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<div>> I'm such an maths / engineering geek I didn't even see the pun in Pole Dancing until just now! help!</div>
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<div>And I'm waiting for the first victim of an angry spouse who looked over one SDIYer's shoulder, seeing the in-box with a lot of headlines reading "pole dancing".</div>
<div>- "But honey, that's just about Slavic folk ceremony!"<br/>
No one out-bad-puns me, ya here me?!</div>
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<div style="margin:0 0 10px 0;"><b>Von:</b> "Andrew Simper" <andy@cytomic.com><br/>
<b>Betreff:</b> Re: [sdiy] Pole Dancing</div>
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<div>I'm such an maths / engineering geek I didn't even see the pun in Pole Dancing until just now! help!
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<div>Andy</div>
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<div>On Wed, 19 Sep 2018 at 06:19, Richie Burnett <<a href="mailto:rburnett@richieburnett.co.uk" onclick="parent.window.location.href='mailto:rburnett@richieburnett.co.uk'; return false;" target="_blank">rburnett@richieburnett.co.uk</a>> wrote:</div>
<blockquote class="gmail_quote" style="margin: 0 0 0 0.8ex;border-left: 1.0px rgb(204,204,204) solid;padding-left: 1.0ex;">> 'Anybody know the positions of the TB-303 real poles?<br/>
<br/>
To a simplification it is electrically just an *un-buffered* cascade of four<br/>
R-C lowpass filter sections. Whatever the resulting cutoff frequencies of<br/>
those sections end up being.<br/>
<br/>
Tim Stinchcombe did a very detailed mathematical analysis of the TB-303<br/>
ladder in a document he put on his website some time ago. He calculated the<br/>
theoretical transfer function and possibly even predicted the feedback gain<br/>
required to achieve self oscillation. I think he also compared Spice<br/>
simulation results of the actual circuit with the mathematical predictions<br/>
but didn't do any measurements on a genuine TB-303 ladder filter.<br/>
<br/>
A real TB-303 ladder filter comes incredibly close to self-oscillation for<br/>
high cut-off frequency settings (less than 0.5dB gain margin), but the<br/>
degree of resonance drops off quickly for lower cut-off frequencies. The<br/>
actual transfer function is more complicated than just 4th order because of<br/>
under-sized coupling capacitors used in several places in the feedback path.<br/>
This results in a much more complicated response which has both LF roll-off<br/>
and HF roll-off. It's a long time since I looked at this stuff, and I can't<br/>
remember if Tim worked out a mathematical expression that took all of this<br/>
into account, or stopped at the 4-pole simplified model.<br/>
<br/>
I remember that from a modelling point of view the effect of the 4th pole in<br/>
the TB-303 filter doesn't kick in until a very high frequency and a point<br/>
where the magnitude response is already well down. Given that the TB-303<br/>
filter is quite noisy, it makes the final transition to -24dB/oct hard to<br/>
observe, so I'm not surprised it's frequently stated to be 3-pole.<br/>
Certainly from an "acoustic perception" point of view it isn't a bad<br/>
simplification to model it as a 3-pole filter, but mathematically it's<br/>
strictly something like a 7-pole filter if I remember correctly!!!<br/>
<br/>
-Richie,<br/>
<br/>
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