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

Tom Wiltshire tom at electricdruid.net
Sun Aug 30 17:08:40 CEST 2015

On 30 Aug 2015, at 13:40, Richie Burnett <rburnett at richieburnett.co.uk> wrote:

>> The TB-303 diode cascade is a 4 pole filter, but the stages are not
>> buffered from each other, so the gain at the cutoff isn't -3dB, it's
>> lower...
> I know what you mean, but we need to be careful with terminology here. Most Electrical Engineer types will say the gain *IS* -3dB at the cutoff frequency, because the -3dB amplitude point is the definition of "cutoff frequency". It's just convention really.
> You could say that the Tb-303 filter's resonance occurs at a frequency several octaves above its cutoff frequency...
> From an EE perspective the cutoff frequency is where the amplitude of the filter with no feedback is 3dB down. The *crossover frequency* is where the phase shift goes through 180 degrees. The latter is the frequency at which the filter self oscillates if it is given enough feedback. These two frequencies don't have to be the same and are often separated. The Tb-303's unbuffered ladder is an extreme example of this.

This is very interesting. I was aware of the effect, but I'd never heard of the "crossover frequency" before. Why don't we use it more? I mean, musically, for filters, it's the frequent where the resonance occurs that's usually the significant thing about it. When people tune a filter to 1V/Oct, they usually do it with the resonance right up so you can hear the filter oscillating, so what they're tuning is the crossover frequency, not the cutoff, right?
This crossover frequency is also the point at which the filter boosts harmonics passing through it, so again, more useful than the cutoff.

The -3dB definition of the cutoff always seemed very arbitrary to me, but I could see that you've got a smooth response curve and you need to define some point on it as the "corner", so -3dB is as good as any.
Crossover frequency offers a much better defined point (nothing arbitrary about 180 degrees) and it makes much more sense in resonant filters.


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