So does that mean symmetry is basically just an offset added to the linear FM signal before it goes into the balanced modulator?Dr. SketchnEtch wrote: ↑Fri Jul 10, 2020 2:20 amSorry 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.
Intellijel Rubicon 2 vs SSF Zero Point Oscillator
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Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator

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Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
DS&E – outstanding description  thanks
Seems EN129 and Rubicon are somewhat similar. Note that the EN129 avoids overramping of the integrator by the R and S asynchronous pins of the flipflop and does not rely on the clock except for direction reversals.
I trust you agree EN129 works; you previously said:
“ One thing I do know is that it gives flawless throughzero FM. “
That yields the essential point: that a given circuit WORKS SEAMLESSLY AS A CONTINUATION of “to zero” linear FM).
Why not leave it there?
Bernie
Seems EN129 and Rubicon are somewhat similar. Note that the EN129 avoids overramping of the integrator by the R and S asynchronous pins of the flipflop and does not rely on the clock except for direction reversals.
I trust you agree EN129 works; you previously said:
“ One thing I do know is that it gives flawless throughzero FM. “
That yields the essential point: that a given circuit WORKS SEAMLESSLY AS A CONTINUATION of “to zero” linear FM).
Why not leave it there?
Bernie

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Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Ari
Would I be wrong if I guessed you never designed/tested a TZVCO based on your interpretation of the math? If you did do it, what happened?
If no hardware, it would seem fairly easy (trivial) to simulate the equation, if not an actual scheme block by block. Would it be “seamless” through zero?
Just a final thought of how to settle the issue.
Bernie
Would I be wrong if I guessed you never designed/tested a TZVCO based on your interpretation of the math? If you did do it, what happened?
If no hardware, it would seem fairly easy (trivial) to simulate the equation, if not an actual scheme block by block. Would it be “seamless” through zero?
Just a final thought of how to settle the issue.
Bernie
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Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Yes. On the Rubicon 2 panel: The raw TZFM input signal goes through a linearized 2164 whose gain is determined by the Index setting and input. The amplified (or attenuated) TZFM signal is then fed to a pair of inverters to generate the VC and VC+ signals which control the multiplier 2164 VCAs. The Symmetry voltage is summed with this amplified signal going into the first inverter.SavageMessiah wrote: ↑Fri Jul 10, 2020 11:51 amSo does that mean symmetry is basically just an offset added to the linear FM signal before it goes into the balanced modulator?
Hence, say the TZFM (Linear FM) signal is a 10Vpp sine wave. Also, say that there is no Index CV, and the Index pot is set halfway. This will send 2.5V to the linearized VCA Index circuit, which will set the TZFM amplifier to a gain of 50%. Hence, the signal coming out of this amplifier is a 5Vpp sine wave.
Now, also assuming no Symmetry CV, if the Symmetry knob is set at exactly halfway, then there is no bias, and the TZFM will be balanced around 0 Hz, with the peak frequencies approximately one octave lower than the base frequency of the VCO. (The base frequency is when there is no TZFM signal, and the Symmetry pot is set to fully CW (or fully CCW).)
If, now, the Symmetry pot is rotated to 3/4, such that the Symmetry voltage is 2.5V, then the attenuated TZFM signal will be biased by 2.5V. Hence, it will now be a 5Vpp sine wave which goes between 0V and 5V. This will give conventional Linear FM and the range of frequencies will be from the base frequency (at the top of the sine wave) to 0 Hz (at the bottom of the sine wave. If the Symmetry pot were turned fully CW, then the sine would go from 2.5V to 7.5V, and the frequency range would be from one octave higher than the base frequency to one octave lower than the base frequency. Get it?
Now, if the Symmetry knob is slowly turned towards the centre, but the Index knob is not changed, then the 5Vpp sine wave will slowly move downwards, and its lower lobe will start to dip into negative voltage territory. This will create throughzero modulation of the VCO. So, by changing the Symmetry setting, the degree of "throughzeroness" of the FM is changed. Once, the modulation starts to pass through zero and back again, the timbre of the VCO really starts to get interesting. That is why the Symmetry control is actually one of the most important on the panel. If the LOCK switch is just left on all the time (which fixes the Symmetry at very nearly 0V, or balanced, while sending a compensating voltage to the CV summer to bring the frequency back to the base frequency), then one gets very deep TZFM (with good tracking), but one really loses a significant degree of timbral control.
Tell me, someone: Alternate view! Alternate view, surely? Surely!?!
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
I personally haven't built one, no, but my "interpretation" of the math (not convinced there's anything here to "interpret") is identical to how the rubicon behaves. I don't need to build (or simulate) anything to know that much. I'm really not sure what your point is here. What I am talking about is achievable, and DS&E has explained precisely how he does it.Bernie Hutchins wrote: ↑Fri Jul 10, 2020 3:38 pmAri
Would I be wrong if I guessed you never designed/tested a TZVCO based on your interpretation of the math? If you did do it, what happened?
If no hardware, it would seem fairly easy (trivial) to simulate the equation, if not an actual scheme block by block. Would it be “seamless” through zero?
Just a final thought of how to settle the issue.
Bernie
To me, the definition of the term "seamless throughzero" is exactly the math I've been talking about. It's what the rubicon (or any other TZ osc with a symmetry/bias/etc. control) implements *directly.* Again, I don't need to simulate anything to know whether an equation matches with its own definition. If we really need a simulation to settle things, I can write one, but I'd like to know first what you mean by "seamless throughzero," so we can agree what we are looking for.
I don't want to be unnecessarily confrontational (we're just talking synths after all!), but so far, you've consistently dodged my questions. I have raised two clear objections to how the EN129 is designed with respect to TZFM, and asked clear questions about interpreting its block diagram (is V_c what I assumed it is?). I haven't received direct responses to my objections, or to my question. If I am wrong on any of these counts, I would appreciate a clear explanation of where I am mistaken (and, if you're willing, how so).

