Page 328 - Power Electronics Handbook

318 D.C. link frequency changers
AdAT and there are as many pulses per cycle as the ratiofdfs. The Fourier
coefficient of this waveform is given by equation (13.13) and the total r.m.s.
content by equation (13.14).

(13.14)

Equations (13.13) and (13.14) have been evaluated in Tables 13.5-13.8
forf+”s = 4,6,10 and 20 respectively. These tables indicate an increase in
total harmonic content with pulse numbers where fdfS = 2 corresponds to
a quasi-square wave. However, the lower harmonics are now considerably
attenuated, and this is illustrated more clearly in Figure 13.38, where the

Tab& 13.5 hnwalc content ufa 4- moddated uddhdod wave withfrlfs = 4

AdAr R.M.S. VOltagt? 11s percentage of d.c. supply
1 3 5 7 9 11 13 15 Total

0 90.0 30.0 18.0 12.9 10.0 8.18 6.92 6.00 100
0.1 82.7 36.2 9.74 17.7 1.11 11.5 2.29 7.84 94.9
0.2 74.8 40.3 0.00 17.3 8.31 6.80 9.31 0.00 89.4
0.3 66.5 42.3 9.74 11.8 13.8 2.70 7.44 7.84 83.7
0.4 57.8 41.9 18.0 2.84 12.6 10.3 1.53 6.00 77.5
0.5 48.7 39.2 23.5 6.% 5.41 10.7 9.05 3.25 70.7
0.6 39.3 34.3 25.5 14.7 4.37 3.58 7.92 8.49 63.2
0.7 29.7 27.6 23.5 18.1 12.1 6.05 0.77 3.25 54.8
0.8 19.9 19.3 18.0 16.2 14.0 11.4 8.72 6.00 44.7
0.9 9.99 9.90 9.74 9.50 9.18 8.80 8.35 7.84 31.6
0.98 2.00 2.00 2.00 2.00 1.99 1.99 1.99 1.98 14.1

Table 13.6 Humonk content of a 4lure moddated uddhdod wave with/& = 6

As& R.M.S. voltage os percentage of d.c. supply
~~ ~
1 3 5 7 9 11 13 15 Total
0 90.0 80.0 18.0 12.9 10.0 8.18 6.92 6.0 100
0.1 81.7 29.6 25.5 4.00 8.93 14.6 2.15 4.22 94.9
0.2 73.2 28.5 31.2 5.36 5.90 16.3 10.3 0.02 89.4
0.3 64.5 26.7 34.8 14.0 1.58 12.7 13.8 4.26 83.7
0.4 55.6 24.3 36.0 20.8 3.07 5.04 11.2 6.02 77.5
0.5 46.6 21.2 34.8 24.9 7.05 4.25 3.57 4.26 70.7
0.6 37.4 17.6 31.2 25.6 9.49 12.2 5.65 0.02 63.2
0.7 28.2 13.6 2S.5 22.9 9.86 16.2 12.4 4.22 54.8
0.8 18.8 9.25 18.0 17.2 8.07 15.0 13.6 5.98 44.7
0.9 9.44 4.47 9.34 9.23 4.52 8.93 8.73 4.22 31.6
0.98 1.90 0.92 1.90 1.90 0.92 1.90 1.90 0.92 14.1