Deep Dive into the Theremin v.2 Audio Amplifier

See YouTube video https://www.youtube.com/watch?v=90T0ZkN-oos&t=3s for further details.

audio_amp_schematic

The Theremin v2 audio amplifier and preview audio amplifier share the same schematic.

The input of the amplifier is on pins P1 and P2, where P2 is the ground connection. The input is supposed to be DC decoupled with a small electrolytic capacitor, as suggested by the data sheet of the integrated circuit TDA2003, which is the main component of this amplifier. However, the capacitor was not put in this schematic because it will find its place directly on the output of the audio generator stage. No reason to have two capacitors in series: one at the output of the audio generator and one at the input of the audio amplifier.

The signal coming from P1 goes to a voltage divider consisting of the resistor R1 and the potentiometer R2. When the potentiometer cursor is all the way toward ground, there will be no signal going to pin 1 of the IC and, therefore, the amplifier will be silent. When the potentiometer cursor is all the way toward resistor R1, the signal coming from P1 is divided exactly in half, since the value of the potentiometer R2 and of resistor R1 are exactly the same. This is the position where the volume will be the maximum possible.

I chose the value of 100K for both R1 and R2 so to have a relatively high impedance toward the audio generator, so its output won’t be affected by the movement of the potentiometer. At the same time, I wanted a value of R2 low enough to keep the input of the amplifier solidly on the ground when there is no input signal.

R2 is a logarithmic potentiometer, which means that its value changes according to a logarithmic scale. This is done to compensate for how we perceive the sound volume: the potentiometer increases the power of the sound wave in the opposite way as our ear perceives it. This way, we feel that the volume increases and decreases linearly when we turn the potentiometer.

The output from pin 4 of the IC goes to the loudspeaker through capacitor C3, which is used to prevent that a DC current goes all the way through. In addition, capacitor C5 and R6 provide a high pass filter that shorts to ground all the high frequencies that are not supposed to go to the loudspeaker. Values of capacitors C3 and C5 and the resistor R6 reflect the suggestion on the data sheet.

data_sheet_schematic

The power supply comes in through pins P5 and P6 and is filtered by capacitors C1 and C2.

C2 takes care of shunting toward ground any unwanted high frequency signal coming from/to the power supply. Capacitor C1, which is a high value electrolytic capacitor, is mostly used to boost the input current when the amplifier requires sudden increases due to peaks of the volume. These capacitors have also the values suggested by the data sheet.

The last part of the amplifier is the negative feedback loop, connected between pins 4 and 2 of the TDA2003. The loop is composed of capacitors C4 and C6, and the resistors R3, R4, and R5.

The negative feedback is used to limit the output power of the amplifier outside the region of frequencies where it is requested, thus preventing auto oscillations of the amplifier, which would otherwise behave like an oscillator.

The values of these components are again those suggested by the data sheet. However, C4 and R5, which correspond to Cx and Rx in the data sheet, are calculated based on the data sheet formulas visible in the above picture, where B is the maximum frequency of the signal that we want to amplify, which I set to 10kHz. I don’t believe we want to hear from the Theremin sounds that are above that frequency.

For further information on this amplifier and for a demonstration on how it works, please refer to my corresponding YouTube video.

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A Tester For Zener Diodes

Zener diodes are used for several purposes, from providing a reference voltage, to protecting sensitive circuits from being destroyed by the wrong input.

Today, I will show you how these diodes work and how to build a simple circuit to measure their most important characteristic, the reverse breakdown voltage. To know more on this topic, please watch the companion video posted on YouTube.

A zener diode looks like a regular diode and actually behaves as such when directly biased (positive voltage on the anode).

However, when inversely biased (negative voltage on the anode), a zener diode behaves in a completely different way.

Let’s take a look at its characteristic I-V diagram:

zener_characteristic

You can see that in the region of direct (or forward) bias, the zener behaves just like any diode. It also seems like in the inverse bias it behaves like a regular diode.  However, there is a big difference between the two.

For a regular diode, the reverse breakdown voltage is very high, in the order of 100V or more, sometimes much more. Such high that you never think at it when you use regular diodes, and you assume that with inverse bias the diode just does not conduct electric current.

For a zener diode, instead, the reverse breakdown voltage is low, in the order of one or two digit volts. Therefore, it is very easy in an electronic circuit to bring this kind of diode to reach the condition when it will start conducing electric current even if inversely polarized.