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Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Thanks for the thorough explanation, this is really useful. And then, if I'm understanding the block diagram you posted earlier, the square wave that the tzfm stuff is scaling then goes through an exponential VCA which would be opened by (tune controls + 1/vo + exp fm). This would determine the base frequency when there's no linear fm, only the symmetry offset. I've heard a bunch of explanations of tzfm before but they were all a bit handwavy. The technical detail here is really helpful.Dr. SketchnEtch wrote: ↑Fri Jul 10, 2020 4:03 pmYes. On the Rubicon 2 panel: The raw TZFM input signal goes through a linearized 2164 whose gain is determined by the Index setting and input. The amplified (or attenuated) TZFM signal is then fed to a pair of inverters to generate the VC and VC+ signals which control the multiplier 2164 VCAs. The Symmetry voltage is summed with this amplified signal going into the first inverter.SavageMessiah wrote: ↑Fri Jul 10, 2020 11:51 amSo does that mean symmetry is basically just an offset added to the linear FM signal before it goes into the balanced modulator?
Hence, say the TZFM (Linear FM) signal is a 10Vpp sine wave. Also, say that there is no Index CV, and the Index pot is set halfway. This will send 2.5V to the linearized VCA Index circuit, which will set the TZFM amplifier to a gain of 50%. Hence, the signal coming out of this amplifier is a 5Vpp sine wave.
Now, also assuming no Symmetry CV, if the Symmetry knob is set at exactly halfway, then there is no bias, and the TZFM will be balanced around 0 Hz, with the peak frequencies approximately one octave lower than the base frequency of the VCO. (The base frequency is when there is no TZFM signal, and the Symmetry pot is set to fully CW (or fully CCW).)
If, now, the Symmetry pot is rotated to 3/4, such that the Symmetry voltage is 2.5V, then the attenuated TZFM signal will be biased by 2.5V. Hence, it will now be a 5Vpp sine wave which goes between 0V and 5V. This will give conventional Linear FM and the range of frequencies will be from the base frequency (at the top of the sine wave) to 0 Hz (at the bottom of the sine wave. If the Symmetry pot were turned fully CW, then the sine would go from 2.5V to 7.5V, and the frequency range would be from one octave higher than the base frequency to one octave lower than the base frequency. Get it?
Now, if the Symmetry knob is slowly turned towards the centre, but the Index knob is not changed, then the 5Vpp sine wave will slowly move downwards, and its lower lobe will start to dip into negative voltage territory. This will create throughzero modulation of the VCO. So, by changing the Symmetry setting, the degree of "throughzeroness" of the FM is changed. Once, the modulation starts to pass through zero and back again, the timbre of the VCO really starts to get interesting. That is why the Symmetry control is actually one of the most important on the panel. If the LOCK switch is just left on all the time (which fixes the Symmetry at very nearly 0V, or balanced, while sending a compensating voltage to the CV summer to bring the frequency back to the base frequency), then one gets very deep TZFM (with good tracking), but one really loses a significant degree of timbral control.
This means that you can simulate the symmetry control on e.g. a Generate 3 by turning off the bias switch and the ac coupling switch and adding an offset to the fm signal. Of course this lacks the extremely helpful Lock function. Neat.

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Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Ah, thanks so much for the super clear explanation! That helps a lot. I see, so this is why with lock engaged it tends to have a ton of side bands and when using symmetry instead you go from linear FM gradually towards adding more and more of that unique timbral modulation. You definitely have a point that you can't really do a demonstration comparing or evaluating this oscillator without exploring this aspect of it.Dr. SketchnEtch wrote: ↑Fri Jul 10, 2020 4:03 pmYes. On the Rubicon 2 panel: The raw TZFM input signal goes through a linearized 2164 whose gain is determined by the Index setting and input. The amplified (or attenuated) TZFM signal is then fed to a pair of inverters to generate the VC and VC+ signals which control the multiplier 2164 VCAs. The Symmetry voltage is summed with this amplified signal going into the first inverter.SavageMessiah wrote: ↑Fri Jul 10, 2020 11:51 amSo does that mean symmetry is basically just an offset added to the linear FM signal before it goes into the balanced modulator?
Hence, say the TZFM (Linear FM) signal is a 10Vpp sine wave. Also, say that there is no Index CV, and the Index pot is set halfway. This will send 2.5V to the linearized VCA Index circuit, which will set the TZFM amplifier to a gain of 50%. Hence, the signal coming out of this amplifier is a 5Vpp sine wave.
Now, also assuming no Symmetry CV, if the Symmetry knob is set at exactly halfway, then there is no bias, and the TZFM will be balanced around 0 Hz, with the peak frequencies approximately one octave lower than the base frequency of the VCO. (The base frequency is when there is no TZFM signal, and the Symmetry pot is set to fully CW (or fully CCW).)
If, now, the Symmetry pot is rotated to 3/4, such that the Symmetry voltage is 2.5V, then the attenuated TZFM signal will be biased by 2.5V. Hence, it will now be a 5Vpp sine wave which goes between 0V and 5V. This will give conventional Linear FM and the range of frequencies will be from the base frequency (at the top of the sine wave) to 0 Hz (at the bottom of the sine wave. If the Symmetry pot were turned fully CW, then the sine would go from 2.5V to 7.5V, and the frequency range would be from one octave higher than the base frequency to one octave lower than the base frequency. Get it?
Now, if the Symmetry knob is slowly turned towards the centre, but the Index knob is not changed, then the 5Vpp sine wave will slowly move downwards, and its lower lobe will start to dip into negative voltage territory. This will create throughzero modulation of the VCO. So, by changing the Symmetry setting, the degree of "throughzeroness" of the FM is changed. Once, the modulation starts to pass through zero and back again, the timbre of the VCO really starts to get interesting. That is why the Symmetry control is actually one of the most important on the panel. If the LOCK switch is just left on all the time (which fixes the Symmetry at very nearly 0V, or balanced, while sending a compensating voltage to the CV summer to bring the frequency back to the base frequency), then one gets very deep TZFM (with good tracking), but one really loses a significant degree of timbral control.
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Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
I'm learning so much in this thread
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Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Yes, and very much looking forward to Bernie’s answers to Ari’s questions.
Ari does bring up a valid point.
