Chebyshev 24db algo need.

Hello Alex,

If all you need is a Chebyshev low or high-pass filter, use the Nth Order Filter which does all the work for you. Here's a 4th order (24 dB) example:

Perhaps, though, you need your microcontroller to calculate coefficients on the fly. Or you need a bandpass filter, which the Nth Order Filter won't do. This is a two-step process: First, given the response you need, find the gain, critical frequency, and Q for each biquad section your filter needs, then calculate the coefficient set for each of these. The easiest way to find the filter stages for a desired response is to use a filter design program -- and AD provides one at: https://www.analog.com/designtools/en/filterwizard/

For example, let's make a filter with 1 KHz center frequency, a 3 dB BW from 707 Hz to 1414 Hz, with 4 stages providing a 24 dB / octave slope, and 0.5 dB passband ripple. The inputs to AD's Filter Wizard might look like this:

Here I set the center frequency to 1 KHz, the upper 3 dB point at 1.41 KHz, and the stopband to -27 dB at 2.82 KHz to provide a 24 dB / octave slope. Then, I moved the Filter Response slider to the left, until it yielded a Chebyshev 0.5 dB ripple result.

Continued below...

The wizard generated four stages, each with the freq, BW, and Q you need to produce the filter. To see these parameters, choose Components at the top menu, and set the View drop-down to Stages::

Note that the last two stages have a higher gain than the first two -- the wizard arranges these for maximum dynamic range of the analog filter. For our purpose, it's easier to multiply all the gains together, convert this to dB and then divide this total gain equally among your stages. With that done, now all you need do is to calculate the IIR Coefficients for each stage. The spreadsheet attached below embeds these formulas in its very last filter type, the Peaking (bandpass) filter -- scroll to the right. Below I show the resulting SigmaStudio schematic with four General 2nd Order Filters -- the top row of filters have been set by the dB gain, frequencies and Q's, the bottom row with the coefficients calculated by the spreadsheet. The two response curves line up nicely.

Once you have the desired Chebyshev response for one frequency, you can produce a similar response at other frequencies by scaling the frequency of all stages together. Thus, you're able to input a desired frequency to your microcontroller and have it calculate a coefficient set. I attached the project file so you can look inside the filter stages as needed, and the spreadsheet containing the coefficient formulas.

This post might also be helpful, near its end there's a link to a more mathematical treatment of this subject:

https://ez.analog.com/dsp/sigmadsp/f/q-a/65394/calculate-coefficients-of-chebyshev-and-notch-filters

Best response,

Bob

Cheby-Fil.zip

3223.Chebyshev_4th-Order.zip