Rectifiers with Capacitor-Input Filters

When the filter has no reactor intervening between rectifier and first capacitor, rectifier current is not continuous throughout each cycle and the rectified wave form changes. During the voltage peaks of each cycle, the capacitor charges and draws current from the rectifier. During the rest of the time, no current is drawn from the rectifier, and the capacitor discharges into the load.

Fig. 49. Voltage and current comparisons in reactor-input and capacitor-input circuits

Comparison between the rectified voltage of reactor-input and capacitor-input filters in a single-phase full-wave rectifier may be seen in Figs. 49(a) and (b), respectively. The two tube currents I₁ and I₂ in (a) add to a constant d-c output, whereas in (b) the high-peaked tube currents flow only while the rectified voltage is higher than the average d-c voltage. Average current per tube in both cases is half the rectifier output. With large values of capacitance, the rectified voltage in Fig. 49(b) increases to within a few per cent of the peak voltage. Ripple, average rectified voltage output, and rectifier current are dependent on the capacitance, the supply line frequency, and the load resistance. They are dependent also on rectifier internal resistance because it affects the peak value of current which the filter capacitor can draw during the charging interval Δt.

Fig. 50. Relation of peak sine voltage to d-c voltage in half-wave capacitor-input circuits.

Analysis of this charge-discharge action involves complicated Fourier series which require a long time to calculate.⁽¹⁾ Satisfactory voltage and current values have been obtained from experimental measurements by Schade ⁽²⁾ and are shown in Figs. 50, 51, and 52 for single-phase half-wave and full-wave rectifiers.

Fig. 51. Relation of peak sine voltage to d-c voltage in full-wave capacitor-input circuits.

Fig. 52. Relation of peak, average, and rms diode current in capacitor-input circuits.

In these figures R_s is the rectifier series resistance, including the transformer resistance.

Results accurate to within 5 per cent are obtained if the rectifier resistance corresponding to peak currentis used in finding R_s. The process is cut-and-try, becausedepends on R_s, and vice versa, but two trials usually suffice. Resistance is in ohms, capacitance is in farads, and ω is 2π times the supply frequency. Three-phase rectifiers are rarely capacitor-input because of their larger power.

In Fig. 52 the peak current indicates whether the peak current of a given tube is exceeded, and the rms current determines the transformer secondary heating. The v-a ratings are greater, but ratios of primary to secondary v-a ratings given in Table VII hold for capacitor-input transformers also.

(1)	See "Diode Rectifying Circuits with Capacitance Filters," by D. L. Waidelich, Trans. A1EE, 61, 1161 (December, 1941).
(2)	Analysis of Rectifier Operation," by O. H. Schade, Proc. I.R.E., 31, 341 (July, 1943).