types of filters (based on circuitry)

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hiawog
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types of filters (based on circuitry)

Post by hiawog » Fri Dec 21, 2012 2:56 pm

hey all. i'm not an electrical engineer, but i want to better understand the different categories of filters as defined by their circuit topologies. obviously there's an infinite number of ways to categorize modules, but i'm hoping to get a better grasp of general approaches to designing a filter and the sonic consequences of those design decisions.

i've heard of a few different types already:

- transistor ladder: thank you bob moog. usually 24db/oct, smooth sound.
- diode: harsher or grittier sounding, i think?
- vactrol-based: vactrol ring and woody tone
- attack-decay: i don't know the right name for this, but i'm talking about the 6db/octave filtering that you can get with a serge-style envelope
- state-variable: don't really understand what this means
- vca-based: i've heard of people designing filters around vca chips, but i don't know how this works.

i'm sure there are plenty of other kinds, and i know that it's never accurate to make sweeping generalizations about a given type of module. i'm just trying to understand the general guidelines and trends, ie. transistor ladder filters tend to have cleaner resonance than diode filters, or whatever. it would also be really cool to know some common or well-known filters of each type.

thanks everyone!

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Post by Cat-A-Tonic » Fri Dec 21, 2012 6:43 pm

- Sallen Key
- Butterworth
- Wien Bridge
- Synthacon multi-mode inputs
- Switched Capacitor
...

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Post by MindMachine » Fri Dec 21, 2012 10:53 pm

Cat-A-Tonic wrote:- Sallen Key
- Butterworth
- Wien Bridge
- Synthacon multi-mode inputs
- Switched Capacitor
...
Do you know of an example of the Butterworth in the Wiggler domain? I am curious if the filter type at all describes the tone it allows. Just curious.

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Post by bouzoukijoe1 » Sat Dec 22, 2012 12:23 am

great topic.

in all the filter discussions I've read, I've always noticed that filter comparisons -- topology notwithstanding -- have always been muddy discussions and rabbit holes. many people attribute various sonic characteristics to filter types, but many descriptions lack any technical explanation or proof. not that I don't believe them, but there's a lack of evidence (histograms, etc.) that actually show the differences. most of it is sort of word-of-mouth style that's hard to distinguish from hearsay.

people endlessly debate this or that sounding similar to x and y, but often at the end of threads all of it still remains voodoo. very few dissections of filter circuitry succeed at really explaining the resulting sonic differences (at least to a end-user like me). there's sort of a "bermuda triangle" between circuit discussions and real world sonic discussions, at least in my opinion.

point being, I personally think it's very challenging to connect real world patches and sounds to filter typologies using only words/language. you often hit dead ends in learning when nobody can really definitively prove that a Moog ladder filter does not sound the same as a Dotcom ladder filter (again, I often believe them despite the lack of visual evidence).

with oscillator waveforms, it's easy to compare and actually show differences (sine shapes for example), but with filters it's much trickier. I almost think you need a combination of scope + histogram(?) to properly show the characteristic differences between filter types. I haven't explored spectrum analyzers that much, but I often wonder about it when I am trying to figure out why I prefer the behavior of one filter vs. another. or why I like the "body" of a 6 db/oct slope vs. a 24 db/oct slope. or why the extreme resonance of a BL diode ladder filter sounds crazier than the resonance of a Dr. Octature "cascading" filter. it's so hard to study.

anyway, I have a Dave Jones O'Tool that has a spectrum view, but I'm not sure it's detailed enough to compare filters with. the display is kind of small. hm...

maybe as a start we can list all the modular filters and organize them by topology/type? someone could start a spreadsheet and pull the list from eurorackdb for starters. I can grab the list and create a Google spreadsheet if you're into the idea.

actually I just went ahead and popped the list into a spreadsheet. if anyone wants to help fill it in, just let me know and I can share it with you.


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Post by NV » Sat Dec 22, 2012 1:08 am

MindMachine wrote:
Cat-A-Tonic wrote:- Sallen Key
- Butterworth
- Wien Bridge
- Synthacon multi-mode inputs
- Switched Capacitor
...
Do you know of an example of the Butterworth in the Wiggler domain? I am curious if the filter type at all describes the tone it allows. Just curious.
The WMD Quad AAF has four -24db butterworth filters. I don't have any personal experience with the WMD myself but other butterworth filters I've heard have generally been rather smooth and simple, as one would expect given the response - more of a functional rather than character filter. The WMD apparently utilizes a vactrol to control the filter's clock so it may have a somewhat different character as a result.

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Post by MindMachine » Sat Dec 22, 2012 1:53 am

^Thank you for the info. I am gonna look at some schematics of different types and try to notice any obvious differences just for fun. I know pretty little about this stuff (design/circuitry), but it should be interesting. I need to look into my old TAB electronics/synth build books.

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Post by Cat-A-Tonic » Sat Dec 22, 2012 4:30 am

The Wiard Boogie is a butterworth filter.

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Post by CJ Miller » Sat Dec 22, 2012 6:02 am

Anything which maps a transform function to the input. More circuits are filters, than are not.

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Post by flashheart » Sat Dec 22, 2012 6:54 pm

bouzoukijoe1 wrote:great topic...


...anyway, I have a Dave Jones O'Tool that has a spectrum view, but I'm not sure it's detailed enough to compare filters with. the display is kind of small. hm...

maybe as a start we can list all the modular filters and organize them by topology/type? someone could start a spreadsheet and pull the list from eurorackdb for starters. I can grab the list and create a Google spreadsheet if you're into the idea.

actually I just went ahead and popped the list into a spreadsheet. if anyone wants to help fill it in, just let me know and I can share it with you.

Anything based on the Korg filter should be a Sallen-Key filter ie. the Manhatten MA-35, The Doepfer Xtreme, AS SY02, pretty sure the Borg is based on the Korg filter type - but with vactrols.
the SV in the Macbeth filter stands for State-variable, the other Macbeth is a transistor ladder. Doepfer A108, A120 and the MFB are all ladder filters. The Elby Bi-n-Tic is a switched capacitor.

Don't think looking at a spectrum analyser will help much in comparing, all you'll see is the slope really.

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Post by CursedFrogurt » Sat Dec 22, 2012 8:22 pm

The moog ladder is a butterworth I think?

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Post by bouzoukijoe1 » Sat Dec 22, 2012 10:46 pm

between the ladder filters, cascading filters, OTA-based filters, etc. it's getting kind of confusing. there should be some kind of filter tree that explains the topological hierarchy of these various circuit designs. there must be a book/author that has attempted to categorize these designs before that can be illustrated like some kind of class diagram. anyone know of any?

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Post by MindMachine » Sun Dec 23, 2012 12:26 am

bouzoukijoe1 wrote:between the ladder filters, cascading filters, OTA-based filters, etc. it's getting kind of confusing. there should be some kind of filter tree that explains the topological hierarchy of these various circuit designs. there must be a book/author that has attempted to categorize these designs before that can be illustrated like some kind of class diagram. anyone know of any?

Image
Excellent idea for a paper even.

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Post by Dr. Sketch-n-Etch » Sun Dec 23, 2012 2:36 am

To really make sense of this topic, one has to have some knowledge of filter "transfer functions". These are simply the ratio of the voltage output of a circuit to the voltage input. The different "filter topologies" give different transfer functions. For me, this is where the action is at in filter design. The transfer function is typically a ratio of polynomials in the "Laplace domain" (a special numerical domain where differential equations in time become algebraic equations in the "Laplace variable"). They are easily derived for any filter simply by carrying out a "current balance" around the filter and solving for the voltages at the outputs relative to the input. When plotted in graphs of log amplitude vs log frequency (so-called "Bode plots") they give the frequency response of the filter. See Don Lancaster's "The Active-Filter Cookbook" for a fairly good discussion of this analysis.

The number of "poles" a filter has refers to possibilties for the denominator of the transfer function to go to zero (and, thereby, for the transfer function itself to tend towards infinity). A typical cascaded-stage filter has as many poles as stages. It bears noting that when a pole coincides with the imaginary axis (which means that it shows up in the actual frequency response of the filter), the filter goes into self-oscillation. The frequency where the pole resides is the frequency at which the filter oscillates. (The Laplace variable s is equal to the angular velocity (related to frequency) omega or w times the imaginary number j (the square root of -1). Hence:

s = jw where the frequency f = w/2*pi = w/6.283

A "Sallen-Key" filter is a certain generic type of two-pole (or "second-order") filter achieved with a single active element (i.e., opamp). This is done by using two capacitors and two resistors (i.e., two RC filtering elements) around a single opamp with the Rs and Cs in certain ratios. AFAIK, this type of filter is rarely used in synths, probably because it is difficult to put it under voltage control (although it would actually be quite easy with 2164 VCAs). Every synth VCF I've ever seen or built had a separate opamp or active element per RC element.

The "State Variable" filter is a special sort of two-pole filter built around three opamps -- an inverter and two integrators. It was originally developed for analog computers, because it's transfer function is also the analytical solution to the classic "mass-spring-dashpot" or "sticky pendulum" problem from Newtonian physics. Indeed, the various outputs represent the position, velocity, and acceleration of the pendulum or mass. It also sounds cool!

Descriptors such as "Butterworth" or "Chebychev" refer to the specific ratios amongst the various Rs and Cs to achieve specific polynomial functions in the denominator of the transfer function, and thereby to obtain an amplitude-vs-frequency response with a certain shape. For example, a Butterworth filter is designed to give the flattest possible passband (no ripples or sudden peaks and/or valleys in the amplitude response below the cutoff frequency in a lowpass filter). A Chebyshev filter has a more ripply passband, but a steeper rolloff, than a Butterworth filter.

The bottom line of all of this is that it probably only matters very much to the designer of the filter.
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Post by dslocum » Sun Dec 23, 2012 6:31 am

Dr. Sketch-n-Etch wrote: A "Sallen-Key" filter is a certain generic type of two-pole (or "second-order") filter achieved with a single active element (i.e., opamp). This is done by using two capacitors and two resistors (i.e., two RC filtering elements) around a single opamp with the Rs and Cs in certain ratios. AFAIK, this type of filter is rarely used in synths, probably because it is difficult to put it under voltage control (although it would actually be quite easy with 2164 VCAs). Every synth VCF I've ever seen or built had a separate opamp or active element per RC element.
I won't claim to be an authority on filter topologies, but I'm pretty sure the Steiner (Synthacon) and the Low-Pass gate are both Sallen-Key. :hmm:

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Post by Xero » Tue Dec 25, 2012 1:30 am

hmm isn't state-variable and multi-mode almost the same thing? at least generally speaking, as far as I know this is usually referring to the switchable 2-pole 12db/oct HP/BP/LP filters? IE: SEM, Wasp, yamaha cs-10/15/30, etc...

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Post by Dr. Sketch-n-Etch » Tue Dec 25, 2012 5:25 pm

Xero wrote:hmm isn't state-variable and multi-mode almost the same thing? at least generally speaking, as far as I know this is usually referring to the switchable 2-pole 12db/oct HP/BP/LP filters? IE: SEM, Wasp, yamaha cs-10/15/30, etc...
Yes, most multimode filters are of state-variable topology. This is because the SVF naturally has LP, BP and HP outputs.

However, the denomination "multimode" can refer to any sort of filter with multiple modal outputs. And, many different filter topologies can be made to give multimode outputs. A good example is the 4-pole cascaded-stage filter, from which virtually any filter mode up to 4 poles can be tapped. Another example is the Korgasmatron, from which a whole host of modes can be derived.
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Post by berfmurret » Tue Dec 25, 2012 10:45 pm

cool thread. good info

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Post by jnlkrt » Wed Dec 26, 2012 2:56 am

Dr. Sketch-n-Etch wrote:To really make sense of this topic, one has to have some knowledge of filter "transfer functions". These are simply the ratio of the voltage output of a circuit to the voltage input. The different "filter topologies" give different transfer functions. For me, this is where the action is at in filter design. The transfer function is typically a ratio of polynomials in the "Laplace domain" (a special numerical domain where differential equations in time become algebraic equations in the "Laplace variable"). They are easily derived for any filter simply by carrying out a "current balance" around the filter and solving for the voltages at the outputs relative to the input. When plotted in graphs of log amplitude vs log frequency (so-called "Bode plots") they give the frequency response of the filter. See Don Lancaster's "The Active-Filter Cookbook" for a fairly good discussion of this analysis.

The number of "poles" a filter has refers to possibilties for the denominator of the transfer function to go to zero (and, thereby, for the transfer function itself to tend towards infinity). A typical cascaded-stage filter has as many poles as stages. It bears noting that when a pole coincides with the imaginary axis (which means that it shows up in the actual frequency response of the filter), the filter goes into self-oscillation. The frequency where the pole resides is the frequency at which the filter oscillates. (The Laplace variable s is equal to the angular velocity (related to frequency) omega or w times the imaginary number j (the square root of -1). Hence:

s = jw where the frequency f = w/2*pi = w/6.283

A "Sallen-Key" filter is a certain generic type of two-pole (or "second-order") filter achieved with a single active element (i.e., opamp). This is done by using two capacitors and two resistors (i.e., two RC filtering elements) around a single opamp with the Rs and Cs in certain ratios. AFAIK, this type of filter is rarely used in synths, probably because it is difficult to put it under voltage control (although it would actually be quite easy with 2164 VCAs). Every synth VCF I've ever seen or built had a separate opamp or active element per RC element.

The "State Variable" filter is a special sort of two-pole filter built around three opamps -- an inverter and two integrators. It was originally developed for analog computers, because it's transfer function is also the analytical solution to the classic "mass-spring-dashpot" or "sticky pendulum" problem from Newtonian physics. Indeed, the various outputs represent the position, velocity, and acceleration of the pendulum or mass. It also sounds cool!

