Butterworth low pass filters

There are so many digital filters like FIR and IIR filter, here this article gives one more analog type batter-worth filter. To shown in figure typical characteristics of batter-worth low pass filter.

This type of response is called a butter-worth response because its main characteristics are that the pass-band maximally flat. It means there are no variations in the pass-band device.

Now the magnitude squared response of low pass butter-worth filters is given by,

  │H(Ω)2  =   1   /  1 + (Ω/Ωc)2N


H(Ω) = Magnitude of analog low pass filter
N = Order of the filter
= Cut of frequency 

Silent features of low pass butter-worth filter :
  • Since the magnitude response is nearly constant at lower frequencies. That means passband and are maximally flat.
  • There are no ripples in the passband and also for stopband.
  • The maximum gain occurs at the value at Ω = 0 and it is │H(0)│= 1
  • The magnitude response is monotonically decreasing.
Application of Butter-worth filter :
  • Butter-worth filter can be used as radar such as in designing the display of radar target track.
  • In high quality, an audio application,s these are used.
  • These are also used in the digital filter for motion analysis.
  • This type of filter most commonly used in anti-aliasing filter in data converter applications