Antenna tuning.

"Oh Fred, that is so last month."

Well, im more up to date than usual, then! ;-)

"Here is the practical method. I just scribbled it on my iPad. You may download it as a PDF file. :-)" - Thierry

Thierry, I have seen something similar to this (The EPE-2008 theremin had a on-board circuit to assist tuning) - but, in playing with the EPE circuit, I found the operation of this circuit unsatisfactory.

My understanding (and my experiments) indicate that maximum loading on the oscillator occurs at the resonant frequency of the antenna circuit (coils + antenna capacitance).. and that one wants the hand capacitance "seen" by the antenna to be at the position one requires for the null point (about 60cm from the antenna)

The resistance inserted between the oscillator and antenna circuit allows the oscillator frequency to be adjusted without being effected by the antenna loading - so one can find (by looking for peak current) the resonant frequency of the antenna circuit.

However, as soon as the 100k (or whatever value is used to 'isolate' the antenna from the oscillator) is replaced with a link (ie, reconnected as it should be) the loading on the oscillator changes the oscillator frequency, so that the antenna / oscillator tunings are no longer at the optimum operating point.

The way I found (with the EPE design) to overcome this 'problem' was (1) to tune for resonance with the isolating resistor fitted, and while still fitted, (2) adjust the reference oscillator so that there was 0 beat (null).. (one wants the users tuning control to be mid position before adjusting the reference oscillator)

(3) Then the antenna circuit was connected to the oscillator (the isolating resistor removed and/or shorted) ,  (4) the (variable)oscillator needs to be re-tuned so that there is 0 beat -

The above works because one has (in steps 1 + 2) set the reference oscillator to the resonant frequency of the antenna - once this is acomplished, one does not adjust the reference oscillator again.. By retuning the variable oscillator (step 4) , one brings it back (when at the null point) to the antennas resonant frequency, by tuning it to the same frequency as the reference oscillator, which has been tuned to the antennas resonant frequency!

It is my belief (hypothesis) that the topology of most theremins is incorrect - to maintain linearity for changing background capacitances, changing the reference frequency is not the optimum method .. The optimum method of tuning a theremin is by setting it up as described above, and then altering the antenna inductance to 're-tune' the theremin - This way linearity is maintained at optimum and sensitivity is not affected.

The most linear theremin I have encountered is the Moog Ether-Vox, and whilst I was not able to reverse-engineer the antenna circuit, I can say that tuning is performed by changing the resonant frequency of the antenna circuit, using a variable capacitor.

I have developed an electronically controlled variable inductance circuit based on saturable reactors - I think this is probably a better topology, as it allows the linearity to be adjusted once - thereafter, regardless of any changes to capacitance seen by the antenna, the theremin can be tuned by adjusting the equalizing coils (effective) inductance, and linearity is unnaffected.. There would be no user adjustment of either reference or variable oscillators, only either user or automated adjustment of the antenna inductance.

I hope to be publishing details about the saturable reactor circuit very soon - I have a couple of prototype reactors which work well, but I cannot get any more - I have now commissioned a UK company (last ones were Chinese made custom parts) to copy these reactors. As soon as I get them, and have tested them, the circuit will be published and the parts available for about £10 I hope.. The reactor is simple in principle, but (like all things theremin) has some constraints not usually encountered in their normal application.

Fred.

Hello Fred,

dewster and I mentioned in the past that just laying a loose wire near the antenna for loose coupling connected to an oscilloscope will indicate when maximum  energy is at the antenna. The p-p voltage in the field around the antenna will rise or fall with tuning of the tank/antenna circuit. On my EWS it did not like maximum p-p so I needed to off tune the tank to the higher freq side or the antenna side oscillator would stop oscillating. 

Edit: The detectable voltage in the field varies quite a bit from one theremin design to the next like 10 volts to 40 volts or more. I found this difference to increase or decrease the number of note intervals that could be played but it had no direct affect on linearity of the playing field.

As always just my humble observation...

