BUTTERWORTH FILTER

Introduction

There are mainly three considerations in designing a filter circuit they are

  • The response of the pass band must be maximum flatness.
  • There must be a slow transition from pass band to the stop band.
  • The ability of the filter to pass signals without any distortions within the pass band.

These distortions are generally caused by the phase shifts of the waveforms. In addition to these three the rising and falling time parameters also play an important role. By taking these considerations for each consideration one type of filter is designed. For maximum flat response the Butterworth filter is designed. For slow transition from pass band to stop band the Chebyshev filter is designed and for maximum flat time delay Bessel filter is designed.

 

                             Butterworth Filter

At the expense of steepness in transition medium from pass band to stop band this Butterworth filter will provide a flat response in the output signal. So, it is also referred as a maximally flat magnitude filter. The rate of falloff response of the filter is determined by the number of poles taken in the circuit. The pole number will depend on the number of the reactive elements in the circuit that is the number of inductors or capacitors used in the circuits.

The amplitude response of nth order Butterworth filter is given as follows

Vout / Vin = 1 / √{1 + (f / fc)2n}

Where ‘n’ is the number of poles in the circuit. As the value of the ‘n’ increases the flatness of the filter response also increases.

‘f’ = operating frequency of the circuit and  ‘fc‘ = centre frequency or cut off frequency of the circuit.

These filters have pre-determined considerations whose applications are mainly at active RC circuits at higher frequencies. Even though it does not provide the sharp cut-off response it is often considered as the all-round filter which is used in many applications.