Hi dpidco, welcome to TW!
I have never played with this particular design, but will try to be helpful.. Take what I say in the following with a big pinch of salt - it may be BS!
1st - you are primarily talking about sensitivity not linearity in the above - linearity is a different matter which you can only start looking at when you have a reasonable playing field.
All the component values for the oscillator / antenna look wrong to me - IMO one needs a much smaller inductor than the 1mH pitch tank inductor (something perhaps in the order of 120uH for the specified frequency) and a MUCH larger capacitance where the variable 0-60pF capacitor sits (something above 1nF, but probably more like 3nF .. I really cant be bothered to do the calculations - check calculations for LC resonance).
The problem is that whoever "designed" this theremin had, AFAICS, absolutely no understanding aboutwhat they were doing ! - The function of the antenna coils in combination with the antenna capacitance is to create a resonator which behaves like a variable INDUCTOR whose inductance changes with change antenna capacitance - This variable inductance is across the tank inductor, and changes the tanks effective inductance NOT its capacitance..
If the tank inductor is large, this "virtual inductance" will have littel effect on the tank frequency (low sensitivity) - if its small, and the tanks capacitance is increased to bring the frequency back to the correct operating point, then the "virtual inductance" of the antenna circuit will be more significant, giving an increase in sensitivity and (if you are lucky or skilled at tuning) an improvement in linearity.
My advice would be to look at the Etherwave technical manual and replace the 1mH inductor with variable / fixed combination as per this theremin, and fit an equivalent (I think its 2n2) capacitor to replace the variable one - or at least see how the EW works so you understand the idea..
My possible quick fix advice: Place an adjustable inductor of perhaps a bit more than 100uH (search for IFT here) across your 1mH inductor to reduce the tank inductance, use this variable inductor for tuning - Replace the 60pF variable capacitor with a 2n2 ceramic, and add capacitance here to lower the frequency... Thats at least where I would start (if I could be bothered) but no gaurantee that it will work at all!
Someone else here may give better advice..
It is a REALLY crap design IMO - Want to find the worst and most ignorant electronic designs on the web ? - Look for theremin circuits! - fine IMO if peeps put these up as "experimental" with appropriate warnings, but not nice if one invests time and money in building something that pretends to be what it isnt.
Sadly, this mistake of tacking an antenna EQ circuit onto a tank which was never designed to operate in this way, thinking that by adding a series inductor linearity will magically appear, is extremely common - Its a mistake I made many years ago when I thought I knew what I was doing, but never had a clue! ... Difference is that when I found it didnt work, I didnt publish the bloody design! I set about finding out why it didnt work, and gained understanding this way.
Fred.
Just a quick update - something you could try with minimum effort..
Get a 42IF106 IFT transformer (Mouser do them, under $2) and connect pins 1 and 3 across the 1mH tank inductor
Remove the tuning capacitor, and fit a 2n2 ceramic ca there... This should bring the oscillator frequency into the right sort of range (172k)..
If this doesnt give required tuning range and/or sensitivity, you could remove the 1mH, and wire the 42IF106 as follows:
Pin 2 to one end (of where 1mH was) connect pins 3 and 4 together but not to anything else, pin 6 to other end (of where 1mH was).. This gives inductance adjustment of 137uH to 254uH aprox.. Make the capacitor about 4.4nF (two 2n2's in parrallel)
with this frequency and 40mH antenna inductance, one needs somewhere 'round 20pF antenna capacitance at the null point - so quite a long and/or fat antenna.. you may want to add another 10mH inductor (bringing total to 50mH) which brings required antenna capacitance down a bit ~17pF
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Final comments:
Just tried running some simulations on this oscillator -
Forget it! .. It looks like the only way to get this to work will be to use the original design, but remove the antenna inductors (you may need to replace these inductors with one small capacitor, perhaps 22pF or even lower to trim sensitivity.. or just a wire link) - it wont work reliably (if at all) with my suggested modifications - and without mods like this, the antenna coils do nothing except reduce sensitivity.
Forget linearity - you wont get it with this "design".
In fact, my advise is put it in a box (or donate it to some recycling centre) - without a lot more knowledge than V=IR, you have no hope! ... Theremins aint a good route to learn basic electronics at the best of times, and enough to put you off electronics for life when you pick a circuit like the one you did!