# 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 simple pi filter, containing a pair of capacitors, an inductor, and a load.

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, RL. 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.

## Operation

The capacitor-input filter operates in three steps:

1. The capacitor C1 offers low reactance to the AC component of the rectifier output while it offers infinite resistance to the DC component. As a result the capacitor shunts an appreciable amount of the AC component while the DC component continues its journey to the inductor L.
2. The inductor L offers high reactance to the AC component but it offers almost zero resistance to the DC component. As a result the DC component flows through the inductor while the AC component is blocked.
3. The capacitor C2 bypasses the AC component which the inductor had failed to block. As a result only the DC component appears across the load RL.

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. 1 mH. A larger value is preferable provided the inductor can carry the required supply current.

In general, the relationship between the resonant frequency (in hertz), which should be less than or equal to one tenth of the minimum AC frequency, in this case 100 Hz, the capacitance (in farads), and the inductance (in henries) can be characterized by the following resonance equation: $f_0 = {1 \over {2 \pi \sqrt{LC}}}.$

## Comparison with other filters

Capacitor input filters can provide extremely pure DC supplies, but have fallen out of favour because inductors tend to be unavoidably heavy, which has led to the often-preferred choice of voltage regulators instead.

• More output voltage
• Ripple-free output