Descriptors such as "Butterworth" or "Chebychev" refer to the specific ratios amongst the various Rs and Cs to achieve specific polynomial functions in the denominator of the transfer function, and thereby to obtain an amplitude-vs-frequency response with a certain shape. For example, a Butterworth filter is designed to give the flattest possible passband (no ripples or sudden peaks and/or valleys in the amplitude response below the cutoff frequency in a lowpass filter). A Chebyshev filter has a more ripply passband, but a steeper rolloff, than a Butterworth filter.

The bottom line of all of this is that it probably only matters very much to the designer of the filter.
good post, thx!

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Post by Grumble » Mon Jul 24, 2017 5:04 am

In my synth I use switched capacitor filters (MAX260), controlled by an Arduino (clone).
And they sound alright to me, even will oscillate if I set the Q-factor high enough. They are easy to tune with the clock frequency but have one big problem:
Especially when f0 at low frequencies the bleed from the clock becomes audible.

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Post by thresholdpeople » Mon Jul 24, 2017 7:07 am

Dr. Sketch-n-Etch wrote: The "State Variable" filter is a special sort of two-pole filter built around three opamps -- an inverter and two integrators. It was originally developed for analog computers, because it's transfer function is also the analytical solution to the classic "mass-spring-dashpot" or "sticky pendulum" problem from Newtonian physics. Indeed, the various outputs represent the position, velocity, and acceleration of the pendulum or mass. It also sounds cool!
Interesting. What does each output correlate to in the mass spring damper model?

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Post by sduck » Mon Jul 24, 2017 10:02 am

Dr. Sketch-n-Etch wrote:The transfer function is typically a ratio of polynomials in the "Laplace domain" (a special numerical domain where differential equations in time become algebraic equations in the "Laplace variable").

s = jw where the frequency f = w/2*pi = w/6.283
I love it when the Doctor gets technical!

Of course you have to factor in how all these different things sound - you know, that reason we use them? One of my favorite filters is the Doctors korgasmatron III, which has more laplaces that any of my other ones.

edit: Doh, didn't realize that this is a necrobumped 5 year old thread.
Last edited by sduck on Mon Jul 24, 2017 8:36 pm, edited 1 time in total.
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Post by addendum » Mon Jul 24, 2017 1:14 pm

Well, the OP back then asked for technical background beyond "sound" which can be subjective. Me I'd love to hear more tech details.

One thing (maybe the thing) that sets State Variable filters apart from filters with one default mode is that they can be used to patch up chaotic systems more easily. I remember someone posting an idea for a "Chua Attractor" (w?) module or something that looked like essentially a SVF. It's been years, I'll see if I can find it.
The same paper included a chaotic patch based around the Moog 904 LPF and one or maybe two Moog VCAs. Those made up for the 904's simplicity by providing differentials ins AND outs, which aids a lot in chaos patches (in an SVF you have phase differences between the four outs "built in").

I think the Wiard Omni Filter hasn't been mentioned here. I seem to remember it's two 2-pole, maybe single-mode, maybe SV filters wired in series for both 2- and 4-pole outs and then there's ultrasonic switching between some outs to get artificial intermediate "states" or "modes" that are different from SVF outs or crossfading different stage outs as in the Boogie. It was partially discussed in the Wiard subforum. Again, I'd love to hear more precise background info. It's one thing to use a module and appreciate it and get great results, but another to have a good idea of what's going on

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Post by auxren » Mon Jul 24, 2017 3:39 pm

This is my go-to document for filter topologies: http://leachlegacy.ece.gatech.edu/ece4435/filtrpot.pdf

Written by one of my favorite professors at GaTech

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Re: types of filters (based on circuitry)

Post by strangegravity » Mon Jul 24, 2017 3:41 pm

hiawog wrote:hey all. i'm not an electrical engineer, but i want to better understand the different categories of filters as defined by their circuit topologies. obviously there's an infinite number of ways to categorize modules, but i'm hoping to get a better grasp of general approaches to designing a filter and the sonic consequences of those design decisions.

i've heard of a few different types already:

- transistor ladder: thank you bob moog. usually 24db/oct, smooth sound.
- diode: harsher or grittier sounding, i think?
- vactrol-based: vactrol ring and woody tone
- attack-decay: i don't know the right name for this, but i'm talking about the 6db/octave filtering that you can get with a serge-style envelope
- state-variable: don't really understand what this means
- vca-based: i've heard of people designing filters around vca chips, but i don't know how this works.

i'm sure there are plenty of other kinds, and i know that it's never accurate to make sweeping generalizations about a given type of module. i'm just trying to understand the general guidelines and trends, ie. transistor ladder filters tend to have cleaner resonance than diode filters, or whatever. it would also be really cool to know some common or well-known filters of each type.

thanks everyone!
908 Posts and you don't know what a state variable filter is? These are filters that have any combination of low, band, and high pass outputs.

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