Theremin v.2 Power Supply Design

theremin-v2-power-supply

For the new version of the Theremin, I have chosen to use a dual 12V power supply. This will have more flexibility because it will allow me to use more sophisticated units, possibly using op-amps.

The circuit is very basic: it uses a dual 14V transformer (not shown in the schematic) capable of providing 1.5A at its output.

A dual transformer is made up as in the following picture.

center-tapped-transformer

Is has a primary winding that is connected to the AC power supply outlet, and a secondary winding with a center tapped wire that is usually put to ground on the low voltage circuit side.

Voltage between either end wire of the secondary and the center tapped wire is usually the same (with the exception of specifically made transformers), which we call V.

The voltage measured between the two end wires of the winding is instead two times V or 2V.

Sometimes, instead of having a single secondary winding, we have two, carrying the exact same voltage. In this case, we can connect together the two closest wires and consider that as the center tapped wire. Then everything works as the first kind of transformer.

transformer-trans64

The AC current of the transformer is converted in to a DC current through the usage of a bridge rectifier and the capacitors C1 and C2.

The bridge rectifier converts the sine wave coming from the transformer into a fully rectified wave.

Full-wave_rectified_sine

Then, the capacitor that follows (in this case C1 and C2) starts charging over the ascending sides of the wave and discharging, partially, over the descending sides of the wave, basically filling the wave in between crests and making it look like more a straight horizontal line with some disturbance in it that we call ripple (the red line in the following picture).

ripple

In general, depending on the use of the power supply, we define a maximum value of the ripple that the circuit can handle.

In our case, we need to make sure that the voltage at the input of the regulators never goes below 14.5V, according to the data sheet, otherwise the regulator will not function properly.

The peak voltage provided by the transformer is its RMS value multiplied by the square root of 2, or:

peak_voltage

The minimum voltage we can have at the input of the regulator is:

regfulator_input_voltage

This is the max value of ripple that we can sustain.

To calculate the capacitor necessary to obtain this ripple, we use the following formula:

capacitance calculation

where f is the frequency of the alternate current which, in the USA, is 60Hz, and Ix is the maximum current that the power supply needs to provide.

So, we would need a capacitance value, for C1 and C2, of 2358uF.

However, the Theremin circuit will really not draw 1.5A from the power supply, so we can stay a little conservative, and use the closest value below the calculated one, which is 2200uF.

At this point we can safely say that the voltage on the output of the regulators will be exactly 12V (positive or negative, depending on the output side).

To further help the regulator, and preventing the current through it to go too close to the 1.5A threshold, where the regulator would not work anymore because the ripple becomes too high, we add to the output of each regulator another electrolytic capacitor, this one with a value at least equal to the capacitance value that we did not put at the input side. Since at the input side we put a capacitance of 2200uF instead of 2358uF, we will need a capacitor of at least 158uF.

However, to stay totally safe, I decided to use a capacitor at least 5 times higher, so I used the value of 1000uF for C3 and C4.

And finally, I added an extra capacitor (C5 and C6) to shunt toward ground any RF frequency that would travel back from the Theremin oscillators toward the power supply. A 0.1uF value is what is suggested by the data sheet of the regulator, so I used just that.

Why did I use this capacitor if there was already a 1000uF in there?

The reason hides in the way the electrolytic capacitors behave. In short, the electrolytic capacitors do not work well at high frequencies, so we need to add the extra 0.1uF capacitor, which is not an electrolytic one, to work in that range of frequencies. And since the range of frequencies is much higher than the one of the 110Vac outlet, a very small capacitance is enough to do the job.

 

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.

capacitor

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

schematic_symbol

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.

capacitor_and_battery

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.

capacitor_and_load

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:

energy

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.

capacitance

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.

spatiul-cosmic

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?

theremin_in_concert

‘Till the next time…

(Watch also the video on YouTube:  https://www.youtube.com/watch?v=jXCCT2xIWcA&feature=share)