Symbolic Representation of General Alternating Waves and of Double Frequency Vector Products.pdf

A payerfresented at the Sixteenth General Meet- ing of the A merican Institute of Electrical Engineers, Boston, June 26th, z899, President Kennelly in the Chair. SYMBOLIC REPRESENTATION OF GENERAL AL- TERNATING WAVES AND OF DOUBLE FREQUENCY VECTOR PRODUCTS. BY CHARLES PROTEUS STEINMETZ. PART 1. a. Graphically alternating currents and E. M. F.s are usually represelnted by vectors. A vector is a quantity having length and direction. The length represents the intensity, the direction the phase of the alternating wave. The vectors generally issue from the center of co-ordinates. In the topographical method, however, which is more conven- ient for complex nietworks, as interlinked polyphase circuits, the alternating wave is represented by the straight line between two points, these points representing the absolute values of potential (with regard to anv reference point chosen as co-ordinate center) and their connection the difference of potential, in phase and in- tensity. Algebraically these vectors are represented by complex quantities. The impedance, admittance, etc., of the circuit is a complex quantity also, In symbolic denotation. Thus current, E. M. F.S impedanee and admittance are related by muultiplication and division of complex quantities similar as current, E. M. F., resistance and conductance are related by Ohms law in direct current circuiits. In direct current circuits, power is the product of current into E. M. F. In alternating current circuits, if . E= +jei 269 Authorized licensed use limited to: NATIONAL LIBRARY OF CHINA. Downloaded on March 12,2010 at 06:08:38 EST from IEEE Xplore. Restrictions apply. 270 STEINMJETZ ON SYMBOLlC REPRESEFNTATION LJune 26, The product: Po0= El (el i ell ill) +± (ell1 + elIt11) is not the power, that is multiplication and divisioni which are correct in the inter-relatioll of current, E. M. F., impedance, do not give a correct result in the inter-relatiorn of E. M. F., current power. The reason is that E I are vectors of