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.


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(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 !!!

Capacitors – Part 1

A brief introduction to capacitors: what they are, how they are made, and their basic functionality.

capacitorsA capacitor is an electric device capable of storing energy in the form of electric charges (electric field).

In the most simple form, a capacitor is made of two conductive plates facing each other and an insulator in between, which is normally called a dielectric. The two plates are then attached to wires, that are used to connect the capacitor in an electric circuit.


The schematic diagram reflects exactly the physical nature of the device:


When a capacitor is connected to a power supply, like a battery, electrons leave the plate that is connected to the positive side of the battery, while the same amount of electrons is pushed into the plate connected to the negative side of the battery. Once the difference of charges at the plates of the capacitor is enough to establish a voltage on the capacitor that is identical to the battery, electrons stop moving around the circuit and an equilibrium is reached.


At this point, if the connection with the battery is severed, the capacitor will retain the amount of charges on its plates: extra charges on the negative plate and defect of charges on the positive plate. If we connect a load to the capacitor, for example a resistor, charges will start moving in the circuit pushed by the voltage at the wires, called electrodes, of the capacitor. So, electrons will leave the negative plate moving toward the load, and an equal amount of electrons will move from the load into the positive plate of the capacitor. The movement of the electrons causes the voltage at the plates of the capacitor to lower until, when an equilibrium of charged is reached, the voltage will be zero and the current will stop flowing through the circuit. At this point all the energy that was stored in the capacitor has been used and the capacitor is said to be discharged.


Both during charge and discharge, the ratio between the amount of charge stored on the capacitor and its voltage remains constant. This can be verified experimentally. We define this constant as the capacitance of the capacitor:

C = Q / V

which is measured in Farad. However, since the Farad is a very big unit, capacitors are normally measured in fractions of Farad, like microFarad (μF, 1 millionth of a Farad)), nanoFarad (nF, one billionth of a Farad), and picoFarad (pF, one trillionth of Farad).

Using the above formula, and calculating the work done to move the charges in and out of the capacitor with the help of some calculus, we can determine the energy stored in a capacitor as:


And, finally, the actual capacitance can also be determined by the physical parameters of the capacitor itself. We can see experimentally that the capacitance is directly proportional to the area of the plates of the capacitor, it is inversely proportional to the distance between the plates, and depends on the type of dielectric in between the plates. The type of dielectric is identified in the formula by the Greek letter ε (epsilon). Each type of dielectric has its own value of ε (permittivity), which is the product of the vacuum permittivity and the relative permittivity of the material.


For more information on this subject, please look also to the corresponding video on my YouTube channel.

Looking At The Future

An overview of the next subjects I will explore in my blog and my YouTube channel.


No, not the future of the human race! Not even the future of the space exploration!

I’m just talking about my plans for future posts on this blog and on my YouTube channel.

I observed that people tend to look mostly at short videos and, when they are too long, watchers soon give up. I attribute this to the fact that people watches YouTube videos in a different way than TV shows and, while TV shows may be long, that is not true for the majority of videos on YouTube. The expectations are just different.

So, rather than proposing long videos that exhaust a subject in all its details, and just gliding over it, it is probably better to have short videos that concentrate on a single detail of the subject. Then I could have several episodes on the same subject, each concentrating on a different detail and made in such a way that someone could watch a specific episode without the need to watch all the previous ones..

Looking back at the resistors video, it could have probably worked better if I had split the video in several pieces, one with the general information, one just for resistors in series, one for resistors in parallel, and so forth.

I could basically have several episodes on different aspects of the same subject!

Based on this assumption, I will publish in the next few weeks several episodes centered on two primary subjects: the capacitor and the inductor, to complete the overview of all the passive components used in electronics. And, maybe, in a later future, I could also provide a number of videos where I show how these components can be used together, and what kind of circuits can be created.

Please let me know what you think of this new setup of my channel by writing a comment. Should I just keep going the way I started? Or should I move on with shorter videos, centered on specific details of a subject? Would this help those people that are only interested in specific details and don’t want to listen to the whole spiel?

Before I go, I would like to finish by introducing a new subject that is very dear to me: I plan to build a functioning Theremin for myself (I play musical instruments as a hobby). It is going to be a complex project, so it wll take some time, but I plan to upload several videos on the progresses I make, until the project is completed. I will also publish the whole design of the instrument, so brave followers can try to build one for themselves too. And, maybe, I could also upload my own performance with the instrument, once completed, playing just some simple tune. Anyone interested?


‘Till the next time…

(Watch also the video on YouTube: