Butterworth Filters
Butterworth filters have the smoothest curve with no ripples, however they have the slowest roll off speed and so may not be selective enough for our purpose.
The roll off rate is defined as 6n dB/octave; where n is the order number. So a 4th order Butterworth filter will roll off with 6x4 = 24dB per octave.
Chebyshev Filters
Chebyshev Filters have a steeper roll off than Butterworth filters however they have ripples. Type 1 has ripples in the pass band and Type 2 (also called inverse Chebyshev) has ripples in the stop band.
Ripples in the pass band shouldn’t effect the level of ‘noise’ in our readings so a type 1 filter could be used, however ripples in the stop band would mean that very small amounts of higher frequency signal could be detected, and so would be noisy.
It is possible for the ripple to be minimised, for example the calculator previously mentioned allows you to select a ripple of between 1dB and 0.01dB. Minimising the ripple has the disadvantage of slowing the roll off speed, so the greater the ripple the faster the roll off, though this effect looks small.
Bessel Filters
These are similar to Butterworth filters in that they have a very smooth roll off with no ripples, however the roll off speed is much too low as it is similar to a simple RC filter.
Elliptic Filters
Elliptic filters are a hybrid of type 1 and 2 Chebyshev filters, where there is a ripple in both the stop band and the pass band, meaning that there is a much steeper roll off. Although the cut off is steep this filter probably wouldn’t be suitable.
Another disadvantage is that each stage of the circuit uses 3 or 4 op amps, so to create a high order filter there would be a huge number of components.
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Cut off frequency : frequency where the magnitude of the signal falls.
Pass band : section of the signal before the cut off frequency
Stop band : section of the signal after the cut off frequency
Ripples : small jumps in the pass band or stop band
Roll off speed : how quickly the magnitude of the signal falls, i.e. the selectivity of the filter.
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