Conductors, Insulators, and Semiconductors

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

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

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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.

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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?

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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.

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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.

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Electric Power Basics

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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.

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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:

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From the voltage we can derive the energy itself:

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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:

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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!

Let’s Talk About Voltage

What is voltage? Where the name comes from? How it makes electric current flow?

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Voltage is a very common word in the context of electrical and electronics engineering. However, common as it is, it is a concept that is often not fully understood.

How many people know that voltage is a concept related with potential energy? The same kind of energy that is so often used in mechanical physics!

When we talked about electrical current in the previous post, we said that current moves from a higher electrical potential energy to a lower one. We also defined the current as the flow of positive charges moving from the positive electrical potential energy to the negative one.

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In order for the charges to move, there has to be a force that puts them in motion in a specific direction. Such force will have to do some sort of work on the charges and the work done by the force can be translated in a change in energy of the charges.

We define Electromotive Force the ratio between the energy change of the charges and the amount of charges. This can be represented with the following formula:

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Note that, despite the name, the Electromotive Force is not a force in the mechanical sense. Instead it is a potential energy per unit of charge, which we also call electric potential, or just potential.

The unit for the emf is called Volt, and is the ratio between one unit of energy, or 1 Joule, and one unit of charge, or 1 Coulomb:

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And that’s where the name voltage comes from: it is a name derived from the measurement unit of the electric potential. Although the correct name is electric potential, to make things easier in the day to day talk, we just call it voltage.

So, again, what is voltage? The voltage is the difference of electrical potential energy that allows a unit of charge to move and produce a current.

Now, do you think it is correct to say that when there is voltage we have a current? Do the two things always go together? Well, the answer is no. You can actually have one without the other.

An example of voltage without a current is the battery. If you don’t connect the battery to a circuit, there is no current involved!

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And what about the current? This example is definitively less intuitive. So, let’s just say for now that if we force a current in a ring of a special material called superconductor and then we remove the cause that generated the current, the current keeps flowing in the superconductor, even in the absence of a voltage. Maybe we can explore this concept a little more in a future post, if I see there is an interest for it. Translation: let me know what you think! Comments are always welcome!

superconductor_ring

Let’s now go back to the battery. The battery provides a voltage between its positive and negative poles. With that, if we connect the battery to an electric load, current starts to flow immediately and the higher the voltage the greater the amount of current (more on that in a future post).

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Like the current, there are two forms of voltage:

  1. The DC voltage

  2. The AC voltage

The DC voltage is the one typically provided by batteries. It is a voltage of a fixed value and of fixed polarity. The plus and minus on the electrodes of the battery never change. One electrode will always be the positive one, and the other electrode will be the negative one.

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When we connect a battery to an electric circuit, we have a flow of DC current.

The AC voltage is the one created for example in the power plants and provided at the wall outlets in your house.

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The voltage at the outlet is not constant as the one in the batteries. Instead, it changes continuously following the shape of a sine wave. Because of that, the polarity at each electrode of the outlet changes over time from positive to negative and vice versa, following the shape of the sine wave.

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When we connect a device to the electric outlet, the current that will flow through that device will be an AC current as well.

The sinusoidal shape of the AC voltage depends on the way the electricity is generated. In the power plants there are devices called alternators, a much bigger version of those that you can find inside your car to recharge the battery, or on a bike, to provide electricity to turn on the lights at night.

Depending on the power plant, a different kind of energy is used to put in motion the alternator. It could be fossil fuel or nuclear energy that heat a reservoir of water and create the steam that makes the alternator rotate.

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Or it could be the rotation of a propeller-like device that is put in motion by the wind.

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Whatever the source is of the mechanical energy, the alternator converts that energy in electrical energy. But, since the rotation translates into a sine wave when described on a Cartesian reference system, the resulting electrical energy acquires that shape too.

DC and AC are both necessary to us to power devices that make our lives easier. Some devices need to be powered with DC, others need the AC.

DC voltage is necessary, for example, to power electronic devices: your smartphone or radio or computer, for example.

AC voltage is used to transmit the electrical energy from the places where it is created to the places where it is used. When AC reaches our home, it can be used as is to power electric motors like those in the refrigerator or the washing machine, or other household appliance. Or it can be converted to DC to power other devices, like your TV set.

Summarizing:

  1. To generate a current, we need to provide some energy to the charges in the conductor.

  2. The potential energy per unit of charge is called emf, or electromotive force. That measures the capability of the generator (a battery, for example) of generating a current.

