[sdiy] Pole Dancing

[Richie Burnett]

> '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,