Theory and calculation of alternating current phenomena . P44S4t 4i Fig. 185. triple and the quintuple harmonic upon the fundamental sinewave. In Fig. 185 is shown the fundamental sine wave and the com-plex waves produced by the superposition of a triple harmonicof 30 per cent, the amphtude of the fundamental, under the rela-24 369 370 AL TERN A TING-C URREN T PHENOMENA tive phase displacments of 0°, 45°, 90°, 135°, and 180°, repre-sented by the equations: sin /3 sin |8 - sin 3 /S sin /3 - sin (3 /3 - 45°) sin /3 - sin (3 /3 ~ 90°) sin )8 - sin (3 /S - 135°) sin ^ - sin (3
Theory and calculation of alternating current phenomena . P44S4t 4i Fig. 185. triple and the quintuple harmonic upon the fundamental sinewave. In Fig. 185 is shown the fundamental sine wave and the com-plex waves produced by the superposition of a triple harmonicof 30 per cent, the amphtude of the fundamental, under the rela-24 369 370 AL TERN A TING-C URREN T PHENOMENA tive phase displacments of 0°, 45°, 90°, 135°, and 180°, repre-sented by the equations: sin /3 sin |8 - sin 3 /S sin /3 - sin (3 /3 - 45°) sin /3 - sin (3 /3 ~ 90°) sin )8 - sin (3 /S - 135°) sin ^ - sin (3 ^ - 180°). ^^.^.. 4i^ft Fig. 186. As seen, the effect of the triple harmonic is, in the first figure,to flatten the zero values and point the maximum values of thewave, giving what is called a peaked wave. With increasingphase displacement of the triple harmonic, the flat zero rises andgradually changes to a second peak, giving ultimately a flat-topor even double-peaked wave with sharp zero. The intermediatepositions represent what is called a saw-tooth wave. In Fig. 186 are shown the fundamental sine wave and the EFFECTS OF HIGHER HARMONICS 371 complex waves produced by superposition of a quintuple har-monic of 20 per cent, the amplitude of the fundamental, under therelative phase displacement of 0°, 45°, 90°, 135°, 180°, representedby the equations: sin /3 sin iS - sin 5 jS sin ^ - sin (5 /S - 45°) sin /3 - sin (5 ^S - 90°) sin 13 - sin (5 /S - 135°) sin 13 - sin (5 i3 - 180°).
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectelectriccurrentsalte
