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VC sine/cosine generator revisited
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frijitz



Joined: May 04, 2007
Posts: 1712
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PostPosted: Wed Aug 08, 2007 10:36 pm    Post subject: VC sine/cosine generator revisited
Subject description: Now with a new 3/4/6/8 phase generating VCO
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Hello --

Many years ago I "invented" a "new" VC quadrature oscillator. A quite simple circuit, it was just a pair of cross-coupled VC integrators, with positive feedback around one of them to build up the oscillations, which reached a maximum when clipped by the power supply rails. This was written up for EN, but not pursued. A couple of years ago while developing my chaos circuitry, I noticed that a nice quadrature oscillator could be built using some of my nonlinear chaos circuits. This I put up on my website and mentioned it on s-diy. Immediately I was contacted by Jim Patchell, who pointed out that he had published the same circuit in Polyphony, 25 years previously. Embarassed Shocked Embarassed

Jim's circuit was based on an original design by RS Burwen, published in the AD Nonlinear Handbook (page 80 in the 1974 edition, but several years older than that).

A current incarnation is shown below. This core requires only two chips: a dual OTA and a dual opamp. No slicing, dicing, pasting, filtering, or any of that. The positive feedback path is provided by the 4.7M resistor and negative-feedback limiting is provided by the back-to-back zeners. I was surprised tonight when I measured the spectral response of a 400 Hz tone. The second harmonic is 60 dB down from the fundamental and the third is down 55 dB. I didn't even look for more. The amplitude is very flat from 8 kHz down to about .3 Hz. Below that the amplitude falls off by about 20% at 0.1 Hz. With larger caps I got good flat response from 800 Hz to .02 Hz, where I got bored with watching the scope.

So why hasn't this beautiful circuit been widely adapted? Who knows. Confused

One EN author criticized it for being unstable. Based on my experience, I don't think this is warranted. Perhaps it got confused with the crank-up-your-filter-Q type oscillator, which can be a bit touchy. But is it stable? You bet!

[extrreeme geekjabber]

The system solves the following nonlinear differential equations:

x' = a y + b x - c x^3 ; y' = -a x.

A quick stability analysis shows that this system undergoes a supercritical Hopf bifurcation as "b" changes from negative to positive. With the cubic term stabilizing the orbits, the system exhibits a stable limit-cycle attractor.

[/extrreeme geekjabber]

Well, maybe I'm just missing something. Perhaps one of you whiteboard wizards would like to give it a try?

Ian

(edited to correct drawing error)


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qosc2.gif



Last edited by frijitz on Mon Aug 20, 2007 2:40 pm; edited 3 times in total
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yusynth



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PostPosted: Thu Aug 09, 2007 2:45 am    Post subject: Reply with quote  Mark this post and the followings unread

Hi Ian

It seems that this schemo is bugged, I reckon that the two 220 ohm resistors shown in parallel at the inverting input of the second OTA (U1b) should be separated, one being connected to the non-inverting input U1b (voltage divider with the 100K resistor...)

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Evan



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PostPosted: Thu Aug 09, 2007 4:56 am    Post subject: Re: VC sine/cosine generator revisited
Subject description: With miscellaneous reminiscences and ruminations
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frijitz wrote:
[extrreeme geekjabber]

The system solves the following nonlinear differential equations:

x' = a y + b x - c x^3 ; y' = -a x.

A quick stability analysis shows that this system undergoes a supercritical Hopf bifurcation as "b" changes from negative to positive. With the cubic term stabilizing the orbits, the system exhibits a stable limit-cycle attractor.

[/extrreeme geekjabber]

Well, maybe I'm just missing something.
I'm sure I am...

I didn't know there would be a maths quiz...
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frijitz



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PostPosted: Thu Aug 09, 2007 5:08 am    Post subject: Reply with quote  Mark this post and the followings unread

yusson wrote:
Hi Ian

It seems that this schemo is bugged, I reckon that the two 220 ohm resistors shown in parallel at the inverting input of the second OTA (U1b) should be separated, one being connected to the non-inverting input U1b (voltage divider with the 100K resistor...)


Arrrrghhhhh. I'll get it fixed. Thanks.

----------------

Edit -- error fixed.
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Evan



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PostPosted: Fri Aug 10, 2007 7:37 am    Post subject: Re: VC sine/cosine generator revisited
Subject description: With miscellaneous reminiscences and ruminations
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frijitz wrote:
A quick stability analysis shows that this system undergoes a supercritical Hopf bifurcation as "b" changes from negative to positive. With the cubic term stabilizing the orbits, the system exhibits a stable limit-cycle attractor.