However, I still can’t get around this logical loophole:
If the symmetry feature permits ‘true’ TZFM. Then what do we call it when the symmetry is perfectly centered (locked)?
In that state it is functionally equivalent to what the EN129 is doing.
When the sum of the offset is sufficiently positive or negative it does not produce timereversals (obviously just normal linear FM).
The answer to true TZFM seems to be the ability to move (the actual transitional movement) from typical linear FM into TZFM.
And the loophole is that if you can’t call EN129 true TZFM, then you can’t really say that any TZVCO is true TZFM while in a static (no change in offset) and symmetrical state.
And that is what loops me back to the criterion that if timereversal is happening, then TZFM sidebands are being produced and it is actually doing TZFM  and I still don’t feel 100% right saying that...
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
When the symmetry is *perfectly* centred and no modulation is incoming, the oscillator is stopped for any value of the other tuning controls. The EN129 is *almost* like this with a formallyinfinite control voltage added (to get it to start oscillating again), whatever this means. (Really, we should be thinking of a tiny offset away from zero symmetry, and a largebutfinite control voltage). The issue is the same thing I brought up about instantaneous frequency before; in true TZFM, this should always be a smooth function of time (assuming that the modulator is smooth). When the symmetry is very near zero, the function changes rapidly, but still smoothly. In the 129, it's discontinuous (from +f to f). I'm not sure whether or not the difference would be basically acceptable in certain synthesizer contexts. In other math/engineering contexts, sometimes this kind of discontinuity has a critical influence, and sometimes it makes no practical difference.analogPedagog wrote: ↑Sat Jul 11, 2020 9:30 amThen what do we call it when the symmetry is perfectly centered (locked)?
In that state it is functionally equivalent to what the EN129 is doing.
Intuitively, I think there could also be problems in the 129 with tuning drift as modulation is increased, since the magnitude of the frequency is only made larger by modulation (never smaller), but I'd need to work through this a bit more to be certain.
In more musical terms, ignoring that possible tuning issue, we might say the following. With the 129, you're basically stuck with "the most extreme" version of TZFM in some sense. As a function of modulation depth (i.e. FM index), there is no smooth transition from ordinary FM to TZFM (though Bernie seems to claim there is, and I hope we'll get some clarification). This is because the reversals happen no matter how small the modulation signal is.
I think that this gives good insight. I would personally say that you don't strictly need to be able to *move* that transition, the transition just needs to exist. But, being able to control it is certainly very useful (the rubicon symmetry knob really opens up a lot of timbral range).analogPedagog wrote: ↑Sat Jul 11, 2020 9:30 am...the answer to true TZFM seems to be the ability to move (the actual transitional movement) from typical linear FM into TZFM.
One way of saying it is that for a real TZVCO, if it really is in a *perfectly* symmetrical state, then it is silent unless modulation is applied, which differs from the EN129 design. I am curious how much of a difference there is between the spectrum one gets out of the EN129 approach and a minimallyasymmetric (i.e. a tiny bit away from perfect symmetry) TZVCO  at small modulation depths, the difference is probably significant, but at larger depths I'm not as sure without doing some math.analogPedagog wrote: ↑Sat Jul 11, 2020 9:30 am...then you can’t really say that any TZVCO is true TZFM while in a static (no change in offset) and symmetrical state.

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Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Ari
Frankly: It is very hard to understand what you write and/or ask. Sorry to say.
I believe that the main difficulty is your failure to understand the difference between frequency F and “instantaneous frequency” (IF). It is IF, exactly proportional to the current from the CA3080 into the integrator, that is being modulated. For example, see S. Goldman “Frequency Analysis, Modulation, and Noise”, Dover (1948) Sect. 5.2, “Angle Modulation  Frequency and Phase Modulation”. Or perhaps see my online http://electronotes.netfirms.com/AES3.PDF which is an AES paper from 1975 (on exponential VCO FM) which has an analogous setup.
You cannot just naively invoke what you SUPPOSE FM “means” and throw out the integral and expect to agree on interpretation. It may look similar, and be audibly acceptable, but is technically wrong and won’t agree with longheld convention.
 Bernie
Frankly: It is very hard to understand what you write and/or ask. Sorry to say.
I believe that the main difficulty is your failure to understand the difference between frequency F and “instantaneous frequency” (IF). It is IF, exactly proportional to the current from the CA3080 into the integrator, that is being modulated. For example, see S. Goldman “Frequency Analysis, Modulation, and Noise”, Dover (1948) Sect. 5.2, “Angle Modulation  Frequency and Phase Modulation”. Or perhaps see my online http://electronotes.netfirms.com/AES3.PDF which is an AES paper from 1975 (on exponential VCO FM) which has an analogous setup.
You cannot just naively invoke what you SUPPOSE FM “means” and throw out the integral and expect to agree on interpretation. It may look similar, and be audibly acceptable, but is technically wrong and won’t agree with longheld convention.
 Bernie
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
<Central question is in bold at end of post>
I have no problem with instantaneous frequency vs frequency (or else I'd lose my job). Nothing in my arguments actually involves throwing out the integral, I just wanted to get to the idea of instantaneous frequency without writing an integral in plain text. Invoking trig functions at all was a mistake, and I would edit all my previous posts to talk about the charging current directly, if the forum rules allowed. Every mention of the word "frequency" in my previous posts should rigorously be interpreted as "instantaneous frequency," i.e. the core charging current.
I'm not really sure what else to say, other than that I should clearly have kept previous questions briefer. So I'll try one more time.
Call the modulator signal m(t). Call the *instantaneous* frequency of the carrier osc f(t). Call the base carrier frequency f0 (i.e. the output freq of the carrier osc when no modulation is applied). FM means f(t) = f0 + m(t). There is no approximation involved here. This is the literal definition of FM. This isn't an opinion.
I claim that EN129 implements f(t) = sign(m(t)) * (f0 +  m(t) ). True or false?
EDIT: For future readers, the answer is false. Will update this post when we get to the bottom of it.
