Author 
State variable filters vs Multimode filters 
sloth713 
What is the the difference between a state variable filter and a multimode filter?
Thanks in advance for helping me fill this gap in my knowledge. 

daverj 
A multimode filter is a filter with multiple "modes". Meaning low pass, high pass, bandpass, and/or notch. (it doesn't have to have them all, but typically has the first three)
They can have multiple simultaneous outputs, or a switch to select the mode of the single output.
A statevariable filter is a specific topology for making a filter. It is a mathematical model involving two or more integrators in a feedback arrangement. The typical circuit implementation includes low pass, high pass, and bandpass, though it's possible to build one where not all modes are brought out to connectors.
A statevariable filter usually has all three outputs, and is therefore usually a multimode filter. If somebody builds one to take advantage of it's characteristics, but only brings out a single output (such as the bandpass output) then in that case it is not a multimode filter.
A multimode filter can be made lots of other ways. So a multimode filter is not necessarily a statevariable filter. 

sloth713 
Thanks for the very informative reply daverj
and on a side note I am glad that you are feeling better. 

milkshake 
You can make multimode filters out of every filter topology. 

Peake 
daverj wrote:  A statevariable filter is a specific topology for making a filter. ... typical circuit implementation includes low pass, high pass, and bandpass, though it's possible to build one where not all modes are brought out to connectors. 
Example: The Buchla 291 bandpass filter. "Clones" are bringing out the other two responses to the front panel. 

wellurban 
I gather that by the nature of the topology, SVFs are always 2 pole (12 dB/octave). I take it that's not always the case for other types of MMF? 

dogoftears 
wellurban wrote:  I gather that by the nature of the topology, SVFs are always 2 pole (12 dB/octave). I take it that's not always the case for other types of MMF? 
right. though often the multimode outs of a 4 pole LPF are not 4 pole themselves. for example i dont think you can get a 4 pole HPF out of a Boogie filter (or am i wrong?).
i'd like to know more about the rarity of 4 pole HPF's in general. is there something in general filter topology that makes this more difficult to achieve in a circuit? 

Dr. SketchnEtch 
In my understanding, state variable filters suck, and multimode filters blow. That's the only difference, really, right? 

daverj 
wellurban wrote:  I gather that by the nature of the topology, SVFs are always 2 pole (12 dB/octave). I take it that's not always the case for other types of MMF? 
The simplest and most common SVF is a 2pole design. But SVFs are not limited to two poles. More integrators can be added to add more poles. If you do a search on "fourth order state variable filter" you'll find some block diagrams and schematics for 24db/oct state variable filters. (and I believe Mattson sells one)
Multimode filters are not a specific topology, so an MMF can consist of a single filter with multiple outputs (like a state variable) or it can be several unrelated filters all working on the same input to provide multiple outputs. So a multimode could be any number of poles, and doesn't even need to have the same number of poles per output. 

milkshake 
Besides the different outputs every filter also has different inputs. This allows for spectral fading of sounds. 

mrand 
old thread here, but seems like an ok place to ask about state variable filters.
Why do they have LP feedback paths as well as BP feedback? I guess they are each 180degrees out of phase with each other, and somehow increasing the BP feedback reduces Q... I think? I'm very puzzled by these filters and don't have the math to understand them properly.
Anyone care to chat a bit about how they work? 

Graham Hinton 
mrand wrote:  Why do they have LP feedback paths as well as BP feedback? I guess they are each 180degrees out of phase with each other, and somehow increasing the BP feedback reduces Q... I think? I'm very puzzled by these filters and don't have the math to understand them properly.
Anyone care to chat a bit about how they work? 
The answers to your questions lie in the maths. The circuit implements the solution to a differential equation. An equation that is quite common in a lot of mechanical systems, e.g. it describes the motion of a damped pendulum. The position of a pendulum being displaced, released and decaying exponentially to rest plotted against time is the same waveform as a SVF being "pinged". It is easy to grasp that intuitively, you need to learn about differential equations to understand it completely.
Dennis Colin wrote an AES paper about the original ARP 1047 SVF, where the background is explained, but he doesn't give anything away.
Don Lancaster's Active Filter Cookbook uses lots of SVF examples and has the maths which is optional. 

