LC Tank / Linearizing Coil Excel Simulation

Spent my day yesterday tinkering with the Excel sim again.  Made the tank series cap and resistor series elements (with each other) rather than parallel (for the capless reference design) and monkeyed with the Linearity phase detect so that sim is working much better & somewhat faster.

I'm toying with the notion of adding a linearity sheet that uses real, measured hand capacitance data, which would essentially remove any issues with hand model fidelity to reality.  Using a simple LC tank with EQ I could calculate capacitance back from frequency.  I suppose a closed fist might be the most generic hand gesture to use, and the rest of my body would have to remain in a very fixed position.

Antenna geometry (length, diameter) might be a confounding factor though, and any target designs that use large air-core EQ coils might not be well represented by the resulting sim (I have a feeling there is significant hand/coil capacitive interaction going on there).

RS, as I understand it, coupling mainly kicks in when the oscillators are very near to each other in frequency, which would be the bass region for a heterodyning Theremin.  My simulation doesn't take this into account (it is a simple a frequency response model) - the only way to model it would be to do a time slice model, much more complex and beyond the scope of what I intend to build.  You could likely use LTspice to model coupling.

What happens in the first 2 to 3 inches to the pitch linearity on your Theremin?  (On most (all?) I believe this region is one of cramped pitch.  On my digital prototype this zone is cramped.)

How wide are your octaves?  (On my digital prototype they are approximately an open / closed hand wide.)

If you set the null point differently does this affect linearity?  (On my digital prototype there is only one null point that gives good linearity, and there is a lot of linearity interaction with where my body is in the field.)

I ask these questions because we may actually have similar scenarios playing out in our circuits.  I believe your spring antenna is acting more like a variable distributed capacitance than a coil.  Iron has a lot of skin effect as well, particularly at the frequencies your Theremin is operating at.

"as I understand it, coupling mainly kicks in when the oscillators are very near to each other in frequency, which would be the bass region for a heterodyning Theremin." - Dewster

This is at least mostly true.. Certainly this is the area that most oscillators go rapidly into sync.

It is a really interesting area to play with, and has lots of effect on both the sound and the linearity. Different oscillators seem to behave differently with regard to the effect of coupling - In my expierience, low frequency (up to about the EW, as in <300kHz) oscillators seem to have a bigger range over which coupling becomes significant.. But please dont trust what I say here, because it certainly isnt always true!

I have gone back to exploring coupling again because of the Lev clone.. Something happens with Lev's theremins which does not happen (or at least not in as nearly as significant way) on other theremins I have played with or whos sounds I have analysed.. This is that the waveshape changes as a function of frequency hugely - and these changes are complex.. I have implemented complex frequency-voltage controlled biasing on the mixer to emulate these effects, but the fact that Lev achieved this without any sophisticated "external" circuitry makesme sure that I am missing something basic.

I think that perhaps the coupling mechanism in Lev's theremins may operate over a much larger frequency range than usual, and that (combined with the special charactaristics of the mixer) this creates its special tone and also improves linearity.

Whilst the Lev oscillator seems to give some (quite substantial perhaps) improvement in linearity, I am not sure that this is enough to explain fully the performance, particularly at the bass end.

Thierry's disclosure about the sophisticated mechanism Bob Moog used to implement coupling on the E-Pro makes me even mor inclined to think that this is important for linearity - As I understand it, the tone generation mechanism for the E-Pro (What I call mixed-signal heterodyning, but some wrongly IMO call digital heterodyning)  could not utilise the analogue waveform changes (because the VFO and REF signals are converted to square waves prior to mixing) generated due to coupling, therefore the only reason such sophisticated coupling is included in the E-Pro must be purely to improve linearity.. If Bob went to that much trouble, there must be a good reason for him doing so!

Fred.

" I believe your spring antenna is acting more like a variable distributed capacitance than a coil. " - Dewster

I agree. It is an adjustable capacitance antenna - identical in function to a whip (telescopic)  antenna whos length can be adjusted, or my stud antenna whos length can be adjusted by rotation.. perhaps the only difference is that it may be possible to adjust the capacitance of a spring more finely - certainly more finely than a whip antenna.

Hi dewster,

Until I meet with a local Thereminist everything about my theremin is just expressing hot gas! You are special as no others will advance your research, there just isn’t anyone.

“What happens in the first 2 to 3 inches to the pitch linearity on your Theremin?  (On most (all?) I believe this region is one of cramped pitch.  On my digital prototype this zone is cramped.)”

This 3” area is cramped but not always as this inside area does change. Outside of that area is linear no matter what the octave width I set too, using say 3” to 6”, octave width is not critical.

I use a closed fist to open hand to set my pitch field before a demonstration and maybe a little wider as it seems better to undershoot than overshoot a musical note but what do I know.

“there is a lot of linearity interaction with where my body is in the field.”

