Brandon Kaplan, Marketing Communications

Summary:

• The theremin was one of the world’s first electronic instruments and perhaps the only instrument you play without ever touching it.
• It uses two simple principles of physics and engineering, capacitance and heterodyning, to convert the musician’s movements into sound.
• While not itself an RF application, the theremin provides an excellent illustration of these concepts, which extend to most RF circuits and systems.

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We live in an electronic world. Leave it to critics and philosophers to debate whether that’s for better or worse, but if art is an expression of experience that’s unique to its time and place, there’s no getting around the fact that contemporary experience is always and increasingly electronic. Examples of art in the electronic age abound nowhere more than in music, where the electronic instruments and effects that appeared in Western popular music around the late 1950s have proliferated into a dizzying array of sub-genres ranging from mainstream electronic dance music (EDM) to experimental forms of sound art where artists, equal parts musicians and engineers, build all manner of esoteric instruments to create original sounds.

An acoustic instrument like a violin, for example, makes sound by vibrating a string which creates vibrations in the air within the audible range of the human ear. Electronic instruments work the same way, except instead of a string, they use an alternating electric current to make a speaker vibrate.  The theremin uses variations in capacitance in a circuit to modulate that alternating current and generate sounds of different pitch (frequency) and volume (amplitude).

At a basic level, the theremin works like the simple circuit shown below, called an “LC circuit,” consisting of an inductor (L) and a capacitor (C).

Illustration of a simple LC circuit.

When a DC voltage is applied to the circuit, a positive charge builds up on one side of the capacitor creating an equal and opposite charge on the other. As the capacitor charges up, the current flows through the circuit at a decreasing rate until the potential across the capacitor is equal to the source voltage. At the same time, the changing current in the circuit creates a changing electrical potential across the inductor until it exceeds that of the capacitor, at which point the current in the circuit changes direction. This process repeats itself indefinitely, causing the current to oscillate at a frequency, ω defined by the equation below:

where L is the inductance of the inductor and C is the capacitance of the capacitor.

Now, capacitance is a function of the surface area of the two conductive surfaces in a given capacitor (A) and the distance between them (d), as well as the permittivity of the dielectric between them, which is defined by the constant ε₀:

Substituting the second equation into the first, we get:

In other words, the frequency of the oscillation is directly proportional to the distance between the two conductive surfaces of the capacitor (or the square root of the distance of you want to be a stickler). The greater the distance, the higher the frequency.

The theremin is designed so that the vertical antenna works as one conductive surface of a capacitor, while the musician’s hand works as the other, and the air between them acts as the dielectric preventing the flow of current from passing through. By moving her hand closer and further from the antenna, the musician is effectively manipulating a variable capacitor, changing the capacitance value, which changes the frequency of the alternating current in the circuit and thus the pitch the instrument emits.

The problem is that the current oscillates at a frequency much higher than our ears can detect. The theremin mixes the current created by the musician’s movements with another internally-generated current to down-convert the frequency into a range we can hear. This process is called heterodyning, and it’s the same process a radio receiver uses to convert RF signals from the airwaves into that Beach Boys song I know you’re still listening to. A side effect of this process is that the frequencies get inverted so higher becomes lower and lower becomes higher.  That’s why the instrument produces a higher pitch when the musician’s hand moves closer to the antenna, opposite what the third equation above denotes. Similar principles apply to the horizontal antenna near the left hand, which controls the volume of the output.

The theremin is an ingenious application of relatively basic concepts in physics and electronics engineering to create an entirely new and original artform. Since its invention, the theremin has featured prominently in contemporary culture everywhere from classical to popular music, film and television to video game soundtracks. Next time you hear that ethereal hum on the radio, hopefully you’ll recognize it and have a greater appreciation for the combination of creativity and technical sophistication that went into the creation of a sound as unique as it is fitting for our electronic world.

And speaking of heterodyning, Mini-Circuits has one of the industry’s largest catalogs of RF mixers, now with RF/LO frequency ranges up to 65 GHz. Browse our full mixer selection >