Bernie, it really feels like you're arguing in bad faith here. For instance, how on earth is my question about what V_c is in EN129 Fig. 1 hard to understand? You've avoided it twice in a row now. It's not a complicated question: is V_c the EXP control, or is it something else?Bernie Hutchins wrote: ↑Sat Jul 11, 2020 2:22 pmAri
Frankly: It is very hard to understand what you write and/or ask. Sorry to say.
I believe that the main difficulty is your failure to understand the difference between frequency F and “instantaneous frequency” (IF). It is IF, exactly proportional to the current from the CA3080 into the integrator, that is being modulated. For example, see S. Goldman “Frequency Analysis, Modulation, and Noise”, Dover (1948) Sect. 5.2, “Angle Modulation  Frequency and Phase Modulation”. Or perhaps see my online http://electronotes.netfirms.com/AES3.PDF which is an AES paper from 1975 (on exponential VCO FM) which has an analogous setup.
You cannot just naively invoke what you SUPPOSE FM “means” and throw out the integral and expect to agree on interpretation. It may look similar, and be audibly acceptable, but is technically wrong and won’t agree with longheld convention.
 Bernie
I have no problem with instantaneous frequency vs frequency (or else I'd lose my job). Nothing in my arguments actually involves throwing out the integral, I just wanted to get to the idea of instantaneous frequency without writing an integral in plain text. Invoking trig functions at all was a mistake, and I would edit all my previous posts to talk about the charging current directly, if the forum rules allowed. Every mention of the word "frequency" in my previous posts should rigorously be interpreted as "instantaneous frequency," i.e. the core charging current.
I'm not really sure what else to say, other than that I should clearly have kept previous questions briefer. So I'll try one more time.
Call the modulator signal m(t). Call the *instantaneous* frequency of the carrier osc f(t). Call the base carrier frequency f0 (i.e. the output freq of the carrier osc when no modulation is applied). FM means f(t) = f0 + m(t). There is no approximation involved here. This is the literal definition of FM. This isn't an opinion.
I claim that EN129 implements f(t) = sign(m(t)) * (f0 +  m(t) ). True or false?
EDIT: For future readers, the answer is false. Will update this post when we get to the bottom of it.
Last edited by ari ellis on Sun Jul 12, 2020 12:03 am, edited 3 times in total.

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Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Ari 
No you don't understand "Instantaneous Frequency" (IF). [ So I don't know what we both might mean by f  hence no T/F.] IF is (1/2*pi)dA(t)/dt where A(t) is the angle of the rotating unit vector. [ The VCO output (after waveshaping) is 5*Sin(A(t)). ] A((t) is an integral. It is not naively (“everyday notion”) just the instantaneous value of f(t) but a derivative; proportional to integrator current. This is a problem of dynamics, and you can't just throw out calculus. You are a physicist – right? Take some time to read.
BTW V_c is of course the exponential control voltage.
Bernie
No you don't understand "Instantaneous Frequency" (IF). [ So I don't know what we both might mean by f  hence no T/F.] IF is (1/2*pi)dA(t)/dt where A(t) is the angle of the rotating unit vector. [ The VCO output (after waveshaping) is 5*Sin(A(t)). ] A((t) is an integral. It is not naively (“everyday notion”) just the instantaneous value of f(t) but a derivative; proportional to integrator current. This is a problem of dynamics, and you can't just throw out calculus. You are a physicist – right? Take some time to read.
BTW V_c is of course the exponential control voltage.
Bernie
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
That's exactly what I mean by instantaneous frequency Bernie. In the equations of my previous post, what I have denoted as "f(t)" is exactly the derivative (of A(t)) that you wrote down. In other words, by f, I mean what you called IF. With that in mind, please answer the true or false question in my previous post, about the behaviour of the EN129.Bernie Hutchins wrote: ↑Sat Jul 11, 2020 5:10 pmAri 
No you don't understand "Instantaneous Frequency" (IF). [ So I don't know what we both might mean by f  hence no T/F.] IF is (1/2*pi)dA(t)/dt where A(t) is the angle of the rotating unit vector. [ The VCO output (after waveshaping) is 5*Sin(A(t)). ] A((t) is an integral. It is not naively (“everyday notion”) just the instantaneous value of f(t) but a derivative; proportional to integrator current. This is a problem of dynamics, and you can't just throw out calculus. You are a physicist – right? Take some time to read.
BTW V_c is of course the exponential control voltage.
Bernie
If you want to talk about calculus, apply the fundamental theorem of calculus to find the derivative of the integral we both agree represents the core integrator. Everything I’m saying follows from doing so.
This is getting ridiculous. Please consider that maybe, in fact, we are having a communication problem, and that I am not simply an idiot who doesn’t understand what he is saying.
(And thank you, that is what I assumed V_c to be, and so my objections stand. V_c then should control the parameter I called f0).

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Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Ari
Back, please, to a point of more obvious disagreement. You said:
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."
{emphasis added}
This is WRONG. The 129 does go to and through zero. The VCO frequency is an exponential function of a control voltage applied to the transistor base, multiplied by a factor (not summed) set by the linear control “reference current to the exponential converter”. This reference can go to zero and “halt” the oscillation, awaiting a restart in the original direction or a time reversal if the sign of linear control has changed. The circuit does exactly that.
So it is the exponential circuit that threw you off? http://electronotes.netfirms.com/s019.pdf Does this help?
Bernie
Back, please, to a point of more obvious disagreement. You said:
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."
{emphasis added}
This is WRONG. The 129 does go to and through zero. The VCO frequency is an exponential function of a control voltage applied to the transistor base, multiplied by a factor (not summed) set by the linear control “reference current to the exponential converter”. This reference can go to zero and “halt” the oscillation, awaiting a restart in the original direction or a time reversal if the sign of linear control has changed. The circuit does exactly that.
So it is the exponential circuit that threw you off? http://electronotes.netfirms.com/s019.pdf Does this help?
Bernie

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Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
@analogPedagog  discussion of the ZPO's implementation seems to have taken a backseat. I'm awaiting on one arriving Monday and keen to understand the technical background in the context of this discussion. I think I understand Bernie's last post about the EN129, halting at 0 and restarting in the direction of a time reversal, which would be TZ modulation. Is this what the ZPO does when you switch TZ on for lin or exp? But it's always mixed in with TZAM as well?
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Alright, now we're getting somewhere! I had Chowning FM in my mind when reading the block diagram and hence expected to find additive modulation, so I wrongly interpreted a sum instead of a multiplication where expo and linear control signals meet (figuring "ref" was some kind of additive reference value). My mistake! Does the EN129 then implement something like f = sign(m) * f0 * (1 + m)?. My first guess was f = f0 * m, but this seems unlikely, since it would suggest the oscillator stops when there's no mod input. Anything obvious I'm missing?Bernie Hutchins wrote: ↑Sat Jul 11, 2020 9:17 pmAri
Back, please, to a point of more obvious disagreement. You said:
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."
{emphasis added}
This is WRONG. The 129 does go to and through zero. The VCO frequency is an exponential function of a control voltage applied to the transistor base, multiplied by a factor (not summed) set by the linear control “reference current to the exponential converter”. This reference can go to zero and “halt” the oscillation, awaiting a restart in the original direction or a time reversal if the sign of linear control has changed. The circuit does exactly that.
So it is the exponential circuit that threw you off? http://electronotes.netfirms.com/s019.pdf Does this help?
Bernie
Do you have any comments on how EN129 compares to Chowningstyle FM (as described in e.g. that wikipedia article I linked), which I still maintain corresponds to f = f0 + m? (For clarity, what I have meant by "true TZFM" is Chowning FM, and I will keep to using that name from now on.) Are the sideband weights roughly like the Bessel functions?
In practical terms, I still believe there are two key features of Chowning FM which differ from EN129:
1) when the modulation depth is small enough, the oscillator should never go through zero, in Chowning FM. On the EN129, any negative modulation signal at all produces a reversal (correct?). This is what I was getting at when I said that I think EN129 probably corresponds to "the most extreme form of TZFM" in some sense  there is no transition from ordinary (reversalfree) analog FM to TZFM as a function of depth, it's always going through zero when the modulator swings negative at all. Like analogPedagog mentioned, it's a little like having a rubicon with the symmetry set very close to zero.
2) Chowning FM is pitchstable when the FM depth varies. Without churning the math, my intuition is that the same may not be true for EN129?
Do you have a different take on any of my bolded (but hopefully not overlybold) questions?
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Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
I gotta say that I'm getting exactly nothing from this extended discussion (argument?) between ari ellis and Bernie Hutchins.
However, I will say that the difficulty that ari ellis seems to be having understanding the basic functioning of the EN129 circuit is exactly the reason why I went a different way with Rubicon.
A musical VCO controls the current to an integrator with an exponential amplifier of some kind, whether this is a conventional exponential converter, or a 2164 VCA. This exponential control sets the pitch of the VCO. However, one has to ask what this amplifier is actually amplifying. The answer is that it is amplifying the current into the integrator. This current is also subject to linear amplification (by putting a linear amplifier in series with the exponential one, either before or after, it matters not). This linear amplifier is what gives Linear FM. This linear amplifier may also generate negative gains, which is what gives TZFM. That's really all there is to it. If the Linear FM signal to the Linear FM amplifier is biased such that it generates negative gains, then one has TZFM (presuming that the oscillator core has been enhanced with the logical circuitry required to accommodate inverse integrator currents).
Here's an experiment that anyone with a Rubicon can do: Feed a Linear FM signal which is a 10Vpp sine wave (which one would obtain from a Dixie). Attenuate it to about 40% by adjusting the Index pot to the 40% point (a bit left of centre). Then, listen to the result, starting with Symmetry at fully CW (100%)  this is Linear FM. Now, slowly turn the Symmetry pot down towards the centre (while also increasing the base frequency of the VCO by increasing the Coarse tuning pot, or the Fine tuning pot and octave switch). When the Symmetry pot is at about 40% right of centre, the FM should just start dipping negative. Do you hear anything different happening? Continue turning the Symmetry pot towards the centre. At 12:00, the Symmetry is at 0% (centred) and the FM is balanced throughzero. Continue turning it CCW slowly until about 40% left of centre. Now the FM is leaving TZ territory and going monopolar. Continue turning CCW to 100% and now we are back to conventional Linear FM, but with "negative frequencies."
I haven't done this, so I don't know how the results would sound. However, the thing to notice is whether there is a fundamentally different sound when the Symmetry pot is between about 2:00 and 10:00, where the FM would be TZ. Of course, the centre frequency of the VCO will decrease dramatically when the Symmetry pot is in this range, so the Coarse control (or octave switches and Fine control for Rubicon 2) will have to be cranked up to compensate and keep the centre frequency about constant, in order for this test to make sense.
I'm gonna make a video a little later today, after I get back from visiting my elder daughter and running some errands. I'm also gonna build a version of EN129 just so I can see how it works and what it does, and I'll make a video of that as well, hopefully within the next few days.
However, I will say that the difficulty that ari ellis seems to be having understanding the basic functioning of the EN129 circuit is exactly the reason why I went a different way with Rubicon.
A musical VCO controls the current to an integrator with an exponential amplifier of some kind, whether this is a conventional exponential converter, or a 2164 VCA. This exponential control sets the pitch of the VCO. However, one has to ask what this amplifier is actually amplifying. The answer is that it is amplifying the current into the integrator. This current is also subject to linear amplification (by putting a linear amplifier in series with the exponential one, either before or after, it matters not). This linear amplifier is what gives Linear FM. This linear amplifier may also generate negative gains, which is what gives TZFM. That's really all there is to it. If the Linear FM signal to the Linear FM amplifier is biased such that it generates negative gains, then one has TZFM (presuming that the oscillator core has been enhanced with the logical circuitry required to accommodate inverse integrator currents).
