Let's Design and Build a (mostly) Digital Theremin!

Why not just stick a few windings at the "cold" end of the field coil?  The windings will mostly just interact with those near it. 
Might need a grounded foil shield between them to kill capacitive coupling.  I thought of doing this a while back.
-- dewster

With sensing coils as a section on the main inductor would require 3 wire connection to the inductor, and sensing connection should be short to minimize the noise.
With on-board sense transformer it's possible to place the main inductor far enough from AFE board, and sinsing amplifier (part of analog multiplier) may be located millimeters from the transformer.

Capacitive coupling could be a concern - it may mix common mode signal (drive) to the sensing signal - shifting sensed phase.
But I believe if transformer coils are located in the same layer (dual spiral), then mutual capacitance should be low (less than 1 pF).
Since one end of sensing coil is connected to reference voltage point, and resistance of the coil is very low, it's hard to influence the voltage on other end of the coil via mutual capacitance.
The amount of energy transferred by inductance will be significantly bigger than one introduced by the capacitance.

I wrote a simple single layer planar transformer footprint generator for KiCAD (github link).

Both coils of the transformer are placed on the same board side, to allow using it on dual layer PCB.

This is a current sensing transformer, to be used in Theremin Current Sensing Oscillator.

First coil (pins 1, 2) is made of wider trace, to allow currents up to 100mA, is intended to drive Theremin LC tank.

Secondary coil - is sensing one (pins 3, 4) is thinner, is supposed to work at currents below 1mA.

Compatible KiCAD schematics symbol is Transformer/TRANSF1

Default values for main coil
* 4.5 turns
* 0.15 mm trace width
* 12 mm inner diameter of coil
* 0.4 mm step
* L = 0.5uH
* Q = 4

Default values for sensing coil

* 5 turns
* 0.08 mm trace width
* 12 mm inner diameter of coil
* 0.4 mm step
* L = 0.62uH
* Q = 2

In current configuration the transformer occupies 12x12mm on PCB.

I've added cut holes similar to ones for planar ferrite core enclosure. But the dimensions of the cutting do not match any real core size.
If core is not used, does it make sense to do the cutting? Any advantage comparing to case when there is no cutting?

Tuning of the parameters

This is simple and dirty java application written in a few hours.
If you want to change the parameters, modify its source file - default values for Options class in the beginning of the file.

"With sensing coils as a section on the main inductor would require 3 wire connection to the inductor, and sensing connection should be short to minimize the noise.  With on-board sense transformer it's possible to place the main inductor far enough from AFE board, and sinsing amplifier (part of analog multiplier) may be located millimeters from the transformer."  - Buggins

Ah, good point.  My brain is in constant remote AFE mode.

I'm experimenting with usage of transformers to implement VCO.
Theremins are about the coils, and modern engineers forgot about them.

So far, I can see that loading of differential cascade on transformers allows to implement SVF (core of VCO) with 6 BJTs + 2 transformers instead of 14 BJTs + 2 opamps + 2 caps.
For free, it can even give you differential outputs for both phases (having all the 0, 90, 180, 270 degrees phases).

12-BJT current mirrors in analog multiplier may be probably replaced with a transformer as well. To be checked. But if so, instead of 19 BJTs, analog multiplier would have 6 BJTs.

I'm thinking about driving of theremin LC tank via transformer. In this case, it will not be required to have large power supply voltage to get kilovolts on the antenna...

Let's get rid of opamps, and create old school oscillator.

Strange unexpected finding with transformer based SVF VCO.
To lower the frequency it's necessary to raise control voltage.
For working ranges of theremin - 500kHz - 2MHz with normal currents (a few mA) it's necessary to have transformer with 500-1000uH inductance.

There are such transformers available like Murata 78615/2JC or 78615/8JC, but they cost about EUR 1.4
Planar transformer ferrite cores probably could boost inductance of PCB planar transformer, but such ferrites are hard to buy.
For the same price it's possible to add 2 BJT pairs and opamp instead.

Attempts to drive LC tank from transformer were unsuccessful as well.

The only case of transformer application in theremin AFE which makes sense is current sensing 5-10uH planar PCB transformer, which outperforms all other current sensing methods, and as well provides 90 degrees phase shift for free.
And the transformer itself is for free - just a PCB trace.

"The only case of transformer application in theremin AFE which makes sense is current sensing 5-10uH planar PCB transformer, which outperforms all other current sensing methods, and as well provides 90 degrees phase shift for free."  - Buggins

I'm playing around with pancake transformers in my t-coil program (https://d-lev.com/research/tcoil_v3_2025-09-25.zip):

I probably don't have the parameters exactly correct, and I can't interleave the windings like your PCB xfmr, but the coupling looks pretty good:

> xfmr: n[5]turns, wd[0.55]mm, wcd[0.15]mm, fd[12]mm, ow[1]turns, oo[0.55]mm, file[pancake]

  L Total       0.000621  0.000621 mH
  N Total              5         5 turns

  Wire Length     0.2317    0.2317 m
  Wire Mass      0.03669   0.03669 g
  Wire AWG          34.6      34.6
  Wire Cu Dia       0.15      0.15 mm
  Wire OD           0.55      0.55 mm

  Form Dia            12        12 mm
  Turns OD          17.5      17.5 mm
  Turns Layers         5         5
  Turns Height      2.75      2.75 mm
  Turns Width       0.55      0.55 mm
  Turns H/W            5         5 (x-section)
  Turns W/OD     0.03143   0.03143 (aspect)

  L/Wire Len        2.68      2.68 uH/m
  L Mutual     0.0003928 0.0003928 mH
  L Self       0.0002281 0.0002281 mH
  L M/S            1.722     1.722
  DCR             0.2203    0.2203 Ohms

  Gap                  0 mm
  LX Mutual     0.000967 mH
  L Total       0.002209 mH
  k               0.7787

> Wrote to file: pancake.scad

Having the windings interleaved and co-planar would most likely increase the coupling.

