Electromagnetics for Electronics Engineers

John Haughton, JLH Systems Ltd


This paper was written as a result of over a decades experience of EMC work on professional audio equipment, mainly digital mixing consoles. During this time I have encountered a few engineers with whom I have experienced great difficulty in presenting the case for and techniques of EMC design. At times it appeared as if we were talking a different language yet I am also an experienced digital design engineer myself.

I have noted that, when in "Hardware Design Mode" I too still make the occasional EMC design error. These are spotted when I later examine my own designs from the perspective of an EMC engineer. This led me to think, ’What are fundamental reasons for this?’ I then started to reduce each discipline to its basic essence. When one does this the underlying truths and parallels are often uncovered.

It is in response to these events that I have written this paper that will hopefully be of use to Electronics engineers who still don’t "get it". It should also be of use to EMC engineers struggling to convince engineering management and directors of the physical principles that enable products to be designed for EMC compliance.


What is it, fundamentally, that an Electronics or Electrical engineer is concerned with?

He is somebody who organises voltages and currents, constrained and guided by conductors, in linear time. This applies equally to digital electronics; the time domain is simply quantised in this application. He is mainly interested in the time and frequency domains.

What is it, fundamentally, that an electromagnetics engineer is concerned with?

He is somebody who organises electromagnetic fields in space. His primary concern within compliance work is preventing untoward EM disturbances from occurring and interfering with other electrical equipment and in preventing the greater EM universe from interfering with the apparatus under consideration. He is mainly interested in wavelength and the spatial domain.

Time is analogous to Frequency:- f = 1/t, t = 1/f.

Distance is analogous to wavelength, λ.

In free space (vacuum or air) Frequency and Wavelength are related by the equation:-

Velocity = C = fλ.

Over a conductor the velocity is divided by εr, the relative permittivity of the conductor medium.

This allows us to draw the table below.


For Electronics engineers Ohm’s law is one of the fundamental relationships. The resistance of the material from which an electrical circuit is comprised sets the relationship between the voltage and current. This hardly needs stating - but here it is for completeness:-

V = IR.

Electromagnetic fields occur when electric charges undergo acceleration, i.e. when they are neither at rest nor in steady motion. This may be from an a.c. source, such as a digital signal or an impulsive event, such as an electrostatic discharge.

In EM engineering the E field component is the direct result of the fluctuating Voltage.

The B field component is the direct result of the circulating current.

In the extreme near field (close to the source) it is possible to have almost pure E or B components.

B = the magnetic flux density.
H = the magnetic field intensity or magnetising force.

μ = Permeability = μ0μr ε = Permittivity = ε0εr

μ0 = Permeability of freespace = 4π/107. ε0 = Permittivity of freespace = 1/36π x 109.

μr = Relative permeability. εr = Relative permittivity.

B = μH.

In the far field, within which all proscribed emission measurements are conducted, there is a fixed relationship between the E and H components. This is determined by a physical property of the universe, the impedance of free space, √(μ0 / ε0), taken to be 377Ω. Between the near and far field there is a translation of E to H component, or vice-versa, until both E and H fields are established at a ratio of 377Ω. The moving E-wavefront generates a moving B-wavefront that in turn supports E, providing that the directions of E, B and the velocity, u, are mutually correct.

If the wavelength of a signal is significantly less than the physical length of the conductor, or the signal is confined to a twisted pair or co-axial type cable, then that signal is confined to the conductor. If it is not then we need to use other means to confine it, as that conductor has become an antenna. Wavelength rules in this world.

An EM wave needs physical space proportionate to its wavelength to exist or propagate yet when confined to a conductor a signal of the corresponding frequency will propagate along the shortest of conductors.

EM phenomena are a basic physical property of the universe we inhabit. ESD and Lightning, which have existed since well before Marconi’s first spark transmissions, have a very wide frequency content extending well beyond a gigahertz. It is for this reason that ESD testing can give a cheap approach to immunity testing - an ESD impulse simultaneously and instantaneously subjects the unit under test to much of the frequency spectrum.

