[sdiy] Sallen Key with input mixing to generate all shapes

Wed Jan 7 02:42:49 CET 2015

On 6 January 2015 at 21:02, Richie Burnett <rburnett at richieburnett.co.uk> wrote:
> I guess so.  I think I would have just replaced the two whole
> "OTA/capacitor/voltage follower" sections with integrator blocks.

Integrator blocks would be fine if all the caps were connected to
ground on one end, but otherwise they would just make everything more
confusing.

> i.e. a
> box with an integrator symbol inside, because that's what those blocks are
> doing.  So it would just be a signal flow diagram then, not an electrical
> schematic/

I don't want to draw a signal flow diagram, I want to draw an
idealised circuit, since this is more useful to me, and hopefully to
people wanting to build actual circuits.

> The part that is most visually confusing for me is the bottoms of C1 and C2
> being connected to something that I don't know the output impedance of.  I'd
> need to think about this some more.  Maybe it's just me that finds it
> difficult to get my head round though, so I wouldn't worry!

All triangles are voltage in, voltage out, idealised amps, they are
voltage controlled voltage sources. They have infinite input impedance
and zero output impedance, infinite bandwidth and zero offset. Their
gain is indicated in the middle of the triangle, in the case of the
sigma the gain is 1, but it makes more sense to show this as a
"summing" amp since in a real circuit these will probably be resistor
divider networks as is common at the input stages of OTAs. The bottom
of the capacitors are connected to voltage sources with zero impedance
that will deliver enough current to keep them at the voltage required.
This is the identical situation to the MS20 v2 KLM-307 where the base
of the caps are connected to the output of op-amps:
http://machines.hyperreal.org/manufacturers/Korg/MS-synths/schematics/KLM-307.GIF

> Have you tried drawing the whole thing out as a complete analogue circuit? I
> know you're mostly interested in digital modelling, so it's probably
> unwanted extra work for you, but many analogue synth enthusiasts might be
> tempted to try and build prototypes of these filters out of op-amps and OTAs
> if a complete electrical schematic was also presented.

Sam has done an entire circuit of the input summing SVF here:
http://houshu.at.webry.info/201202/article_2.html

For the SKF version most of the same circuit can be recycled with
minor changes to routing and a single additional op-amp to invert one
of the high pass signal paths. I would love to publish a full
schematic for the input summing SKF (and also another couple of filter
circuits I've designed), but I'm loath to do so without also building
the circuit to make sure it works. I have a couple of months work to
finish before I will have enough spare time to do this. I hope to be
able to contribute the designs to Mutable Instruments' collection of
open source circuits, and get Olivier's help if he has time to fix all
my mistakes and get something that will be robust as I have no
experience in real world circuit design and all the touches needed to
limit currents so things don't get fried.

> Thanks again for sharing your work,
>
> -Richie,

You're welcome, and thanks for the feedback.

