Uh, Pro1 definitely sounds fatter than a Nord Lead 1Prunesquallor wrote: ↑Tue Jul 07, 2020 8:46 am
Nothing to do with the fattest sound necessarily. Life's too short and there's too many modules.
Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Moderators: luketeaford, Joe., lisa, Kent
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
 Dr. SketchnEtch
 Super Deluxe Wiggler
 Posts: 7846
 Joined: Thu Jan 21, 2010 1:46 pm
 Location: Vancouver, BC, Canada
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
As requested, here is a block diagram of the Rubicon core (as first envisioned from the comfort of our downstairs washroom toilet):
Starting from the upper left, the Expo VCA is a 2164 VCA, and VC Expo is the exponential voltage coming from the CV summer which sets the pitch of the VCO at 1V/octave.
The triangle wave is generated at the integrator, then goes to the positive/negative opamp which is controlled by the JFET.
The output of the +/ opamp goes to the core comparator, which generates a raw square wave which is about 20Vpp. The square wave (and all the other waves) are limited by the zener bridge to about 10Vpp.
The sum of the limited square wave and the triangle wave is the zigzag wave, which actually drives the comparator.
The square wave and its inverse are sent to a pair of opposing linearized 2164 VCAs, which act as a balanced modulator. The VC signals to these VCAs are the TZFM signal. The straight signal is sent to FM VC+, and its inversion is sent to FM VC. The linearized VCAs are at unity gain at +5V and zero gain at 0V and below. Hence, if the TZFM signal is a 10Vpp sine wave, then when this sine wave is positive, it turns on the positive VCA, and when it is negative it turns on the negative VCA. If the sine wave is centred around 0V, then each VCA will just reach unity gain (thus giving the baseline frequency of the VCO) when the sine wave reaches its apices.
The FM VC signals are compared at a comparator, and the output of this comparator (which switches when the FM VC signals cross zero) drives the JFET to change the polarity of the triangle going to the core comparator.
This arrangement gives very good TZFM, and is pretty cheap. The multiplier is two linearized 2164 VCAs, which can be built from a single 2164 IC and a dual opamp (total cost, about $4). The multiplier can actually be built from a single 2164 VCA, but the result is harder to calibrate for 1V/octave with changing symmetry.
I haven't shown the Linear FM circuit which generates the FM VC signals, but suffice it to say that the incoming signal goes through yet another linearized 2164 VCA, and this provides the TZFM Index (i.e., for triggering with an envelope to get bell sounds, etc). Also, the Symmetry control biases the indexed TZFM signal to change the centre point relative to zero frequency.
I hope this clarifies things.
Starting from the upper left, the Expo VCA is a 2164 VCA, and VC Expo is the exponential voltage coming from the CV summer which sets the pitch of the VCO at 1V/octave.
The triangle wave is generated at the integrator, then goes to the positive/negative opamp which is controlled by the JFET.
The output of the +/ opamp goes to the core comparator, which generates a raw square wave which is about 20Vpp. The square wave (and all the other waves) are limited by the zener bridge to about 10Vpp.
The sum of the limited square wave and the triangle wave is the zigzag wave, which actually drives the comparator.
The square wave and its inverse are sent to a pair of opposing linearized 2164 VCAs, which act as a balanced modulator. The VC signals to these VCAs are the TZFM signal. The straight signal is sent to FM VC+, and its inversion is sent to FM VC. The linearized VCAs are at unity gain at +5V and zero gain at 0V and below. Hence, if the TZFM signal is a 10Vpp sine wave, then when this sine wave is positive, it turns on the positive VCA, and when it is negative it turns on the negative VCA. If the sine wave is centred around 0V, then each VCA will just reach unity gain (thus giving the baseline frequency of the VCO) when the sine wave reaches its apices.
The FM VC signals are compared at a comparator, and the output of this comparator (which switches when the FM VC signals cross zero) drives the JFET to change the polarity of the triangle going to the core comparator.
This arrangement gives very good TZFM, and is pretty cheap. The multiplier is two linearized 2164 VCAs, which can be built from a single 2164 IC and a dual opamp (total cost, about $4). The multiplier can actually be built from a single 2164 VCA, but the result is harder to calibrate for 1V/octave with changing symmetry.
I haven't shown the Linear FM circuit which generates the FM VC signals, but suffice it to say that the incoming signal goes through yet another linearized 2164 VCA, and this provides the TZFM Index (i.e., for triggering with an envelope to get bell sounds, etc). Also, the Symmetry control biases the indexed TZFM signal to change the centre point relative to zero frequency.
I hope this clarifies things.
You do not have the required permissions to view the files attached to this post.
this night wounds time,
 Dr. SketchnEtch
 Super Deluxe Wiggler
 Posts: 7846
 Joined: Thu Jan 21, 2010 1:46 pm
 Location: Vancouver, BC, Canada
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Also, Bernie, I incorporated a dualcore version of the Rubicon into my Frequency Shifter design, and set the two cores up in a way to give perfect 90degree quadrature of the two outputs. Here is the first of three videos about that module. If you skip to about 7:30 in the video, I put the dualcore VCO into throughzero FM, and the time reversal is very clearly shown on the scope at 7:45 in the video.
this night wounds time,

 Learning to Wiggle
 Posts: 23
 Joined: Sat Jun 27, 2020 3:19 pm
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
DS&E  looks good  thanks
The block diagram (although cumbersome and expensive – terms often applicable to some of my work!) would seem functionally equivalent to Doug’s (canonic) timereversal, and the video is definitive proof of TZFM.
Bernie
The block diagram (although cumbersome and expensive – terms often applicable to some of my work!) would seem functionally equivalent to Doug’s (canonic) timereversal, and the video is definitive proof of TZFM.
Bernie
 Prunesquallor
 Veteran Wiggler
 Posts: 549
 Joined: Wed Nov 11, 2009 3:08 am
 Location: Valencia, Spain
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Yeah, in your example, but we're talking about TZFM VCOs. In my case, I love the sound of the Rubicon, clear to gloopy (your word, brilliant!); and the Teezer, spooky. Nothing phat in either of these. The EN129 also sounds amazing. My point is that technical comparisons are all fine, but at the end of the day, if there's a choice, take the module that speaks to you, especially if it's going to be a centrepiece. Personally, the ZPO doesn't do it for me (and neither do the Generate 3 or Brenso, for that matter), although it looks like a very well designed module. It's the core sound that matters.daphnid wrote: ↑Tue Jul 07, 2020 1:54 pmUh, Pro1 definitely sounds fatter than a Nord Lead 1Prunesquallor wrote: ↑Tue Jul 07, 2020 8:46 am
Nothing to do with the fattest sound necessarily. Life's too short and there's too many modules.
If at first you don't succeed read the instruction manual.
 Dr. SketchnEtch
 Super Deluxe Wiggler
 Posts: 7846
 Joined: Thu Jan 21, 2010 1:46 pm
 Location: Vancouver, BC, Canada
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
I just had a look at EN129, and that circuit seems far more complicated than the Rubicon. The thing I like about the Rubicon (and what I strive for in most of my designs) is that it uses just three different ICs: 2164 quad VCAs (which I strongly prefer to OTAs), TL07X JFETinput opamps, and LM311 comparators. The 2164s are about $3 (and two are required), but the opamps and comparators are dirt cheap and work well. Everything else is just passives and a few diodes (no matched transistor pairs, no tempco resistors, no white goop). The other thing I like about it is that I think the TZFM concept is very easy to understand from this implementation.Bernie Hutchins wrote: ↑Tue Jul 07, 2020 8:28 pmDS&E  looks good  thanks
The block diagram (although cumbersome and expensive – terms often applicable to some of my work!) would seem functionally equivalent to Doug’s (canonic) timereversal, and the video is definitive proof of TZFM.
Bernie
this night wounds time,

 Learning to Wiggle
 Posts: 23
 Joined: Sat Jun 27, 2020 3:19 pm
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
ari ellis wrote: ↑
Tue Jun 23, 2020 10:27 pm
“Yep, that's the EN I had in mind. That's not TZFM, and I'm not swayed just because they called it such. Right now, multiple options exist which implement actual, nocaveats TZFM. The two most common analog TZ oscs I've encountered in euro are the rubicon and the doepfer quadrature osc (can't remember it's # offhand). Both of these offer TZFM as per its unambiguous mathematical definition.”
Ari (or anyone else), please point out what you think is the “unambiguous mathematical definition” of TZFM. How would such a notion differ from that used in EN129?
Thanks  Bernie
Tue Jun 23, 2020 10:27 pm
“Yep, that's the EN I had in mind. That's not TZFM, and I'm not swayed just because they called it such. Right now, multiple options exist which implement actual, nocaveats TZFM. The two most common analog TZ oscs I've encountered in euro are the rubicon and the doepfer quadrature osc (can't remember it's # offhand). Both of these offer TZFM as per its unambiguous mathematical definition.”
Ari (or anyone else), please point out what you think is the “unambiguous mathematical definition” of TZFM. How would such a notion differ from that used in EN129?
Thanks  Bernie

 Learning to Wiggle
 Posts: 23
 Joined: Sat Jun 27, 2020 3:19 pm
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
DS&E –
You said “The other thing I like about it is that I think the TZFM concept is very easy to understand from this implementation.”
Which one – seriously.
What could be simpler than taking a very standard (Tricore) exponential VCO (with excellent tracking), which already has linear FM, and putting a flipflop in the loop to reverse direction : (1) when a triangle limit is reached (2) when the FM control changes sign (3) both simultaneously.
Please DO explain how yours works in anywhere near such simple terms.
Bernie
You said “The other thing I like about it is that I think the TZFM concept is very easy to understand from this implementation.”
Which one – seriously.
What could be simpler than taking a very standard (Tricore) exponential VCO (with excellent tracking), which already has linear FM, and putting a flipflop in the loop to reverse direction : (1) when a triangle limit is reached (2) when the FM control changes sign (3) both simultaneously.
Please DO explain how yours works in anywhere near such simple terms.
Bernie
 Dr. SketchnEtch
 Super Deluxe Wiggler
 Posts: 7846
 Joined: Thu Jan 21, 2010 1:46 pm
 Location: Vancouver, BC, Canada
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
I don't know, Bernie. You win. Nobody will ever design anything that is as good as what is in Electronotes, so we shouldn't even try.
All I know is that it was easier for me to design my own circuit based on my own understanding of the concept of TZFM, rather than trying to decipher how EN129 works.
And, as far as simplicity, for the Rubicon, I took an existing (and very successful) VCO design  the Dixie  and added a linear VCA, a comparator, and a JFET to the linear FM circuit.
All I know is that it was easier for me to design my own circuit based on my own understanding of the concept of TZFM, rather than trying to decipher how EN129 works.
And, as far as simplicity, for the Rubicon, I took an existing (and very successful) VCO design  the Dixie  and added a linear VCA, a comparator, and a JFET to the linear FM circuit.
this night wounds time,
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Hate to interrupt these bickering engineers with my fuzzy musician's language, but I hooked up the Rubicon (1) and did some sine on sine FM with it next to the ZPO this evening (using a DIxie 2+ as modulating VCO) and in terms of the TZFM the Rubicon had a more rich and round, bubbly character to it in that context. It really is a beautiful sounding oscillator. The ZPO sounds more "dry" or something under the same settings. I also noted that the saw on the Rubi seemed to be fuller or have more harmonics. Perhaps because the ZPO is saw core so it's a more pure waveform? Idk. Just an observation.
And as noted by several people, the sync on the ZPO sounds great. The Rubi is a lot more buzzy under the same sync conditions. And it's a lot easier for me to get sounds out of the ZPO I've never quite heard from an analog VCO before (granted, that was true of the Rubi when I first used it too). Lots of strange scratchy and gravelly, broken glass textures that aren't what I'd call harsh but aren't smooth either. I personally find them very useful for industrial/noise/techno. Someone said something about their ZPO sounding like sandpaper in another thread and yeah, it kinda does (or can). The brilliance of this thing is the amount of these strange tones you can get to track pitch in a musically useful way.
To get anything near the Serge NTO's variable wave morphing I need to be mixing it with different waves from another oscillator with the same tuning. The wave morphing just isn't that exciting on its own, despite having 2 variable morphing waveforms that you can morph between. A lot of the strange sound come from audiorate modulating the wave morphs on the ZPO though, esp when doing FM. I thought I'd be able to get better results out of slowly modulating all the morph inputs but there's a lot of dead space in between the shapes.
And as noted by several people, the sync on the ZPO sounds great. The Rubi is a lot more buzzy under the same sync conditions. And it's a lot easier for me to get sounds out of the ZPO I've never quite heard from an analog VCO before (granted, that was true of the Rubi when I first used it too). Lots of strange scratchy and gravelly, broken glass textures that aren't what I'd call harsh but aren't smooth either. I personally find them very useful for industrial/noise/techno. Someone said something about their ZPO sounding like sandpaper in another thread and yeah, it kinda does (or can). The brilliance of this thing is the amount of these strange tones you can get to track pitch in a musically useful way.
To get anything near the Serge NTO's variable wave morphing I need to be mixing it with different waves from another oscillator with the same tuning. The wave morphing just isn't that exciting on its own, despite having 2 variable morphing waveforms that you can morph between. A lot of the strange sound come from audiorate modulating the wave morphs on the ZPO though, esp when doing FM. I thought I'd be able to get better results out of slowly modulating all the morph inputs but there's a lot of dead space in between the shapes.
 brandonlogic
 Super Deluxe Wiggler
 Posts: 2681
 Joined: Tue Jan 27, 2015 9:17 am
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Thanks for the comparison. If you (or anyone) have the ability to do a video or audio demo comparison focusing on sine on sine tzfm that would be neat to hear.
Just make sure to use a wide variety of frequencies and fm attenuation (so the fm isn’t just wide open always).
I noticed with the rubicon, when the lock switch is on the fm depth of the tzfm input gets really deep, and lots of the sweet spots are waitin the first 25% of its range (makes it a little hard to dial in!).
Just make sure to use a wide variety of frequencies and fm attenuation (so the fm isn’t just wide open always).
I noticed with the rubicon, when the lock switch is on the fm depth of the tzfm input gets really deep, and lots of the sweet spots are waitin the first 25% of its range (makes it a little hard to dial in!).

 Learning to Wiggle
 Posts: 23
 Joined: Sat Jun 27, 2020 3:19 pm
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
DE&S –
You said: “ Nobody will ever design anything that is as good as what is in Electronotes, so we shouldn't even try.” I never said anything remotely like that. Why the uncalledfor sarcasm?
What I feel EN did “better” was to provide detailed descriptions of the theory, design procedures, and circuit functioning with the genuine intention that those with certain minimums of savvy and a modicum of ambition (and who tried) could benefit.
 Bernie
You said: “ Nobody will ever design anything that is as good as what is in Electronotes, so we shouldn't even try.” I never said anything remotely like that. Why the uncalledfor sarcasm?
What I feel EN did “better” was to provide detailed descriptions of the theory, design procedures, and circuit functioning with the genuine intention that those with certain minimums of savvy and a modicum of ambition (and who tried) could benefit.
 Bernie
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
EDIT: double post, please delete!
Last edited by ari ellis on Thu Jul 09, 2020 12:02 pm, edited 1 time in total.
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Very cool to see you here Bernie!Bernie Hutchins wrote: ↑Wed Jul 08, 2020 9:18 pmari ellis wrote: ↑
Tue Jun 23, 2020 10:27 pm
“Yep, that's the EN I had in mind. That's not TZFM, and I'm not swayed just because they called it such. Right now, multiple options exist which implement actual, nocaveats TZFM. The two most common analog TZ oscs I've encountered in euro are the rubicon and the doepfer quadrature osc (can't remember it's # offhand). Both of these offer TZFM as per its unambiguous mathematical definition.”
Ari (or anyone else), please point out what you think is the “unambiguous mathematical definition” of TZFM. How would such a notion differ from that used in EN129?
Thanks  Bernie
The following equation is a crude description of what I mean by "true TZFM:"
<output signal> = cos((f_0 + <modulation signal>) * t),
where f_0 is the frequency of the oscillator with zero modulation index (maybe set by a panel knob, or incoming V/oct). <modulation signal> is measured *after* the index VCA if there is one.
The real definition involves an integral, which I don't feel like writing out in plain text, but see the first equation here: https://en.wikipedia.org/wiki/Frequency ... l_analysis. I believe that the oscillators I mentioned directly implement the first linked equation, maybe with other waveforms in place of the sine's. I believe that DX synths implement the approximation given by the second set of equations at the link.
Correct me if I'm wrong, but I'm fairly confident that the EN129 doesn't do this. My understanding is that the polarityreversal of the 129 happens when <modulation signal> is negative, *not* when (f_0 + <modulation signal>) is negative. This is different. Also, turning up the FM always increases the absolute value of the instantaneous frequency (with overall waveform polarity reversed when the modulator is negative).
In other words, the crude equation would be
<EN129 output> = (sign of <modulator signal>) * cos((f_0 +  <modulator signal> ) * t),
where  ...  denotes the absolute value. Again, this is wrong in the same way that the first equation I wrote is wrong (we need an integral), but I hope it gets the idea across  let me know if it doesn't!
But I'm a physicist, not an engineer. Am I misunderstanding something?
EDIT: The equations as I've written them here are pretty unclear. The trig functions are unnecessary, and were just meant to convey the notion of "instantaneous frequency," which they don't successfully do. See my posts below for statements which are both simpler and more accurate.
Last edited by ari ellis on Thu Jul 09, 2020 7:51 pm, edited 2 times in total.
 analogPedagog
 Steady State Fate
 Posts: 966
 Joined: Wed Apr 14, 2010 10:56 pm
 Location: New York
 Contact:
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
The sign of the modulator is always positive. That’s what the rectifier is for. That is why the frequency goes back up at the zero crossing of the modulator, at the same point that the time reversal occurs.ari ellis wrote: ↑Thu Jul 09, 2020 12:00 pmVery cool to see you here Bernie!Bernie Hutchins wrote: ↑Wed Jul 08, 2020 9:18 pmari ellis wrote: ↑
Tue Jun 23, 2020 10:27 pm
“Yep, that's the EN I had in mind. That's not TZFM, and I'm not swayed just because they called it such. Right now, multiple options exist which implement actual, nocaveats TZFM. The two most common analog TZ oscs I've encountered in euro are the rubicon and the doepfer quadrature osc (can't remember it's # offhand). Both of these offer TZFM as per its unambiguous mathematical definition.”
Ari (or anyone else), please point out what you think is the “unambiguous mathematical definition” of TZFM. How would such a notion differ from that used in EN129?
Thanks  Bernie
The following equation is a crude description of what I mean by "true TZFM:"
<output signal> = cos((f_0 + <modulation signal>) * t),
where f_0 is the frequency of the oscillator with zero modulation index (maybe set by a panel knob, or incoming V/oct). <modulation signal> is measured *after* the index VCA if there is one.
The real definition involves an integral, which I don't feel like writing out in plain text, but see the first equation here: https://en.wikipedia.org/wiki/Frequency ... l_analysis. I believe that the oscillators I mentioned directly implement the first linked equation, maybe with other waveforms in place of the sine's. I believe that DX synths implement the approximation given by the second set of equations at the link.
Correct me if I'm wrong, but I'm fairly confident that the EN129 doesn't do this. My understanding is that the polarityreversal of the 129 happens when <modulation signal> is negative, *not* when (f_0 + <modulation signal>) is negative. This is different. Also, turning up the FM always increases the absolute value of the instantaneous frequency (with overall waveform polarity reversed when the modulator is negative).
In other words, the crude equation would be
<EN129 output> = (sign of <modulator signal>) * cos((f_0 +  <modulator signal> ) * t),
where  ...  denotes the absolute value. Again, this is wrong in the same way that the first equation I wrote is wrong (we need an integral), but I hope it gets the idea across  let me know if it doesn't!
But I'm a physicist, not an engineer. Am I misunderstanding something?

 Learning to Wiggle
 Posts: 23
 Joined: Sat Jun 27, 2020 3:19 pm
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Ari 
It is charming that an “unambiguous mathematical definition of TZFM” begins with: “the following equation is a crude description of what I mean by ‘true TZFM:’ ”. You then discard the integral (nearly everyone gets this wrong the first time, me included)!
You need the integral (or the corresponding derivative). The oscillator model is a revolving unit vector at angle A(t) so that the output is Sin(A(t)). If omega is constant, there is no FM and A(t) = omega*t, so the “instantaneous frequency” is dA(t)/dt=omega – just rotating at omega. If not constant, the vector rotates at the instantaneous frequency, which is exactly proportions to the slope of the integrator of the tricore VCO. This slope rate is an exponential function of the “keyboard” control voltage and a linear function of the magnitude of the FM control.
The key to understanding is that the DIRECTION (NOT the polarity) of the ramp (up or down) is a function of the SIGN of the linear control. The output, given a sign change of the linear control, looks like it is REVERSING IN TIME. For a simple example:
X(f,t) = Sin(2*pi*f*t)
X(f,t) = Sin[2*pi*(f)*t] = Sin[2*pi*f*(t)]
The flipflop (idea of Doug Kraul) in the EN129 is the upordown memory and reverses the ramp at the triangle limits, and midcycle if a FM polarity change occurs. Hence the diagnostic Ms and Ws midcycle shapes seen on a scope.
I hope you are convinced.
Bernie
It is charming that an “unambiguous mathematical definition of TZFM” begins with: “the following equation is a crude description of what I mean by ‘true TZFM:’ ”. You then discard the integral (nearly everyone gets this wrong the first time, me included)!
You need the integral (or the corresponding derivative). The oscillator model is a revolving unit vector at angle A(t) so that the output is Sin(A(t)). If omega is constant, there is no FM and A(t) = omega*t, so the “instantaneous frequency” is dA(t)/dt=omega – just rotating at omega. If not constant, the vector rotates at the instantaneous frequency, which is exactly proportions to the slope of the integrator of the tricore VCO. This slope rate is an exponential function of the “keyboard” control voltage and a linear function of the magnitude of the FM control.
The key to understanding is that the DIRECTION (NOT the polarity) of the ramp (up or down) is a function of the SIGN of the linear control. The output, given a sign change of the linear control, looks like it is REVERSING IN TIME. For a simple example:
X(f,t) = Sin(2*pi*f*t)
X(f,t) = Sin[2*pi*(f)*t] = Sin[2*pi*f*(t)]
The flipflop (idea of Doug Kraul) in the EN129 is the upordown memory and reverses the ramp at the triangle limits, and midcycle if a FM polarity change occurs. Hence the diagnostic Ms and Ws midcycle shapes seen on a scope.
I hope you are convinced.
Bernie
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
I explicitly accounted for the rectifier in my second equation (the one describing 129style modulation). I was talking about the modulation signal on its way in (but after whatever attenuation might happen outside).analogPedagog wrote: ↑Thu Jul 09, 2020 3:28 pm...
The sign of the modulator is always positive. That’s what the rectifier is for. That is why the frequency goes back up at the zero crossing of the modulator, at the same point that the time reversal occurs.
It might be clearer if I restate things in terms of instantaneous frequencies, which will also help address Bernie's points. Let's denote the instantaneous output frequency of the carrier osc by c. When there is no modulation applied, we have some base frequency f.
When there is modulation present, say a signal m(t), FM means that we want the instantaneous carrier frequency to become c(t) = f + A * m(t), for some modulation depth parameter A. I think this is uncontroversial so far.
Let's assume that m(t) oscillates between 1 and +1 for convenience.
When A = 0, the carrier just oscillates at f, i.e. c(t) = f + 0 = f.
When the modulation depth is small  in our notation, when A < f  notice that negative frequencies are never produced: c(t) = f +/ (something smaller than f) > 0.
When the modulation is large enough, i.e. A > f, we start to have some time windows where c(t) < 0, i.e. the modulation pushes the instantaneous frequency *through zero.* Two critical points:
1) The "time reversals" happens when A * m(t) =  f_0, not when m(t) itself passes through zero.
2) The transition from "ordinary" FM to "throughzero" FM happens at a particular nonzero value of the modulation depth, A = f in the units we've been working with. For modulation depths below this, there is no time reversal at all.
The EN129/ZPO/etc. design misses both of these criteria. It corresponds to an instantaneous frequency c(t) = sign(m(t)) * (f + A * m(t)). (Notice that I've included both the rectification of the modulator, and the timereversal). This is a different animal from the "correct" version.
I'm not claiming it isn't musically useful. But it isn't the same thing.
Still not convinced! Discarding the integral is definitely not legitimate, I agree, and I think I was clear about that (hence why I linked to the legitimate equation on wikipedia). Really, the rough equations I wrote were only intended to get the intuition of instantaneous frequency across, and I shouldn't have involved the trig functions at all. My error. But thinking in terms of instantaneous frequency, i.e. the derivative, not only does my point stand, but it is both clearer and more rigorous.
c(t) in my response to analogPedagog corresponds to the rotation rate you're talking about.
You claim that "the DIRECTION ... of the ramp (up or down) is a function of the SIGN of the linear control." This is incomplete  it is a function of the sign *AND AMPLITUDE* of the linear control. My points 1) and 2) above are especially important. If the modulation depth is small enough, *there is no change of direction at all*. For small modulation depths, the speed of the rotating vector changes in time, but it always rotates in the same direction. It only starts spinning backwards when the modulation depth is turned up sufficiently to overcome the initial rotation rate f. This makes a *huge* difference in what happens when the FM depth is dynamically adjusted, particularly when the depth (A) varies both above and below the "throughzero threshold." I'm fairly confident that this isn't how the 129 behaves. Am I mistaken?
Last edited by ari ellis on Thu Jul 09, 2020 5:00 pm, edited 1 time in total.
 analogPedagog
 Steady State Fate
 Posts: 966
 Joined: Wed Apr 14, 2010 10:56 pm
 Location: New York
 Contact:
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
ari ellis wrote: ↑Thu Jul 09, 2020 4:17 pmYou might want to reread my post; I explicitly account for the rectifier in my second equation (the one describing 129style modulation). I'm talking about the signal on its way to get rectified.analogPedagog wrote: ↑Thu Jul 09, 2020 3:28 pm...
The sign of the modulator is always positive. That’s what the rectifier is for. That is why the frequency goes back up at the zero crossing of the modulator, at the same point that the time reversal occurs.
It might be clearer if I restate things in terms of instantaneous frequencies, which will also help address Bernie's points. Let's denote the instantaneous output frequency of the carrier osc by c. When there is no modulation applied, we have some base frequency f.
When there is modulation present, say a signal m(t), FM means that we want the instantaneous carrier frequency to become c(t) = f + A * m(t), for some modulation depth parameter A. I think this is uncontroversial so far.
Let's assume that m(t) oscillates between 1 and +1 for convenience.
When A = 0, the carrier just oscillates at f, i.e. c(t) = f + 0 = f.
When the modulation depth is small  in our notation, when A < f  notice that negative frequencies are never produced: c(t) = f +/ (something smaller than f) > 0.
When the modulation is large enough, i.e. A > f, we start to have some time windows where c(t) < 0, i.e. the modulation pushes the instantaneous frequency *through zero.* Two critical points:
1) The "time reversals" happens when A * m(t) =  f_0, not when m(t) itself passes through zero.
2) The transition from "ordinary" FM to "throughzero" FM happens at a particular nonzero value of the modulation depth, A = f in the units we've been working with. For modulation depths below this, there is no time reversal at all.
The EN129/ZPO/etc. design misses both of these criteria. It corresponds to an instantaneous frequency c(t) = sign(m(t)) * (f + A * m(t)). (Notice that I've included both the rectification of the modulator, and the timereversal). This is a different animal from the "correct" version.
I'm not claiming it isn't musically useful. But it isn't the same thing.
Still not convinced! Discarding the integral is definitely not legitimate, I agree, and I think I was clear about that (hence why I linked to the legitimate equation on wikipedia). I shouldn't have involved the trig functions. But thinking in terms of instantaneous frequency, i.e. the derivative, my point stands (and is in fact both clearer and more rigorous).
c(t) in my response to analogPedagog corresponds to the rotation rate you're talking about.
You claim that "the DIRECTION ... of the ramp (up or down) is a function of the SIGN of the linear control." This is incomplete  it is a function of the sign *AND AMPLITUDE* of the linear control. My points 1) and 2) above are especially important. If the modulation depth is small enough, *there is no change of direction at all*. For small modulation depths, the speed of the rotating vector changes in time, but it always rotates in the same direction. It only starts spinning backwards when the modulation depth is turned up sufficiently to overcome the initial rotation rate f. This makes a *huge* difference in what happens when the FM depth is dynamically adjusted, particularly when the depth (A) varies both above and below the "throughzero threshold." I'm fairly confident that this isn't how the 129 behaves. Am I mistaken?
Ari,
Speaking just about the ZPO  no it isn't the same thing. Its a totally different design approach than the EN129. It does show time reversals but by quite different means. Totally happy to call it TZFMlike, as we already established. Apologies for misreading your post. The two equations were identical with the exception of ‘sign of the modulator.’
But as far as the EN129 goes, I really don’t see what the hangup is. Even without the math (I know you need that to be convinced), but both the rubi and the en129 and all the others exhibit the same functionality and there isn't any marked improvement either way. Am I wrong?
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
No worries! But also, note that the equations aren't quite identical other than the sign() function  notice the absolute value on the modulator in the latter case only.analogPedagog wrote: ↑Thu Jul 09, 2020 4:59 pm[...]
Ari,
Speaking just about the ZPO  no it isn't the same thing. Its a totally different design approach than the EN129. It does show time reversals but by quite different means. Totally happy to call it TZFMlike, as we already established. Apologies for misreading your post. The two equations were identical with the exception of ‘sign of the modulator.’
But as far as the EN129 goes, I really don’t see what the hangup is. Even without the math (I know you need that to be convinced), but both the rubi and the en129 and all the others exhibit the same functionality and there isn't any marked improvement either way. Am I wrong?
My hangups are about what happens for small depths, and what happens when the FM depth is dynamic. The onset of TZFM in the rubicon/etc. design is smooth, transitioning from "normal analog FM" at small depths to "TZFM" at large depths (because the two are identical at small depths, when c = f + A * m(t) is always positive). I think the 129 misses this (waiting for Bernie's reply), and if I understand the ZPO, it does as well  no matter what else is happening, a rectifier on the modulator will get things wrong  you'd need to rectify *after summing with the expo control,* to get  f + A * m(t) , not just f + A * m(t). The two are different when m(t) is negative.
(You'd also need to trigger the timereversals based on the summed control, not just based on the modulator.)
Like we've agreed, none of this makes the designs any more or less musically useful. They just sound very different to me, *especially* when modulated dynamically.
Last edited by ari ellis on Thu Jul 09, 2020 5:16 pm, edited 1 time in total.
 analogPedagog
 Steady State Fate
 Posts: 966
 Joined: Wed Apr 14, 2010 10:56 pm
 Location: New York
 Contact:
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
ari ellis wrote: ↑Thu Jul 09, 2020 5:06 pmNo worries! But also, note that the equations aren't quite identical other than the sign() function  notice the absolute value on the modulator in the latter case only.analogPedagog wrote: ↑Thu Jul 09, 2020 4:59 pm[...]
