms are in general obvious. Therefore, there are very often the fixed relationships between the amplitudes and phase angles of the harmonics. Further, in polyphase a.c. circuits, there are often the fixed relationships between corresponding harmonics in the wave forms of the respective phases. When the wave forms of those circuits are discussed, the new method investigated in this paper may offer a useful key.