On Theremin Sensitivity

I ran across this a while ago:

http://www.dogstar.dantimax.dk/theremin/thersens.htm

It's an interesting exercise, and I think his conclusion in the sense that there is such a thing as too much sensitivity is valid.  But the analysis is fundamentally flawed because it doesn't take the presence of any EQ inductance into account.  Sensitivity can often be greatly increased in many designs with it.  No one would go to the trouble of winding those huge crazy air coils in the RCA and its clones, and Bob M. wouldn't have included them in his designs if it didn't do something highly significant to the pitch response (and it does: external capacitance interacting with the EQ coil is responsible for much of the pitch response).  Many of the sensitivities he lists are way too low because of this.

This is an elephant in the room (or on the Theremin schematic) that is difficult to ignore, but I suppose difficult to analyze without sims or more extensive math beyond simple LC resonance.  And to get the analysis really right one has to include parasitics, because they can have a profound influence (to the point where excess coil self capacitance can put the kibosh on it working at all).

"But the analysis is fundamentally flawed because it doesn't take the presence of any EQ inductance into account" - Dewster

I dont think that the late Fred Nachbaur ever used Equalizing coils on his theremins - he did quite extensive modifications on the PAiA theremax, and quite a lot of tube stuff including a theremin from an old tube AM radio if I remember correctly, and I think his "theremin sensitivity" article was intended for those building or modifying "direct capacitance" (as in, uncompensated) theremins.

And yes - his "analysis" is completely useless for any theremin which has an inductor between the tank and the antenna -

But I think he was the first to at least give us something, and his tube circuits and  descriptions of them really helped me to get back into the "feel" for these components..

I believe that your spreadsheets are the only source of data related to theremin sensitivity and linearity which are of any use for equalized theremins! - Until these appeared, there was a pile of impossible maths or painstaking simulations.

Fred.

I think that when using eq inductors, the "trick" is in balancing sensitivity and linearity - one could make an absurdly sensitive theremin which is completely unplayable with or without equalizing inductors.. I also think that, for unequalised theremins, it is easier to obtain the "right" sensitivity if one operates at a higher frequency (400k up) simply because of the lower tank capacitance requirement with a sensible LC ratio - somewhere between 100pF and 300pF || inductance 400uH to 800uH, which determines the proportional effect of antenna capacitance... The smaller the tank capacitance, the more sensitive the theremin.

I think his argument is worse than I initially thought!  Unless I made an grievous error in my spreadsheet (entirely possible) or the hand model is crap (entirely possible) I believe the sensitivity issue itself as presented on his web page is wrong. 

After playing around for several hours with entirely different designs that have entirely different topologies, operating points, and kHz/pF "sensitivities" I was puzzled to find that all looked qualitatively extremely similar on the Linearity worksheet - i.e. they all had roughly the same hand spacing per octave.  Increasing kHz/pF had the effect of moving the quasi-linear range up in frequency, but that's it. 

At first I thought something was wrong, but the answer I believe is in our logarithmic sense of pitch.  Increasing kHz/pF is a simple multiplication, which in the logarithmic domain is adding, hence the simple frequency offset I saw.  Real sensitivity in terms of octave per hand spacing is %F/pF (which is the ratiometric sensitivity I use for digital Theremin design).  All of the designs I was playing with had roughly the same %F/pF sensitivity (-4.3 to -5.5) hence the same Linearity graph shape.

So: kHz/pF sets the linearity center frequency and has nothing to do with note / hand spacing.  %F/pF sets note / hand spacing.

"The smaller the tank capacitance, the more sensitive the theremin" is not true for the parallel tank EWS which has a relatively huge tank capacitor and relatively tiny tank inductor (compared to the EQ coil) but still manages a quite respectable -4.5 %F/pF.  However I believe that quote does apply to parallel tanks without EQ, and to series tanks with or without EQ. 

The EWS has been my "design to beat" in terms of %F/pF for a quite a while - I've done as well with the series tank and may finally beat it with the capless tank.