Ari,
Speaking just about the ZPO  no it isn't the same thing. Its a totally different design approach than the EN129. It does show time reversals but by quite different means. Totally happy to call it TZFMlike, as we already established. Apologies for misreading your post. The two equations were identical with the exception of ‘sign of the modulator.’
But as far as the EN129 goes, I really don’t see what the hangup is. Even without the math (I know you need that to be convinced), but both the rubi and the en129 and all the others exhibit the same functionality and there isn't any marked improvement either way. Am I wrong?
My hangups are about what happens for small depths, and what happens when the FM depth is dynamic. The onset of TZFM in the rubicon/etc. design is smooth, transitioning from "normal analog FM" at small depths to "TZFM" at large depths (because the two are identical at small depths, when c = f + A * m(t) is always positive). I think the 129 misses this (waiting for Bernie's reply), and if I understand the ZPO, it does as well  no matter what else is happening, a rectifier on the modulator will get things wrong  you'd need to rectify *after summing with the expo control,* to get  f + A * m(t) , not just f + A * m(t). The two are different when m(t) is negative.
(You'd also need to trigger the timereversals based on the summed control, not just based on the modulator.)
Like we've agreed, none of this makes the designs any more or less musically useful. They just sound very different to me, *especially* when modulated dynamically.
All I can say is you are correct about the ZPO. It uses a TZVCA to accomplish the phase reversals. And hence, when the modulation source is sitting at 0V, the output is 0V and not sitting on some DC value at the point where oscillation hangs.
While it can produce a lot of tzfm sounds  there are two things going on at once and the VCA behavior is much more dominant at low mod frequencies.
The dynamic aspect is all accomplished by the VCA (zero point) and not with the FM itself  like a normal TZVCO would.
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
There's another analogy that might help clear this up to someone. It's basically the same as the spinning wheel analogy.
Imagine you're driving a car with a throttle control that can go forward and backward. In the middle, the engine idles. Imagine you're cruising along at constant forward speed, with the throttle somewhere in the forward half of its travel. Imagine now that you start wiggling the throttle forward and backward around the forward point you started from. If the wiggles are small, the car will always be driving forward, just speeding up and slowing down relative to its initial cruising speed. When you start wiggling enough to go past the middle (where the car stops), the car will start spending some time moving backwards. If we wanted to be fancy, we could call this "throughzero velocity modulation."
With EN129/ZPO/etc.style modulation, the car would never slow down beyond its starting speed. As we push forward from the starting speed, it would speed up, and as we pull back to the starting speed, it would return to that speed. But next, instead of smoothly reducing the velocity (towards zero and possibly beyond), we would suddenly jolt the throttle back into reverse, and move at the same speed we started from but backwards, then repeating the above cycle but in reverse. We would never spend any time moving more slowly than we were before we started wiggling the throttle.
A major limit of the analogy is that the car has inertia, so the two approaches would in fact produce somewhat similar results for a real car. In the electronic side of this analogy, the "inertia" is negligible. Without inertia, the car would repeatedly jolt from moving forward to backwards in a way that looks very different from the first scenario. (For those concerned, the velocity of the car corresponds to the instantaneous frequency, and its position corresponds to the instantaneous phase).
Imagine you're driving a car with a throttle control that can go forward and backward. In the middle, the engine idles. Imagine you're cruising along at constant forward speed, with the throttle somewhere in the forward half of its travel. Imagine now that you start wiggling the throttle forward and backward around the forward point you started from. If the wiggles are small, the car will always be driving forward, just speeding up and slowing down relative to its initial cruising speed. When you start wiggling enough to go past the middle (where the car stops), the car will start spending some time moving backwards. If we wanted to be fancy, we could call this "throughzero velocity modulation."
With EN129/ZPO/etc.style modulation, the car would never slow down beyond its starting speed. As we push forward from the starting speed, it would speed up, and as we pull back to the starting speed, it would return to that speed. But next, instead of smoothly reducing the velocity (towards zero and possibly beyond), we would suddenly jolt the throttle back into reverse, and move at the same speed we started from but backwards, then repeating the above cycle but in reverse. We would never spend any time moving more slowly than we were before we started wiggling the throttle.
A major limit of the analogy is that the car has inertia, so the two approaches would in fact produce somewhat similar results for a real car. In the electronic side of this analogy, the "inertia" is negligible. Without inertia, the car would repeatedly jolt from moving forward to backwards in a way that looks very different from the first scenario. (For those concerned, the velocity of the car corresponds to the instantaneous frequency, and its position corresponds to the instantaneous phase).
 analogPedagog
 Steady State Fate
 Posts: 966
 Joined: Wed Apr 14, 2010 10:56 pm
 Location: New York
 Contact:
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
But really, the car should just do the opposite of what it is doing moving forward, when it is going fully backwards in time.ari ellis wrote: ↑Thu Jul 09, 2020 5:56 pmThere's another analogy that might help clear this up to someone. It's basically the same as the spinning wheel analogy.
Imagine you're driving a car with a throttle control that can go forward and backward. In the middle, the engine idles. Imagine you're cruising along at constant forward speed, with the throttle somewhere in the forward half of its travel. Imagine now that you start wiggling the throttle forward and backward around the forward point you started from. If the wiggles are small, the car will always be driving forward, just speeding up and slowing down relative to its initial cruising speed. When you start wiggling enough to go past the middle (where the car stops), the car will start spending some time moving backwards. If we wanted to be fancy, we could call this "throughzero velocity modulation."
With EN129/ZPO/etc.style modulation, the car would never slow down beyond its starting speed. As we push forward from the starting speed, it would speed up, and as we pull back to the starting speed, it would return to that speed. But next, instead of smoothly reducing the velocity (towards zero and possibly beyond), we would suddenly jolt the throttle back into reverse, and move at the same speed we started from but backwards, then repeating the above cycle but in reverse. We would never spend any time moving more slowly than we were before we started wiggling the throttle.
A major limit of the analogy is that the car has inertia, so the two approaches would in fact produce somewhat similar results for a real car. In the electronic side of this analogy, the "inertia" is negligible. Without inertia, the car would repeatedly jolt from moving forward to backwards in a way that looks very different from the first scenario. (For those concerned, the velocity of the car corresponds to the instantaneous frequency, and its position corresponds to the instantaneous phase).
