[sdiy] Pole Dancing
Andrew Simper
andy at cytomic.com
Wed Sep 19 15:15:56 CEST 2018
I'm such an maths / engineering geek I didn't even see the pun in Pole
Dancing until just now! help!
Andy
On Wed, 19 Sep 2018 at 06:19, Richie Burnett <rburnett at richieburnett.co.uk>
wrote:
> > 'Anybody know the positions of the TB-303 real poles?
>
> To a simplification it is electrically just an *un-buffered* cascade of
> four
> R-C lowpass filter sections. Whatever the resulting cutoff frequencies of
> those sections end up being.
>
> Tim Stinchcombe did a very detailed mathematical analysis of the TB-303
> ladder in a document he put on his website some time ago. He calculated
> the
> theoretical transfer function and possibly even predicted the feedback
> gain
> required to achieve self oscillation. I think he also compared Spice
> simulation results of the actual circuit with the mathematical predictions
> but didn't do any measurements on a genuine TB-303 ladder filter.
>
> A real TB-303 ladder filter comes incredibly close to self-oscillation for
> high cut-off frequency settings (less than 0.5dB gain margin), but the
> degree of resonance drops off quickly for lower cut-off frequencies. The
> actual transfer function is more complicated than just 4th order because
> of
> under-sized coupling capacitors used in several places in the feedback
> path.
> This results in a much more complicated response which has both LF
> roll-off
> and HF roll-off. It's a long time since I looked at this stuff, and I
> can't
> remember if Tim worked out a mathematical expression that took all of this
> into account, or stopped at the 4-pole simplified model.
>
> I remember that from a modelling point of view the effect of the 4th pole
> in
> the TB-303 filter doesn't kick in until a very high frequency and a point
> where the magnitude response is already well down. Given that the TB-303
> filter is quite noisy, it makes the final transition to -24dB/oct hard to
> observe, so I'm not surprised it's frequently stated to be 3-pole.
> Certainly from an "acoustic perception" point of view it isn't a bad
> simplification to model it as a 3-pole filter, but mathematically it's
> strictly something like a 7-pole filter if I remember correctly!!!
>
> -Richie,
>
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