A matrix approach to the Moog ladder filter

[Music Engineer]

yes, the terminology in the audio processing domain is sometimes rather inaccurate. i agree that "state variable filter" does not make much sense as term, since all filters have one or another kind of state variables. "moog filter", on the other hand, is much more valid - it just credits the inventor. he may have built and used others as well - but so what? this just happens to be the most popular and famous one. there are also butterworth-filters, linkwitz/riley filters etc. frequency-modulation is also regularly misused to denote phase-modulation. and then there are a lot of strange marketing buzzwords - think of "linear arithmetic" synthesis. seriously - who came up with this term and why? WTF? but when a term is established for something, it's unfortunately hard to change that. i would also advocate to rename "real" numbers into "continuous" numbers and "complex" numbers in something like 2D or "planar" numbers. it would make things much easier to understand, if the terms actually say what they mean. saves one mental mapping indirection. you would guess that mathematicians value an accurate and descriptive terminology. but we are stuck with weird and meaningless terminology

[Music Engineer]

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hey, was looking for a long time for a way to embed proper math formulas into forum posts. how are you doing these?
...and sorry for the distraction from the original topic

[aciddose]

The issue using the term "moog filter" is that there are many different filters designed by moog.

Which one are you referring to?

The problem using "moog filter" to replace "four-pole filter" is one is generic while the other is entirely pointless.

(He did not invent what you seem to think he invented. Such filters existed long before. Try reading the patent. The patent applies to the complete device described in the patent including all the terms. This is why merely changing a small component of the circuit such as a capacitor avoided the patent.)

For example a cascaded OTA with four poles, in which way has this anything to do with the minimoog filter?

What it is when people use this sort of jargon is a clear demonstration that they do not know what they're talking about.

My demand is that people ought to use the generic term "four-pole filter" when they mean that, and use other terms when they mean something else. "Moog filter" is hopelessly ambiguous. Not only did it never carry a valid meaning, but it never will.

Take into account the fact that the balanced ladder used in the minimoog is unlike any other unbalanced cascaded four-pole filter based upon OTAs or otherwise. Also take into account that the complete circuit has many more properties that I am absolutely certain you are not referring to as well as I suspect you are completely unaware of.

"Moog filter" is a bad choice.

[juha_p]

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hey, was looking for a long time for a way to embed proper math formulas into forum posts. how are you doing these?
...and sorry for the distraction from the original topic

Hmm... thoes are normal images linked/added using forums "Img" tool.

If you need to prepare those equations/formulas by yourself, there are even online editors available (...if you don't have some office stuff (w/ equation/formula editor) in hands (MS/OO/etc.).
Her's one online editor you could try - https://www.codecogs.com/latex/eqneditor.php
How to get the equation/formula embedded into your post:
- get/prepare the equation/formula
- if needed, make it an image file (export, capture, etc.) (png, jpeg, etc. supported by forum)
- (if needed) edit the image size (paint, gimp, etc.) so it fits well into your post
- upload the image to some site which hosts image files (http://tinypic.com/, etc.)
- use forums "Img" tool to link the image (paste the link to image between the Img start and end tags

[JCJR]

Well, state variable is the name thunk up decades ago by smart engineers with slide rules in pocket protectors-- For the three opamp circuit with 2 integrators in series on the back end and a feedback mixer in front.

A less flexible three opamp setup with integrators on the front and back, with an inverting amp in the middle, the front integrator also doing feedback mixing, was in the old days called a biquad.

I considered "ladder filter" only the moog transistor ladder, or close equivalent. They may be functionally equivalent to four series ota integrators, but sounded different. Perhaps because the ladder filter had more distortion. Or maybe just different, rougher distortion than ota's.

I generally preferred the quad series ota filter. The ladder was great on some sounds but had an "electronic edge" making imitative patches difficult. Some of the old analog synths could get "kinda close" to a guitar or string or clarinet, but I was never able to coax even "kinda close" out of a ladder filter.

[aciddose]

State-variable wasn't "thought up" for that particular circuit.

That circuit is one circuit that fits into the abstract label "state-variable filter" along with numerous other state-variable filter circuits.

This is why the term is ambiguous.

If you are referring to that particular circuit, use the proper name: Kerwin-Huelsman-Newcomb or KHN filter.

Any filter defined based upon the ratio of two quadratic functions is a biquad. The KHN filter is also biquadratic. It is a biquadratic state-variable filter.

"Ladder" is a very old term used in radio engineering. An unbalanced ladder is the proper name for a passive RC low-pass filter circuit.

By including a balanced input it becomes a balanced ladder.

A balanced signal can be generated using (in current) an amplifier with differential output (often a LTP, usually two transistor), or (in amplitude) a phase-splitting amplifier (usually one transistor).

People that mistakenly use these abstract terms to refer to concrete ideas, or use concrete terms to refer to abstract ideas demonstrate that they do not know what they are talking about. I urge such people to research the meaning of these terms and to either ask for and discuss the proper terms and develop a valid rational nomenclature to clearly describe what they actually mean, or look up the proper nomenclature and understand its rationale before attempting to apply the terms.

[aciddose]

The differences you describe between cascaded OTA stages and the minimoog filter circuit are likely due to a combination of input and output distortion.

An OTA circuit can be made to produce very similar results to the minimoog filter if given identical levels of input voltage/current (especially note the balanced current at the differential inputs for each stage) and an identical output stage.

This is another example of why the term "ladder filter" is a bad choice. Not only is the minimoog filter a ladder topology along with an OTA cascade, a passive RC low-pass is also a ladder topology! Yet there are very important differences between these circuits although they have similar or identical topology which will be overlooked if they are named by referring to the circuit topology alone. A topology is useful to describe only the topology of a circuit and is otherwise completely ambiguous.

The circuit in the minimoog is naturally more prone to error due to poor matching of the devices in the ladder, due to being a differential circuit dealing in current rather than voltage it is more prone to unbalanced current on either side of the ladder as well as to unbalanced input or output in the output buffer stage.

A series of OTA stages is quite different. It is unbalanced. Although prone to the same sort of distortion due to the LTP inputs and balancing, OTA based circuits are far easier to balance. OTA circuits are internally matched at the factory which reduces any error due to unmatched components on either side of the balanced circuit.

The error that does exist is often balanced in terms of phase due to the common configuration of an OTA cascade where in each stage produces a 180 degree phase inversion.

Error in each individual stage is very well balanced internally, and the minor variations in each OTA in the unbalanced ladder tend to cancel out by averaging much like in a resistor ladder.

[JCJR]

Thanks aciddose.

I don't much care what things are named. Nowadays perhaps there is scholarly refinement over concepts from the past. Information is easier to come by today and some people take great advantage of it.

In the past information was sparser. And pehaps less refined except among professors one might never hear about. My old calculus course was 1.67 years long and IMO rather difficult, but unless my memory is real bad, I see math articles on dang wikipedia with calculus details never mentioned in that old course. Wonder how many years it would take to THOROUGHLY cover any small specialty?

All I know is that I have several filter books from the 1970's and they name one circuit a state variable and another a biquad, etc. Maybe the authors knew more than they were telling, or maybe that was the extent of their own understanding of the words. Information was sparse even with access to a good library.

Maybe there is a more proper scholarly name for "hammer"? Or "wheelbarrow".

Haven't any objection to proper scholarly nomenclature, but can't see getting all huffy about naming a particular implementation with the same moniker it has had for decades, even if maybe there is a better name.

[aciddose]

The problem is that it hasn't had that name, its name is "minimoog filter", not "moog filter".

Now the real problem: that isn't what people mean when they say "moog filter". They mean "four pole filter".

The only problem with this name is it is perhaps a bit too abstract. There are configurations other than a single series cascade of four poles tuned at the same frequency with negative feedback which fall under "four pole filter".

So, to be more specific you need to say more. Why complain that you need to use more than one word to describe a complex topic?

I suggest if people really want a short name for this sort of filter where they do not care to be specific, "four pole filter" is entirely valid. It is ambiguous, but no more so than "moog filter" ever was. Most importantly it is obvious that it is intended to be ambiguous.

When we're discussing the topic of this thread, a proper name such as "lossy integrator cascade" is a better name. In greater detail it can be specified that there are four stages and that negative feedback is applied.

If people want to use the name "minimoog filter" by all means please do. Although you are then being very specific and any discussion of this specific circuit which is ignorant of the majority of specific details of the circuit seems misplaced. I have yet to see any real discussion, ever, of the minimoog filter circuit in reasonable enough detail to be considered a genuine attempt at modelling this circuit.

This is the real problem. "Moog filter" doesn't mean something different from "minimoog filter" really, it is in my opinion the result of people being lazy to the point that they've dropped four letters from the name without caring about the resulting ambiguity.

