Polyphase Rectifiers

The effect of rectifying more than one phase is to superpose more voltages of the same peak value but in different time relation to each other. Figures 82 (a) and (b) give a comparative picture of the rectified output voltage for three-phase half-wave and full-wave rectifiers.

Fig. 82. Polyphase rectifier output waves.

Increasing the number of phases increases the value of E_dc, increases the frequency of the alternating components, and decreases the amplitude of these components. Ripple frequency is p times that of the unrectified alternating voltage, p being 1, 2, 3, and 6 for the respective waves. Roughly speaking, p may be taken to represent the number of phases, provided that due allowance is made for the type of circuit, as in Fig. 83.

Fig. 83. Rectifier ripple voltage.

Rectifiers with p = 3 or 6 are derived from three-phase supply lines, and, by special connections, rectifiers with p = 9, 12, or more are obtained.

The frequency of any ripple harmonic is mp, where m is the order of the harmonic.

Ripple voltage for any of these rectifiers can be found by the Fourier relation:

[45]

where

A_n = amplitude of nth ripple harmonic
T = ripple fundamental period
t = time (with peak of rectified wave as t = 0)
ω = 2π/Tp = 2π · supply line frequency
f(t) = ripple as a function of time = E_pk cos ωt, (T/2 > ωt > - T/2).

The voltage peak is chosen as t = 0 to obtain a symmetrical function f(t) and eliminate a second set of harmonic terms like those in equation 45, but with sin nωt under the integral.

Ripple amplitude is given in Fig. 83 for the ripple fundamental, and second and third harmonics with reactor-input filters. In this curve, the ratio P_A of ripple amplitude to direct output voltage is plotted against the number of phases p. It should be noted that P_A diminishes by a considerable amount for the second and third harmonics. In general, if a filter effectively reduces the percentage of fundamental ripple across the load, the harmonics may be considered negligibly small.