High frequency energy flowing on conductors ’dislikes’ sharp changes in impedance, you tend to get reflections of energy, rather than energy flow in these situations. This is because the current flowing establishes a magnetic field that resists attempts to abruptly alter them. This is why we should use curves or 45-degree angles on high-speed tracks. A good analogy here is trying to change the direction of a car on a road - you can follow a curved path much faster than a tight corner without your forward momentum carrying you off the road. The same phenomena occur at other discontinuities in a signal path such as at connectors or vias on a circuit board.

The distance at which this ratio is reached and properly established EM fields occur is known as the Rayleigh distance and is taken to be

D = 2 L2 / λ where L = length of the radiating element.

What we must remember is that when we construct an electronic system we can not avoid creating an electromagnetic system. The wires and conductors of our circuits are simply a framework that we hope the EM fields our circuits generate will prefer to follow rather than radiating into freespace. An antenna engineer has the opposite problem - he wants to maximise the efficiency of his antenna’s EM radiation.

A capacitor is an E field device. Current flow through the capacitor is entirely down to the electric field between its plates and all the energy is stored in this field.

An inductor is an H field device. The very name conveys this - current flow through it induces a magnetic field. It is this magnetic field that impedes the flow of high frequencies through the device and all the energy is stored in this field.

Near field magnetic fields are attenuated at 1/D3 and electric fields attenuate at 1/D2. One consequence of this is that electric fields within a system are able to couple via capacitance at greater distances than the magnetic components that couple via current loops.

From Fourier analysis remember that any conceivable waveform or function can be synthesised from a series of sine waves. The most useful Fourier transform to keep in mind is that for a square wave, e.g. the clock of a digital system.

Consider an ideal square wave, with infinite slope, at frequency f0:-

Square wave of frequency f0 = f0 + 1/3. ( 3f0 ) + 1/5. ( 5f0 ) + 1/7. ( 7f0 ) + 1/9. ( 9f0 ) etc


Note that the Fourier series for square waves or any waveshape that, in its ideal form has infinite slope, has a Fourier spectrum that extends to infinity. Fig 1.

In the real world it is impossible to create an infinite slope. PCB capacitance, inductance and the output impedance of real drivers prevents this from being the case. This is one reason for adding series terminators, they, in conjunction with board capacitance, will act as an LP filter. Board capacitance is pure, inductance free, plate capacitance and will work to infinity without the restrictions encountered in real world components. For this reason some PCB manufacturers offer to incorporate cores in a PCB to maximise capacitance between the boards voltage planes and ground at extra cost.

Consider signal integrity. Ideally we want our signals to arrive at their destinations with the same waveform with which we sent them. We have all seen high frequency clocks that started out as square waves and look more sinusoidal when they arrive - what has happened to this signal? In many cases the higher frequency harmonics have radiated away from the conductor as an EM wave.

The rise times of real signals are now sub nano second and the spectrum of a 100MHz clock signal will extend to well beyond 1GHz. The fundamental frequency and the rise time of its edges determine the spectrum of a real world digital signal. The rise time introduces a break point along the frequency axis. Fig2.


Frequency Wavelength
1MHz 300m
10MHz 30m
100MHz 3m
1GHz 0.3m

The consequence of this is that as digital circuits operate at ever-increasing speeds and rise times then the higher the frequencies and the shorter the wavelengths that have to be considered. As equipment operates at ever-higher frequencies and wavelengths get ever shorter apertures and cable lengths that were once entirely acceptable can now be problematic. Each time a product takes an evolutionary step this fact needs careful consideration. Any engineer who thinks the techniques applied successfully to one generation of product will be adequate for the next will find to his cost that this is generally not the case.