I think the confusion is what happens when a TZVCO is about to go in either direction. Technically, the oscillation does slow down and stops during the transition to going backwards (or forwards) in time. Which is equivalent to the freq slowing down to 0Hz.

 Learning to Wiggle
 Posts: 23
 Joined: Sat Jun 27, 2020 3:19 pm
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
What happens when the linear FM control (sum of all contributions) goes through zero is seen in http://electronotes.netfirms.com/EN206.pdf, Fig 4a (typical), Fig 4c, 4d, and 4e (special cases) but not Fig 4b (no timereversals). As we go THROUGH zero, proper TZ is smooth and SONICALLY UNREMARKABLE; just additional depth (audible sidebands) .
Does anyone disagree?
This is the case with EN129 as in http://electronotes.netfirms.com/EN129.pdf and above.
Does anyone disagree?
I know very little of the Rubicon and nothing at all about ZPO.
Bernie
Does anyone disagree?
This is the case with EN129 as in http://electronotes.netfirms.com/EN129.pdf and above.
Does anyone disagree?
I know very little of the Rubicon and nothing at all about ZPO.
Bernie
 Dr. SketchnEtch
 Super Deluxe Wiggler
 Posts: 7846
 Joined: Thu Jan 21, 2010 1:46 pm
 Location: Vancouver, BC, Canada
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Sorry about the sarcasm, Bernie, but I must confess that this whole discussion was starting to piss me off a little bit.
Also, I found that whole discussion about "what is TZFM" to be very confusing. My understanding of TZFM is much simpler than any of that. Let me explain (although the entire explanation is really encapsulated within the block diagram I posted above).
Start with a normal tricore VCO oscillating at some frequency. In my case, this is a trisquare VCO, so a square wave comes from a comparator and zener limiter back to an integrator. When the square wave is high, the integrator ramps down (integrators are inverting), and when the square wave is low, the integrator ramps up. When the triangle hits +5 or 5, the comparator flips states and so does the square wave.
Now, if this square wave is put through a linear VCA, and that VCA's gain is, say, 50%, then the square wave will be half as large as it was. If it was originally a 10Vpp square wave (with levels of +5 and 5V) it will now be a 5Vpp square wave (with levels of 2.5 and 2.5V). Because the voltage of the square wave is half what it was, the ramp of the triangle will be half as steep as it was, and the frequency of the oscillator will decrease by one octave. Hence, a linear change in the gain of the VCA has generated a linear change in the amplitude of the square wave, which creates a linear decrease in the slope of the triangle wave, and a linear change in the frequency.
If the gain of this VCA is put under voltage control, now we have Linear FM. However, the gain of this VCA can only go to zero. It cannot go into negative territory. At a gain of zero, the VCA shuts off, there is no square wave at all, and the VCO stops oscillating. This is the limit of normal Linear FM. If the VCA is modulated to zero gain, there will be dead spots where the VCO is silent. (What I'm describing here is the Dixie.)
However, let's create the inverse of the square wave so that, now, there are two square waves 180 degrees out of phase. Let's put this second, inverted, square wave through a second VCA. Also, let's rig up this second VCA so that it turns on when the control signal is negative. Hence, say, the first VCA goes from off to unity gain with a control signal of 0 to 5V, and the second VCA goes from off to unity gain with a control signal of 0 to 5V. How is this possible? Easy: The two VCAs are actually identical, but one is driven by the Linear FM signal directly, and the other is driven by the inverse of the Linear FM signal.
So, picture the Linear FM signal as a sine wave. When it goes positive, one VCA goes on, and sends the positive square wave to the integrator. When the sine wave hits its apex (say, +5V), then this VCA is at unity gain and the VCO oscillates at its base frequency. As the sine wave falls, the first VCA starts to shut off. As the sine wave goes through zero, the first VCA shuts off completely and the second VCA comes on, sending the inverted square wave to the integrator. The VCO is now oscillating at "negative frequencies" which is stupid, because there is no such thing as negative frequency. The waveforms are simply inverted.
The twoVCA system I have described is a "balanced modulator" and this is the key to getting TZFM in a trisquare VCO. The nice thing about this arrangement is that it relates the TZFM depth to the gain of the VCAs and thus gives a level of control to the whole situation which is very easy to understand and manipulate, and, in the case of my designs (for Intellijel or otherwise), all linear VCA gains are set to a 5V unitygain standard, and all VCO waveforms are 10Vpp, so any raw waveform will just exactly turn on any linear VCA to unity gain at its peak.
Now, there's something I haven't mentioned yet. If the negative square wave is sent to the integrator, the triangle will start rising or falling in the opposite direction. However, the comparator is still being driven by the noninverted square wave summed to the triangle. Hence, the triangle may be rising towards +5V, but the comparator will only flip at 5V. This means that, when the integrator is being driven by the negative square wave, then the triangle being summed into the comparator's input must also be inverted for the comparator to catch the threshold and flip the triangle. If this is not done, then the triangle will blow past 5V and go all the way to the rail (12V or 15V or whatever) and hang there. The VCO will stop. So there needs to be something which senses that the VCO is in negative territory and inverts the triangle going to the comparator. In the Rubicon, this sensor is a second comparator comparing the final Linear FM signal driving the VCAs to 0V. When this signal goes negative, then the VCO is in negative territory, and the second comparator activates a JFET switch to change an opamp from a follower to an inverter. This really has nothing to do with TZFM, but is just a thing that has to be done to allow the oscillator to oscillate in negative territory.
The other thing I like about it is that it recognizes that TZFM is really nothing more than balanced AM applied to the gain of the integrator current in a tricore VCO.
Also, I found that whole discussion about "what is TZFM" to be very confusing. My understanding of TZFM is much simpler than any of that. Let me explain (although the entire explanation is really encapsulated within the block diagram I posted above).
Start with a normal tricore VCO oscillating at some frequency. In my case, this is a trisquare VCO, so a square wave comes from a comparator and zener limiter back to an integrator. When the square wave is high, the integrator ramps down (integrators are inverting), and when the square wave is low, the integrator ramps up. When the triangle hits +5 or 5, the comparator flips states and so does the square wave.