I reach out 1’ then play the field width of 18” up to 3” from the antenna. I leave my body behind from entering the pitch field (sounds like astral projection)

Eight years ago is when I first made the statement on my webpage that hand capacitance alone between the hand and antenna does not fully explain the linearity phenomena of why the field is relative to a musical scale.

My first experiments with the coiled antenna to understand how perfect pitch field linearity came about used a series capacitor and inductor inline with the coil antenna. My oscillator was a parallel Hartley tank circuit.  I used the ferrite rod and a variable capacitor from a RS Crystal Radio kit.

For perfect pitch field linearity the inline tuning was added to match the pitch oscillator frequency. At a specific point of tuning the octaves next to the antenna became wider in response than the outside octaves which compress inward. There was a specific point in the pitch field that was a “different” NULL than we are accustom too which needed to be moved away from the antenna out beyond the Thereminist. You could tell where the “different” null was in the pitch field because it created a flat spot in the pitch where the audio note went steady until you passed through it towards the antenna. This is why this different null was moved out and placed behind the Thereminist. Later I found this series critical tuning was unnecessary and did away with the inline LC. The theremin had seemed to want to show me something.  Later on the Linearity next to the antenna did not seem important. I don’t think a theremin sound above 3 kHz is enjoyable and preferably I like less than 1500 Hz and better yet below 1000 Hz where it is more natural and vocal.

With my direct single spring, sometimes the inside 3” is perfectly linear and on some days my theremin voice is wonderful yet these two are variables and on any given day they will be slightly different. I monitor room humidity but have not made a connection yet.

My tube front end theremin had ideal linearity and I could pick up the amplitude 12” from the antenna. My present solid state has measurable amplitude only within 1” from the antenna. Both demonstrated the same perfect linearity. A theremin running hot around the antenna is going to interfere with other equipment as I use separate pitch and volume oscillators. You sure don’t want them talking to one another.

I removed the webpage that may be an incorrect observation as I removed the webpage of the possibility of FM heterodyning. The later developed a triangular wave yet perfect linearity off of a straight wire. The IF coils used were forced to fight each other more than usual. It was fascinating stuff but viewed as blasphemy and there are better things to focus on than to waste time explaining.

One last observation, the L1 and L2 oscillators respond opposite of each other (corrected). If I place a one foot length of antenna wire in the other oscillator opposite the pitch antenna side and direct it towards the floor, the playing is normal but the inside 3" become perfectly linear, almost overly linear or nullified, along with the pitch field being wonderful. The sound is horrifying but about as good as the Distant Voices theremin that some people like. (-'

Christopher

I think that perhaps the coupling mechanism in Lev's theremins may operate over a much larger frequency range than usual, and that (combined with the special charactaristics of the mixer) this creates its special tone and also improves linearity.  - FredM

Theremin did his development without a scope, correct?  Talk about flying blind.  No sims, no scopes, no frequency counters, no DMMs, no easy to use LCR meters.  Plus early tubes, hand wound coils, what look like hand made caps (?) - knives and bearskins.  Must've had the patience of Job.

"Until I meet with a local Thereminist everything about my theremin is just expressing hot gas! You are special as no others will advance your research, there just isn’t anyone."  - RS Theremin

Have you tried sending the mountain to Mohammed?  If anything ever crawls out of my lab alive I hope some of the good players around here will oblige me by giving it a whirl.

"the L1 and L2 oscillators are 180 degrees out of phase" - RS

L1 and L2 being pitch and reference? How can the phase relationship of these two oscillators be any way locked and one get any sound?.. the only time one has a fixed phase relationship is when both frequencies are the same!

"Theremin did his development without a scope, correct?  Talk about flying blind.  No sims, no scopes, no frequency counters, no DMMs, no easy to use LCR meters.  Plus early tubes, hand wound coils, what look like hand made caps (?) - knives and bearskins.  Must've had the patience of Job." - Dewster

Yes - But more importantly I think, is that he REALLY knew what he was doing - Reading as much as I can find about the man recently, and he is absolutely astounding - not just in electronics, but also in all physics and science - incredibly "broad spectrum"

I also think that the education system was probably greatly superior to anything students encounter today (or at least what they encounter in "standard" universities - most universities are "degree factories" me thinks - churning out graduates that, in Lev's day, would hardly qualify  as  technicians)  - In those days, to get into physics one needed to be the cream - to have a mind way above the average.. Lev certainly had such a mind!

BUT - He was also as mad as a hatter IMO! - When one reads about his ideas on ressurecting Lennin (possibly a reason Stalin locked him away? - or perhaps the real story is that he was certified as a loony ;-) one realises he was no ordinary individual!

Fred.

Fred said: "L1 and L2 being pitch and reference? How can the phase relationship of these two oscillators be any way locked and one get any sound?.. the only time one has a fixed phase relationship is when both frequencies are the same!"

I may misstate the operation but it does not take away from it operating correctly. I would think all heterodyning LC oscillators worked the same way. The only thing I can say with certainty is if I approach one oscillator the pitch goes up and when I approach the other it goes down. Like wise the coil tuning direction is reversed when L1 is compared to L2.