Andy

>
>
> -----Original Message----- From: Andrew Simper
> Sent: Tuesday, January 06, 2015 1:52 AM
> To: Richie Burnett
> Cc: synthdiy diy
>
> Subject: Re: [sdiy] Sallen Key with input mixing to generate all shapes
>
> Richie, do these look better?
>
> http://cytomic.com/files/dsp/SvfInputMixing2.jpg
> http://cytomic.com/files/dsp/SkfInputMixing2.jpg
>
> Andy
> -- cytomic -- sound music software --
>
>
> On 6 January 2015 at 09:28, Andrew Simper <andy at cytomic.com> wrote:
>>
>> On 5 January 2015 at 21:50, <rburnett at richieburnett.co.uk> wrote:
>>>
>>>
>>> Hi Andy,
>>>
>>> Thanks for sharing this interesting work.
>>
>>
>> Your welcome!
>>
>>
>>> In the discretization technical paper it would have been interesting to
>>> see the resulting z-domain frequency responses for the digital realisations
>>> of the filters, so that comparisons can be made with the original s-domain
>>> analogue prototypes as the cutoff frequency approaches the Nyquist limit.
>>> (The s-domain frequency responses are "textbook" analogue 2nd order shapes,
>>> so aren't particularly interesting by themselves.)
>>>
>>> -Richie,
>>
>>
>> It is trapezoidal integration, which gives a cramped response which is
>> equivalent to the bi-linear z transform which is why I didn't bother.
>> Please read the other papers I wrote for derivations and plotting of
>> the z-domain transfer function. I show the derivation of forming the
>> z-domain transfer function directly from trapezoidal integration here:
>> http://cytomic.com/files/dsp/SvfLinearTrapOptimised2.pdf in the
>> section "Transfer functions for low, band, high, notch, and peak,
>> continuous and discrete"
>>
>>
>>> PS. The mixture of "electrical schematic" and "signal flow"
>>> representations in the same diagrams might be a little confusing to some.
>>> I'm an electronics engineer so am familiar with looking at both, but they
>>> usually aren't mixed in the same diagram.
>>
>>
>> I originally had little triangle amp blocks but things looked messy.
>> Donald posted a link to this paper:
>> http://www.ka-electronics.com/images/pdf/Steiner_Filter.pdf , which
>> uses a square with a sigma sign in the middle to show a summing block,
>> so I used this idea but instead used a more modern + sign in a circle.
>> Should I switch it to how Steiner does it with a square and sigma? Is
>> that more standard for idealised circuit diagrams? I show the
>> development of the notation I used here:
>> http://cytomic.com/files/dsp/OnePoleLinearLowPass.pdf with the full
>> resistor divider network to use a circle with a + instead, but I am
>> happy to change it if there is something just as succinct and more
>> standard.
>>
>> All the best,
>>
>> Andy
>>
>>
>>>
>>>
>>>
>>>
>>>
>>>
>>> On 2015-01-05 13:25, Andrew Simper wrote:
>>>>
>>>>
>>>> I've taken Sam's ARP transposed SVF design with input mixing and
>>>> written a discretization technical paper on it. I've also updated the
>>>> SKF (Sallen Key Filter) design I did with input mixing to more
>>>> explicitly address using different input signals.
>>>>
>>>> Idealized circuit diagrams:
>>>> http://cytomic.com/files/dsp/SkfInputMixing.jpg
>>>> http://cytomic.com/files/dsp/SvfInputMixing.jpg
>>>>
>>>> Technical papers:
>>>> http://cytomic.com/files/dsp/SkfInputMixing.pdf
>>>> http://cytomic.com/files/dsp/SvfInputMixing.pdf
>>>>
>>>> All the best,
>>>>
>>>> Andrew Simper
>>>> -- cytomic -- sound music software --
>>>>
>>>>
>>>> On 24 December 2014 at 23:44,  <houshu at muj.biglobe.ne.jp> wrote:
>>>>>
>>>>>
>>>>> Hello Andy and list,
>>>>>
>>>>> I'm grad you like my schematics.
>>>>>
>>>>> Multiple point signal injection is a very interesting idea.
>>>>> I guess you can get any response from famous filter structure
>>>>> keeping the original sound.  Four pole filter such as ladder
>>>>> filter may be a good target.
>>>>>
>>>>> Sam HOSHUYAMA
>>>>> Saitama, JAPAN
>>>>>
>>>>>
>>>>>
>>>>> ----- Original Message -----
>>>>> From: "Andrew Simper" <andy at cytomic.com>
