Fundamentals Of Electric Circuits

Some basic nomenclature and information on electric circuits.

When we think of an electric circuit, the first thing that comes to mind is a bunch of electric and electronic components put together to make a device that provides a certain functionality.

This is totally right, of course, but it is not a precise definition of an electric circuit. In fact, circuits can be defined in different ways, depending on the particular aspect of them that we want to highlight.

If we want to define a circuit with respect to the wave length of the voltage and current that the circuit handles, we will distinguish between “lumped” and “distributed” circuits.

If instead we want to highlight the kind of electric or electronic components the circuit is made of, then we need to talk about linear and non-linear circuits.

And, finally, depending on the temporal stability of the components, we can talk about “time-invariant” and “time-variant” circuits.

And, of course, we can consider combinations of the properties and, therefore, combinations of different circuit types.

In this article, I will go through the above list of circuit types and provide a proper definition and description of each one of them. Combination of those types will lead to combined definitions and descriptions of the basic types. However, in this context, I will go through only the basic types of circuit, leaving to you the task to provide definitions and descriptions of the combinations.

Lumped and Distributed Circuits

Let’s go now into more details about these kind of circuits. What differentiates these circuits is the size of their components compared to the size of the wavelength of the electric current flowing through them. Hum, well, I guess we need to back up a little bit first. Let’s start with the types of current.

We have two kind of currents: the direct current, or DC, and the alternate current, or AC. DC current always flows in the same direction and never changes. AC current has usually the shape of a sine wave, or some other shape that periodically inverts the direction of the current. The number of times the current inverts its flow depends on the number of times the voltage flips its polarity. When the Voltage goes from positive to negative n number of times in a second, we say that its frequency is n and it is measured in Hertz.

Since the flow of the current in a conductor is not instantaneous, it makes sense to think that a change in the voltage at the ends of a conductor makes the current change progressively through the conductor. And if the voltage keeps changing back and forth, so does the current. At the end, both the instantaneous values of the current and the voltage across the length of the conductor follow in space the same shape of the voltage changes (in time) applied at the ends of the conductor. So, if the voltage changes in time like a sine wave at the ends of the conductor, it will follow a similar shape in space throughout the length of the conductor. The length of such a sine wave in space throughout the conductor is called wavelength of the voltage, or the current. Such length in space depends on the length in time of the corresponding voltage applied at the ends of the conductor.

We can calculate the wavelength using the following formula:

The Greek letter “lambda” represents the wavelength, the f represents the frequency of the voltage, which is how many times the voltage goes from positive to negative and back in one second. And, finally, the letter ‘c’ represents the speed of light. Yes, you got it right, it is the speed of light!

When the wavelength is much longer than the physical size of the components of the circuit, we say that it is a lumped circuit, because the components are just small lumps with respect to the wavelength itself. In such a case voltage and current are practically constant across the whole length of the component.

When the wavelength is comparable with the physical size of the components of the circuit, we say that it is a distributed circuit, because the components are so big compared with the size of the wavelength that the wave itself is distributed across them. In such a case voltage and current will be different in different sections of the component, at any instant in time.

Distributed circuits cannot be analyzed with normal algebra equations. For those, it is necessary to heavily use calculus. Example of such circuits are the microwave circuits, those used to deal with radars and satellite signals.

Linear and Non-Linear Circuits

A component is defined as linear if it can be represented in a I-V (current-voltage) diagram with a straight line.

A component is defined as not linear if its representation on a I-V diagram is not a straight line.

Simply put, a linear circuit is one made with only linear components, while a non-linear circuit is one that has at least one non-linear component.

Note the difference: for a circuit to be linear, ALL the components must be linear; for a circuit to be non-linear, it is enough that ONLY ONE component is non-linear. All the other components can be linear and still the whole circuit is non linear.

Time-Invariant and Time-Variant Circuits

Difference between time-invariant and time-variant circuits is also straightforward.

A time-invariant component is one for which the measurements that define it never change over time.

A time-variant component is one for which the measurements that define it can change over time.

As a result, a time-invariant circuit is one made only with time-invariant components. A time-variant circuit is one made with at least one time-variant component. This is a subtle definition, very similar in its form to the one for linear and non-linear circuits.

Circuits in Series and in Parallel

One last thing I would like to discuss about circuits in general is related on their topology or, in other words, on how the components in a circuit are connected to each other.

There are two main configurations of connected components:

  1. components in series
  2. components in parallel

Components are said to be connected in series when they are traversed by the same current.

Components are said to be connected in parallel when the voltage on each one of them is the same.

When we talk about connections in series and in parallel, of course, we refer to components directly attached to one another, at least on one terminal, or lead. Components that are far away in the circuit diagram, or that are not directly connected together cannot be defined as in series or in parallel.

So, now, can you tell me what kind of circuit is the one at the very beginning of this article? Put your answer in the comments and let’s see who gets it right.

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.