## Electromagnetic Interference and Shielding

Whenever a current flows through a wire, it creates a magnetic field surrounding it and, if the current is variable, so will be the magnetic field.

Conversely, if we put a wire in a variable magnetic field, an electromotive force will be generated in the wire, in other words: a voltage. This voltage, in turn, produces a current in the wire when it forms a closed circuit, like a loop.

Another way to describe this phenomenon is this: if we have a variable magnetic field in a volume of space, a variable electric field will be automatically generated in that same space. It is that electric field that generates the voltage on the wire and causes current to flow through it. Again, this concept presents a duality. If I generate a variable current in a wire, a variable electric field will be present on the wire and its surroundings. As a result, a variable magnetic field will be generated in the same volume of space.

In fact, whenever there is a variable electric field, there is also a corresponding variable magnetic field and viceversa. Each of the two variable fields cannot exist without the other. They always both exist at the same time. It is for this reason, that we usually refer to them as a single field called Electromagnetic field.

And because the electromagnetic field changes over time, it also affects its surrounding space and the space surrounding that space, and so forth. Basically, the effects of the electromagnetic field is visible over long distances and so we say that electromagnetic fields propagate in space. We call this an electromagnetic wave.

Light, for example, is an electromagnetic wave and propagates in space at what we call the speed of light.

A physicist named James C. Maxwell, back in 1861, put together all the knowledge of the time and elaborated a set of 4 equations that completely describe how electromagnetic fields work and how electromagnetic waves propagate. These equations are known today as the Maxwell’s Equations.

The concept of electromagnetic waves is widely used in electronics to make devices that can receive and transmit information using this physical property. You know very well these devices. They are called radios, and they can be used on their own or inside a wide variety of more complex devices, like TV sets and cellphones.

Without the electromagnetic waves, the global telecommunications system we enjoy today would not exist.

However, there is a negative side of the electromagnetic fields and waves. Electromagnetic waves are continuously transferred from one circuit to another, or from one part of the same circuit to another as long as variable currents is produced. The problem is that, most often than not, we do not want these kind of interactions.

Whenever an unwanted signal is generated in a circuit because of the electromagnetic fields that surrounds it, we call it a noise, and we try our best to remove it.

The generation of these unwanted signals is generally called Electromagnetic Interference or, in short, EMI.

The action we take to avoid and prevent EMI is called Electromagnetic Shielding, or EMS.

Basically, it works by putting a shield in between the area where the source of the Electromagnetic field is located, and the circuit that is negatively affected.

There are several sources of EMI, some occur in nature, others are created by humans, as a by-product of the machines and devices we use daily.

Since the production of EMI is a bad thing, the governments all over the world provide guidelines to help reduce the generation and the effects of EMI. They also define rules that specify the maximum amount of EMI that any device can generate.

This helps manufacturers in creating compatible devices that do not influence each other.

If we had to make a list of all possible sources of EMI, that list would be incredibly long.

Here are just some examples.

Some natural occurring EMI:

– solar magnetic storms, that occur from time to time on the surface of the sun and may cause huge electromagnetic waves that can propagate toward Earth and cause a disruption of electric and electronic devices.

– lightning, especially during thunderstorms.

– Earth’s magnetic field flux, which is caused by moving an electric device across the magnetic field generated by the Earth, thus creating unwanted electric fields and currents inside the device.

And here are some human-created sources of EMI:

– TV sets

– cell phones

– brush motors

– fluorescent bulbs

– computers

– tablets

– microwave ovens

– power generators

– internal combustion car engines

– arc welders

– brownouts and blackouts in the power grid

– electrical power lines, causing the well known humming that can be even heard when getting close to a high voltage power line.

– voltage sags and spikes in circuits

… and the list goes on and on. And each item in this list is potentially a noise generator that can affect and even totally disrupt the functionality of an electronic circuit.

That’s why, all the electronics equipment that is sensitive to EMI needs to be protected with shields. We call this protection “ElectroMagnetic Shielding” or “RF Shielding”.