I am sick of seeing threads that use the name "moog filter" which contain absolutely no discussion of any of the circuits designed by moog, having absolutely nothing to do with the minimoog filter.

I just really think people should use the term "lossy integrator cascade" as a generic for this filter type which includes a single pole (one) or sallen-key (two stages) as well as three and four stage variations, or any further number of stages.

To be more specific, "lossy integrator cascade (4p)" might be used.

Alternatively, "lossy-∫ cascade (4p)".

[aciddose]

I urge anyone who wants to use the term "moog filter" to read the patent. If people don't mean the filter from the minimoog, the only filter I can see them referring to by "moog" is the one to which the patent applies from the moog modular.

This circuit is actually a combination of CV mixing, biasing and signal mixing stages including both a four cascaded stage high-pass as well as a low-pass.

It is significantly distinct from the minimoog circuit which includes a modified version of the low-pass stage with feedback but lacks much of the supporting circuitry.

It is also important to drop "ladder" as it is entirely pointless. Specifying the circuit topology really adds no meaning at all to the name.

[Richard_Synapse]

I have yet to see any real discussion, ever, of the minimoog filter circuit in reasonable enough detail to be considered a genuine attempt at modelling this circuit.

True, part of the reason might be that devs don't want to give away their secrets, or they tune their models to particular hardware units and thus they are not universally valid. And btw if we're really pedantic then Minimoog isn't perfectly accurate (Model D, early, late? Voyager?)

Richard

[Z1202]

In the lack of a commonly accepted terminology, my approach would be, rather than being pedantic, to use whatever term will have the "highest ratio" of being understood vs. misunderstood, even if the "understanding" may be challenged as being not 100% correct.

In this regard a "moog ladder" is a useful shortcut for "a series of 4 buffered 1-poles with feedback". A "diode ladder" is a useful shortcut for a specific kind of non-buffered 1-poles. Even for fully linear models. Getting into the nonlinear range, one could further distinguish between "transistor" and "OTA" "moog ladders", differing by the placement of the saturators within the 1-poles. As long as the names "work" as a definition, they are fine with me.

I can agree that e.g. Antti's "moog vcf" is not a 100% model of a "moog vcf", but then I doubt that such 100% model can even exist. There will be always some fine details not covered by a particular model. And those can even vary from one hardware instance to another. So instead of reserving the term "moog vcf" for a (using a Russian expression) "spherical horse in a vacuum", which never exist, I prefer to use it, where it works "well enough" (whatever it means) as a term. The specifics of the meaning can be picked up from the context.

[aciddose]

I don't care that it is 100%, it isn't even 1%. The aim of the code was never to attempt to emulate any characteristic of the circuit itself. Rather the only thing they have in common is that they are both a cascade of four lossy integrators with negative feedback!

Thus I urge people to use the term "lossy integrator cascade" to describe both circuits and code with this topology in a generic way.

If people don't understand the meaning of the term (which is self-descriptive) I doubt they'll understand anything else. Most importantly people who misunderstand the meaning of the misuse of the term "moog filter" will no longer misunderstand what is represented by use of the term "lossy integrator cascade".

In my opinion this is not about what is accurate or most likely to be understood. To think that people understand the meaning of "moog filter" is really quite ridiculous and requires an amazing amount of assumptions to be made about how they interpret meaning.

I believe this is due to the brand being highly sought after. This is nothing more than a sneaky way to leech off bob moog's name by applying his brand to other circuits or software that bears no resemblance to his circuits.

This is what I believe established this nomenclature and this is what we must eliminate for the sake of accuracy, to eliminate confusion and make real progress in the future. Please do not continue to fall victims to sleazy marketing buzzwords.

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Note that these trademarks are in full effect on audio related websites or with regard to audio products both in software and electronic circuitry.

[Smashed Transistors]

Maybe we could start a thread on the subject of nomenclature, it's not at all the topic of this one.

[aciddose]

Well I thought a single post would do it. There isn't much to discuss on my side. If people want to continue to disagree I'll continue to stand firm with regard to what the most accurate nomenclature is. This is nomenclature in common use in electrical engineering and my argument is essentially that we should adopt this established nomenclature rather than halfheartedly attempt to develop our own.

If people have anything to discuss they can post a new topic. I can't see myself adding anything further outside simply repeating what I've already said.