Ok, I'm starting to get my head around this. Just starting, though.

http://www.scholarpedia.org/article/Bifurcations

I think I may have to see this circuit in action, to get much further.
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Scott Stites
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PostPosted: Fri Aug 10, 2007 10:35 am    Post subject: Reply with quote  Mark this post and the followings unread

This is very groovy, Ian! Do you plan to do PCBs?

Cheers,
Scott

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frijitz



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PostPosted: Fri Aug 10, 2007 9:10 pm    Post subject: Re: VC sine/cosine generator revisited
Subject description: With miscellaneous reminiscences and ruminations
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Evan wrote:

Ok, I'm starting to get my head around this. Just starting, though.
http://www.scholarpedia.org/article/Bifurcations
I think I may have to see this circuit in action, to get much further.


Well, we don't need the fancy math theorems to understand how it works. If you have just the cross-coupled integrators, then each signal is (+) or (-) the integral of the other, so the signals are sine and cosine functions. Ideally they could have any amplitude. But in a real world system there will be damping, offsets, etc., so the system will damp out to zero or else fly off to the rails.

To stabilize the amplitudes, two feedback signals are added. Positive feedback (the 4.7M resistor) ensures that small oscillations will grow in amplitude. Eventually they will be limited by the rails.

The second feedback is provided by the two Zener diodes. When the signal amplitude gets above ~5 V, the diodes break down and the resulting negative feedback prevents the oscillations from growing any further. At some amplitude these "push" and pull" signals balance out to give a stable, fixed amplitude signal. As long as the feedback signals are weak, the oscillations are very nearly sinusoidal.

Very Happy

Ian
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frijitz



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PostPosted: Sat Aug 11, 2007 10:29 am    Post subject: Reply with quote  Mark this post and the followings unread

Scott Stites wrote:
Do you plan to do PCBs?


Since there are other quad osc designs out there it probably doesn't make sense right now to do a board for this one, at least as it stands.

I'm thinking it might be interesting to extend this circuit to more stages. Two integrators could be added to the chain to get an eight phase sinusoidal generator. A bypass switch could be added to make it a six phase osc. (The four original phases would be included in the eight-phase circuit.)

Would this be interesting to anybody?

The multiple phases are useful for wave mixing -- just run the various phases into different VCAs with different sources. This would be basically the same as what I did here (with multi-phase chaos signals).
http://home.comcast.net/~ijfritz/demoB.mp3

As an aside, I have been working a bit on a VC wave mixer circuit. This uses FETs as VC attenuators to vary the amplitudes, obviating the need for many VCAs. So it will be simple and non-precise, but perhaps useful.

Ian
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Nosferatu



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PostPosted: Sat Aug 11, 2007 12:27 pm    Post subject: Reply with quote  Mark this post and the followings unread

>an eight phase sinusoidal generator.
>Would this be interesting to anybody?

I'm sure it can as soon as people realize what it can be used for.

>The multiple phases are useful for wave mixing -- just run the various
>phases into different VCAs with different sources. This would be
>basically the same as what I did here (with multi-phase chaos signals).
>http://home.comcast.net/~ijfritz/demoB.mp3

Indeed, a neat additive oscillator!

>As an aside, I have been working a bit on a VC wave mixer circuit. This
>uses FETs as VC attenuators to vary the amplitudes, obviating the need
>for many VCAs. So it will be simple and non-precise, but perhaps useful.

I have seen a DC to RF mixer made out of two mosfets back to back, it
had a BW of 80Mhz, i haven't tested it and im not entirely clear on how
this back to back actually works?! Any idea?

Last edited by Nosferatu on Tue Aug 21, 2007 12:14 pm; edited 1 time in total
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vtl5c3



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PostPosted: Sun Aug 12, 2007 8:47 am    Post subject: Reply with quote  Mark this post and the followings unread

Nice sample, Ian. It reminds me of early Kluster.

I'd be interested in a PCB, whatever form this circuit ends up taking.

Romeo
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Dave Kendall



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PostPosted: Sun Aug 12, 2007 1:20 pm    Post subject: Reply with quote  Mark this post and the followings unread

Frijitz wrote;
Quote:
As an aside, I have been working a bit on a VC wave mixer circuit. This uses FETs as VC attenuators to vary the amplitudes, obviating the need for many VCAs. So it will be simple and non-precise, but perhaps useful.


That sounds interesting. Something to mix the many outputs from VCOs and waveshapers under VC would be v. useful IMO.

cheers,

Dave (intruiged.........)
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Evan



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PostPosted: Sun Aug 12, 2007 2:52 pm    Post subject: Re: VC sine/cosine generator revisited
Subject description: With miscellaneous reminiscences and ruminations
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frijitz wrote:
Well, we don't need the fancy math theorems to understand how it works.

No danger of this happening.

If I ever understand the math, it will be a happy consequence of seeing the curcuit in operation.

It's just that a 'supercritical Hopf bifarcation' sounds so cool...
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frijitz



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PostPosted: Mon Aug 13, 2007 7:16 pm    Post subject: expo for the 3-4-6-8 phase generators Reply with quote  Mark this post and the followings unread

EDIT: SEE LATER POST BELOW FOR COMPLETE SCHEMATIC, INCLUDING THE EXPO.



Beavering away at this project.

Here is a schematic for the basic expo converter. It should be mostly familiar. One thing to note is the high-frequency tracking circuit. Looking through my old EN's and other notes, I see that nobody ever seems to add this feature to their OTA-based filters and oscillators. Also, the usual FM inputs may easily be added -- these should be obvious from other designs.

{SNIP}

The full-blown, switchable six/eight phase generator is now breadboarded, tested and tracked. Both go down to below .02 Hz and up to 3-4kHz at the top end. This is a better than 5-decade response, which is about as far as I like to push an OTA. A full range unit could easily be done using a cap switch.

Again, just three chips for the basic quad unit, or five for the complete 3/4/6/8 phase unit. Very Happy

I'll try to get the full circuit drawn up in a couple of days.

Enjoy Exclamation

Ian

Last edited by frijitz on Mon Aug 20, 2007 2:46 pm; edited 1 time in total
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PostPosted: Mon Aug 13, 2007 9:41 pm    Post subject: Re: expo for the 3-4-6-8 phase generators Reply with quote  Mark this post and the followings unread

Very interesting project. Just what I need to test my wave shaping idea.

frijitz wrote:
I see that nobody ever seems to add this feature to their OTA-based filters and oscillators.


I wouldn't have thought to put one in because I had the idea that the HF track was mainly required to compensate for the fixed reset time of a sawtooth core.
I guess it must be useful if you want to get the best tracking over the widest range.
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frijitz



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PostPosted: Tue Aug 14, 2007 7:04 am    Post subject: Re: expo for the 3-4-6-8 phase generators Reply with quote  Mark this post and the followings unread

g2ian wrote:
frijitz wrote:
I see that nobody ever seems to add this feature to their OTA-based filters and oscillators.


I wouldn't have thought to put one in because I had the idea that the HF track was mainly required to compensate for the fixed reset time of a sawtooth core.
I guess it must be useful if you want to get the best tracking over the widest range.

Actually the primary purpose of the HF track is to compensate for the base-emitter resistance of the converter transistor, which is a non-ideality in the transistor response that causes the tuning curve to go flat at high current levels. This correction involves some positive feedback of a voltage proportional to the current.

It can also at the same time compensate for reset errors, provided they are small. But the proper way to correct for reset error is to build the correction into the core. You may sometimes see small resistors in series with the integrating cap. These are for reset-time correction.

Ian
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frijitz



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PostPosted: Tue Aug 14, 2007 6:40 pm    Post subject: Full circuit, 3/4/6/8 phase generator. Reply with quote  Mark this post and the followings unread

Here is the full circuit as it now stands.

Just a word about operation, since this kind of system seems to be widely misunderstood and is rarely used the EM world.

At first glance this looks like a four-pole filter with feedback. But look again -- it is really quite different and more subtle than that. The difference? This circuit has negative feedback around each individual stage. The feedback resistors are carefully -- painstakingly actually -- chosen so that the linear part of the system (small signals) oscillates, but just barely. On startup the oscillations build up slowly over dozens of cycles.

At large signal amplitudes the zener diodes begin to conduct, adding additional negative feedback that prevents further growth in amplitude. In other words, large amplitude signals decay over time. The subtle and delicate balance between these opposing gentle forces cause the system to perform stable, high-purity sinusoidal oscillations at a finite amplitude. The amplitudes are adjusted by the two "Level" trimmers, which vary the strength of the nonlinear feedback.

Contrast this operation with that of the four-pole filter with feedback. In that case the positive feedback is highly regenerative and the first stage is clipped by the hard limiting of the power supply rails. The subsequent stages filter this signal somewhat, so the second and fourth stages can be used for a crude quadrature oscillator, but distortion is still quite high.

In the current system, all four stages give sine waves that look the same on a scope trace. This means that all stages can be used, yielding an eight-phase oscillator, rather than the usual quadrature signals obtained from the regenerating four-pole filter.

The six-pole switch (Sa-Sf) allows a choice between six phase and eight phase operation. Using alternating outputs give three and four phase operation.

Next I will be working on soldering this circuit up so I can free up my whiteboard for the part of the project, the development of an eight stage dynamic wave scanner.

