[sdiy] Ladder filters and gain drop, that old chestnut

rsdio at audiobanshee.com rsdio at audiobanshee.com
Fri Aug 28 21:12:53 CEST 2015

I think that one potential issue thwarting understanding here is that too many texts and articles refer to "polarity inversion" and "180 degree phase shift" as if they were exactly the same thing. They're not. At least they're not the same for anything but a pure sine wave or precise harmonics of a fundamental frequency. In the latter case, it's still not accurate to say "180 degree phase shift" because the shift is actually different for each harmonic.

Polarity Inversion is the same as subtracting or using the negative input of a differential amplifier. It even happens when you connect your speaker terminals backwards and swap the red and black wires. If you electrically mix a signal with a polarity-inverted copy of the same signal, it will completely cancel out at all frequencies. If you acoustically mix a signal with a polarity-inverted copy of the same signal, then the results are much more complex due to the speed of sound and the position of the speakers in the room.

Phase Shift is frequency dependent, so I think it's unnecessarily confusing to refer to inversion as a 180-degree phase shift. If you have a signal running through a filter, each frequency will have a different amount of phase shift. It's true that some frequencies will see a 180-degree phase shift, and that may be where the filter has its most pronounced effect, but other frequencies will see 179 or 18 or 0 degrees of phase shift. It's all over the place. So, when problems occur with resonance because some frequencies completely reinforce due to shifting and inversion while other frequencies are attenuated, it's not possible to simply fix this with additional inversion because that will just change the frequencies where the phase shift causes reinforcement.

The only fix would be an all-pass filter where only the phases of individual frequencies are changed, and not their amplitude. Analog all-pass filters are difficult to control precisely - at least not in a way where you can easily get exactly what you want.


>> When it comes to the gain drop, shouldn't it be possible to add more
>> poles & phase shifts somewhere else in the frequency range in order to
>> avoid some of the cancellations?

On Aug 27, 2015, at 9:31 AM, Richie Burnett <rburnett at richieburnett.co.uk> wrote:
> If you cascade more than four poles in the forward path, you get to your 180 degrees of phase lag required for resonance quicker, and with *less attenuation*. Hence you need less gain in the feedback path and therefore suffer less attenuation in the passband at the onset of self-oscillation. But of course a higher order filter will have a much steeper rolloff slope in the stopband too.
> Conversely a 3-pole filter like the Tb-303 requires a *LOT* more gain to get close to self-oscillation. And the drop in the passband gain at high resonance settings is even more pronounced than the moog ladder! You get about 26dB drop without any measures used to compensate it.

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