Now that you mention it, saying it is phase relationship shift makes better sense.

Christopher

Edit: If the L1 oscillator pushes the audio frequency higher then the L2 oscillator pushes the audio frequency lower which would be a 180 degree shift for the audio frequency.

Edit2:  Fred said: "NO! - Nothing is "pushing or pulling" the audio frequency!"

I speak metaphorically as I am not technical, I would hope the average individual that follows this board will understand me.

"Now that you mention it, saying it is phase relationship shift makes better sense." - Christopher

In simplistic terms, it is the waves from both oscillators moving and mixing with each other which produces the audio (difference) output waveform..

Phase relationships are reletive to some fixed point or to another wave.. So if we have two identical fixed frequencies, one which at its peak and the other which is crossing zero (mid) and going positive at a given instant, then the two waves are 90 degrees out of phase.. They will remain 90 degrees out of phase if there is no change to either frequency..

If one wave is crossing zero going in a +Ve direction, and the other is crossing zero going in a -Ve direction, these waves are 180 degrees out of phase. If there is no distortion and the peak amplitudes are the same and the frequencies are the same, then adding (subtracting, multiplying) these waves will cancel them out resulting in zero.

Fred.

"Edit: If the L1 oscillator pushes the audio frequency higher then the L2 oscillator pushes the audio frequency lower which is a 180 degree shift for the audio frequency." - Christopher

NO! - Nothing is "pushing or pulling" the audio frequency!

You have two oscillators, the audio is the frequency difference between these oscillators.. that is all! Forget "phase shift" in the audio - you cannot hear phase shift, you do not know and do not care what the phase of your audio is! All you care about is its frequency and waveform!

Have a look at this applet..

Set Freq1 to 3000, Freq 2 to 3100, ms per 1000 pixels to 20. Tick Show snd 1, snd 2 and mix..

With this you will see how heterodyning works

Play with this applet, change Freq 1 to 3100 and Freq 2 to 3000 and note the lack of difference!

You can see that phase is not the issue - the difference in the frequency of the two oscillators is the issue! - prove this by changing the 3100 to 3200.

"I speak metaphorically as I am not technical, I would hope the average individual that follows this board will understand me." - Christopher

When you make statements like "which would be a 180 degree shift for the audio frequency" there is no metaphor - you are talking technical.. Anyone who "understands" what you are saying is on the path to greater confusion.. because what you are saying is wrong.

I am just trying to help you and others to not get lost in bogus ideas - there is no shame in getting things wrong - I do it all the time.. sure, there may be a moment of embarrasment and feeling like a fool, but this soon passes - and one is rewarded by having better understanding - But there is folly in clinging to wrong ideas when you have been shown how things actually work, and in clinging to and proclaiming a wrong idea to be valid when it has been clearly shown as flawed or false.

If I am honest, I think you are probably beyond help - So my posting here is more to help others to understand and to steer them away from the confusion which, IMO, you could easily cause.

The reference oscillator should be tuned such that, at the null distance, its frequency is the same as that of the variable oscillator. At all other times (if one is actually playing the theremin between the null distance and the antenna, and not away from it) the variable oscillator frequency is lower than that of the reference oscillator - how much lower depending on how much capacitance is "seen" by the antenna, capacitance increasing as the player moves anything towards the antenna.

It is the difference in frequency between the reference oscillator and the variable oscillator which determines the pitch.. for example, reference at 256kHz and variable at 255kHz will give a difference (audio) frequency of 1kHz.

If one lowers the reference oscillator frequency, but it is still above the variable oscillator frequency, the pitch (difference frequency) will reduce (get lower).. This applies whether lowering the reference oscillator is caused by tuning it or otherwise imposing any capacitance which affects its frequency. (this action is equivalent to moving the null point closer to the antenna)

If the reference oscillator drops below the frequency of the variable oscillator, then any further lowering of the reference oscillators frequency will cause the difference frequency to increase. (this is operating on the "wrong side" of the null point - it is not usable [as in, one should not tune the null point to the antenna - the lowest variable oscillator frequency] and playing in this way, with pitch going higher as one moves away from the antenna, is always extremely non-linear)

These are the most basic, fundamental, rudamentary elements of standard heterodyning theremin operation.

None of this has anything to do with phases, being 180 degrees out of phase, audio phase or any such descriptions - all of these type of "metaphors" are utterly meaningless, as are metaphors such as "pulling and pushing" the audio.

What I have said is not highly technical and should be a lot easier to understand than meaningless erronious statements like "If the L1 oscillator pushes the audio frequency higher then the L2 oscillator pushes the audio frequency lower which would be a 180 degree shift for the audio frequency" as phase shifting is "technical" and, apart from which,the whole statement is completely and utterly wrong in every possible way! - Subtracting one frequency from another to determine the audio frequency is comparatively non-technical, and is correct.

Fred.