Now, if this square wave is put through a linear VCA, and that VCA's gain is, say, 50%, then the square wave will be half as large as it was. If it was originally a 10Vpp square wave (with levels of +5 and 5V) it will now be a 5Vpp square wave (with levels of 2.5 and 2.5V). Because the voltage of the square wave is half what it was, the ramp of the triangle will be half as steep as it was, and the frequency of the oscillator will decrease by one octave. Hence, a linear change in the gain of the VCA has generated a linear change in the amplitude of the square wave, which creates a linear decrease in the slope of the triangle wave, and a linear change in the frequency.
If the gain of this VCA is put under voltage control, now we have Linear FM. However, the gain of this VCA can only go to zero. It cannot go into negative territory. At a gain of zero, the VCA shuts off, there is no square wave at all, and the VCO stops oscillating. This is the limit of normal Linear FM. If the VCA is modulated to zero gain, there will be dead spots where the VCO is silent. (What I'm describing here is the Dixie.)
However, let's create the inverse of the square wave so that, now, there are two square waves 180 degrees out of phase. Let's put this second, inverted, square wave through a second VCA. Also, let's rig up this second VCA so that it turns on when the control signal is negative. Hence, say, the first VCA goes from off to unity gain with a control signal of 0 to 5V, and the second VCA goes from off to unity gain with a control signal of 0 to 5V. How is this possible? Easy: The two VCAs are actually identical, but one is driven by the Linear FM signal directly, and the other is driven by the inverse of the Linear FM signal.
So, picture the Linear FM signal as a sine wave. When it goes positive, one VCA goes on, and sends the positive square wave to the integrator. When the sine wave hits its apex (say, +5V), then this VCA is at unity gain and the VCO oscillates at its base frequency. As the sine wave falls, the first VCA starts to shut off. As the sine wave goes through zero, the first VCA shuts off completely and the second VCA comes on, sending the inverted square wave to the integrator. The VCO is now oscillating at "negative frequencies" which is stupid, because there is no such thing as negative frequency. The waveforms are simply inverted.
The twoVCA system I have described is a "balanced modulator" and this is the key to getting TZFM in a trisquare VCO. The nice thing about this arrangement is that it relates the TZFM depth to the gain of the VCAs and thus gives a level of control to the whole situation which is very easy to understand and manipulate, and, in the case of my designs (for Intellijel or otherwise), all linear VCA gains are set to a 5V unitygain standard, and all VCO waveforms are 10Vpp, so any raw waveform will just exactly turn on any linear VCA to unity gain at its peak.
Now, there's something I haven't mentioned yet. If the negative square wave is sent to the integrator, the triangle will start rising or falling in the opposite direction. However, the comparator is still being driven by the noninverted square wave summed to the triangle. Hence, the triangle may be rising towards +5V, but the comparator will only flip at 5V. This means that, when the integrator is being driven by the negative square wave, then the triangle being summed into the comparator's input must also be inverted for the comparator to catch the threshold and flip the triangle. If this is not done, then the triangle will blow past 5V and go all the way to the rail (12V or 15V or whatever) and hang there. The VCO will stop. So there needs to be something which senses that the VCO is in negative territory and inverts the triangle going to the comparator. In the Rubicon, this sensor is a second comparator comparing the final Linear FM signal driving the VCAs to 0V. When this signal goes negative, then the VCO is in negative territory, and the second comparator activates a JFET switch to change an opamp from a follower to an inverter. This really has nothing to do with TZFM, but is just a thing that has to be done to allow the oscillator to oscillate in negative territory.
The other thing I like about it is that it recognizes that TZFM is really nothing more than balanced AM applied to the gain of the integrator current in a tricore VCO.
this night wounds time,
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
My response refers to the block diagram in Fig. 1 on page 3 of EN129. On a quick glance I couldn't find any description of what V_c is; I assumed that it is the exponential control input (including, for example, any V/oct that might be present). Please let me know if my assumption is wrong, as it may affect the following argument.Bernie Hutchins wrote: ↑Thu Jul 09, 2020 10:44 pmWhat happens when the linear FM control (sum of all contributions) goes through zero is seen in http://electronotes.netfirms.com/EN206.pdf, Fig 4a (typical), Fig 4c, 4d, and 4e (special cases) but not Fig 4b (no timereversals). As we go THROUGH zero, proper TZ is smooth and SONICALLY UNREMARKABLE; just additional depth (audible sidebands) .
Does anyone disagree?
This is the case with EN129 as in http://electronotes.netfirms.com/EN129.pdf and above.
Does anyone disagree?
I know very little of the Rubicon and nothing at all about ZPO.
Bernie
From the block diagram, it seems clear that my previous objections hold. As you say, the time reversals in the 129 happen when the linear part of the control current changes sign: this is manifestly not what is supposed to happen. The reversals should happen when the sum of the linear AND EXPONENTIAL control currents changes sign, *not just the linear contributions.* In other words, the reversals should happen when the negative excursion of the linear control *overwhelms* the (positive) expo control. Were this to be done, the fullwave rectification would correspondingly need to be applied to the SUM OF LINEAR AND EXPO controls. In the 129 design, the total instantaneous frequency never approaches zero. It seems clear from the block diagram that the absolute value of the instantaneous frequency is never lower than the frequency that the expo control alone is asking for. This differs from "real TZFM."
Take home point: the correct reversals cannot be deduced from the modulator alone, which the 129 tries to do  the timing reversals associated with TZFM depend on the relationship between the modulator and the exponential control current. The 129 design ignores this relationship.
In other words: when you're trying to determine when and how the reversals should happen, separating the "FM" part of the control signal (i.e. charging current) from the rest of the charging current (e.g. V/oct, exp FM, etc.) is *not valid.*
Again, the math is trivial. Ignoring the modulation gain for simplicity (i.e. including A in the definition of m), TZFM means c = f + m, in the notation I previously introduced. The 129 implements c = sign(m) * (f + m). When m < 0, these equations *never* agree (unless f = 0, and we generally care about nonzero f).
EDIT: Dr. SketchnEtch said it in much clearer engineering terms than all of the math I'm invoking:
Dr. SketchnEtch wrote: ↑Fri Jul 10, 2020 2:20 am[...]TZFM is really nothing more than balanced AM applied to the gain of the integrator current in a tricore VCO.
Last edited by ari ellis on Fri Jul 10, 2020 11:58 am, edited 2 times in total.