We actually exploit this behaviour to create reference voltages, or to provide a protection against unwanted voltages at the input of certain circuits, or a ton of other things.

The behaviour of a diode depends in fact upon the way it was fabricated, and in particular upon how it was doped. Regular diodes are lightly doped, while zener diodes are heavily doped. Depending on the amount of doping on both the P and the N side of the junction, the reverse breakdown voltage changes. That way, manufacturers can create zener diodes within a large range of breakdown voltages.

Problem is, manufacturers often don’t put the value of the breakdown voltage on the body of the components. Instead, they put some internal code or, sometimes, nothing at all.

So, if you had a number of such diodes on your workbench, how to distinguish them from one another?

Meet the zener tester.

It is a device that allows you to measure the reverse breakdown voltage, so you know if the diode works and what that voltage is.

How such a tester works? From the I-V diagram above, you can see that the characteristic of the zener diode is an almost vertical line when polarized in the reverse bias region. For any current value in that vertical line, the voltage is always the same and corresponds to the breakdown voltage. So, if we circulate a current at any point of that vertical line, we can measure at the terminals of that diode its breakdown voltage.

The zener tester I’m showing you today does just that: forces a current into the zener diode so we can measure the value of the breakdown voltage. We choose this current in such a way that it is high enough to stay away from the point where the characteristic is not linear, but low enough to avoid dissipating inside the diode a power that the diode itself cannot handle.

The following link allows you to download an archive containing the schematic of such device, along with the OpenSCAD code to 3D print the box for the device.

zener_diodes_tester_files

In the schematic you’ll see that I used a ready-made boost converter and a digital voltmeter. Here are the links to the store where I bought them. Of course you are free to use any other equivalent component. It will work as well.

BOOST CONVERTER

DIGITAL VOLTMETER

Please make sure to watch the YouTube video that completes the information I provided in this post. Between the two, you should have a complete view of the design of the device and should be able to build it.

Happy experiments!

 

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.

 

Theremin v.1 Pitch Reference Oscillator Analysis

This is my first post of this kind, which I plan to use to give insights on how an electronic circuit is designed. In the future, I plan to post a similar article for every new circuit I design and present on my YouTube channel.

This way, people who are interested in such details can go to this site to get them, thus sparing all the others that don’t care from watching them on the original video.

Today, to get started with the new series of posts, I will go into the insights of the design of the Pitch Reference Oscillator used in the Theremin version 1.

I decided to use the Pitch Reference Oscillator because all the other Theremin’s oscillators are based on the same principle, although for the variable ones, an antenna is added to the resonant circuit to make its capacitance increase based on the position of the hand on the player with respect to the antenna. In fact, the antenna adds up to 8pF to the resonating tank, based on the position of the hand of the player.

For reference, you can watch any of the YouTube videos on my channel related to oscillators in the Theremin Project playlist.

Here is the link to the playlist:

https://www.youtube.com/watch?v=moT9iAaZU-I&list=PL3SNC7XyKklYZOs48Qfh16nTO4t8edDPU

I began the design of the oscillator starting from the base concept of positive feedback amplifier, which can be represented as follows:

feedback_amp

We have an amplifier with a positive gain, which should be 1 when there is an oscillation, and we have a feedback impedance Zf that takes part of the output signal and brings it back to the input of the amplifier. Zf is supposed to be chosen to obtain a positive feedback at the oscillation frequency.

This basic configuration needs now to be modified to insert in it an LC resonating tank. This should be on the output of the amplifier, so its oscillations can be fed back to the input and be sustained with no decay.

oscillator_block_diagram

The amplifier can now be replaced with a real circuit made with a transistor. I choose in this case a common base configuration, which gives me the required gain of almost 1, which is enough to sustain the oscillation.

The Zf will need to provide a phase shift of 90° to compensate for the internal capacitance of the transistor, which will add another 90° for a total of 180°, thus providing a positive feedback, considering that the transistor has actually a negative value of amplification (-1).

Therefore, Zf can be replaced with a simple capacitor that will bring the output signal back to the input with the desired 90° phase shift.

And once all the polarization resistors are added, the circuit looks like the following:

oscillator

In this circuit, R2, R3, R4 and R5 are the polarization resistors, which are calculated based on the specs of the transistor itself.

L1, C4, C6, C7 constitute the resonating tank. The Two variable capacitors are added to allow for a fine tune of the frequency.

