Here we are again with another post about the Theremin, which can be considered the first electronic musical instrument ever invented, almost 100 years ago, in 1919, by the Russian physicist Leon Theremin.

At that time the Theremin was made out of thermionic valves and used a lot of space and electric power.

Today, thanks to the evolution of electronics in the last century, we can make one that can occupy much less space while also consuming much less power. In fact, this is one of several articles that I have already published on the design and construction of such musical instruments, using solid state components.

Please consult this site archives for the previous articles on the subject and THIS link for schematics and diagrams, which I keep updating as I go in designing and building the pieces of the instrument

A corresponding series on the Theremin is also available on YouTube at THIS link. There, I describe every detail of my project, explaining how the various parts of the device work and how I built everything so far in a very inexpensive way.

In this article I will explore the **Mixer** stage of the Theremin, describing how it works and how it is used within the Theremin itself.

The mixer is the Theremin stage that combines together the signals from the pitch variable oscillator and the pitch reference oscillator, to create an audio signal that is essentially the sound that the Theremin produces.

The combination of the two input signals is done with a process called heterodyne. It basically consists in multiplying the two input signals by exploiting the non-linear characteristic of transistor Q1, which is carefully polarized outside its linear zone. The result of the multiplication is a new complex signal containing frequencies that are the sum and the difference of the frequencies of the original input signals. Since the frequencies of those input signals are close to each other, their difference falls in the audible range, which is what produces the peculiar sound of the instrument.

Looking at the schematic, you can see that the two input signals are mixed together at the base of transistor Q1, which they reach passing through capacitors C4 and C8, used to decouple the mixer from the direct current superimposed to the input signals.

Transistor Q1 is polarized in the non-linear zone of its characteristics. Because of the non-linearity of the transistor, the two signals end up being multiplied with each other, producing a new, more complex, signal that contains both the sum and the difference of the frequencies of the input signals. This heterodyne process, therefore, applies the following equation to the two input signals:

**sin(2πf _{1}t) * sin(2πf_{2}t) = 1/2 cos(2πf_{1}t – 2πf_{2}t) – 1/2 cos(2πf_{1}t + 2πf_{2}t)**

where the factors on the left side represent the two sinusoidal input signals, and the resulting complex signal is on the right side of the equation. The above formula is actually a simplification, because it does not take into account the phase shift between the two input signals, which should appear as a phase factor in the parameters of each of the sine waves on the left side of the equation. However, if we did the full calculations, we would see that we would still obtain the same output waves, but each would have an extra amplitude factor that depends on the initial amplitude of the input signals and on their phase shifts.

Anyway, the complex signal obtained at the collector of transistor Q1 is supplied to a Low Pass filter, made up of the components R4, R7, R8, R9, C2, C3, C5, C6 and C7. The filter produces an attenuation of the high frequency element of the complex signal, effectively leaving only the one at low frequency **cos(2πf _{1}t – 2πf_{2}t)**, which is the audio signal.

That output signal is then passed to the next stage of the Theremin, the VCA, where it acquires the dynamics of the music sound. We will talk about the VCA in a future post.

If you are interested in more information on the Theremin Mixer and how I built it, please watch this companion VIDEO on YouTube.

And, as always,

Happy experiments !!!