Here's an experiment that anyone with a Rubicon can do: Feed a Linear FM signal which is a 10Vpp sine wave (which one would obtain from a Dixie). Attenuate it to about 40% by adjusting the Index pot to the 40% point (a bit left of centre). Then, listen to the result, starting with Symmetry at fully CW (100%)  this is Linear FM. Now, slowly turn the Symmetry pot down towards the centre (while also increasing the base frequency of the VCO by increasing the Coarse tuning pot, or the Fine tuning pot and octave switch). When the Symmetry pot is at about 40% right of centre, the FM should just start dipping negative. Do you hear anything different happening? Continue turning the Symmetry pot towards the centre. At 12:00, the Symmetry is at 0% (centred) and the FM is balanced throughzero. Continue turning it CCW slowly until about 40% left of centre. Now the FM is leaving TZ territory and going monopolar. Continue turning CCW to 100% and now we are back to conventional Linear FM, but with "negative frequencies."
I haven't done this, so I don't know how the results would sound. However, the thing to notice is whether there is a fundamentally different sound when the Symmetry pot is between about 2:00 and 10:00, where the FM would be TZ. Of course, the centre frequency of the VCO will decrease dramatically when the Symmetry pot is in this range, so the Coarse control (or octave switches and Fine control for Rubicon 2) will have to be cranked up to compensate and keep the centre frequency about constant, in order for this test to make sense.
I'm gonna make a video a little later today, after I get back from visiting my elder daughter and running some errands. I'm also gonna build a version of EN129 just so I can see how it works and what it does, and I'll make a video of that as well, hopefully within the next few days.
Tell me, someone: Alternate view! Alternate view, surely? Surely!?!

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Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
1) Ari  you said: "On the EN129, any negative modulation signal at all produces a reversal (correct?)." Of course.
Negative values of the SUM: initial + enveloped.
2) The “pitch” of an FM sound is fairly weak in the general case of the generation of belllike (clangorous) sounds (like setting the carrier and the modulation frequencies more or less at random) (not trying). If the two frequencies are set to an integer ratio, the sidebands form a harmonic spectrum with a pitch that is generally the spacing of the sidebands (the modulating frequency). The “carrier” is the zeroth sideband. This is a bit tedious to achieve. If both the main carrier VCO (TZ or not) (and the separate modulating VCO) track, pitch tracks, as does the general timbral impression.
Note that Chowning said that a negative frequency was just an inversion [ Sin(omega*t)) = Sin(omega*t) ]! Problem is Cos(omega*t) = Cos(omega*t). For a general phase angle, fi this means Sin(omega*t – fi) =Sin(2*omega*to)Cos(omega*t) + Cos(2*omega*to)Sin(omega*t) where to is the time when the transition of polarity occurs. Here 2*omega*to = fi. This is the time reversal at the modulation polarity transition time. This is NOT obvious from the equations  you need a good plot
Bernie
Negative values of the SUM: initial + enveloped.
2) The “pitch” of an FM sound is fairly weak in the general case of the generation of belllike (clangorous) sounds (like setting the carrier and the modulation frequencies more or less at random) (not trying). If the two frequencies are set to an integer ratio, the sidebands form a harmonic spectrum with a pitch that is generally the spacing of the sidebands (the modulating frequency). The “carrier” is the zeroth sideband. This is a bit tedious to achieve. If both the main carrier VCO (TZ or not) (and the separate modulating VCO) track, pitch tracks, as does the general timbral impression.
Note that Chowning said that a negative frequency was just an inversion [ Sin(omega*t)) = Sin(omega*t) ]! Problem is Cos(omega*t) = Cos(omega*t). For a general phase angle, fi this means Sin(omega*t – fi) =Sin(2*omega*to)Cos(omega*t) + Cos(2*omega*to)Sin(omega*t) where to is the time when the transition of polarity occurs. Here 2*omega*to = fi. This is the time reversal at the modulation polarity transition time. This is NOT obvious from the equations  you need a good plot
Bernie
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
this is really not meant to disturb here any of the discussions going on:
since my picture i got out of this thread and debate is that there are several ways to acomplish a type of FM that i´d like to call from now on: "double sided FM": ( well, "double sided non stalling FM" is even better )
I got under the "opinion" that not all of these types of FM would really need the core of the VCO to go into a ZeroHertz (frequency) state and in that sense going "thru" it (thru zero).......to pick then up speed again.
it seems that some techniques nicely overcome the "stalling" aspect on the commonly found (fully unsymmetrical) "LinFM" by other means.
I phrase it out with: ".....need the core to go....." , since it has zooming again deeper in two aspects:
the "need" to go thru a zerohertzfrequenzy state, and on the other the "ability" to achive that "zerohertz state at all.
I think the first point that matters here is to avoid the "stalling effect" within the Frequenzy modulation.
Not saying the aspect of achieving a zerohertz state in real has no impact or no importancy.
How important the achievment of "going thru zero" is, in a music making context would in my opinion much depend on the frequenzy ratios that Carrier and modulator are set to.
in that sense, looking to all this, and this debate too, coming from the "music making" side of the things,
and having had alots of patch experience with TZFM VCOs plus digital 2OPFM VCOs would i say:
we do not deal here with problems
other than to stick to the same understanding of the wording and how to phrase out formulas so that a clear communication can happen.
but technically speaking, *in regards to the music making aspect* are here no problems !
just different approaches to deal with FM, respectivly how a carrier and a modulator can interact, one with the other.
further: from a music making point of view do we indeed deal with *one* problem, and thats here in my opinion the most important determing aspect if things sound good or not, assoon we have reached the state of "double sided (non sdtalling) FM":
its the Frequenzy Ratio aspect between carrier and modulator !
and so far, we have not seen any tools implemented in the VCOs to overcome this, real, "problem"
But all the different technical approaches to get to have a "non stalling double sided FM" do just create "different sounding" VCOs, thats it.
there is not one of these VCOs a problem cause it is notsetup like the formula has to be.
my take on that *very interesting" debate.
super interesting ! i got me into a total new understand of what we deal with, when we deal with FM
this is a interesting statement !Bernie Hutchins wrote: ↑Sat Jul 11, 2020 9:17 pmTHE TOTAL INSTANTANEOUS FREQUENCY NEVER APPROACHES ZERO.
since my picture i got out of this thread and debate is that there are several ways to acomplish a type of FM that i´d like to call from now on: "double sided FM": ( well, "double sided non stalling FM" is even better )
I got under the "opinion" that not all of these types of FM would really need the core of the VCO to go into a ZeroHertz (frequency) state and in that sense going "thru" it (thru zero).......to pick then up speed again.
it seems that some techniques nicely overcome the "stalling" aspect on the commonly found (fully unsymmetrical) "LinFM" by other means.