C5 is the feedback impedance, or Zf.

The resonating frequency is calculated based on the following formula:

resonating_frequency

where L = L1, and C = C4//C6//C7//CBE = C4 + C6 + C7 + CBE

and CBE is the capacitance between emitter and base.

Temporarily excluding CBE from the calculations, the frequency therefore can vary between 258.2 kHz and 312 kHz. The CBE can be obtained from the transistor data sheet, adjusting for the polarization between base and emitter.

Also, we can slightly affect the resonating frequency of the oscillator by changing the polarization point of the transistor. This can be achieved by a potentiometer added on the base of the transistor itself, as per the following schematic.

final schematic

All the other capacitors in the schematic are used to make the polarization point of the transistor independent from the oscillation frequency, by shunting the oscillation signal toward ground. Thus, their value is such that they behave like conductors with respect to the high frequency of the oscillator.

At the end, considering the increase in capacity given by CBE, the frequency ends up to be centered around 400kHz, which was the required frequency for the pitch reference oscillator.

DC Electronic Load V.3

Back in August 2018, I presented a DC electronic load on my YouTube channel (V.2). For that, I used an old 2N3055 transistor in a Darlington configuration with 2 more transistors to be able to get enough gain to use it.

100W_el_load_v2

Although declared useful for 100W, I was never able to make it work at those powers due to the limited dissipation capabilities of the power transistor and the heat sink. The max power dissipation I could have from that device was about 20W.

Today, at the anniversary of that presentation, I have created a new version of of the DC electronic load. This new version is based on a MOSFET that can work alone as a load, adjusting the current only through an appropriate voltage on its gate, avoiding the need of having a Darlington circuit with multiple transistors.

The schematic of this new version of the DC electronic load is based on a single MOSFET capable of driving the necessary current, up to 5A and a voltage divider connected to the battery, providing the appropriate voltage to the gate of the MOSFET.

electronic_load-v.3

In order to make it work correctly, the trim-pot RV1 needs to be tuned to obtain a voltage of 1.5V on pin 3 of the potentiometer that regulates the amount of current flowing through the MOSFET, which provides a better use of the multi-turn potentiometer that regulates the actual value of the current.

A combination of digital voltmeter and am-meter, like in the previous version of the DC load, takes care of providing information about the power supply under test.

The device is powered through a 9V battery and it is connected in such a way that the voltage is measured through the yellow wire of the digital voltmeter, wile the current is measured putting the am-meter in series with the MOSFET, with the thick red wire on the source, and the thick black wire toward the negative connector, through a 5A fuse that is used, mostly, to protect the am-meter itself against currents too high of those it can handle.

I made a new case for this new version of the DC load. The main difference is the location of the heat-sink, which is now located on the back panel rather than the top of the device. The new heat-sink is also attached to the back panel through 4 separators, which allow for a better air flow and cooling of the unit when it is used for long period of times.

Here is an OpenSCAD view of the box and the corresponding code to create it.

v3_box_view

$fa=0.5;
$fs=0.5;

//main section
rotate([180, 0, 0]) translate([0, 10, -2])
{
// front panel
difference()
{
cube([150, 80, 2]);
translate([27.5, 40, -1]) cube([45.8, 27.7, 4]);
translate([52, 20, -1]) cylinder(d=6.2, h=4);
translate([120, 60 , -1]) cylinder(d=9, h=4);
translate([108, 20 , -1]) cylinder(d=9, h=4);
translate([132, 20 , -1]) cylinder(d=9, h=4);
translate([3,3,0.5]) linear_extrude(height=2) text(“eleneasy.com – DC load – 25W max.”, size = 6);
translate([36,18,0.5]) linear_extrude(height=2) text(“off”, size=5);
translate([61,18,0.5]) linear_extrude(height=2) text(“on”, size=5);
translate([109,44,0.5]) linear_extrude(height=2) text(“current”, size=5);
}
translate([102.25, 15, 0]) cube([2, 10, 2]);
translate([126.25, 15, 0]) cube([2, 10, 2]);
translate([111.75, 15, 0]) cube([2, 10, 2]);
translate([135.75, 15, 0]) cube([2, 10, 2]);
translate([12, 20, -36]) cube([27, 2, 35]);
translate([39, 4, -36]) cube([2, 18, 35]);

// left panel
translate([0, 0, -60]) cube([2, 80, 60]);