The EMC directive imposes legal requirements upon manufacturers to construct equipment that can co-exist in an ever more complex EM universe. Essentially it says "Thou shalt be good neighbours and co-exist with the rest of the world. Thou shalt not shout or be aggressive, nor be overly sensitive to those around you. If you want to communicate with a family member then use a private channel that is yours by agreement (i.e. an allocated part of the spectrum ) or one that is impervious to the rest of the world ( e.g. a screened and/or filtered cable) of appropriate construction."

Up to the end of the 1970s very little equipment had a microprocessor in it. People had a record deck, television, cooker - all of this was analogue equipment. Now even the toaster has a processor inside! It is only relatively recently that speeds for microprocessors have risen above 100 MHz and those for microcontrollers above 30 MHz. Now 4 GHz processors are on the horizon. Wavelengths are getting shorter and shorter and are comparable with track and cable lengths as well as the physical dimensions of equipment,

For E-fields:- As long as physical sizes of conductors are significantly less than the shortest wavelength of the signal then the energy remains contained around that conductor. In reality we need to be less than around a 1/10th of the wavelength, below this the efficiency of the antenna becomes very poor.

For H-fields:- As long as the loop area is less than that required to support a half cycle of alternating current of a given frequency then the magnetic field does not propagate away from the circuit with any appreciable efficiency.

In modern digital electronics the signal currents are ideally very small and by using ground planes on PCBs we can effectively limit the loop areas of these currents:- i.e. the H field generated is kept very small.

It is the rapidly fluctuating voltages of the 1’s and 0’s, generating E field, that are more of a problem. Lower voltage rails (1.8, 2.5, 3.3V etc) are better in this respect than the older 5V standards. What we must be aware of is the physical dimensions of the conductors that these signals are flowing on. Cables in particular pose a problem in this respect.

For power supplies and power cables the current is much higher and the H field DOES matter. With these we need to be particularly careful of loop areas and to carefully control current flow.

As a rule of thumb cables and PCB tracks need to be 1/10th to 1/20th of the wavelength of the highest Fourier component of concern.

Some basic principles to be mindful of are the following ones:-

1. It is voltage fluctuating on a cable of greater than 1/4 λ ( in practice 1/10th or 1/20th ) that causes the near field E component to arise. You need no current flow for this to occur.

2. With cables it is their physical length and construction that cause them to pose problems. View all cables as potential aerials. The same applies to slots or openings in enclosures.

3. It is current flow that causes the near field H component to arise. It is the area of the loop traversed by this current that determines its effectiveness as a transmitter. You need no voltage fluctuation (other than that created by the current flowing through the finite impedance of the circuit loop) for this to occur.

4. Near field pure E or H components will cause corresponding H or E components, in the proper ratio of 377 ohms, as measured in the far field.

The Electromagnetic Universe

As human beings we are primarily concerned with the physical universe that our own senses of touch, sight, smell, taste and hearing keep us informed of. We need radios, televisions, mobile phones, computers etc. to connect these senses via the EM universe. There is also the natural EM world that exists independently of human beings. This natural world contains phenomena such as static electricity, gamma ray bursts, lightning and solar flares. Whenever we construct an electrical system we also create an EM system. We must make it such that these systems do not interact within themselves or with each other in an uncontrolled manner. We also need to ensure that they are insignificant too, or isolated from, the natural EM environment.

Consider first the concept of a Faraday cage. This is a concept that describes the screening, shield or enclosure of an electronic system.

A Faraday cage can be considered as a perfectly conducting sphere or bubble. As such no potential difference can exist between any two points on the inside, or any two points on the outside, of the surface of this bubble. Hence the term equipotential surface. Examining the boundary conditions of the mathematical functions that describe such a system will derive this.

If no potential can exist then no current can flow. Without fluctuating voltage, or circulating currents no E or H field can be supported, or propagate through the conducting surface. This means that we can consider the inside of a Faraday cage as isolated from the rest of the E.M. universe.

Consider the diagram below (Fig 3) as containing the whole EM universe within the box. If we introduce an electronic system without an enclosure into this then it is entirely at the mercy of the outside EM universe. Also, in this situation, any radiated emissions can escape into the world at large. If these are above the regulatory limits then we have a problem.