""The smaller the tank capacitance, the more sensitive the theremin" is not true for the parallel tank EWS which has a relatively huge tank capacitor and relatively tiny tank inductor (compared to the EQ coil) but still manages a quite respectable -4.5 %F/pF.  However I believe that quote does apply to parallel tanks without EQ, and to series tanks with or without EQ. " - Dewster

Absolutely! (or perhaps not.. Just seen what I highlighted above.. Let me think about that! ;-) - The sensitivity derived from Fred Nachbaur's calculations are only extremely crude "ball park" calculations and do not apply at all for topologies which include any equalizing method.. the "The smaller the tank capacitance, the more sensitive the theremin" applies only to non-compensated "direct antenna capacitance" designs.. Hz/pF is an utterly useless 'parameter' as both variables have a non-linear relationships - for music, Hz needs to be exponential, and for distance pF is inverse square law.. Put these together and one gets the (musically) non-linear response of distance <-> difference frequency.

This is why I have split theremin front-end designs into two groups -

(1) those where the antenna capacitance is "part" of the tank circuit directly - as in, the antenna capacitance is in parrallel with the tanks fixed capacitance - in these designs, the tanks fixed capacitance must be small (<500pF, but usually in the order of 220pF or even less) and the tank inductance needs to be large, and the operating frequency is usually high so that the tank inductance can be kept managable and to reduce the troublesome effect of inductance variation due to temperature (the bigger the inductance, the more thermal effects on this inductance will influence the oscillator frequency I think)..

The size of the fixed tank capacitor will directly influence the sensitivity - it is easy to change the sensitivity simply by increasing or decreasing the size of this capacitor.. but low frequency operation will require a bigger inductance, as one cannot reduce the operating frequency by increasing the tank capacitance, as this will impact sensitivity.. The SC front end has typical (and well selected) values of 680uH and 180pF for the tank, giving an operating frequency of 455kHz - and the change in antenna capacitance is "seen" as a change in total tank capacitance, and due to the small size (180pF) of the tanks fixed capacitance, is significant enough to give reasonable sensitivity.

(2) those where the antenna capacitance is not directly "seen" by the tank circuit - with these, changes in the antenna capacitance are converted to larger changes in the "virtual inductance" imposed across the tank inductor by the antenna equalizing circuit.

With these designs, even for low frequency oscillation, the tank inductance is small.. Sensitivity is determined by the ratio of the change in the antenna circuits inductive reactance || the tanks inductive reactance, so the antenna circuit can be seen as a "virtual variable inductor" in || with the tanks fixed inductor. The tank capacitance can be extremely large and the combination of tank L and C forms an oscillator which is, effectively, inductively tuned.

My conclusion:

The two different topologies are mirror images of each other, and completely incompatible.. The "direct antenna capacitance" topology is better suited to higher frequencies, has small capacitance and large inductance, and has no equalization mechanism of any kind.

The "antenna with seperate resonator" topology requires small tank inductance and large tank capacitance, is well suited to lower frequency operation, and the conversion process from capacitance change to imposed inductive reactance change confers some linearization.

Sensitivity is easier to adjust / control in the "direct antenna capacitance" topology because this topology is far simpler - there are no complex interactions and only a single network defining the operating frequency.

Fred.

Yes.  From my simulations and experience with series tanks, the tank inductor must be large, the tank capacitance tiny (on the order of the antenna & hand capacitance), and the EQ inductance (if used) on the order of the tank inductance.  This gives well defined phase at resonance and roughly double the tank voltage swing at the antenna.

From my simulations of parallel tanks with EQ and limited experience with the EWS, the LC of the EQ coil and antenna & hand capacitance set the resonance point, and the tank LC resonance must be set slightly above this for the best %F/pF sensitivity (and to keep the tank current from getting too high).  Large tank inductance / small tank capacitance gives poor Q, small tank inductance / large tank capacitance gives good Q.

"... the bigger the inductance, the more thermal effects on this inductance will influence the oscillator frequency I think..."

I don't think this is necessarily true because a proportional change in the inductance will change the LC resonance point proportional to the inverse square root of the change.  And ppm (e.g. thermal dependence) is proportional to the nominal value.