Capacitor-input filter

The capacitor-input filter, also called the pi filter due to its shape that looks like the Greek letter π, is a type of electronic filter. Filter circuits are used to remove unwanted or undesired frequencies from a signal.

A typical capacitor input filter consists of a filter or reservoir capacitor C₁, connected across the rectifier output, an inductor L, in series and another filter or smoothing capacitor, C₂, connected across the load, R_L. A filter of this sort is designed for use at a particular frequency, generally fixed by the AC line frequency and rectifier configuration. When used in this service, filter performance is often characterized by its regulation and ripple.

The capacitor-input filter operates in three steps:

The component value for the inductor can be estimated as an inductance that resonates the smoothing capacitor(s) at or below one tenth of the minimum AC frequency in the power supplied to the filter (100 Hz from a full-wave rectifier in a region where the power supply is 50Hz). Thus if reservoir and smoothing capacitors of 2200 microfarads are used, a suitable minimum value for the inductor would be that which resonates 2200 microfarads (μF) to 10 Hz, i.e. 115 mH. A larger value is preferable provided the inductor can carry the required supply current.

In general, the relationship between the resonant frequency, which should be less than or equal to one tenth of the minimum AC frequency, in this case 100 Hz, the capacitance, and the inductance can be characterized by the following resonance equation: ${\displaystyle f_{0}={1 \over {2\pi {\sqrt {LC}}}}.}$

...
Wikipedia