That was quite some thesis!
Thank you for such a concise and comprehensive (and simply presented) exposition! Much respect.
However - I do feel a little bit peeved - Over the last couple of days I have spent several hours preparing a document covering much of what you have just said.. And your thesis is far better than what I had written! (I had not, for one thing, determined the optimum ratios for linearity - simply used data on a few theremins as examples)
So I would like to ask a favour of you - Can I have permission to copy what you have just posted, compile it to a .pdf, and place this (with authorship obviously assigned to you) in the document collection at Element 14 ?
Alternatively (better) if you could place a copy of what you have written on Element 14, that would be great!
"Not sure why the oscillator would stop – I have never managed to stall an EW oscillator, and have abused then so severely that lovers of the EW would probably have me stoned! - When the antenna is in resonance (as in, when the oscillator is running at the antennas resonant frequency) the loading on the oscillator is at maximum, so I suppose if its going to stall, it probably would be at this point!" - FredM
I haven't managed to stall the oscillators in my EWS but I haven't actually monkeyed around with it all that much.
The thing that bugs me the most about the EW oscillator design is that the LC tank feedback is in phase with the drive - the tugging point is the same as the sensing point. I believe this necessarily leads to a small gain (negative resistance?) drive, which in this case is single ended.
This is mode 1 in my Theremin spreadsheet simulator - a bandpass design. It can theoretically produce fairly pure sine waves. How important is oscillator spectral purity in an analog Theremin?
" How important is oscillator spectral purity in an analog Theremin?" - Dewster
In my view, and this may well be blasphemy to many, spectral "purity" is not a good idea - control of the spectrum is a good idea..
The audio wave shape and harmonic content comes from several sources.. and its the mixer which determines the importance of the oscillator waveform in the final output..
A true multiplier (mixer) will only output the sum and difference of the input signals - forget the sum components - these are thrown away.. the difference components will be the difference of all the components of the two input signals - therefore..
1:) the output harmonics will only be harmonics which appear on both input signals - if either signal is a pure sine wave, there can only be a sine wave output
2.) harmonics are multiplied - so assuming the fundamentals are at amplitude "1" and the 2nd harmonics of both input signals are at level "0.5", the output will be a fundamental with an level of "1" (1*1=1) and the 2nd harmonic will be at a level of "0.25" (0.5*0.5)..
It can be seen that a filtering action takes place with true multiplication - this, IMO, is one reason why analogue theremins using true 4Q multipliers have a more sine output than others.
In order to get more harmonics out, one needs to put more harmonics in from both oscillators.
However - most analogue theremins do not use a perfect mixer - the diode mixer in the EW distorts the hell out of the input waveforms mix.. And with these, I think that the input waveforms are quite insignificant in terms of contribution to the output harmonic content - It is only when these inputs become severely distorted (as when the oscillators pull / sync to each other, as can happen when their frequencies are close - at the bass end) that their harmonic contributions become really significant.
It should, however, be stated that some harmonics are particularly unmusical, and if these appear even at quite low levels on the input waveforms, they can make the sound unpleasant even through a diode mixer..
Then there is deliberate post-mixer distortion added in many theremins, and distortion added deliberately by changing the bias on multipliers like the MC1496..
Without doing anything to the waveform produced by the MC1496 (as in, just using it as a true multiplier) one gets a nearly pure sine output from standard oscillator inputs.. One really needs to distort the input waveforms quite significantly to make a noticable difference.
So I dont think spectral purity needs to be too critical - I think that controlled distortion of the oscillator waveforms is desirable for tone coloration, and avoidance of musically unpleasant harmonics existing on the input waveforms is important .
I think the "unmusical harmonic" is an unsuccessful expression. All the harmonics are musical ones. Maybe Fred meant something like combination frequencies and "ghost tones".
For example, if we put non-pure 100 and 103 kHz to mixer the most significant result will be 3 kHz plus multiple harmonics 6, 9, 12... kHz. But the resulting spectrum will also contain such non-musical overtones, as
36*100 - 35*103 = 5 kHz,
35*100 - 34*103 = 2 kHz,
34*100 - 33*103 = 1 kHz,
33*100 - 32*103 = 4 kHz,
32*100 - 31*103 = 7 kHz,
31*100 - 30*103 = 10 kHz,
and so on.
"Fred, I bow to you for your extensive yet concise and informative answer to my question!" - Dewster.
Please dont bow! my answer, particularly WRT "unmusical harmonics" may well be complete BS!
I am much more knowlegable about engineering than I am about music..
I was in fact referring to normal integer harmonics - to my ears, there are some which, if too predominant or in the "wrong" context, sound horrible and can be "heard" as a seperate tone - but I do not know if this has any foundation other than in my ears / brain - I just assumed (mostly from experimenting with synthesis) that these harmonics, if predominant, would sound horrible to everyone else!
To me, particularly the 7th harmonic (and also the 9th), is almost always at least a 'distraction' and most often 'unmusical' .. But it (to me) all comes down to the fine balance of the other harmonics - A spectrum where every ascending harmonic reduces in amplitude is much more likely to sound "right" to me than one where any higher harmonic has greater amplitude than lower harmonics.. When a higher harmonic appears at greater amplitude than a lower one (particularly if the 6th, 7th or 9th) I tend to hear these as seperate tones.
Until I get to the 6th harmonic, having higher harmonics with greater amplitude than lower ones can be really pleasant (to my ears) if the mix is right - And removing the fundamental and 2nd harmonics can really boost the bass effect - Take a ramp, chop off its 2nd harmonic and fundamental, and one (IMO) gets a tone which sounds like a lovely deep growling 25Hz bass when in fact the first actual frequency being played is 75Hz .. I was messin about with this concept with the idea that I could extend the playable bass range of a theremin by changing the harmonics of a higher difference frequency to give a lower sound.
But I think Ilya is absolutely right - there is no such thing as a harmonic (as in, integer harmonic) which is unmusical.
Just one thing I need to say, having re-visited this thread..
I stated "I have never managed to stall an EW oscillator, and have abused then so severely that lovers of the EW would probably have me stoned! " and this is true - what I failed to mention is that I never absolutely follow someone elses design unless I am looking for faults - I did not use (and rarely use) the 2n3904 transistors .. I have my favorite transistors (The Zetex ZTX range) which have much better current and dissipation ratings than the 2n3904.
On some thread Thierry mentioned that wrongly tuning the new EW's could damage the transistors, as the antenna inductances have now changed, causing the loading on these transistors to increase.
IMO, a design which can be adjusted to self destruction is inexcusable, particularly when all it takes to prevent such a possibility is changing 4x 5p components to 4x 25p components.
But I just felt that, in the light of Thierrys revelation and my saying "I have never managed to stall an EW oscillator" I should warn that my oscillator used different transistors - You may not stall the oscillator - but its transistors may die - a permanent "stall" I suppose.
(it is also interesting to me that on all the high-end Moogs I have seen, great big beefy transistors are used in the oscillators)