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

Richie Burnett rburnett at richieburnett.co.uk
Tue Jan 6 14:02:36 CET 2015

I guess so.  I think I would have just replaced the two whole 
"OTA/capacitor/voltage follower" sections with integrator blocks.  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 

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!

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.

Thanks again for sharing your work,


-----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?


-- 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.
>>>> 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
>>>>> 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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