// right panel
translate([148, 0, -60]) cube([2, 80, 60]);

// bottom panel
translate([0, 0, -60]) cube([150, 2, 60]);

// top panel
translate([0, 78, -60])
{
cube([150, 2, 60]);
}

// screws supports
translate([2, 2, -58]) difference()
{
cube([10, 10, 58]);
translate([5, 5, -1]) cylinder(d=2, h=16);
}
translate([138, 2, -58]) difference()
{
cube([10, 10, 58]);
translate([5, 5, -1]) cylinder(d=2, h=16);
}
translate([2, 68, -58]) difference()
{
cube([10, 10, 58]);
translate([5, 5, -1]) cylinder(d=2, h=16);
}
translate([138, 68, -58]) difference()
{
cube([10, 10, 58]);
translate([5, 5, -1]) cylinder(d=2, h=16);
}
}

// back cover
translate([0, 10, 0]) difference()
{
cube([146, 76, 2]);
translate([5, 5, -1]) cylinder(d=4, h=4);
translate([5, 71, -1]) cylinder(d=4, h=4);
translate([141, 5, -1]) cylinder(d=4, h=4);
translate([141, 71, -1]) cylinder(d=4, h=4);
translate([73, 38, -1]) cylinder(d=40, h=4);
translate([126, 60, -1]) cylinder(d=12.5, h=4);
translate([130.5,51,0.5]) rotate([0, 0, 180]) linear_extrude(height=2) text(“5A”, size=5);
translate([(146-55)/2, (76-50)/2, -1]) cylinder(d=4, h=4);
translate([146-(146-55)/2, (76-50)/2, -1]) cylinder(d=4, h=4);
translate([146-(146-55)/2, 76-(76-50)/2, -1]) cylinder(d=4, h=4);
translate([(146-55)/2, 76-(76-50)/2, -1]) cylinder(d=4, h=4);
}

Assembling the circuit is pretty straightforward, and it is done partially in the air and partially  on a perforated board.

We just need to make sure we provide the cables with the right thickness for the current we need to support.

In my case, I used stranded cables with an 18 gauge. These cables are necessary between the thick am-meter cables, the MOSFET source and drain, and the external connectors.

Every other connection can be made with 22 gauge cables.

And finally, the heat-sink should have a resistance of 0.82 Centigrade degrees per watt or less, to prevent the MOSFET from becoming too hot. Note that this will not save the MOSFET in case you draw a current too high. The product between the current and the voltage as provided by the measurements display must never exceed 25W, and the current should never exceed 5A, or the MOSFET will burn.

The tuning is done by measuring the voltage between the terminal 3 of the potentiometer and the ground, with the circuit on, but not connected to any external power supply. The trim-pot has to be adjusted such that the measured voltage equals 1.5V, which is just below the minimum voltage necessary to make the MOSFET conduct current. This way, when turning on the apparatus with the potentiometer all the way to the counter-clockwise position, there will be no current. Then, moving the potentiometer in the clockwise direction, current will start flowing.

Testing of the unit is done attaching it to a power supply that provides different test voltages while we adjust the current with the multi-turn potentiometer on the DC load unit. Just make sure not to exceed 25W of power at any given time. Doing so could damage the MOSFET itself.

I plan to use this DC load in all my future projects that require a power supply of 25W or less, to test the power supply itself. Besides checking that the power supply works fine, you could also check that the ripple of the output voltage does not exceeds your requirements. That can be done connecting the power supply output to an oscilloscope while the DC load draws the current.

And finally, here are a couple of picture of the finished device.

20190816_112540.jpg

20190816_112614

Happy experiments!

 

Conductors, Insulators, and Semiconductors

cpu-3061923_1280

Everybody knows that an electric wire, usually made of copper, is a conductor. And everybody knows that all metals are conductors.

copper-72062_1280

Everybody also knows that plastic is a good electrical insulator, as well as other materials such as glass and rubber.

insulators-3838730_1280

But how about semiconductors? What are they? And how do we really distinguish among conductors, semiconductors and insulators?

To answer all these question we need to look deeper inside the materials.We know that matter is made of atoms, and atoms are made of protons, neutrons and electrons. Protons and neutrons reside at the center of the atom structure, called the nucleus. Electrons are allocated all around the nucleus, at a long distance from it, relatively to the scale of the nucleus itself.