mrand 
Thanks, Graham.
I checked out the Dennis Colin article. You're right it doesn't reveal much for me, but I love his misc application notes!
Shopping now for used copy of Lancaster's book. Hopefully in a couple years when I'm finished my current degree I will endeavor to learn the maths. For now, I will have to accept intuition and analogies.
I get what you are saying about pinging. I suppose the cutoff is akin to the radius of the pendulum's arc, and the resonance would be...hmmm... the inverse of the mechanical resistance to the pendulum's motion.
Well it makes a nice picture, anyways. 

slow_riot 
The 360 degrees feedback from integrator 2 inverted back to integrator 1 establishes the transfer function of the complete SVF. This is at full resonance, but without it you would not get a bandpass response from integrator 1. Feedback around integrator 1 back into itself damps the response, but without compromising the transfer function that allows multiple outputs.
You could get very similar behaviour by deleting the feedback around integrator 1, and varying the level of the 360 degree feedback path to adjust resonance/oscillation, but this would defeat the bandpass output which is established by the 360 feedback path at unity gain.
The maths, or rather description of the behaviour at the algorithmic level is important, circuit design for music purpose is engineering which is applied maths. It's worth putting the time in to understand the maths if you wish to design your own circuits, and the SVF in particular is the main building block for complex periodic functions.
Simulation using a SPICE or similar package (LTSpice is free and has features that some very pricey industry standard packages do not) may fall short in describing circuit behaviour in intimate detail, but you will always get a good idea of the big picture. An afternoon with an SVF, both as oscillator in transient analysis mode, and as filter in AC sweep mode will be very enlightening. 

Graham Hinton 
mrand wrote: 
I checked out the Dennis Colin article. You're right it doesn't reveal much for me, but I love his misc application notes!

I was able to build my first SVF from the maths that he did give away, and actually I'm glad that I never knew his circuit at the time.
I have some notes somewhere that I made doing the maths of SVF from first principles. I'll dig them out and scan them.
Quote: 
Hopefully in a couple years when I'm finished my current degree I will endeavor to learn the maths.

The level of maths required is entrance level for a technical degree.
The differential equation also describes the behaviour of an LCR series circuit, but that isn't intuitive as to what will happen when given a signal. It works the other way, analysing the circuit shows that it will behave like a pendulum analogue (by recognising the similarity of the equations) which then allows us to predict and exploit the circuit.
Quote: 
I suppose the cutoff is akin to the radius of the pendulum's arc, and the resonance would be...hmmm... the inverse of the mechanical resistance to the pendulum's motion.

Right on the second. The arc distance is the amplitude of the initial signal. The resonant frequency comes from the mass and length of the pendulum and the gravitational acceleration. Think about it: frequency has one dimension, [T]^1, so the factors contributing to it have to cancel out and be dimensionally consistent. Acceleration contains [T]^2 and a square root gets that to [T]]^1. The same principle applies if you are doing it with resistances and capacitors. 

modularblack 
milkshake wrote:  You can make multimode filters out of every filter topology. 
This.
And it is quite easy. You just have to take the Lowpass to an Attunuverter and mix it to the original signal signal.
You can get everything but the bandpass/bandstop/peak out of it.
A bandpass is just a lowpass and a highpass together. And a Bandstop is the original signal minus the bandpass signal. And the Peak signal is a bandpass plus the original signal. 

mrand 
slow_riot wrote:  The 360 degrees feedback from integrator 2 inverted back to integrator 1 establishes the transfer function of the complete SVF. This is at full resonance, but without it you would not get a bandpass response from integrator 1. Feedback around integrator 1 back into itself damps the response, but without compromising the transfer function that allows multiple outputs.

OK it is becoming a bit clearer now, thanks!.
slow_riot wrote:  You could get very similar behaviour by deleting the feedback around integrator 1, and varying the level of the 360 degree feedback path to adjust resonance/oscillation, but this would defeat the bandpass output which is established by the 360 feedback path at unity gain. 
Am I mistaken that this makes the ms20 type filter?
slow_riot wrote:  It's worth putting the time in to understand the maths if you wish to design your own circuits, and the SVF in particular is the main building block for complex periodic functions. 
wonder where to start... it's been 20 years since learning calculus. Many of the concepts stuck, but the practice is lost. 

