## Filter Design Theory

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trtlmnky
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### Filter Design Theory

I've looked around pretty thoroughly on this subject, I feel, and didn't really come up with much in the way of what I was looking for. Maybe I missed something so forgive if this has been answered before.

Anyway, regarding filter circuitry, I haven't found much in the way of theory of operation/schematics regarding Variable (& Voltage Controlled) filter slopes, i.e. how it's done at all with analog circuitry.

Also very interested in ways of implementing an analog "morphing" filter, a feature to allow a "stepless" transition from low-pass to high-pass or on some kind of "gradient" I suppose where you could have a potentiometer changing filter topology from closed lowpass at full ccw, bandpass-ish at 12:00 and fully filtered high-pass at fI'll cw? For instance.

Any help with this or direction towards relevant reading materials would be very much appreciated.

cyberdine
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### Re: Filter Design Theory

I can’t help you but just to say I appreciate you asking this question and I’ll watching this thread with eager eyes. For something so run of the mill, filters are remarkably complex.

loderbast
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### Re: Filter Design Theory

2 ideas of where to start:
https://mutable-instruments.net/archive ... alysis.pdf

i hope you like math

KSS
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### Re: Filter Design Theory

trtlmnky wrote:
Fri Apr 03, 2020 11:33 pm
Anyway, regarding filter circuitry, I haven't found much in the way of theory of operation/schematics regarding Variable (& Voltage Controlled) filter slopes, i.e. how it's done at all with analog circuitry.
Don Lancaster's Active Filter Cookbook is online in PDF -from him, and Bernie Hutchin's Electronotes Newletters are another great resaource.

For variable slope, visit J Haibles legacy website for his project of that name. Read more about its development at the Electro-music site in the DIY section. Serge is another example to look into.
Also very interested in ways of implementing an analog "morphing" filter, a feature to allow a "stepless" transition from low-pass to high-pass or on some kind of "gradient" I suppose where you could have a potentiometer changing filter topology from closed lowpass at full ccw, bandpass-ish at 12:00 and fully filtered high-pass at fI'll cw? For instance.
Several classic examples of this. See the schematics for the Oberheim SEM,the EML 101 VCF, the ARP 2500 1047 MMf to get started.

If you want to do it under CV or preset control, then look at some of the later Oberheim polys -Matrix12- to see how filter pole mixing -also described in the Electronotes and for a manual example see Craig Anderton's Multiple Identity Filter DIY paper.

cygmu
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### Re: Filter Design Theory

Pole-mixing as mentioned by KSS is the most direct way to gain access to a range of different filter outputs. I believe Electronotes is the earlier reference for this (Electronotes 85 from 1978) but I'd love to know if there is an earlier one. Emilie Gillet wrote up the same ideas: https://mutable-instruments.net/archive ... mixing.pdf
You could achieve voltage-controlled filter response by means of VC-mixing. In the end this might not be very different from crossfading between pre-defined outputs though. For crossfading between more than one response, you could use an interpolating scanner (See J Haible or D Tillman's designs for that.)

The Serge "Variable Slope" filter is very interesting because it is just a regular VC state-variable filter with some careful control of the gain. It is not variable-slope at all, in fact: it's a 12dB/Oct SVF. But it has variable bandwidth (which is the same thing as saying it has variable Q) and as you narrow the bandwidth, the filter slope gets steeper for frequencies close to the centre frequency. I find it quite entertaining that Serge's three late-70s filters are called the "Variable Q", "Variable slope" and "Variable bandwidth" filters, when in fact they are all varying the bandwidth (They are different filters, don't get me wrong)

EATyourGUITAR
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### Re: Filter Design Theory

I use this website for everything. great for learning the basics of RC low pass high pass band pass filters. LC, RLC etc..
https://www.electronics-tutorials.ws/

supplement with this
http://www.muzique.com/lab/notch.htm
http://www.muzique.com/lab/swtc.htm
http://www.muzique.com/lab/swtc3.htm
https://www.ampbooks.com/mobile/classic ... tonestack/
http://www.duncanamps.com/tsc/

then finally a college level text book

you will definitely NEED to learn this to do the math in the book
https://en.wikipedia.org/wiki/Angular_frequency

optional big boy math probably more useful for digital filters and hybrid systems or switched capacitor filters.
https://en.wikipedia.org/wiki/Laplace_transform
https://en.wikipedia.org/wiki/Fourier_transform
https://en.wikipedia.org/wiki/Nyquist%E ... ng_theorem

this is probably obvious but you will need to be good at applied math using calculus and trigonometry to do any of the basic filter math.
WWW.EATYOURGUITAR.COM <---- MY DIY STUFF

bitflip
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### Re: Filter Design Theory

TI has this "Basic Introduction to Filters"

http://www.ti.com/lit/an/snoa224a/snoa224a.pdf

jorg
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### Re: Filter Design Theory

Analog Devices Linear Circuit Design Handbook is amazing; chapter 8 on filters is indispensable.
https://www.analog.com/en/education/edu ... dbook.html#
https://www.analog.com/media/en/trainin ... apter8.pdf

petkost
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### Re: Filter Design Theory

Moog Ladder Filters Analyzed (Analog Circuits for Music Synthesis, Spring 2020, NOT 2019)

Aether Machine
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### Re: Filter Design Theory

Conceptually, the state variable filter is really the ultimate analog computing building block. You can get simultaneous BP, LP, HP and AP outputs, and it can also be used as a Sine oscillator. Most morphing filter types are SVFs with simple crossfading with VCAs.

In practical terms, the SVF has been considered to lack depth or character by some designers (e.g. Grant Richter is known to dislike the neutral/clinical sound), where Sallen Key or ladder (transistor or diode) types are preferable in this respect.

snowday
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### Re: Filter Design Theory

+1 for Lantermann.
Here’s a lecture he posted a few days ago on the Moog ladder.