The only way to achieve compliance in this situation is to make our system insignificant when considered against the greater EM world. The way to do this is by making loop areas as small as possible (e.g. by using ground planes), by keeping the energy of our systems low and by employing filters to isolate the circuitry from wavelengths below which connected cables will be effective antennas due to their physical sizes.


Next, consider Fig 4 a single system within an enclosure:-


Here the enclosure shorts out EM fields on the inside and prevents them propagating to the outside world. Conversely, EM fields from the outside world are shorted out and prevented from entering the enclosure.

Considering the enclosure, the only point at which the field can be zero is on the surface of the enclosure itself. The EM fields contained within excite all other points within the enclosure. This is an important point. It is a point to which the whole concept of chassis, screen termination and common mode noise can be referred. Using this concept the ideas of common mode noise etc. can be more easily understood. We can also infer from this that the ideal placement for filters and screen terminations is right on this boundary and that you must never cross the filters with any tracks. One side of the filters must be zoned entirely in the outside EM world, the other within your products EM environment.

Consider the classic feed through filter with its threaded body, Fig 5 - this is the perfect design for bolting through the enclosure wall of equipment as are the integrated mains filters intended for mounting on an enclosure.


Two, or More, Interconnected Systems

In the real world virtually every system (apart from simple battery powered equipment) has to connect to the outside world. Many consumer and industrial systems are comprised of several such interconnected boxes.


In this example, Fig 6, we see that a screened cable connects the two subsystems, each in their own enclosures. No filters are employed at either enclosure boundary. The screen of the cable should be thought of as a continuous extrusion of the enclosures - the ideal is a 360o crimp. A short pigtail on a screen termination will compromise the effectiveness of the enclosure at frequencies as low as 10MHz upwards.

In Fig 7 we have interconnected the systems with an unscreened cable. This is penetrating the enclosures and allows radio frequency below the wavelengths associated with its length to freely enter and leave the system. Within the enclosure we will be within the nearfield in many instances and pure capacitive coupling can dominate. Noise currents and coupled r.f. from the sub systems, including ground noise, flows freely on the unscreened cable. The cable is exposed to the outside world and can carry any interference it is subjected to directly to or from the circuits at which it terminates - it has effectively bypassed the enclosure completely.


In the next example, Fig 8, we have added a filter at the exit point of the cable from each enclosure. In order to use an unscreened cable the shortest wavelength (highest frequency) of the desired signal must be significantly less than the length of the connecting cable. This obviously implies that the filters must have a cut off frequency that is low enough to accommodate this requirement, and that the signal we wish to convey is suitable for this type of conditioning.


The above concept of imagining a bubble around your product, which in many products will equate to a metallic enclosure, can still be applied to circuits that do not have an enclosure as such. A circle or sphere can still be around the circuit under consideration enclosing your local EM environment and separating it from the world at large. Filters are then placed on this circle or sphere as required to keep the inside and outside separate. No tracks must cross the filters, as doing so would capacitively bypass them, connecting the inside and outside worlds. Common mode chokes and ferrites are particularly useful when there is no metallic enclosure, as such, to call chassis.

If we introduce an aperture into the enclosure, as we inevitably need to do to accommodate displays, connectors, controls, access panels etc. then we will compromise the Faraday cage. As long as the dimensions of the aperture are smaller than 1/10th wavelength of the highest significant harmonics then the enclosure will still function as such. In the special case where the aperture is the same size as a half wave of the field under the consideration then we have resonance and the presence of this aperture makes the situation far worse than were it not there at all. If apertures of a certain size have to be introduced (e.g. to accommodate a certain LCD display) then we ought to ensure that these do not coincide with the half wavelength of a significant frequency (e.g. a clock, or an harmonic of a clock).

It is the major dimension of an aperture that determines its resonant frequency. A vanishingly thin slot is as bad as a round opening of the equivalent diameter in this respect. This comes as a surprise to many on first learning of this fact.