mrand 
Graham Hinton wrote:  The resonant frequency comes from the mass and length of the pendulum and the gravitational acceleration. 
OK yeah, I guess I meant length of the arm when I said radius, but I didn't think about initial acceleration.
Graham Hinton wrote: 
Think about it: frequency has one dimension, [T]^1, so the factors contributing to it have to cancel out and be dimensionally consistent. Acceleration contains [T]^2 and a square root gets that to [T]]^1. The same principle applies if you are doing it with resistances and capacitors. 
I'm thinking... but its foggy! I will need to come back to this afew times before it clarifies.
Thanks for the replies, folks, this is very helpful 

slow_riot 
The MS20 is a Sallen and Key architecture, but there are more similarities than differences with the SVF . Here is a full analysis of the topology.
http://www.timstinchcombe.co.uk/synth/MS20_study.pdf
I'm being somewhat hypocritical in advocating starting with the maths, I personally learn by doing and seeing more than anything else. But the maths does underpin everything, more so in continuous processing circuits like filters and oscillators, and will allow you to expand your understanding beyond the limits set by other people's work. Most of the industry is built upon only minor variations in topology, transconductor with no changes at the mathematical level. At the moment these variations in topology are sort of moot anyway because modern low distortion variable gain cells like THAT2180 and V2164 require a virtual ground input and SVF is the only topology that will allow this.
Further explorations around the basic calculus of the state variable equation allow realisation of linear and non linear ordinary differential equations such as Legendre or Bessel, high order chaotic equations, and even partial differential equations. It is incredibly powerful.
Aside from the Don Lancaster book on filters, I would recommend (some of which you can find PDFs of):
Jim Williams Linear Tech application notes e.g. AN47
Bob Pease has some interesting ideas about real time computation
Sergio Franco Design with Operational Amplifiers and Analog Integrated Circuits
Walt Jung Opamp Cookbook and Basic Linear Design (free PDF)
Analog Devices Nonlinear Circuits Handbook
Stanley Fifer  Analogue Computation
Ian Fritz  http://ijfritz.byethost4.com/?i=1 

Dr. SketchnEtch 
slow_riot wrote:  I'm being somewhat hypocritical in advocating starting with the maths, I personally learn by doing and seeing more than anything else. But the maths does underpin everything, more so in continuous processing circuits like filters and oscillators, and will allow you to expand your understanding beyond the limits set by other people's work. Most of the industry is built upon only minor variations in topology, transconductor with no changes at the mathematical level. At the moment these variations in topology are sort of moot anyway because modern low distortion variable gain cells like THAT2180 and V2164 require a virtual ground input and SVF is the only topology that will allow this. 
Not true. The 2164 requires virtual ground, but if one is clever one can adapt just about any filter topology to use with 2164. The trick is to derive transfer functions using the stock 2164based filter stage which are mathematically equivalent to the topology being considered. Doing this with the MS20 filters was the basis of the Korgasmatron (now the Morgasmatron). And I can confirm that the Korgo can sound identical to the MS20  the main difference in sound between a real, vintage MS20 and a eurorack setup with a Korgasmatron is the VCA  the simple VCA in the MS20 is pretty noisy and colours the sound a lot. 

Rex Coil 7 
Ack ... all you smartysmart guys crack me up! All of this talk of math and brains .... when everyone knows the difference between a multi mode and a state variable is that one goes WOOP WOOP and the other one goes BOING BOING.
GEEZ!
...uhm .... I'll just see myself out ....


mrand 
still reading with interest and enjoying the techtalk and comedic relief in equal measure!
Thanks for the reading list, btw, slowriot. 

Graham Hinton 

Llouwelyn 

arthurdent 
Graham Hinton wrote:  An equation that is quite common in a lot of mechanical systems, e.g. it describes the motion of a damped pendulum. The position of a pendulum being displaced, released and decaying exponentially to rest plotted against time is the same waveform as a SVF being "pinged". It is easy to grasp that intuitively, you need to learn about differential equations to understand it completely. 
OH MY GOD! Takes me back to 1965, my freshman year in college, had to take a course called Dynamic Systems, and that's where we started  the damped pendulum model. EVERYTHING could be modeled from the damped pendulum  LC circuits, LR circuits, LRC circuits, mechanical assemblies. And it worked, you could understand it, if/once you got through all of the math explaining it. Brings back a lot of memories... 