>>>>> To: houshu at muj.biglobe.ne.jp
>>>>> Cc: "synthdiy diy" <synth-diy at dropmix.xs4all.nl>
>>>>> Sent: Tuesday, December 23, 2014 13:00:39
>>>>> Subject: Re: [sdiy] Sallen Key with input mixing to generate all shapes
>>>>>
>>>>> Sam you're a legend!
>>>>>
>>>>> You just saved me an IEEE membership just to look at one paper and
>>>>> some pain in "fixing" the schematics in it. I was really interested in
>>>>> the SVF with mixing inputs and you just delivered it straight to me
>>>>> with a wonderfully clear LTSpice schematic, thank-you!
>>>>>
>>>>> I hope I can come up with some more interesting designs to help
>>>>> contribute to the synth community like you are doing.
>>>>>
>>>>> The positive feedback path around the Band section and that you noted
>>>>> is from the ARP 4023, it looks like the OSCar also copied this idea -
>>>>> thanks for pointing out the original.
>>>>>
>>>>> Andy
>>>>>
>>>>> -- cytomic -- sound music software --
>>>>>
>>>>>
>>>>> On 23 December 2014 at 09:34,  <houshu at muj.biglobe.ne.jp> wrote:
>>>>>>
>>>>>>
>>>>>> Hello list,
>>>>>>
>>>>>> Input mixing structure is possible with state-variable-like filter.
>>>>>>
>>>>>> http://houshu.at.webry.info/201202/article_1.html
>>>>>>
>>>>>> HPF response is 12dB/oct not 6dB/oct. Multiple functions with
>>>>>> beautiful frequency response can be obtained from this very
>>>>>> simple circuit.
>>>>>>
>>>>>> Basic structure is like ARP4023, which can be derived from
>>>>>> ordinary state variable filter:
>>>>>> http://houshu.at.webry.info/200602/article_1.html
>>>>>>
>>>>>> I built a module with satisfactory results:
>>>>>> http://houshu.at.webry.info/201202/article_2.html
>>>>>> http://houshu.at.webry.info/201411/img22_1.141731631693745480177.html
>>>>>> Power consumption is as small as 5mA.
>>>>>>
>>>>>> I designed it for single supply operation.
>>>>>> Bipolar supply operation is possible by changing the
>>>>>> exponential converter (Untested):
>>>>>> http://www5b.biglobe.ne.jp/~houshu/synth/VcSvf01a.gif
>>>>>>
>>>>>> Sam HOSHUYAMA
>>>>>> Saitama, Japan
>>>>>>
>>>>>> ----- Original Message -----
>>>>>> From: "Andrew Simper" <andy at cytomic.com>
>>>>>> To: "synthdiy diy" <synth-diy at dropmix.xs4all.nl>
>>>>>> Sent: Sunday, December 21, 2014 16:54:23
>>>>>> Subject: [sdiy] Sallen Key with input mixing to generate all shapes
>>>>>>
>>>>>> Hey guys,
>>>>>>
>>>>>> I've noticed many Sallen Key synth filters can generate different
>>>>>> responses by sticking the input into various points of the circuit,
>>>>>> but they only ever deliver a 1 pole high pass, and a very weak notch.
>>>>>> I've worked out the theory for generating all the same responses as
>>>>>> you can get by mixing the outputs of an State Variable, but instead
>>>>>> mixing the inputs to a Sallen Key. I've put together a technical paper
>>>>>> on it here:
>>>>>>
>>>>>> https://cytomic.com/files/dsp/SkfLinearTrapezoidalSin.pdf
>>>>>>
>>>>>> and I've sketched the basic structure of what is going on here (taking
>>>>>> an MS20 v2 type OTA Sallen Key as the basis):
>>>>>>
>>>>>> www.cytomic.com/files/dsp/SkfInputMixing.jpg
>>>>>>
>>>>>> the important voltages are:
>>>>>>
>>>>>> vamp1 = (m0*v0) - (m1*v0 + v1)
>>>>>> vamp2 = (m1*v0 + v1) - (v2)
>>>>>> vcap1 = (v1) - (res*v2 + m2*(-v0))
>>>>>> vcap2 = (v2) - (m2*v0)
>>>>>>
>>>>>> where m0 = low mix, m1 = band mix and m2 = high mix
>>>>>>
>>>>>> Also for those interested in a digital implementation I've also
>>>>>> included in the paper is also a trapezoidal integrated linear circuit
>>>>>> model use state space increments and high precision coefficient
>>>>>> calculation.
>>>>>>
>>>>>> Andy
>>>>>> _______________________________________________
>>>>>> Synth-diy mailing list
>>>>>> Synth-diy at dropmix.xs4all.nl
>>>>>> http://dropmix.xs4all.nl/mailman/listinfo/synth-diy
>>>>
>>>>
>>>> _______________________________________________
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>
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