I phrase it out with: ".....need the core to go....." , since it has zooming again deeper in two aspects:
the "need" to go thru a zerohertzfrequenzy state, and on the other the "ability" to achive that "zerohertz state at all.
I think the first point that matters here is to avoid the "stalling effect" within the Frequenzy modulation.
Not saying the aspect of achieving a zerohertz state in real has no impact or no importancy.
How important the achievment of "going thru zero" is, in a music making context would in my opinion much depend on the frequenzy ratios that Carrier and modulator are set to.
in that sense, looking to all this, and this debate too, coming from the "music making" side of the things,
and having had alots of patch experience with TZFM VCOs plus digital 2OPFM VCOs would i say:
we do not deal here with problems
other than to stick to the same understanding of the wording and how to phrase out formulas so that a clear communication can happen.
but technically speaking, *in regards to the music making aspect* are here no problems !
just different approaches to deal with FM, respectivly how a carrier and a modulator can interact, one with the other.
further: from a music making point of view do we indeed deal with *one* problem, and thats here in my opinion the most important determing aspect if things sound good or not, assoon we have reached the state of "double sided (non sdtalling) FM":
its the Frequenzy Ratio aspect between carrier and modulator !
and so far, we have not seen any tools implemented in the VCOs to overcome this, real, "problem"
But all the different technical approaches to get to have a "non stalling double sided FM" do just create "different sounding" VCOs, thats it.
there is not one of these VCOs a problem cause it is notsetup like the formula has to be.
my take on that *very interesting" debate.
super interesting ! i got me into a total new understand of what we deal with, when we deal with FM
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Thank you for these answers Bernie!Bernie Hutchins wrote: ↑Sun Jul 12, 2020 2:34 pm1) Ari  you said: "On the EN129, any negative modulation signal at all produces a reversal (correct?)." Of course.
Negative values of the SUM: initial + enveloped.
2) The “pitch” of an FM sound is fairly weak in the general case of the generation of belllike (clangorous) sounds (like setting the carrier and the modulation frequencies more or less at random) (not trying). If the two frequencies are set to an integer ratio, the sidebands form a harmonic spectrum with a pitch that is generally the spacing of the sidebands (the modulating frequency). The “carrier” is the zeroth sideband. This is a bit tedious to achieve. If both the main carrier VCO (TZ or not) (and the separate modulating VCO) track, pitch tracks, as does the general timbral impression.
Note that Chowning said that a negative frequency was just an inversion [ Sin(omega*t)) = Sin(omega*t) ]! Problem is Cos(omega*t) = Cos(omega*t). For a general phase angle, fi this means Sin(omega*t – fi) =Sin(2*omega*to)Cos(omega*t) + Cos(2*omega*to)Sin(omega*t) where to is the time when the transition of polarity occurs. Here 2*omega*to = fi. This is the time reversal at the modulation polarity transition time. This is NOT obvious from the equations  you need a good plot
Bernie
I think Chowning could get away with it because a digital platform affords essentially perfect phase stability, letting him pick an arbitrary phase reference for the carrier (so he could choose fi = 0). But it's an important general distinction, I agree.
I'm not sure what you're referring to by initial and enveloped  are these a pair of inputs?
EDIT: I think I figured this out after reading EN129 one more time in detail. There is an offset voltage, I think what Bernie called "initial" here, and I think by "enveloped" he means the (probably oscillating) modulation signal after passing through a VCA. With this said, I withdraw all objections. This approach should give pretty similar output to the rubicon in principal (initial = symmetry). It's all about the offset, baby! The block diagram is blockier than I appreciated  needed to RT(entire)FM again.
I'm not sure I agree that FM sounds can't have a useable sense of pitch without perfect harmonic tuning, but understanding the 129 properly now, it shouldn't drift more than anything else.
Funky40: Please note that Bernie was quoting me when he wrote the statement about 129 never decreasing in frequency, and he then refuted the statement, explaining how I had misinterpreted an element of the block diagram.

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Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
Since we are talking quite a bit about my EN129 and everyone has (online) http://electronotes.netfirms.com/EN129.pdf the writeup, it makes sense to use the component markings and descriptions already there rather than try (with some difficulty) to just use words. Even though I have become aware that many here do not readily recognize oncefamiliar circuit elements, this would seem a better approach.
Accordingly, by “initial and enveloped” I mean the output of OA8 which is a sum of INITIAL LINEAR and MOD IN (as enveloped by OTA2 through OA12 back through R67. It is this OA8 that is the total modulation signal that is rectified (OA5 and OA6) and edge detected (OA9, OA10, 4070) to trigger reversals (pin 3 of 4013).
Ari asks “Would you agree that EN129 is doing….”? All questions of this nature require extensive study to see what you are defining and assuming. I always decline. I have written in detail exactly what the AN129 does.
“there must be some equation relating the core instantaneous frequency.” It is the voltage output of OA5 divided by 150k (R7), the “reference current” reratioed http://electronotes.netfirms.com/s019.pdf eqn (8)
by the exponential converter to drive pin 5 of OTA1k, which “directions” the output current to ramp up/down.
“not quite pitch) that can be kept consistent as the modulation depth changes,” This is because the sideband SPACING is unchanged by depth.
” I was asking about stability w.r.t. changing modulation intensity.” Everything that happens as depth changes is stable and perceptually just incremental.