  3. Most used synonyms of the emf are: voltage, difference of potential, and potential. Somebody also uses the name “tension”.

  4. The measurement unit of the potential is the Volt, which is the potential energy of 1 Joule per unit of charge, or 1 Coulomb.

  5. The Volt is a differential measure, not an absolute one. You always measure Volts with respect to a point that we arbitrarily define as 0V, or ground.

  6. Emf can be DC or AC and, correspondingly, it can generate a DC or an AC current when connected to an electrical circuit.

  7. DC voltage is normally generated through chemical reactions in a battery, or can be obtained from the AC through a process called “rectification”.

  8. AC voltage is normally generated with alternators like those used in power plants.

If you want to know more on this topic, I suggest you to watch the companion video of this article, which I posted on my YouTube channel:

https://www.youtube.com/watch?v=vPX-B4xAdtk

Thank you for reading this article and, as always,

Happy Experiments!

Electric Current The Easy Way

Electric Current The Easy Way: a very simple and qualitative approach to understanding what electric current is and how it flows.

Watching a number of YouTube videos, I realized there is some misconception regarding the electric current and how it flows. Some people don’t understand what the current is made of and whether it flows from positive to negative or vice versa.

So here I am, trying to shedding some light to clear the obscurity on this subject.

This post approaches the subject in a very basic qualitative way. No formulas and no calculations are involved.

Here it is!

From the Webster Dictionary

Current:
A flowing or passing; onward motion. Hence: A body of
fluid moving continuously in a certain direction; a
stream; esp., the swiftest part of it; as, a current of
water or of air; that which resembles a stream in motion;
as, a current of electricity.

So, current is the flow of something, some kind of material thing like the molecules of water in a river.

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But, what is the material that makes the electric current?

Electric current is made of electric charges. These charges have the ability of moving in a medium like, for example, an electric wire. Like the water in a river, charges have to move from a higher level to a lower level of potential energy.

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For a river, the higher level of potential energy is the higher ground, and so the water flows from a higher ground to a lower ground, from a mountain or a hill toward the valley below or the sea, or the ocean.

Similarly, for an electric current, charges have to move from a higher ground of electric potential energy to a lower ground.

The problem with the electric current is that different kind of charges can make it, depending on the medium, and depending on the kind of charges. So, the definition of higher ground may change.

This seems utterly complicated, and it is. Think if we had to consider the kind of medium and/or the kind of charge every time we need to describe what happens with a current.

So, since we don’t like complications, we make some simplification. We always define a higher ground as a positive electric potential energy level, and we always say that the current flows from the positive potential energy level to the negative.

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Hum… Positive? Negative?

Well, yes, because charges can only be positive or negative. Think at the electrons and the protons in the atoms. Those are the basic charges and they are negative for the electrons and positive for the protons.

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Wait, what we just said? Electrons are charged negatively and protons positively? How do we know that?

We don’t!

Positive and negative are just made up names that we use because it is convenient to do so.

We could have as well said that electrons are positively charged and protons are negatively charged. But, historically, we have defined the polarity of the charges in a certain way and therefore we continue to do so, because we don’t like changes, and we like concepts to be simple.

So, here we are, saying that an electric current is made of charges. That the charges can be positive or negative. That positive charges like to go from their kind of higher ground, a positive electric potential level, to a lower ground, which is a lower positive electric potential level that we call negative, to distinguish from the other one. And, finally, we say that negative charges like to go from their kind of higher ground, the negative electric potential level, to their kind of lower ground, which now we understand we can call positive electric potential level.

Hum, it seems too much, isn’t it?

And yes, it is: too complicated to use it in every day conversations.

Simplification? Sure, let’s do that. Let’s say that whenever an electric current is involved, we will always say that it is made up of positive charges, and that positive charges always go from positive to negative electric potential level. How’s that? Simple enough?

Now doesn’t matter the medium being an electric wire, were the current is made up of electrons moving through it, or the acid solution in a car battery, where the electric current is made of ions, of both positive and negative kinds, creating two different currents flowing simultaneously in opposite directions.

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Lesson learned: we like to make things simple. We define the electric current as the flow of positive electric charges in a medium, whatever it is, going from the positive potential level to the negative.

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And that’s it. That’s enough for us. With this definition we can address problems involving electric currents always the same way, without worrying what is really happening behind the scenes. This is a very important concept. All about electrical engineering is based on this definition of current. Well… at least part of it.

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!