The theremin is a unique electronic musical instrument that one plays without touching. Traditionally, the theremin consists of a box and two metal antennas that create an electric field. Each of the performer’s hands forms with one of the antennas a capacitor. As the player moves their right hand in the vicinity of the vertical antenna, the capacitance of the field varies with the distance between their hand and the antenna, changing the frequency of a resonant pitch circuit inside the box. The vertical antenna is thus used for controlling pitch. On the other hand, the movement of the left hand in the vicinity of the loop antenna controls volume by changing the control voltage of the volume circuit.

For this project, we will focus on building just the pitch circuit of the theremin and delegate volume control to an external speaker. We will get to learn about several main components of the pitch circuit: fixed pitch oscillator, variable pitch oscillator, mixer, amplifier and low-pass filter. We will also design a wooden box that holds all electronic components. Then, we will put all parts together, along with a power supply and a speaker, tune the theremin to the audible frequency range, and play!

Disclaimer: We followed the instructions in “Physics of the Theremin” by Skeldon et al. (1998) and added our own modifications.

Acknowledgments: We would like to acknowledge and thank our Professor Janice Hudgings, Mark, and Hardy for all the work they put in to help us make our vision of our theremin come to life. Additionally, we want to thank our Electronics classroom for supporting us in our journey, especially when it came to us tuning our theremin (it got pretty loud and high pitched at times.) Lastly, our thanks goes to the Pomona Physics Department for always inspiring us to take our projects a step further and for always supporting us in every way possible!

Supplies

Resistors:

47 Ω x 1

100 Ω x 4

330 Ω x 2

1 kΩ x 3

3.3 kΩ x 2

4.7 kΩ x 2

10 kΩ x 3

22 kΩ x 2

100 kΩ x 2

Capacitors:

15 pF variable capacitor x 1

33 pF x 2

100 pF x 2

1 nF x 3

10 nF x 2

15 nF x 1

1 μF x 2

1.5 μF x 2

22 μF x 2

47 μF x 2

*More capacitors in the 10–200 pF range will help tune the theremin.

Other parts:

1 mH inductor x 2

BFY51 transistor x 2

JFET 3819 transistor x 2

Op-amp x 1

Pitch antenna (brass rod ~40–50 cm long, ~5 mm in diameter) x 1

SBL-1 frequency mixer x 1

+12 V and -12 V power supply, as well as a ground x 1

Insulated box (we chose wood) x 1

Step 1: Building the Pitch Circuit

Here is the circuit diagram we will use for building the pitch circuit. It looks insane at first glance… don’t fret over its complexity! We promise it will make sense. Broadly speaking, the pitch circuit consists of a fixed pitch oscillator, a variable pitch oscillator, a frequency mixer, and an active low-pass filter. The fixed and variable pitch oscillators are almost exactly the same. The outputs of these two oscillators are two pure sine waves of slightly different frequencies in the radio range (~0.5 MHz). The SBL-1 mixer multiplies these two signals, producing an output voltage that can be written (via trigonometric identities) as a term that oscillates at a high frequency (the sum of the oscillator frequencies) added with another term that oscillates at a much lower frequency (the difference of the oscillator frequencies). We can use an active low-pass filter to get rid of the signal at the sum frequency, leaving only the signal at the difference frequency, which is in the audible range. More details about the math can be found in Skeldon et al. (1998) (linked in the introduction).

The active low-pass filter also serves to amplify the output signal of the mixer and send the audio output to a speaker. We want to use a speaker that has its own volume controller so that we don’t need to build a separate volume circuit. If you fancy building a volume circuit, though, you should look at Skeldon et al. (1998) – the design of that circuit is very similar to that of the pitch circuit, so it shouldn’t be hard to build once you understand the workings of the pitch circuit!

Now, you may ask yourself, how does this circuit control the pitch of the theremin’s audio output? The answer lies in the very subtle difference between the fixed and variable pitch oscillators. The fixed oscillator, as its name suggests, produces a signal of a fixed radio frequency. There’s a variable capacitor in the fixed oscillator that allows you to tune this fixed frequency, but other than that, this oscillator does not respond to the movement of your hand around the pitch antenna.

Meanwhile, the variable oscillator is connected to the pitch antenna and hence produces a signal of a radio frequency that varies with the distance between your hand and the antenna. The pitch antenna is connected to an LC resonant circuit, and it is this LC circuit’s resonant frequency that can be modified. Initially, the resonant frequency of the variable oscillator matches the resonant frequency of the fixed oscillator. Your hand, which is an electrical conductor that is grounded by its connection with the rest of your body, forms with the pitch antenna a variable capacitor, such that movement of your hand toward the antenna changes the antenna capacitance very slightly (by just a few picofarads). Variation in the antenna capacitance changes the resonant frequency of the variable oscillator’s LC circuit. Since both the signals produced by the fixed and variable oscillators have very high frequencies in the radio range (~0.5 MHz), a few picofarad difference in capacitance can vary the difference frequency by a kilohertz, which is a noticeable variation in pitch in the audible range.

Each oscillator has a bipolar junction transistor (BJT), its base connected to an LC resonant circuit and a voltage divider powered by a +12 V DC supply, that produces a high-frequency radio signal. We recommend building the BJT portion of each oscillator first and display the transistor’s output at its collector with an oscilloscope to ensure that you’re getting what you expect – a sine wave signal oscillating at ~0.5 MHz. The BJT’s output is then passed through a junction field-effect transistor (JFET), which buffers the signal so that it can be safely fed into the frequency mixer. Again, check the output of each oscillator’s JFET buffer on the oscilloscope screen – it should look exactly the same as the output from the BJT step.

