[sdiy] 36dB VCF output drop while increasing emphases

[Richie Burnett]

For this type of filter with a cascade of first-order poles inside a global 
negative-feedback loop, the "volume-drop" that you get as you increase 
resonance becomes smaller the more poles you cascade inside the loop. 
(Assuming that all sections track each-other and have the same cut-off 
frequency.)

Basically the more poles you have, then the quicker you get your total 180 
degrees of phase shift required for resonance, before you go so far past the 
knee in each 1-pole frequency response that you loose all the amplitude.  In 
summary you need less gain around the feedback loop to make it 
self-oscillate the more poles you have inside the feedback loop, and this 
squashes the remaining audio in the pass band down less as you turn up the 
resonance control.

For example, in a classic moog 4-pole cascade, each section contributes 45 
degrees of phase lag and reduces the amplitude by 70.7%.  That gives the 
require 180 degrees of phase shift at resonance and an amplitude drop down 
to 25%.  Therefore to achieve self-oscillation you need a gain of 4 around 
the loop, and that makes the passband gain drop to 1/5 of what it was 
without resonance.  A volume drop of almost 14dB!

Conversely, for a 6-pole cascade (-36dB/oct filter,) each section would 
contribute 30 degrees of phase lag and reduce the amplitude by 86.6%.  That 
still gives the required 180 degrees of phase shift at resonance, but now 
with an amplitude drop of only down to 42.2%.  Therefore to achieve 
self-oscillation in the 6-pole filter you only need a gain of 2.37 around 
the loop, and the passband only drops to 1/3.37 of what it was without 
resonance.  That's a volume drop of about 10.6dB.  More than 3dB louder than 
the moog filter without any resonance compensation.

If you cascade more stages the volume drop with resonance will be even less, 
although the benefit of each new stage diminishes when you have lots.  You 
can also compensate for the drop by either boosting the gain after the 
filter (like in the TB-303) or boosting the signal into the filter (like in 
the Juno-106.)  Personally i favour boosting the drive signal with resonance 
as this tends to make the filter saturate slightly as it approaches 
self-resonance and stops it squealing too loudly compared to typical audio 
levels.  It's also easy to achieve by mixing some of the input signal with 
the output signal before it's fed through the feedback VCA that controls 
resonance level.  That means that as you increase the resonance level by 
feeding back more of the output from the filter cascade, you also compensate 
for the volume drop by feeding in progressively more of the input.  One of 
the Juptier filter schematics shows how this is done, and it's also in the 
Juno 106 filter module stylised schematic too.

As for whether 8-poles sound better than 6-poles, I guess it comes down to 
personal preference.  High order filters definitely sound more un-natural. 
1-pole, 2-pole, 3-pole and 4-pole all sound quite natural to my ears, but 
higher order filters tend to sound un-naturally mellow and artificial to me. 
I'd almost say they sounded "digital" because digital filters are where most 
people are most likely to have heard such an aggressive filter roll-off. 
e.g. Alesis Ion.

Hope this helps,

-Richie,

-----Original Message----- 
From: Quincas
Sent: Friday, April 17, 2015 3:53 PM
To: Harald
Cc: synth-diy at dropmix.xs4all.nl
Subject: Re: [sdiy] 36dB VCF output drop while increasing emphases

Maybe you can use another 13700, make a vca and a voltage follower as an 
output compressor? 36db seems already very steep, I'm a 2 pole man myself :) 
don't know how much difference you'll get with 48, but I think you should 
try it and hear for yourself, maybe the sonic character becomes something 
quite unique...

Sent from my iPad

> On 17/04/2015, at 7:08, Harald <sdiy at haraldswerk.de> wrote:
>
> I am just working on a 36dB VCF. Plain forward design with LM13700. First 
> steps here:  http://www.haraldswerk.de/wrdprs/ . As we know, output level 
> decreases with feedback (Q). This can be compensated with increasing the 
> output gain while increasing Q. But then the peak level of the output will 
> be way higher as the normal output. Which might cause distortion in the 
> next stage. Is there a compromise to avoid this or do i need to select: 
> Lower output or increased distortion?
>
> Second thought: The filter works quite good. Does it make sense to go for 
> 48dB musicaly?
>
> Harald
>
> www.haraldswerk.de
> _______________________________________________
> Synth-diy mailing list
> Synth-diy at dropmix.xs4all.nl
> http://dropmix.xs4all.nl/mailman/listinfo/synth-diy
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