# Constant-K LC Low Pass Filter Circuit Design & Calculations

### Design considerations, circuit and formulas for a constant-k 3 pole LC low pass filter for RF applications.

It can often be difficult to design a simple LC low pass filter as the calculations may be difficult to perform or tables of normalised values may not be available.

Although there are some filter calculators on the web, the equations for a simple filter can be easy to handle and they give an insight into the workings of the filter.

## Low pass filter design basics

Low pass filters are used in a wide number of applications. Particularly in radio frequency applications, low pass filters are made in their LC form using inductors and capacitors. Typically they may be used to filter out unwanted signals that may be present in a band above the wanted pass band. In this way, this form of filter only accepts signals below the cut-off frequency.

Low pass filters are normally built up using a number of sections. They can be arranged in either a Pi (Π) or T configuration. For the Π section filter, each section has one series inductor and either side a capacitor to ground.

The T network low pass filter has one capacitor between the RF line and ground and in the signal line, there are two inductors, one either side capacitor. The T section is not always as convenient, because even when additional sections are present, it still required more inductors and these are more expensive to buy or require individual winding.

## Low pass filter design equations

There is a variety of different filter variants that can be used dependent upon the requirements in terms of in band ripple, rate at which final roll off is achieved, etc. The type used here is the constant-k and this produces some manageable equations:

Where:
Z0 = characteristic impedance in ohms
L = Inductance in Henries
fc = Cutoff frequency in Hertz