Electrons have a certain amount of energy, that is always an integral value of a certain amount that is called quantum of energy. Depending on the amount of energy they posses, they are locate closer or farther away from the nucleus. The more energy, the farther they are.

Based on quantum mechanics, which we are not going to talk in details in this context, electrons occupy bands of energy. The farther bands in the atom are the so called Valence Band and Conduction Band.

The valence band contains all those electrons that allow the atoms to stick together and forming molecules by bonding with other atoms of the same or a different substance.

water-40708_1280

For certain materials, rather than having molecules, the atoms form what is called a crystalline lattice, which is the case we are more interested in this context. It is worth noting that a new theory, highly based on quantum mechanics, is also distinguishing between actual crystalline lattices and material networks. However, for all the scope and purpose of this context, we will make a simplification and name both of them as crystalline lattices.

lattice(This picture, courtesy of Wikipedia)

In certain conditions, electrons in the valence band can jump to a higher level of energy, thus moving in what is called the conduction band. In the conduction band, electrons are no more stuck to their own atoms, but can start moving freely in the lattice that makes up the material. When that happens, we can control their movement by applying an electric field by the means, for example, of a battery. The voltage of the battery, applied to the two ends of the same block of material (for example a wire), produces the electric field inside the material and forces the electrons to move toward the positive electrode of the battery while, in the mean time, the negative electrode of the battery provides electrons to the material, to replace those that have entered the positive electrode of the battery.

Don’t think that electrons move very fast when they do that. Electrons, in fact, move very slowly, but it is the huge amount of them that help creating a measurable current.

Then you would ask: but when I turn the switch on, the light comes out of a lamp instantly. If the electrons move slowly, shouldn’t a lamp emit light only after a while?

lamp-18869_1280

Well, yes and no. In fact, the lamp does not light up immediately. It takes a certain amount of time to do that. But that time is so small that for us the event happens instantly.

Also, when you turn the switch on, the electrons closest to the positive electrode move into it almost immediately, not because they are fast, but because they are so close to it. At the same time, new electrons are fed to the material from the negative electrode. So, at the end, all the electrons in the wire start moving simultaneously inside of it, causing the current to start flowing immediately.

But I am digressing. Let’s go back to our primary subject.

We have talked about electrons in the valence band and the possibility they have to jump to the conduction band and, thus, helping creating a current if we apply a voltage.

But how much energy do the electrons need to jump to the conduction band?

Here it comes the definition of conductors, semiconductors and insulators.

conductors_semiconductors_insulators

In the materials called conductors, the level of energy that the valence electrons need to jump to the conduction band is basically ‘0’. In fact, valence band and conduction band overlap each other and, therefore, some or all the electrons in the valence band are also, already, in the conduction band. This happens mostly with metals, like copper, iron, aluminum, and so forth. Depending on the particular metal, the conduction and valence bands are more or less overlapped. Those material where there is more overlap are those that conduct electricity better. Those material where there is less overlap, are those that are worst to conduct current, although still conductors.

In the materials called insulators, the gap between the valence band and the conduction band is so high that electrons cannot jump from the valence band to the conduction band, and so they cannot generate an electrical current.
Of course, if we apply a voltage high enough, we can still provide them the energy to make the jump. However, in that case, because of the very high voltage, electrons jump from one band to the other in a disruptive way, causing the material to break. Once that happened, the insulator loose its property and it is no good anymore as such.

Finally, in the materials called semiconductors, the valence band and the conduction band are separated, but close together. It is relatively easy for an electron in the valence band to jump to the conduction band if we only heat a little bit the semiconductor, maybe just with our bare hands. The heat provides enough energy to the electrons to jump to the conduction band. However, not many electrons will do so, unless we keep heating the semiconductor. So, at the end, although capable of conducting some current, semiconductors are not good in doing so. Thus the name of their category.

In this article, we have talked about energy bands in materials, and how materials behave based on the position of the two highest energy band levels.

We have said that conductors are those were valence and conduction bands are partially overlapping.

Conversely, insulators are those that have a high gap in between the valence and the conduction bands.

And finally, semiconductors are those somewhat in between. For them, the valence and conduction bands are separated with a gap, but that gap is small enough to allow, under certain conditions, for the electrons to jump from the valence to the conduction band. That’s why they perform poorly both as conductors and insulators. However, we will see later on how semiconductors can be of great advantage for us, as long as they are treated in a certain way. They are those that allow us to build all the wonders of modern electronics.

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!