Appendix A

RMS Values of Commonly Observed Converter Waveforms

The waveforms encountered in power electronics converters can be quite complex, containing modulation at the switching frequency and often also at the ac line frequency. During converter design, it is often necessary to compute the rms values of such waveforms. In this appendix, several useful formulas and tables iire developed which allow these rms values to be quickly determined.

RMS values ofthe doubly-modulated waveforms encountered in PWM rectifier circuits are discussed in Section 18.5.

A.1 SOME COMMON WAVEFORMS

DC, FtE. A.l:

rms = /

(A, I)

Fig. Л.1

DC plus linear ripple, Fig. A.2:

Square wave, Fig. A.3:

Sine wave. Fig. A.4:

rms = I

CA.2)

Fig. Л.2

T. t

rms = /

(A3)

Fig. A.3

(0

(A.4)

Fig. A.4

Pulsating waveform, Fig. A.S:

rm.f = I/D

(a.5)

Fig. Л.5

Pulsating waveform with linear ripple. Fig. A.6:

(A.6)

Fig, A.6

Triangular waveform. Fig. A.7:

(A.7)

Fig. A.7

0 D,r, D{r T, ,

Triangular waveform. Fig. A.S:

(A.S)