Whenever we have an electronic device that is sensitive to electrical noise, we need to provide it with some sort of electromagnetic shielding, or EMS, to make sure that the electrical noise generated by the EMI is reduced below a value, or threshold, that the device can safely handle. Sometimes, very sophisticated and sensitive instruments have really low thresholds, a condition that is very difficult to achieve but, nonetheless, necessary.

Examples of electronic devices that need EMS are:

– electric wires used to transport audio, video and radio frequency signals: to protect them we usually do things like surrounding them with a metallic shield. Such cables are called coaxial cables.

– RF equipment: radios, cellphones, TV sets, and so forth, need to be shielded from unwanted noise. In fact, EMI can make sounds difficult to understand, or it can distort pictures and videos, for example.

– Audio equipment: again we don’t want to hear noise when we are listening to our preferred song or band.

– medical equipment: EKG machines, diagnostic equipment and the sort affect human life and we don’t want that the wrong noise at the wrong time causes somebody to die.

– Avionics: what if the airplane instruments stop working during landing because some EMI was generated by the unshielded device of a passenger? That’s why they don’t want you to use any sort of electronic devices during take off and landing.

– certain lab tools, like oscilloscopes: we want them to measure the signals of our circuits under test, not the noise produced by electromagnetic fields in the room where the instrument is located.

And again, the list goes on and on.

Whenever we create a new device, we always need to make sure, first, that it will not cause EMI that can affect other devices; and, second, that it will not receive too much EMI from the surroundings.

The ability of creating Electromagnetic shielding depends on two different properties of the materials: the conductivity, which is the capability of allow the movement of electric charges, and the magnetic permeability, which is the capability of a substance to facilitate the flow of a magnetic field through it. In other words, the permeability works for the magnetism like the conductivity works for the electricity.

The conductivity property allows to shield from electric fields and the permeability property allows to shield from magnetic fields.

Unfortunately, there are no materials that have simultaneously a good conduction and a good permeability. So, we choose one material or another depending on what aspect we need to give priority.

Shielding due to conductivity is achieved by the property of what is called the Faraday Cage.

Michael Faraday was a British scientist that invented the device in 1836. The cage was capable of shielding people from electric strikes and from electrostatic discharges. That device is today known with his name, the Faraday’s cage, and its principle is extensively used to provide electric shielding of all sorts.

It is basically a cage made of conductive material and is capable of shielding whatever is inside of it against electrostatic and electric fields.

It works because an external electric field causes modifications in the distribution of the charges in the conductor. Once the charges are redistributed, they produce on their own another electric field that cancels out the original field and prevents it to enter inside the cage. The better is the conductor of which the cage is made of, the better the cage works.

Note, however, that the cage is supposed to be a continuous covering of conductive material, without holes. Only that way it can prevent electric fields from going inside. In practice, we do need openings in the cage, otherwise it would not be possible to put anything inside of it. But, as long as the openings have a size much smaller than the length of the electric waves that we want to shield, the Faraday’s cage will work as if it was a continuous covering.

So, for lower frequencies we can have bigger openings, but for higher frequencies we need to make them smaller and smaller, up to the point that for very high frequencies we really need a continuous covering.

Another aspect of the Faraday’s cage is its bad efficiency at the higher frequencies due to what is called the skin effect.

When a constant current flows inside a conductor, all the movable charges inside the conductor participate in creating the current.

But, when we have an alternate current, the center of the conductor is used less and less with the increase of the frequency. So, at the highest frequencies, if we don’t have a very good conductor, since the current will only move in a thin outer layer of the whole conductor, or the skin, the resistivity will be so high that the electrons inside will not move fast enough to counterbalance the electric field and so the shield will not be effective.

That’s why at the highest frequencies shields are usually made with an external layer of copper or even silver, which is the best known conductor.

When we need to create a shield for a magnetic field, a good conductor doesn’t do any good. For magnetic fields, we need to use materials with high permeability to magnetic fields which, conversely, are poor conductors.

The big difference with magnetism is that we cannot separate north and south poles like we do with the positive and negative charges, Therefore, the lines of a magnetic field always go from the north pole to the south and cannot be interrupted.

