Category: voltage

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.

 

Electric Power Basics

electricity-3442835_1280

Power.

That is the word commonly used in every day language to refer to electricity. But what is really the electrical power?

To describe the meaning of electrical power, we need to dig into our knowledge of mechanical physics. In physics, power is the ratio at which energy is consumed or, in other words, is the number representing the energy used divided by the time needed to actually consume it.

Another way to say it is in terms of work. The energy consumed is, in fact, the work done on the system, so we can say that the power is the work done on the system in a certain amount of time.

In mechanical physics, the power is measured in Joules/Second, and the unit for it is called Watt, in honor of James Watt, a Scottish inventor, engineer and chemist of the 18th century that did a lot of work on the subjects of energy and power in mechanical systems.

power

Now that we have refreshed our knowledge on the concept of power, let’s see if we can find an equivalent way of defining it in the realm of electricity.

In terms of electricity, we need to consider the energy used to move the electrical charges, which is still a work, and it is done by the generator that powers the electrical circuit.

We know already how to measure the electric potential energy in electrical circuits: that is done by the voltage, which provides the energy per unit of charge:

voltage

From the voltage we can derive the energy itself:

energy

Now we have our energy consumed in the system to move the charges around. The electrical power is that energy divided by the time spent to use that energy:

el_power

Very interesting result, isn’t it? To calculate the electrical power we just need to multiply the voltage used to power the circuit by the current that flows into it. And, again, this power is measured in Watts, so the product of Volt and Ampere gives us the amount of watts used by the circuit.

Now that we have the formula for the power, it is easy to figure out how much power a generator provides when connected to a circuit. We just multiply the voltage of the generator by the current that is flowing through it.

And the power consumed by a load is the product of the voltage applied to the load and the current that flows through it.

Is the power provided by a generator the same as the one consumed by a load?

Well, in both cases we can measure it in Watts. However, in the first case the power goes out of the generator, while in the second case the power goes in to the load. We just need to establish a rule to make sure we can distinguish the direction in which the power flows.

We say that the power is negative when it goes out of a device and it is positive when it goes in.

So, in an electrical circuit with a generator and a load, the power is negative at the generator and is positive at the load. But the absolute amount in both cases is the same, and the sum of the two powers is therefore zero.

In fact, we have just verified the physics law of conservation of energy: in a closed system (the electric circuit), the total amount of energy never changes. The amount of energy produced by the generator equals the amount of energy absorbed by the load and, therefore, in any time interval (thus the power), the total is zero and never changes.

To conclude, we have talked about the electrical power. We have compared the way the power is calculated in mechanical systems with the way the power is calculated in electrical systems.

We have stated the rule to provide a sign to the power, and we have verified that this rule satisfies the law of the conservation of energy.

These concepts are general enough to apply to both DC and AC circuits. However, I will come back on these concepts in a future article to see how calculations are affected by loads having different electrical properties.

In the mean time, you can get some more information by watching the companion video on the Electrical Power that I recently published on my YouTube channel.

And, as always…

Happy Experiments!