I probably don't have the parameters exactly correct, and I can't interleave the windings like your PCB xfmr, but the coupling looks pretty good
-- dewster

Interesting tool.
Have you placed two coils with big spacing between wires one above another on the same distance as inter-wire space to simulate case close to one when both spirals are in the same plane?
What if there is a PCB thickness distance between them (placed on front and bottom Cu layers) - does the coupling change significantly?
What if inter-coil distance is reduce twice, but both spirals are on different sides of PCB one on top of another?

According to your simulation, what inductive coupling coefficient should I use in LTSpice simulation? The default is 1, but what value should be specified in simulation to get closer to your simulation results?

"Have you placed two coils with big spacing between wires one above another on the same distance as inter-wire space to simulate case close to one when both spirals are in the same plane?"  - Buggins

That's what I did above, the one pancake right on top of the other.  But now that I think of it, I could interleave them by specifying the second former diameter as one wire with larger than the first former diameter:

Which gives a coupling k=0.9

> xfmr: n[5]turns, wd[0.55]mm, wcd[0.15]mm, fd[12]mm, ow[1]turns, fd2[12.55]mm, file[pancake]

  L Total       0.000621 0.0006528 mH
  N Total              5         5 turns

  Wire Length     0.2317    0.2403 m
  Wire Mass      0.03669   0.03805 g
  Wire AWG          34.6      34.6
  Wire Cu Dia       0.15      0.15 mm
  Wire OD           0.55      0.55 mm

  Form Dia            12     12.55 mm
  Turns OD          17.5     18.05 mm
  Turns Layers         5         5
  Turns Height      2.75      2.75 mm
  Turns Width       0.55      0.55 mm
  Turns H/W            5         5 (x-section)
  Turns W/OD     0.03143   0.03047 (aspect)

  L/Wire Len        2.68     2.716 uH/m
  L Mutual     0.0003928 0.0004144 mH
  L Self       0.0002281 0.0002384 mH
  L M/S            1.722     1.738
  DCR             0.2203    0.2285 Ohms

  Gap             -0.275 mm (COLLISION!)
  LX Mutual     0.001154 mH
  L Total       0.002428 mH
  k               0.9065

Coupling very much an "inverse distance squared" thing, even 0.5 mm between the coils above gives a k of 0.66

Interleaving PCB traces is probably a really good thing for minimizing the capacitance between the drive and sense windings as they present thin little edges to each other.

"Theremins are about the coils, and modern engineers forgot about them."  - Buggins

So true!  EE undergrad exposed me to the theoretical model of the transformer, but we didn't have any practical hands-on lab experience with them.  Much like so many things EE (which encompasses diverse multitudes!) there is limited time to be exposed to the basics during one's formal education, and hopefully that will be enough to take things further if one ends up designing switching power supply or similar.  Inductors aren't exactly the average EE's bread and butter, and they're fraught with complex non-idealities, so I get how most technical folks aren't exactly eager to deal with them.  And yes - Theremins are all about the coils!

Cloudland Revisited

Ran across the paper "How the Theremin Fell by the Wayside" by John Waymouth again.  I started a discussion about it here back in 2012 (!): 

http://www.thereminworld.com/forums/T/28532?post=192548#192548

Not trying to blow my own horn or anything, but I believe the D-Lev addresses almost all of the issues listed in that paper.

1. Theremin went missing, so for a long time there was no one promoting the instrument.
2. Few compositions written for it.
3. Lack of good instruments, RCAs were a limited run and quite expensive.
4. Which led to few able to teach the instrument (Clara's lament).
5. Requires great dexterity from the player.
6. Player must stand like a statue.
7. Requires perfect pitch, or very good relative pitch.
8. Lacks feedback / physical reference points.
9. It lacks timbre variation with volume.
10. Few creative deviations from intended use.
11. Sharp note attack difficult / impossible.
12. Thermal drift of fields.

We can't really do a lot about issues #1 thru #4 as they are historic in nature.  Though modern instruments can be made quite a bit less expensively.

Issues #5 & #6 can be greatly relieved by relaxing the pitch field.  I believe a reversed volume field would help noobs too.

Issue #7 can be largely addressed by using the built-in pitch correction.

As for #8, the player can get valuable real-time pitch feedback from the LED tuner.

issues #9 and #10 are addressed via pitch and volume field modulation of the DSP synth.

Volume field variable knee and velocity enable sharp percussive attacks of issue #11, and reversing the volume field gives a "drum" on the floor rather than on the ceiling.

Issue #12 is largely addressed with low tempco air core coils and digital phase locked oscillators.

The paper has many really interesting points beyond this, e.g. Theremin's return to Russia.