I just recently discovered how to use the Butterworth coefficients to simulate a low pass filter and it couldn't be easier. The schematic shows an Eighth order Butterworth filter where the resistors are the Butterworth coefficients that are published in tables. There are 4 second order filters in series and each second order filter gets a coefficient value for its resistor, The coefficients never need changing as long as every inductor equals every capacitor in value. The filter frequency is changed by changing all the Ls and Cs keeping L=C while applying the equation 2*(pi)(Freq)(SQRT(L*C))=1. All the Cs must equal all the Ls for the coefficients to work. This filter works well for measuring the harmonic distortion of a Class D amplifier when using a simulator and it is very straightforward to set its cutoff frequency. The pattern is the same for all even order low pass Butterworth filters. I hope that some one finds this information useful.
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These coefficients are useful only for filters with buffers in between adjacent sections. The table for a passive filter (without buffers) is given below. You'd first make a 1Hz filter and then scale the LC values to obtain the actual filter at the required cutoff frequency using
http://www.crbond.com/papers/btf2.pdf
http://www.crbond.com/papers/btf2.pdf
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