[sdiy] Pole Dancing
Richie Burnett
rburnett at richieburnett.co.uk
Wed Sep 19 00:19:47 CEST 2018
> '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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