Stay tuned. Very Happy

Ian


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frijitz



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PostPosted: Mon Aug 20, 2007 2:58 pm    Post subject: Reply with quote  Mark this post and the followings unread

BUMP

Attachments put back in.
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bugbrand



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PostPosted: Mon Aug 20, 2007 5:42 pm    Post subject: Reply with quote  Mark this post and the followings unread

Frijitz,

I keep on kicking myself 'cos I still haven't had a chance to try out any of your circuits.
They look so fine! Really exciting, really interesting



..sometime..sometime..!...

[edit --- I should learn to read people's names properly!]

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PostPosted: Mon Aug 20, 2007 6:48 pm    Post subject: Reply with quote  Mark this post and the followings unread

Thanks Ian
i was going to try the basic version, but am very happy to put together the extended version.
i don't see 6 pole switches very often, would it work to use SPDT cmos analog switches(....and then drive them with a gate input)?

cheers
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frijitz



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PostPosted: Mon Aug 20, 2007 8:23 pm    Post subject: Reply with quote  Mark this post and the followings unread

andrewF wrote:
Thanks Ian
i was going to try the basic version, but am very happy to put together the extended version.
i don't see 6 pole switches very often, would it work to use SPDT cmos analog switches


Great! I'm having a lot of fun with the 6-phase right now. There is no end to what you can do with wave mixing, and it sounds pretty good, at least to me. I'll get some clips up soon.

CMOS switches should work OK, I think. But Mouser has the inexpensive Alpha rotary units:

105-SR2511F-62RN

Good luck!

Ian
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yusynth



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PostPosted: Tue Aug 21, 2007 3:40 am    Post subject: Reply with quote  Mark this post and the followings unread

Nice circuit, it looks very promising. It might give it a go and design a PCB for it...
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frijitz



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PostPosted: Tue Aug 21, 2007 7:09 am    Post subject: Reply with quote  Mark this post and the followings unread

bugbrand wrote:
I keep on kicking myself 'cos I still haven't had a chance to try out any of your circuits.
They look so fine! Really exciting, really interesting
..sometime..sometime..!...


Ah, well, many thanks for the kind words. You still have the opportunity to be among the first to work with these circuits. Wink

Ian
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frijitz



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PostPosted: Fri Aug 24, 2007 9:57 am    Post subject: some 6-phase demos Reply with quote  Mark this post and the followings unread

Here are three audio clips of the 6-phase scanner in action.
The first clip demonstrates straightforward scanning among three slightly different waveforms.
The second involves varying the timber of four waves using four stages of the scanner..
For the final clip, the scanner is used to vary the amount of vibrato (FM) of three VCOs along with the modulation of two VCF's and a VCA.

Lots of interesting uses for this unit beyond just audio signal scanning.

Very Happy
Ian


wavescanA.mp3
 Description:
Phases 1, 3, and 5 (120 deg spacing) apply AM to different waveforms. Section 1: VCA bias at zero, large AM depth. Section 2: medium VCA bias, medium AM depth. Section 3: Large VCA bias, small AM depth. Sections 4 and 5: Modulation at audio frequency.

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 Filename:  wavescanA.mp3
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buildup01.mp3
 Description:
Section 1: Modulated Double Pulse Waveform Generator. Section 2: Tri-Saw modulation using the Snicster waveshaper. Section 3: XOR signal from two modulated 5Pulsers. Section 4: All three mixed together.

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 Filename:  buildup01.mp3
 Filesize:  460.45 KB
 Downloaded:  714 Time(s)


vibscan.mp3
 Description:
Phases 1,2 and 5 amplitude-modulate three LFOs, which then modulate three VCOs. Phases 3, 4, 6 modulate 2 VCFs and a VCA. Four sections for four different scan rates -- two sub-audio, two audio.

Download
 Filename:  vibscan.mp3
 Filesize:  518.82 KB
 Downloaded:  683 Time(s)


Last edited by frijitz on Fri Aug 24, 2007 1:19 pm; edited 3 times in total
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EdisonRex
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PostPosted: Fri Aug 24, 2007 12:33 pm    Post subject: Reply with quote  Mark this post and the followings unread

Fascinating as usual. You're always up to something new and unusual. It's an inspiration.
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Scott Stites
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PostPosted: Fri Aug 24, 2007 10:05 pm    Post subject: Reply with quote  Mark this post and the followings unread

Oh, dear, I came across this thread again and realized I'd downloaded DemoB last...what, August 12....and never listened to it (such is the begin-download-check-back-later life of crappy dial-up).

Just listened to it - whoa, Nelly!

Time to download more....

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