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.

A Few Words On DC And AC: What Exactly Are They?

A few disorganized concepts about direct and alternate current.

There are two main variations of the electrical current: the Direct Current, or DC, and the Alternate Current, or AC. But what does that mean?

The DC is the one you obtain when you power a device using batteries, for example. Batteries provide what is called Direct Voltage and that generates a Direct Current once applied to an electric circuit. If we draw a diagram of the voltage and, correspondingly, the current that flows in a circuit powered with DC, here is what we obtain:

This diagram basically tells us that the value of the voltage, and of the current, does not change over time. We usually define the current as flowing from the positive to the negative pole of the battery and that flow never changes over time.

The AC works like the DC, going from the positive to the negative voltage. The difference is that the voltage keeps switching: positive becomes negative and then becomes positive again, and so forth. And so the current keeps changing its direction accordingly.

Also, the AC does not change suddenly back and forth, but it does that progressively, following a shape called sine wave. All electrical energy distributed in our homes has this shape.

In USA, the AC current changes direction 120 times per second, which means that in one second there are 60 full periods of the sine wave. We say that the frequency of the current is 60 Hertz, abbreviated 60 Hz.

In Europe, 50 Hz is used instead. Other parts of the world either use one or the other.

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

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.

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

Whatever is the source 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.

But, why do we need both forms of voltage, DC and AC?

First of all, DC voltage is necessary to power up any electronic device, from your TV to your smartphone or radio or computer.

AC voltage, from the electrical engineering perspective, is used to transmit the electrical energy from the places where it is created to the places where it is used.

Back to the time where the first experiments of electricity transmission were conducted, there was a famous diatribe between Thomas Edison and Nikola Tesla.

Edison believed that the safest way to transmit electricity was to do that with cables powered with DC current.

Tesla argued that it was better to use AC current because it allowed much less waste of energy during the transportation, thanks to the fact that it is easier to convert the voltage from a low value to a higher one and vice versa, when using AC. And it is also very simple to convert the AC into DC when DC is needed, through a process called rectification.

As history tells us, Tesla won that battle, rightfully. And so, today, AC is used to bring the electrical energy to our homes from the power plants.

How To Choose A Resistor

How do we choose the right resistor when designing and building an electronic circuit? Here are the major parameters that should be kept into account.

bunch_of_resistors

A resistor is a component made out of a poor conducting material, so that it can offer a resistance to the flow of the current.

You can think to resistance in terms of the obstacles that charges encounter when moving from one end to the other of a conductor. The more obstacles, the higher the resistance. In a metallic wire, for example, the charges are the electrons of the conduction band (see this post and this other one for further details).

In today’s post I would like to address an issue that sometimes is underestimated when designing an electronic circuit: how to choose the right resistor for the job.

Resistors are not all the same. Besides the resistance value that distinguishes one from the other, there are other factors that are important as well.

Here is a list of all the important factors, why they are important, and what are the consequences of not choosing a resistor based on each specific factor.

  • The first thing that comes to mind is the tolerance, which is usually provided on the body of the resistor itself, along with its resistance value.

resistor_color_bands

In color coded resistors, the tolerance is defined by the band that is far away from all the others. In the above picture, for example, it is the gold band, which means that the tolerance is of 5%. In other resistors, where the resistance is explicitly written on the body of the resistor, the tolerance is usually written in clear along with the resistance. More in general, you’ll have to refer to the data sheet provided by the constructor to figure out its tolerance.
Tolerance is an important factor for those circuits that require very precise resistors, like measuring instruments and the like. It is also important when the resistor is used for the polarization of a critical component. If the resistors used in the project have a tolerance that is too high, the whole circuit may not function properly because the actual value of the resistor is too different from the one that was required.

  • Operating Temperature. This depends both from the ambient conditions and by the temperature raise produced by the power dissipation. There are two reasons to keep the temperature range into account. First, resistors slightly change their resistance with the change of the temperature. Using the resistor outside its temperature range would cause a variation greater than the one considered by the tolerance. Second, but not last, when the resistor is traversed by current it heats up. As long as the current stays within a range for which the power dissipation is not exceeded, everything is fine. Otherwise, the resistor can easily overheat and burn.

scorched_resistor

  • Maximum Voltage. Operating a resistor above its maximum voltage rating may cause sparks that would destroy the resistor.

burned_resistor

Resistors used in low power circuits usually have a maximum voltage in the order of at least 100V, and that’s why people usually don’t care or it doesn’t even know that there is such a parameter. In fact, low voltage circuits will normally never exceed the maximum voltage of any resistor. However, there are specific applications where voltages in the circuits can be above the 100V threshold. In such cases, it is important to verify that the resistors used in the circuit can withstand those voltages.

  • Temperature coefficient. This is the parameter that tells us how much the resistance changes per degree Celsius. It depends on the material the resistor is made of, but also on the heat dissipation capability of the component. Some resistors are built with an embedded heat sink to reduce the value of this factor.

power_resistor

This information becomes important in those cases where it is known that the resistor is going to dissipate a considerable amount of power. Based on that, it is possible to figure out if the resistor needs an external heat sink and, eventually, the heat sink thermal resistance.

  • Parasitic Capacitance and Inductance. A real resistor does not have only a resistance but also a very low value of capacity and inductance that may affect its functionality at high frequencies.

equivalent_resistor

These parasitic capacitance and inductance are caused by the physical dimensions and shape of the component and cannot be avoided. When working at high frequencies, these values need to be taken into account, since they will generate both capacitive and inductive reactance that will affect the value of the resistor at the particular frequency it is going to be used.

  • Packaging. This keeps into account where and how the resistor is going to be mounted. It can be a through holes resistor, which is provided with two leads to make the connections. The leads are usually inserted in the holes of a perforated board or of a Printed Circuit Board (PCB). Or, the resistor can be a Surface Mounted one. This has no wires, just two pads that can be directly soldered on a Surface Mounted technology (SMT) PCB. Other factors affecting the packaging include the possibility of attaching it to an external heat sink, and/or the necessity to properly ventilate it, to guarantee enough heat dissipation.