More on the Theremin: The Heterodyne Mixer

The heterodyne mixer is the stage of the Theremin where the high frequency signals coming from the pitch reference oscillator and the pitch variable oscillator are combined together to obtain the audio signal.

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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.

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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(2πf1t) * sin(2πf2t) = 1/2 cos(2πf1t – 2πf2t) – 1/2 cos(2πf1t + 2πf2t)

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(2πf1t – 2πf2t), 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 !!!

Behind The Scenes Of The Theremin Design

How I design my electronic circuits and prepare the videos to show them to you.

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Did you ever ask yourself where I get the schematics of the Theremin circuits and other gadgets that I present on my YouTube videos? The answer is simple: I do some research on books, on specialized magazines and on the Internet. I see solutions created by other people, if any, and then I think about what would better work for my case. Sometimes it ends up to be a modification of something that somebody else did, maybe for a totally different purpose. Sometimes, I just use the general idea to create something different, new, my own design that is more appropriate for my needs.

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Either way, I usually build a number of prototypes of what I need, then I take some measurements in lab, then I start making further modifications to my original design, until I obtain exactly what I am looking for.

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Also, more often than not, I figure that the circuit I am testing is too sensitive to certain parameters of the circuit itself. Maybe is a capacitor which value needs to be adjusted a little bit, or a connection between two or more components that causes issues because of capacitive or inductive coupling with other components. That is when I try to change my design to reduce such sensitivities, so that the circuit can be assembled by anyone with the exact same results as mine. And this is what is called engineerization, or adjusting the design for mass production.

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And sometimes, to do so, it is not enough to test the single circuit. Instead, I need to connect the circuit with other pieces that have to work together with it, and see if further unwanted interactions happen, so that I can eliminate them or, at least, reduce them so that they become negligible.

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Sometimes this process goes fast, sometimes takes a long time. And that’s why my videos are not published at fixed intervals. Unfortunately, since this is done only as a hobby, I don’t always have enough time to dedicate to my project, so days go by until, finally, I am done. Then I finalize my schematics, I build the last prototype and the final product and, in the process, I also record all these activities so I can end up making a video out of them.

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Then the video editing process starts and, once the video is finally ready, I release it on YouTube for you to watch it.

One day I will be able to do this full time. Who knows, maybe when I retire. Or, maybe, if you all give me a hand, this could become my new full time job (donations, donations, donations). We’ll see.

Thank you for reading this article. And, as usual, happy experiments!

Another Theremin Post

Announcing the new video on the design, implementation and testing of the power supply module of the Theremin.

You can find the video at this link.

Also, refer to the link on the right column about the Theremin project to find all the files so far published on the construction of this unusual electronic musical instrument (schematics, 3D designs, work art).

And, finally, don’t forget to look also at the other videos on my YouTube channel.