# Pi Filter Design For Power Supply (with Calculator)

Power supplies generate noise and voltage ripple. This can interfere with other circuits they are connected to. A Pi filter (configured like the symbol π) is often required to eliminate high frequency noise in switching power supplies.

## Introduction

The first step is to determine either through analysis or prototyping, the frequency of the noise.

For the purpose of the design, let’s assume the filter is to be designed for a cut off frequency of Fc. At this frequency the signal attenuation will be 3 dB or half the power. Frequencies lower will pass through with minimum loss in power.

The filter attenuation (or gain) curve will look like the picture below. The frequencies to be eliminated are much higher than Fc.

For instance to eliminate noise having frequency components that are 1 MHz and higher, a reasonable Fc might have to be 10 kHz. It all depends on how much attenuation is desired. If Fc is 100 kHz, the noise attenuation won’t be as high compared with if Fc = 10 kHz.

## Pi Filters

The next step is to design a Pi LC filter to eliminate unwanted noise generated by the supply from entering circuitry on either side of the power supply (input or output).

A Pi filter is popular on account of its simplicity and performance. The low pass filter consists of two capacitors and one inductor as shown in the picture below. The components are configured like the Greek letter π.

There are two Pi filter designs depending on the input and output impedance values.

### Power Supply Pi Filter Calculator (equal Zo)

In this case, the input and output impedance is the same – Zo.

For a cutoff frequency of Fc, the values of the inductor and capacitor are given by the formulas

L = Zo/(π*Fc)

C = 1/(Zo*π*Fc)

As well, the following tool computes the capacitor and inductor values in the same scenario.

#### Example Calculation

To eliminate noise frequency of 1 MHz, we can design a low pass filter with 10 kHz cutoff frequency. Use an impedance value of 50 ohm in the calculator above. This results in an inductor value L = 1.6 mH and equal capacitor values C = 0.64 uF.

The components are arranged in a Pi configuration with two caps to ground (one at the input and the other at the output) and an inductor in between.

### Power Supply Pi Filter Calculator (unequal source and load impedance)

The source and load impedance can sometimes be unequal and a Pi filter can be used in this situation as well. The equations to calculate C1, L2 and C3 are derived by Horowitz and Hill in .

Enter the Load Impedance in Ohms and the Cut-off frequency Fc.

This calculator applies when the source resistance (RS) is much greater than the load resistance (RL)

This particular filter is a Butterworth filter .

#### Example Calculation

For a small load resistance of 10 ohm and Fc = 10 MHz, the values for the Pi filter are as follows:

• C1 = 1.6 nF
• L2 = 0.32 uH
• C3 = 1.6 nF

If the source resistance is much smaller than the load resistance, then a T filter consisting of one capacitor and two inductors will have to be used.

Either the T or Pi configurations can be used when the source and load impedances are identical. However a Pi is preferred as it uses fewer inductors. Inductors are more expensive than capacitors and the Pi filter is therefore more economical than a T Filter.