What we can do is to merely deviate the field lines and force them to go through a high permeable material, away from the device that we want to protect.

This is a totally different approach from the electric fields, where we actually cut the field lines and prevent them to go inside the Faraday’s cage.

Materials

As we already said, there are two kind of shielding: those that work better against electric fields, and those that work better against magnetic fields.

Different materials have been adopted over time to achieve these two goals.

To shield from electric fields, we need to use good conductors. The best conductors, however, like silver and copper, are very expensive. So, whenever possible, the tendency is to use slightly less conductive metals that are still very efficient at the particular frequencies where the shield is supposed to work.

And so you can see shields that are made of aluminum, steel or nickel, and only when strictly necessary copper or even silver is used.

Shields for electric fields can then be shaped as a solid box, or as a mesh, or a metallic foil, depending on the mechanical and electrical needs. To protect plastic boxes, there are even certain conductive paints that can be used to coat the plastic and obtain a relatively good shielding.

To shield from magnetic fields, we need to use a material that is permeable to magnetic fields.

Iron and steel are the obvious examples, but there are some alloys that are particularly good for magnetic shielding, like silicon-iron and mu-metal.

Just to give you an idea, the relative permeability of the air is defined as 1.

Iron with 0.2% impurities has a relative permeability of 5000.

Silicon-iron has a permeability of 7000.

And mu-metal has a permeability of 100,000.

Depending on how thick we can make the shield and the amount of magnetic energy that we want to stop, we will need to choose one solution or the other.

For electronic circuits, however, we deal most of the time with electromagnetic waves and not with constant or quasi-constant fields.

Since electromagnetic waves have both an electric and a magnetic component, and since one cannot exist without the other, it is enough to shield from one of the two component to block the whole wave.

That is why, electronic devices are usually only shielded against the electric fields, which are the easiest shields we can obtain. Doing so, we can stop or reduce the electric component of the waves and, therefore, the whole waves, since the magnetic component will go away as well, just because the electric component is not there anymore.

When creating an EMS, or an electromagnetic shielding device, we need to be careful to make it in such a way that it will actually shield our electronic circuit, rather than actually collect even more noise. Unfortunately, it is very easy to obtain the opposite effect.

For example, if the shielding of a device is not connected to ground, the current that flows in the shield will non be able to be discharged anywhere. As a result, all the energy will be reflected in the surrounding space, thus defeating the purpose of having a shield or, even worst, causing some resonating effect that could create even more noise.

Another cause of trouble is when the shielding is done in such a way that the internal currents move around in a loop. If that happen, the loop will actually cause a concentration of the eletromagnetic waves, thus causing more trouble than not having a shielding at all.

The last issue I would like to mention is the one of the gaps in the shielding which, if too large compared to the wave length of the noise, will not be able to prevent the noise itself to go through. We therefore need to be very careful when making holes in the shielding, for example, to allow wires to go through. Or to allow us to see the display of an instrument. If the opening is too large, compared to the wavelength, the noise will no through and the shielding will be ineffective.

EMS is always a hot topic in electronic devices, whether they are low or high frequencies. We need to spend a lot of thoughts when designing the case of a device and, in case of radio frequency, even the design of the PCB deserves a lot of attention to prevent unwanted coupling of the signals from one section of the PCB to another, which is basically noise that is generated and distributed internally to the circuit itself.

It is also important to distinguish cases where the device is supposed to deal with very low signals versus those cases where the signal is higher.

When dealing with low signals, we may end up with noise that has the same magnitude of the signal being treated, and so we have to put a particular attention to the suppression of the noise, which could otherwise overwhelm the wanted signal.

When dealing with higher level signals, the surrounding noise could sometimes be considered negligible and, in such a case, the EMS becomes less of an issue.

It is important, therefore, to address each case individually. There is no common solution that can be adopted for everything.

## White And Pink Noise: What You Should Know

Noises are sound effects, they have nothing to do with the light. So, why are we talking about white and pink noise?

The reason comes from the knowledge that white light is the composition of all the colors in the visible spectrum. By association, a noise composed by all the frequencies in the audible spectrum was defined as white as well. From there, it became easy to extend this concept to other kind of audio noises, and assign a different color to each one of them.

