How to design Shelf and Butterworth HP or LP 6db/oct, 12db/oct filter?

Hello everyone,

I search the SigmaStudio wiki, and I still not figure out how to make a filter that contain db/oct design

If I want to design a High or Low pass Shelf / Butterworth filter with db/oct design, which block should I use (I am using AD1701)?

I only find the butterworth design in the Crossover block.

sorry I am noob on SigmaStudio EQ design

Hope you guys can help me! 




  •      Hello Alvis,

         Here's what blocks to use in order to implement these filters:

    Lowpass & Highpass

         Six dB per octave filters can be implemented with the First-Order Filter Block:

    By definition these are Butterworth filters ("maximally flat in their passband.").  They're analogous to the simple RC filters in the analog world.

    You can also do these filters with the General Second-Order Filter block.  Here you get the advantage of two selectable filters in one -- for example, a Lowpass and a Highpass together:

         If the General Second-Order Filter has enough "horsepower" to build two 6 dB filters, it's reasonable to expect it could make one 12 dB filter.  And it does!  Here we can select a Second-Order Butterworth filter:

    The "horsepower" comes from a more sophisticated algorithm involving two delays and two feedbacks (compared to one each for the First-Order filters).  With the whole block dedicated to one filter, it becomes analogous to Second-Order analog filters which include either an inductor or an extra cap plus an op-amp.

         Need even more dB per octave?  You can cascade several filters.  Though you can do this manually, you'll need to choose differing Q and sometimes frequency for each section to get optimal results.  The Nth-Order Filter block does this math for you.  The last time I looked it only works for even-numbered N -- in other words, it cascades only Second-Order filters, although the theory allows you to mix First-Order and Second-Order filters.

    Shelving Filter

         Choose the General Second-Order Filter and set its drop-down menu to Shelving.  You can change the slope with the knob as shown below.  Likely there's a  formula to translate dB per octave to the setting of this knob, but it hardly matters since the slope cannot be entered numerically anyway.

         Best regards,


  • Hello Bob,

    This is very useful information for me! Big thanks!

    I have another question about shelf EQ, last question is HP/LP Shelf filter, this only adjust the Frequency and Gain value

    If I want to make a "HP/LP Shelf EQ", this can adjust the Frequency, Gain and Q value, but the General filter only give me shelf filter and I can not enter the Q value which I want, the only way is using "Slope" .

    Any suggestion for the Shelf EQ? or using Parametric filter with General HP/LP filter to simulate the  Shelf EQ?




  •      Hello Alvis,

         The relationship between slope factor S and  quality factor Q is rather complicated.  Robert Bristow-Johnson's reference provides this formula relating them:

    1.   1/Q = sqrt((A + 1/A)*(1/S - 1) + 2)

    2.        where  A  = 10^(dBgain/40)

    We can solve this algebraically for S:

    3.   S = (A + 1/A)   { (1/Q^2) - 2 + A + 1/A  }

        It appears from the reference that dBgain in Equation 2 refers to the position of the slider in the filter (the "boost").  I don't see why either the boost or the static gain of the filter would enter into the relationship between S and Q -- since Q relates to the sharpness of the filter, not its gain.  On the other hand, dB per octave slope is definitely affected by these -- a shelving or parametric filter with zero boost has a flat response without any visible slope!  If we set dBgain to zero (unity linear gain), then Equation 1 simplifies to:

    4.   S = 2 * (Q^2)               Example:  Q = 0.707, then S = 1.

    This could be the most useful formula for you to work with.  S = 1 is a good setting for a shelf EQ -- it's the highest slope factor (sharpest filter) without overshoots in the response curve (akin to a Butterworth response).

         Best regards,


  • Hello Bob,

    I have some new questions about db and octave relationship.

    Sometimes I see some Amps spec has "1/36 octave steps" in some parts of Low/High pass filter,

    what does "1/36 octave steps " mean? 

    My opinion is 36 db/octave (Nx6 order, N is 6, which means there are 6 first order block chaining), anything wrong on this? Can you help me to realize the real meaning about "1/36 octave steps"?

    Second question is:

    How to mapping the LP/ HP filter type 12 or 18 db/octave Bessel and Butterworth to the 12 or 24 db/octave Linkwitz Riley 4th or 8th order? (any example?) 

    The above condition, I think it is using crossover block to implement it, but I am not really sure about it.

    Please help me answer these two question, Thank you!

    Best regards,


  •      Hello Alvis,

       I've got time for your first question before heading to work.

    One octave is defined as a pitch range from a given frequency to double that frequency -- for example, middle A is 440 Hz, while 880 Hz is one octave above middle A.  I'm no musician for sure, but I believe the term stems from the eight notes in a scale covering this span.

       A piano has 12 keys covering an octave because its extra notes allow for all scales, not just C-major (the white keys).  The frequency of each note is the twelfth root of two [2^(1/12)] above the previous one.  Equalizers and such with 12 bands per octave use the same formula.

       Thus, a filter featuring 36 per octave steps has 36 frequency choices in each one-octave range.  To do this evenly, start with the lowest frequency and keep multiplying by 2^(1/36) or approximately 1.019441.  You'll end up with frequencies like: 20,  20.4,  20.8,  21.2,  21.6,  22.0,  22.4,  22.9 ...  You can easily calculate these with a spreadsheet (or MATLAB -- but that would be like using a cannon to kill a housefly).

       Best regards,