Hi Chris,

"dewster and I mentioned in the past that just laying a loose wire near the antenna for loose coupling connected to an oscilloscope will indicate when maximum  energy is at the antenna. The p-p voltage in the field around the antenna will rise or fall with tuning of the tank/antenna circuit. On my EWS it did not like maximum p-p so I needed to off tune the tank to the higher freq side or the antenna side oscillator would stop oscillating." -Christopher

Yes - provided the wire used to pick up the signal does not actually add too much capacitance, the above is a good scheme. Field strength meters are also useful for this - they can often be held at 60cm from the antenna and give reasonable indication of peak signal. 

I needed to off tune the tank to the higher freq side or the antenna side oscillator would stop oscillating

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!

Tuning the oscillator frequency to a  higher frequency than antenna resonance is normal  - At the “null” distance, these frequencies should be as close as possible.

Just a reminder - As I have often stated - I am not an EW expert!

"The voltage in the field varies quite a bit from one theremin design to the next like 10 volts to 40 volts or more. I found this difference to increase or decrease the number of note intervals that could be played but it had no direct affect on linearity of the playing field."

With a linearizing inductor, you can get really high voltages on the antenna at resonance (more than 200V P-P is easily possible) - without this inductor, and with a LC oscillator, one can still get supply voltage * 2 easily. RC oscillators (without any inductors) will only give at maximum the supply voltage.

I think the "number of note intervals that could be played" is reference to sensitivity, which, as you say, not directly linked to linearity (although with LC oscillators driving equalizing inductors, it tends to be).

Fred.

Hi Fred,

a bit another aspect: what is the optimal ratio between the osc LC and antenna LC wave impedances, in terms of your theory of linearisation and tuning?

There is a rule of thumb which allows you to set up a system of equations which can then be easily solved (or modified if you get impractical values):

Given the oscillator's frequency f_osc and the maximal deviation of the variable oscillator delta_f (= maximum audio frequency when you grasp the pitch antenna after the oscillators were nulled before). If the whole circuit is well tuned, you will reach about a fifth lower than that (2/3 of delta_f) with the hand at 1cm of the pitch antenna.

These equations are simplified and assume no parasitic capacitance of the linearization coils, but it's a first design aid. In practice (even with parasitic capacitance) you will obtain the best stretching of the highest octave when tuning the variable oscillator for the calculated delta_f by alternatively grasping the pitch antenna and running out of the field. 

There is a curious phenomenon in the Etherwave Pro: With the present component values for linearization, the top octave would be ways too stretched. That's why Moog has put a small variable capacitor in parallel of the first (from 4) linearization coils in order to add parasitic capacitance and thus to "worsen" the over-linearization somewhat.

L_osc, C_osc => oscillator's tank circuit
L_lin => inductance of the linearization coil
C_ant => static capacitance of the pitch antenna with no player in the field

I) f_osc = 1/(2*pi*Sqrt(L_osc*C_osc))

II) f_ant = f_osc = 1/(2*pi*Sqrt(L_lin*C_ant))

III) 2*delta_f ~ 1/(2*pi*Sqrt(L_lin*C_osc))

Let's take the example of the Etherwave Standard or Plus for an empiric view on that:
C_osc = 3.3nF, L_osc = +/-94uH, L_lin = 30mH
I) f_osc ~285kHz 
II) allows us to roughly estimate C_ant since L_lin is known: ~10pF (thanks to the grounded aluminum foil)
III) 2*delta_f ~15.8kHz => delta_f ~7.9kHz which means that one could theoretically tune an Etherwave for a maximum pitch range of 7.9*2/3 ~5.3kHz

In reality it will become unstable when you go beyond 4kHz (about a third lower than the theoretical maximum) due to secondary effects.

Explanation:

We have a parallel tank circuit in the oscillator and directly in parallel the series tank circuit formed by the linearization inductance and the antenna capacitance.

The series resonant circuit will behave like a frequency dependent inductor above its proper resonant frequency and has an upper limit: the linearization inductance itself. That means that the bigger you make the antenna capacitance (i.e. by approaching your hand) the lower the self-resonant frequency and thus the higher the inductance seen by the oscillator.