Finally, feed the two oscillator signals into the frequency mixer and build the op-amp amplifier and low-pass filter. Check the output of each step – the harmonic signal that comes out of the mixer should have a high-frequency component riding on top of a low-frequency component, and the signal that comes out of the op-amp amplifier and low-pass filter should retain only the low-frequency component. Connect this final output to a speaker to convert the electrical signal into sound. Now you’re ready to move onto the next step – building a theremin box!

Step 2: Building the Box

A beautiful circuitry must have a beautiful house to go along with it! That is why we chose a wooden box to store our circuit and hold our pitch antenna. You can really choose any protective insulative space to store your theremin circuitry and you could even add a personal flare or design to it. The material must be insulative because if it is conductive, it will affect the pitch antenna by having the box be the “capacitor plate” instead of your hand. If you prefer not to use a wooden box and go with another design such as a plastic box, you may omit this section and fast forward to the “Drilling Holes” subsection. We will now explain and give instructions about the building of our chosen design for our wooden box.

The Wooden Box

The design of our box is a treasure chest design that has a hinge at around the ¾ mark of the box to swing open the top to show our circuitry. Our basis of wood is plywood, which we used to construct the whole box except the pins of the hinges which were made out of a skinny piece of metal that we found, so we are unsure of the actual metal material so any should be fine. You could also design this box with other materials such as acrylic as long as it is compatible with your laser cutter.

We decided on a jigsaw design for our box where each side would fit into each other through the little jigsaw legs. We were able to do this design due to the lovely help of Pomona College’s Machinist who helped us use a pre-made program for the jigsaw box on a laser cutting machine. If you have access to a laser cutter, there are premade programs for boxes such as ours which can be found in different websites by just looking up “hinged laser cut box.” For ours, as mentioned previously, we went with the treasure box design where even the hinges were printed (excluding the pins for the hinges as the pins had to be cylindrical and of the length of the 5 hinges together).

Once you have the pieces of wood, it is time to put them together. Due to the design of the wooden sides, you essentially put them together as a jigsaw puzzle. It might be a little hard to piece it together due to discrepancies with the laser cutter, but if need be, feel free to sand the wood a bit to make it fit better. Once you have the pieces built together, super glue the inside to ensure that the sides stay together as we want a safe and reliable house for our theremin circuitry. Additionally, you should attach the hinges in the correct spot to the bottom half of the box and the top half of the box, but before attaching make sure the metal pin is inside the hinges. Once all of this is done, you have your box which will house your circuitry!

The Wooden Block

We decided to have the theremin antenna in a separate wooden block which we would wood-glue to the side of our theremin box. We drilled an L-shaped hole into the rectangular block from the top and exited out one of its sides. We soldered the antenna with some wire that would connect directly to the circuit and place the whole thing so that the antenna would be emerging from the top side of the block and the wire emerging from the side of the block.

Drilling Holes

We drilled a few holes in the box to have successful connections with everything. The first hole we drilled was the hole that would connect the antenna block to the inside of the circuitry. This hole is special because it must go parallel with the hole we drilled on the block so the antenna connection could thread successfully into the circuitry. Then we also drilled a hole for the speaker connection since we used an exterior speaker with a volume output knob of its own. And we also drilled a hole for the actual power supply which also connected directly to the circuit.

Step 3: Putting It All Together

Now that we have our house for our theremin, it is time to put the circuitry in the box. If you did not solder your circuit and use a raw breadboard like we did, this has to be done with extreme precaution as one mistake could lead to the destruction of all your hard work constructing the circuit. First, you must disconnect the power supply, the speaker, and the antenna. Next, you are going to want to carefully pick up the breadboard – or multiple breadboards if you decide to build the different circuit components in different breadboards and if so you might need multiple hands to do this – and place it in the box. Now you must reconnect the power supply, the speaker, and the antenna by threading them through the holes we have drilled in the box and connecting them to their corresponding places in the breadboard inside. Lastly, secure your breadboard by gluing it down with double-sided tape or any adhesive of your choosing to the bottom of the box. Voila, visually and aesthetically, you are at the end of the road for the construction of your theremin!

Step 4: Tuning

After we finish building the fixed and variable pitch oscillator, the mixer, the amplifier, and the box, we are ready to tune the theremin. Ultimately what we want is for the mixer to produce a frequency in the audible range, that is, 20 Hz to 20 kHz.

If you have an oscilloscope, you can check the frequency passed into the mixer by each pitch oscillator separately, and you will find they are almost half a million hertz. How then do we tune this input frequency into the audible range? Well, the mixer works by outputting the multiplied waveform of the two input waves, thus producing two frequencies, with the one we are interested in as the frequency difference between the two input waves. In other words, as long as we get the two input frequencies (from the fixed and variable pitch oscillators) very close to each other, we can significantly lower the output frequency to the audible range!

Thus, to tune the theremin, we want to tune our two input waves to similar frequencies. Now, remember that each input frequency is determined by the resonant frequency of the LC circuit in the respective oscillator, and that resonant frequency is determined by the total capacitance in the LC circuit. For starters, connect the speaker to the final output and turn the knob on the variable capacitor. In the best-case scenario, you will be able to hear a sound when the capacitance is tuned to the right place. Otherwise, you might need to tweak the circuit by adding to or subtracting from the total capacitance of the fixed oscillator’s LC circuit. Follow these rules:

To add to the total capacitance, switch out the current capacitor for one with a larger capacitance, or add another capacitor in parallel with the current capacitor.
To subtract from the total capacitance, switch out the current capacitor for one with a smaller capacitance, or add another capacitor in series with the current capacitor.

Hopefully, by changing the capacitance of the LC resonant circuit of the fixed oscillator, a sound will eventually come out of the output, and it will change pitch when your hand moves closer or further away from the antenna. See the video for a demonstration. Yay!