Capacitor Effect

If the rectifier had no filter capacitor, the rectifier would deliver the average value of the rectified voltage wave, less regulation components 1 and 2 of Section 51. But with a filter capacitor, there is a tendency at light loads for the capacitor to charge up to the peak value of the rectified wave. At zero load, this amounts to 1.57 times the average value, or a possible regulation of 57 percent in addition to the IR and IX components, for single-phase full-wave rectifiers. This effect is smaller in magnitude for polyphase rectifiers, although it is present in all rectifiers to some extent.

Suppose that the rectifier circuit shown in Fig. 80(a) delivers single-phase full-wave rectifier output as shown in Fig. 80(b) to an inductor-input filter and thence to a variable load. In such a circuit, the filter inductor keeps the capacitor from charging to a value greater than the average E_dc of the rectified voltage wave at heavy loads. At light loads the d-c output voltage rises above the average of the rectified wave, as shown by the typical regulation curve of Fig. 89.

Fig. 89. Rectifier regulation curve.

Starting at zero load, the d-c output voltage E₀ is 1.57 times the average of the rectified wave. As the load increases, the output voltage falls rapidly to E₁ as the current I₁ is reached. For any load greater than I₁ the regulation is composed only of the two components IR and IX. It is good practice to use a bleeder load I₁ so that the rectifier operates between I₁ and I₂.

Filter elements X_L and X_c determine the load I₁ below which voltage rises rapidly. The filter, if it is effective, attenuates the a-c ripple voltage so that across the load there exists a d-c voltage with a small ripple voltage superposed. A choke-input filter attenuates the harmonic voltages much more than the fundamental, and, since the harmonics are smaller to begin with, the main function of the filter is to take out the fundamental ripple voltage. This has a peak value, according to Fig. 83, of 66.7 percent of the average rectified d-c voltage for a single-phase full-wave rectifier. Since this ripple is purely a-c it encounters a-c impedances in its circuit. If we designate the choke impedance as X_L, and the capacitor impedance as X_C, both at the fundamental ripple frequency, the impedance to the fundamental component is X_L - X_c, the load resistance being negligibly high compared to X_c in an effective filter. The d-c voltage, on the other hand, produces a current limited mainly by the load resistance, provided that the choke IR drop is small.

Fig. 90. A-c and d-c components of filter current.

A-c and d-c components are shown in Fig. 90, with the ripple current I_ac superposed on the load direct current I_dc. If the direct current is made smaller by increased load resistance, the a-c component is not affected because load resistance has practically no influence in determining its value. Hence a point will be reached, as the d-c load current is diminished, where the peak value of ripple current just equals the load direct current. Such a condition is given by d-c load I₁ which is equal to I_ac. If the d-c load is reduced further, say to the value I_x, no current flows from the rectifier in the interval A-B of each ripple cycle. The ripple current is not a sine wave, but is cut off on the lower halves, as in the heavy line of Fig. 91.

Fig. 91. Capacitor effect at light load.

Now the average value of this current is not I_x but a somewhat higher current I_y. That is, the load direct current is higher than the average value of the rectified sine wave voltage divided by the load resistance. This increased current is caused by the tendency of the capacitor to charge up to the peak of the voltage wave between such intervals as A-B; hence the term capacitor effect which is applied to the voltage increase. The limiting value of voltage is the peak value of the rectified voltage, which is 1.57 times the sine-wave average, at zero load current.

To prevent capacitor effect the choke must be large enough so that I_ac is equal to or less than the bleeder current I₁. This consideration leads directly to the value of choke inductance. The bleeder current I₁ is E₁/R₁, where R₁ is the value of bleeder resistance. The ripple current is the fundamental ripple voltage divided by the ripple circuit impedance, or

Equating I₁ and I_ac we have, for a single-phase full-wave rectifier,

[52]

Here we see that the value of capacitance also has an effect, but it is minor relative to that of the choke. In a well-designed filter, the choke reactance X_L is high compared to X_c. Therefore, the predominant element in fixing the value of R₁ (and of I₁) is the filter reactor.

Polyphase rectifiers have similar effects, but the rise in voltage is not so great because of the smaller difference between peak and average d-c output. The bleeder resistance for eliminating capacitor effect can be found in general from

[53]

where P₁ is the fundamental ripple peak amplitude from Fig. 83, and X_L and X_c are the filter reactances at fundamental ripple frequency.

Between load I₁ and zero load, the rate of voltage rise depends upon the filter. Figure 92 shows the voltage rise as a function of the ratio (X_L - X_C)/R_L for a single-phase full-wave rectifier. A curve of ripple in terms of ripple at full load is given. Figure 92 is a plot of experimental data taken on a rectifier with IR + IX regulation of 5 percent. Reactances X_L and X_c are computed for the fundamental ripple frequency.

Capacitor-input filters have the voltage regulation curves shown in Figs. 50, 51, and 53) (pp. 64, 65, and 68) for their respective circuits. At light loads these filters may give reasonably good regulation, but it is possible to get very poor regulation at heavier loads, as can be seen from the curves. Rectifier series resistance plays an important part in the voltage regulation of this type of filter. The effect of anode transformer leakage inductance can be found from Fig. 92.

Fig. 92. Voltage rise in single-phase full-wave rectifier at light loads.