The parallel resonant circuit of the oscillator will behave like a frequency dependent capacitor above its proper resonant frequency.

What happens now if you connect a linearized antenna circuit to the oscillator whose self resonant frequency is slightly higher than the one of the antenna circuit?

The oscillator will see an inductance in parallel which will cause him to go up in frequency. You can check this on an Etherwave with a frequency counter when you disconnect the first linearization coil. (oh miracle!)

If you add now capacitance to the antenna circuit, its self resonant frequency will go down and the inductance seen by the oscillator will thus increase. When you grasp the antenna it will see almost the whole linearization inductance in parallel. Since the linearization inductance (and its impedance) is much larger than the one in the oscillator's tank circuit, it will have less impact in the parallel circuit and the oscillator's frequency will go down and approach its initial value in the extreme case.

And here we are: Finally the linearization coil does nothing other than limiting the frequency deviation by lifting up the oscillator by a defined amount (delta_f) without hand capacitance and by allowing it to fall back no more than until its own resonant frequency. This fallback happens in an asymptotic way, that means it gets "slower" towards the end. And that makes that bigger capacitance changes as they happen with the hand near the antenna have a smaller impact on the resonant frequency of the entire system, which stretches the tone spacing in the high register.

It is difficult to calculate in an understandable way a predictable linearization behavior inside of the frequency bounds cited above. We have a resonant system oscillating above the resonant frequency of both initial tank circuits with a virtual and frequency dependent capacitance formed by the oscillator's parallel tank circuit and a virtual and frequency (and hand capacitance) dependent inductance formed by the antenna series tank circuit. This leads already to 4th order equations (without parasitic capacitances taken into account) which are not trivial to solve.

It should be clear that the fixed pitch oscillator will have to be tuned to the upper frequency which is taken by the variable o/c when the antenna circuit is connected.

On the Etherwave Pro for example, you will have to tune the variable oscillator to 276kHz without the pitch arm (which contains the linearization coils) and the fixed oscillator to 282kHz. As soon as you connect the pitch arm and the antenna, the variable oscillator will jump up to 282kHz and things are fine... ;-)

So the idea of linearization is to choose your components and resonant frequencies in a way that you get the desired maximum frequency deviation and thus the upper limit of the pitch range AND a nice tone spacing near the antenna. The tone spacing in the lower register is then easily to adapt with the pitch knob which acts on the fixed pitch oscillator, because the latter causes a constant frequency difference which will naturally have much more impact in the low register than in the high register... Adding 50Hz to the lowest Cello octave (initially 65 to 130Hz) will give 115 to 160Hz which is now only a fifth, while adding the same 50Hz in the highest register (2040 to 4080Hz) will make 2090 to 4130Hz which is sell very close to the 1:2 ratio.

Linearity is thus: Giving the instrument a useful tone spacing in the higher register by properly designing the linearization circuit and allow to converge this "tone spacing by design" through the whole pitch range with the help of the pitch knob.

Finally, you will now also understand why it makes no sense to add a linearization circuit to an oscillator which has not been designed for that. The capacitors in the oscillators' tank circuits of linearized theremins are most times much bigger in order to meet the delta_f requirement from equation III and would not allow an important frequency deviation with just the antenna connected and without linearization coil. In reverse, the trial to linearize a theremin with a "classic" oscillator and low capacitance in order to be more sensitive to the small capacitance changes of the antenna would need impractically high linearization inductances in order to meet the delta_f requirements, but this would too much lower the resonant frequency of the antenna circuit so that this "linearization" would not have the desired effect.

Мerci beaucoup, Thierry, for your mega answer,

 and summing up the above (especialy relation III), it turns out that "the less the difference between L_lin and  L_osc ---  the wider the pitch range of instrument (under same conditions -- operating freq,  antenna, linearization inductance). 

The experiment (and I've made a lot of that) shows that best linearization results are obtained with a L_lin/L_osc ratio of > 150:1 ...