Single-Phase Rectifiers

Single-phase half-wave rectified voltage across a resistive load R is shown in Fig. 77.

Fig. 77. Half-wave rectifier voltage.

It may be resolved by Fourier analysis into the direct component whose value is 0.318E_pk or 0.45E_ac, and a series of alternating components. The fundamental alternating component has the same frequency as that of the supply.

Single-phase half-wave rectifiers are used only when the low average value of load voltage and the presence of large variations in this voltage are permissible. The chief advantage of this type of rectifier is its simplicity. A method of overcoming both its disadvantages is illustrated in Fig. 78 where a capacitor C shunts the load. By using the proper capacitor, it is often possible to increase the value of E_dc to within a few per cent of the peak voltage E_pk.

Fig. 78. Capacitor filter.

The principal disadvantage of this method of filtering is the large current drawn by the capacitor during the charging interval as shown in Fig. 49(b) (p. 63). This current is limited only by transformer and rectifier regulation; yet it must not be so large as to cause damage to the rectifier. The higher the value of E_dc with respect to E_ac, the larger is the charging current taken by C (see Figs. 50 and 52). Therefore, if a smooth current wave is desired, some other method of filtering must be used.

To obtain less voltage variation or ripple amplitude, after the limiting capacitor size has been reached, an inductive reactor may be employed. It may be placed on either the rectifier or the load side of the capacitor, depending on whether the load resistance R is high or low respectively. See Figs. 79(a) and (b). In the former, the voltage E_dc has less than the average value 0.45E_ac, because the inductor delays the build-up of current during the positive half-cycle of voltage, and yet the inductor in this case should have a high value of reactance X_L, compared to the capacitive reactance X_C, in order to filter effectively. When R is low, reactance X_L should be high compared to R.

Fig. 79. (a) Inductor-input filter; (b) capacitor-input filter.

In Fig. 79 (a) the ripple amplitude across R is -X_C/(X_L - X_C) times the amplitude generated by the rectifier, if R is high compared to X_c. Also, in Fig. 79(b), the ripple amplitude across R is R/X_L times the ripple obtained with capacitor only. R here is small compared to X_L. Large values of inductance are required to cause continuous current flow when the inductor is on the rectifier side of the capacitor in a half-wave rectifier circuit. Since current tends to flow only half the time, the rectified output is reduced accordingly. This difficulty is eliminated by the use of the full-wave rectifier of Fig. 80.

Fig. 80. (a) Single-phase full-wave rectifier; (b) rectified full-wave voltage.

The alternating components of the output voltage have a fundamental frequency double that of the supply, and the amplitudes of these components are much less than for the half-wave rectifier. The higher ripple frequency causes L and C to be doubly effective; the smaller amplitude results in smaller percentage of ripple input to the filter. Current flow is continuous and E_dc has double the value that it had in Fig. 77. For these reasons, this type of rectifier is widely used.

A full-wave rectifier uses only one-half of the transformer winding at a time; that is, E_ac is only half the transformer secondary voltage. A circuit which utilizes the whole of this voltage in producing E_dc is the single-phase bridge rectifier shown in Fig. 81.

Fig. 81. Bridge rectifier.

The output voltage relations are the same as those of Fig. 80(b). Although this circuit requires more rectifying tubes, it eliminates the need for a transformer midtap.