“frequency is modulated. In nonsynth contexts, FM typically means that the frequency is shifted in an additive way. This is also true in digital FM synths. But (as is tradition), analog synths can be different! Analog *linear* FM seems to refer to a sort of multiplicative FM (modulating gain applied to the integrator current, as has been described in this thread). “
The processes are neither additive or multiplicative and the same AF or RF. The magic is that something apparently continuous is discrete (sidebands)
Accordingly, by “initial and enveloped” I mean the output of OA8 which is a sum of INITIAL LINEAR and MOD IN (as enveloped by OTA2 through OA12 back through R67. It is this OA8 that is the total modulation signal that is rectified (OA5 and OA6) and edge detected (OA9, OA10, 4070) to trigger reversals (pin 3 of 4013).
Ari asks “Would you agree that EN129 is doing….”? All questions of this nature require extensive study to see what you are defining and assuming. I always decline. I have written in detail exactly what the AN129 does.
“there must be some equation relating the core instantaneous frequency.” It is the voltage output of OA5 divided by 150k (R7), the “reference current” reratioed http://electronotes.netfirms.com/s019.pdf eqn (8)
by the exponential converter to drive pin 5 of OTA1k, which “directions” the output current to ramp up/down.
“not quite pitch) that can be kept consistent as the modulation depth changes,” This is because the sideband SPACING is unchanged by depth.
” I was asking about stability w.r.t. changing modulation intensity.” Everything that happens as depth changes is stable and perceptually just incremental.
“frequency is modulated. In nonsynth contexts, FM typically means that the frequency is shifted in an additive way. This is also true in digital FM synths. But (as is tradition), analog synths can be different! Analog *linear* FM seems to refer to a sort of multiplicative FM (modulating gain applied to the integrator current, as has been described in this thread). “
The processes are neither additive or multiplicative and the same AF or RF. The magic is that something apparently continuous is discrete (sidebands)
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
It's multiplicative in the sense that it's linear gain applied to the core charging current (and the flipflop/rectifier enable multiplication by negative numbers). For static V_c, it's equivalent to the basic formal definition, IF = some frequency + some modulation: EN129 core current is proportional to exp(V_c) * (initial + enveloped) = (some constant frequency) + (some modulation signal), so the distinction is purely one of implementation. I just thought it was an interesting way of realizing the formal (additive) expression one sees in a lot of discussions of FM synthesis (many of which assume a digital platform).
As a further aside, it's always seemed to me like one could even more directly implement said formal definition by just adding the linear modulation signal directly into the core (after enveloping, without any initial/offset), and using a window comparator instead of a normal comparator to detect when the core hits a triangle limit. This would be a direct implementation of the integral. Must be a matter of cost/complexity/stability? Is gain control preferable to / simpler than accurate summing from an engineering POV?
As a further aside, it's always seemed to me like one could even more directly implement said formal definition by just adding the linear modulation signal directly into the core (after enveloping, without any initial/offset), and using a window comparator instead of a normal comparator to detect when the core hits a triangle limit. This would be a direct implementation of the integral. Must be a matter of cost/complexity/stability? Is gain control preferable to / simpler than accurate summing from an engineering POV?
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Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
I feel the discussion about what is/isn't true TZFM (no matter how convoluted it has become) is still important as it applies to the ZPO.AugustusArnone wrote: ↑Sat Jul 11, 2020 9:47 pm@analogPedagog  discussion of the ZPO's implementation seems to have taken a backseat. I'm awaiting on one arriving Monday and keen to understand the technical background in the context of this discussion. I think I understand Bernie's last post about the EN129, halting at 0 and restarting in the direction of a time reversal, which would be TZ modulation. Is this what the ZPO does when you switch TZ on for lin or exp? But it's always mixed in with TZAM as well?
In the context of how the ZPO functions, as compared to both the EN129 and Rubicon method, the functional goal was to take advantage of the 'timereversal' concept. Specifically, the fact that additional sidebands are created when the waveform reverses direction and goes back up in frequency.
Both the EN129 and Rubicon are strictly TZFM as defined. The rubicon also employs the symmetry feature  which IMHO is a feature enhancementbut they both operate on the principle of directing the current, controlling the integrator in the vco core.
The ZPO has the "Zero Point' function. This is implemented using a balanced modulator with a linear offset control, like the Rubicon. But rather than being tied to the current controlling the integrator, it is only controlling the VCO direction and therefore decoupled from affecting the pitch. This is similar to symmetry without affecting the pitch.
If Zero Point is centered, the output is null for SIne, Pulse, Triangle, Upsaw and Even waveforms, but due to the wave shaping circuitry, Saw and Ripsaw are half amplitude square waves.
This null output is similar to a TZVCO stalling at some DC level, except it will always be at ground potential. Either way you get silence.
There are components of both TZFM and TZAM through applying 'TZMOD' on the ZPO.
If you were to use a linear 4quadrant multiplier in the Zero Point circuit, the output would always be dominated by Ring Modulation. So the 'trick' of the design is to make sure that the timereversal happens very quickly to produce a similar, but definitely different approach to 'timereversal side band generation. It is tuned to be as smooth of a transition as possible within a given modulator/carrier frequency ratio.
The rise/fall time of the modulation source determines how quickly/smoothly this phase reversal occurs. Hence, the dominance of the amplitude modulation component increases as the mod/carrier frequency ratio deviates from 1:1, in either extreme.
As far as comparing the Rubicon/EN129 to the ZPO, although they employ similar functional blocks (viewed in isolation), and can perhaps sound similar at times, they really are quite different overall.
Re: Intellijel Rubicon 2 vs SSF Zero Point Oscillator
One last quick comment before I stop pulling the thread away from its original topic  in the last few posts, I ultimately realized that EN129 does actually have a control equivalent to symmetry, what Bernie called "initial." It's implicitly included in the linear modulation in the 129 block diagram (and explicitly later in the electronote).analogPedagog wrote: ↑Mon Jul 13, 2020 11:21 amBoth the EN129 and Rubicon are strictly TZFM as defined. The rubicon also employs the symmetry feature  which IMHO is a feature enhancementbut they both operate on the principle of directing the current, controlling the integrator in the vco core.
So that nobody thinks there is remaining disagreement: my previous objections to 129 were rooted in a misunderstanding of its design. It should be pretty much equivalently to rubicon, in principle. Like analogPedagog said, ZPO is something different.