The reality as we know today, however, is quite different. Today we know that any audible noise is obtained by mixing together all the possible frequencies of the audible spectrum. The difference lays in the perceived intensity of the sound at each frequency or interval of them.

We know know that the white noise is characterized by having a constant amplitude at all the frequencies, which translates in saying that the power of the various frequency of the white noise is constant. Or, even better, the power spectral density of the white noise is the same at all frequencies.

Or is it?

Well, the problem of us humans is that we do not believe in something unless we can prove it to be true.

The fact is: our ear does not perceive the sound linearly. The ear perceives the sound logarithmically. In particular, our ear can perceive much better the high frequencies than the low frequencies. As a result, when we listen to the white noise, we perceive it as very rich of high frequencies, but that is just because we cannot hear well the lower frequencies of the white noise spectrum.

The proof of that? Look at the screen of a spectrum analyser for the white noise.

Look at the top crests. Those are the ones that represent the amplitude of the signal at each frequency. Do you see how it remains constant at all the frequencies?

Let’s now talk a little bit about the so called pink noise. When we listen to the pink noise we perceive it as filled of all those low frequencies that were missing from the white noise.

However, the reality is quite different. The pink noise intensity changes with the frequency. In particular, it is such that it decreases with the increase of the frequency at a rate of -3dB per octave. Incidentally, this is the same rate at which our ears work, but in the opposite direction: when the frequency increases, our ear becomes more sensitive to the intensity of the sound at a rate of about +3 dB per octave. The two rates are the exact opposite and so they cancel each other and, to our ear, the pink noise seems to contain all the frequencies of the audible spectrum and all with the same intensity. Weird, isn’t it?

Here is the proof of that.

Do you see how the top crests at the various frequencies become smaller and smaller at the increase of the frequency?

So, contrary to the white noise, the pink noise presents a reduction in the intensity of the sound that is inversely proportional to the frequency of the sound itself and, specifically, when the frequency doubles, the signal becomes 3dB smaller. in other words, the power spectral density of the pink noise decreases with the increase of the frequency with a ratio of -3dB per octave.

If you like, go watch this video on YouTube, where I describe how to build a generator of white and pink noise for the lab. You’ll be able to hear both the white and the pink noise several times throughout the video, so you can get an idea on how we perceive each one of these noises.

Let’s now talk about how these noises are actually used in lab and in the real world.

Let’s begin from the white noise. Because of its characteristic of providing a constant intensity at all the frequencies, it becomes really useful when we want to measure the frequency response of an audio amplifier, for example. We inject the white noise into the input of the amplifier and we attach to the output a spectrum analyser. The analyser will tell us the range of frequencies that the amplifier is capable of handling, but it will also tell us if the amplifier has a flat frequency response, or if it amplifies better certain frequencies rather than others. This information can then be used to tune the amplifier to make it work with a flat response at all frequencies.

Another usage is in filters measurements. Again, putting at the input of the filter the white noise and attaching the output to a spectrum analyser, we can actually visualize in a single shot if the filter works in the required range of frequencies and if it provides the right attenuation at each frequency.

And what about the pink noise? Pink noise becomes very useful when installing professional sound systems in a room. Such systems normally posses what is called a graphic equalizer, which allows to change the response of the system to various frequencies. We input a pink noise into the sound system and we let it fill the room with its sound. Then, using some microphones in the strategic places of the room, we can convert the actual sound back into electrical signals and send them to a spectrum analyser. Then we start playing with the graphic equalizer to obtain a flat response on the analyser. Because the pink noise has a distribution of power density which is a complement of the sensitivity of our ears, when we obtain a flat response we have actually adapted the sound system to the most appropriate way to generate sound pleasant to our ears. Without doing so, the sound system would amplify the sound linearly, therefore changing it from what it was originally intended during its recording. Remember, we want the electronic instruments behave like our ears, because that is how we perceive the musical instruments and the voice of people, not linearly. The pink noise allows us to tune the sound system in exactly that way.

## 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.