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# Half-Wave Rectifier with Filter

A power supply filter greatly reduces the fluctuations in the output voltage of a half-wave or full-wave rectifier and produces a nearly constant dc voltage. Filtering is necessary because electronic circuits require a source of constant dc voltage and current to provide power and biasing for proper operation, as we saw in the CD/DVD power supply application. Filtering is done using capacitors, inductors, or combinations of both.

The circuit works as follows.

** During the positive input half-cycle:** The diode is forward-biased, allowing the capacitor to charge to within a diode drop of the input peak. When the input voltage drops below the capacitor voltage the diode becomes reverse-biased and the capacitor discharges via the load resistor.

** During the negative input half-cycle:** The capacitor continues to discharge through the load resistor at a rate determined by the RLC time constant. The larger the time constant, the less the capacitor will discharge.

** During the first quarter of the next input cycle:** The diode will again become forward-biased when the input voltage exceeds the capacitor voltage by approximately the diode barrier voltage and the capacitor will be charged again.

The role of an inductor is to additionally reduce the ripple voltage, because it has a high reactance at the ripple frequency, and the capacitive reactance is low compared to both **X _{L}**and

**R**. The two reactances form an ac voltage divider which tends to significantly reduce the ripple from that of a pure capacitor filter. However, an LC rectifier produces an output with a dc value approximately equal to the average value of the rectified input. A capacitor filter produces an output with a dc value approximately equal to the peak value of the input. Another point of comparison is that the amount of ripple voltage in the capacitor filter varies inversely with the load resistance. Ripple voltage in the LC filter is essentially independent of the load resistance and depends only on

**X**and

_{L }**X**as long as

_{C}**X**is sufficiently less than

_{C}**R**.

The inductance **L** is chosen to offer high impedance to the ac ripple voltage and low impedance to the dc component. Therefore, for the ac ripple, a very large voltage drop occurs across the inductor and a very small voltage drop across the load** R _{L}**. For the dc component, however, a very small voltage drop occurs across the inductor and a very large voltage drop across the load. The capacitor

**C**bypasses the ac component which the inductor fails to block. As a result only the dc component appears across the load

**R**.

_{L}For a filter with an inductor, the ripple decreases when **L** is increased and **R _{L}** is decreased. Thus the inductor filter is more effective only when the load current is high (small

**R**). The larger value of the inductor can reduce the ripple; at the same time, the output dc voltage is lowered as the inductor has a higher dc resistance. Since the action of an inductor is to oppose any change in current flow, the inductor tends to keep a constant current flowing to the load throughout the complete cycle of the applied voltage.

_{L}