[sdiy] Pole Dancing

Richie Burnett rburnett at richieburnett.co.uk
Wed Sep 19 22:49:05 CEST 2018

I found a note here that the TB-303 ladder filter needed a feedback gain of 
about 20 to make it self-oscillate at high frequencies.  You can contrast 
this to the gain of 4 required to achieve self-oscillation for the Moog 
ladder filter.

The increased gain requirement is a direct consequence of the filter poles 
being spread out further to start with in the TB-303 diode ladder filter 
because there is no buffering between stages.

Another interesting side effect of this is that the much higher negative 
feedback gain required to achieve significant resonance in the TB-303 ladder 
causes a much greater drop in the pass-band gain.  This has the effect of 
making the output from the filter get quieter as the resonance is turned up. 
(Often described as the bass dropping out when the resonance is turned up.)


-----Original Message----- 
From: Donald Tillman
Sent: Wednesday, September 19, 2018 9:30 PM
To: Richie Burnett
Cc: synth-diy mailing list
Subject: Re: [sdiy] Pole Dancing

> On Sep 18, 2018, at 3:19 PM, 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.

It's a straightforward calculation... but it's *very* error prone.

> 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.

Ah, here:

    Diode ladder, 4-pole low-pass

Tim says the TB-303 filter poles are at: (-3.53,0), (-2.35,0), (-1.0,0), 

So you can pop those in and see what happens.

Now... I'm not a Roland fetishist, so I don't know anything about these 
guys.  Are the caps the same value?
Are there variations?  Tim says his equation is for the same value caps.


And if anybody is looking for an interesting project; is there are set of 
cap values to use in a diode ladder that brings the poles closer together? 
Is there an optimum?

  -- Don
Donald Tillman, Palo Alto, California

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