Theory and calculation of alternating current phenomena . 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
Theory and calculation of alternating current phenomena . 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°).. Fig. 187.—Some characteristic wave-shapes. The quintuple harmonic causes a flat-topped or even double-peaked wave with flat zero. With increasing phase displacementthe wave becomes of the type called saw-tooth wave also. Theflat zero rises and becomes a third peak, while of the two former 372 ALTERNATING-CURRENT PHENOMENA peaks, one rises, the otlier decreases, and the wave graduallychanges to a triple-peaked wave with one main peak, and a sharpzero. As seen, with the triple harmonic, flat top or double peakcoincides with sharp zero, while the quintuple harmonic flat topor double peak coincides with flat zero. Sharp peak coincides with flat zero in the triple, with sharpzero in the quintuple harmonic. With the triple harmonic, thesaw-tooth shape appearing in case of a phase difference betweenfundamental and harmonic is single, while with the quintupleharmonic it is double. Thus in general, from simple inspection of the wave-shape,the existence of these first harmonics can be discove
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