[sdiy] Ladder filters and gain drop, that old chestnut

[Russell McClellan]

This was a fascinating discussion, thanks for all your insights!

I was curious, so I went ahead and translated Andrew Simper's
directions for calculating the needed gain into python code here:

https://gist.github.com/russellmcc/c0b0eb8ab7920fe5aee2

Feel free to play around with it as you like, it works for an
arbitrary transfer function, including diode filters - it turns out
for a standard diode filter you need a gain of 18 or so.

I provided code for either numerical evaluation with numpy and
symbolic evaluation with sympy - sympy doesn't seem to be able to deal
with high pole order transfer functions, though.

Thanks,
-Russell

On Mon, Aug 31, 2015 at 9:25 AM, Richie Burnett
<rburnett at richieburnett.co.uk> wrote:
>> Also my point is that dB to me seems like an arbitrary unit, it makes
>> more sense to me to see on a plot a drop of 1 unit per octave
>> (incidentally which is another power of 2) for a 1 pole filter, or a
>> rise of 1 unit per octave for a 1 pole high pass filter, 1 pole = 1
>> doubling / halving per octave. It just makes things easier to count in
>> my head instead of having to multiply and divide by 6 all the time.
>
>
> I totally agree, Andy.  As an EE I have to deal with things in dB all the
> time, so have just gotten used to it.  But for students learning I get them
> to plot their bode-plots on log-log paper where the y-axis is amplitude in
> volts, and the x-axis is frequency in Hertz.  Then we talk about 1st order
> (1-pole) low-pass filters having a stop-band slope of minus one, 2nd order
> low-pass having a slope of minus two, high-pass filters having a positive
> stop-band slope, etc...
>
> As you said, one factor of 2 change in amplitude for a factor of 2 change in
> frequency for a 1-pole filter, or two factors of 2 change in amplitude for a
> factor of 2 change in frequency for a 2-pole filter.  It is more intuitive
> than saying -6dB/octave or -12dB/octave, but that's what they will encounter
> in EE circles so they need to know about that too.  And then to confuse them
> even more there's slopes quoted as 20dB/decade, etc...
>
> -Richie,
>
> PS. Tim Stinchcombe those 3D animated root-locus plots are cool.  I only
> just realised you could click on them and make them come to life!
> _______________________________________________
> Synth-diy mailing list
> Synth-diy at dropmix.xs4all.nl
> http://dropmix.xs4all.nl/mailman/listinfo/synth-diy