Current flowing on a shield or enclosure tries to follow its easiest path to satisfy Kirchoff’s law. The preferred direction creates its own magnetic field, ideally cancelling the fields of any impinging EM field that created the surface currents in the first place. If we create a discontinuity in this path by introducing an aperture then the current must divert to flow around it, as in Fig 9. When this happens the magnetic fields can not cancel and we have reduced the effectiveness of the enclosure.


In the EM world we can visualise fields that have physical wavelengths associated with them. If the aperture is bigger than the wavelength then the field slips through as if the hole was not there. If it is smaller than the aperture then it is like trying to get through a door that is too small - it is an effective barrier to the propagation of the field.

Cables and noisy circuits should be kept as far away from any apertures as possible by careful routing or positioning of the item under consideration.

If we can not keep the sizes of apertures insignificant, because, for example the display is physically too large, then we need to consider other methods, such as a conductive mesh or coating incorporated into an optical filter. We could also mount the problem component outside the main enclosure and filter the connections to it.

By utilising the above facts about apertures ’loose enclosures’ can be constructed around modules that are to be mounted in a frame, See Fig 10. The rear of the main circuit board is covered with a chassis plane and mounted to a front panel with metal pillars around the edge of the circuit board. As long as the spacing of the pillars is less than the highest frequency / tenth wavelength of concern then for relatively simple microcontrollers etc this type of enclosure is sufficient. It also provides a good chassis plane to terminate our connectors screens or filters to. If any pair of pillars is further apart than the around a tenth of the shortest wavelength of concern then this approach WILL NOT work.


A similar approach can also work for racks. The outside surface of the backplane is covered in a chassis plane that is bonded to the top, bottom and sides of the rack. The top and bottom are easily bonded using the normal mounting screws to the fixing rails. The sides are a little more difficult. One approach that has worked well here is to use an inner layer of the backplane to provide a strip of chassis plane, stitched with many vias to the outer chassis plane. This strip of chassis is brought right to the side edges of the backplane and these edges are the plated - a process which many PCB manufacturers can perform. These plated edges can then mate to a beryllium-copper gasket or a compressible conductive cloth gasket bonded to the inner surface of the rack sides.

Some Practical Application Guidelines

From the above perspectives it should be clear that we are trying to create a separate, island universe for our system to exist in - to stop the outside world getting in, and the inside from leaking out. In order to do this we need a control plan to carefully control the placement of filters, the coupling between tracks, the sizes of apertures, which cables need screening and those that do not. With such a plan in place, and all in agreement to apply it, then the task of achieving and maintaining compliance can be a relatively easy one. Without it the task can be impossible.

As a rule of thumb each via has 10nH of inductance, as does an inch of copper trace or wire.

Another point to remember is that r.f. does not respect our neat concepts of a system. Interference is happy to exit on an input cable or enter a system on an output cable. R.f. is quite happy to travel on a mains or audio cable - it does not seek out and use nice coax cable that we have carefully designed in to convey our intended r.f. signal.

A twisted pair cable works because it minimises loop areas. Each twist effectively reverses the current flow, cancelling with the previous loop’s H field. Because these cables are generally used to send balanced signals the E field from one conductor is equal and opposite to the other causing mutual cancellation. Because of this the net voltage change on the cable is zero, causing no E field to be emitted. Because of their loop area cancelling construction these cables also offer benefits to immunity. Any magnetically coupled interference tends to cancel and, again, because of their use for balanced signals any E field interference tends to be common mode only - i.e. both conductors experience the same interfering signal whilst the intended, differential, content remains the same. Think about Ethernet connections. They are unscreened, twisted pair cables denoted Cat3, Cat4, Cat5/5e and now Cat6. As the frequencies go up so does the number at the end. This number actually represents the number of twists per foot - with increasing frequency we need ever smaller loop areas (and therefore more twists per foot) to make the connection work reliably and meet EMC standards.

Putting ’extra’ grounds in ribbon cables works because this minimise the loop area (and hence inductance) for any signal return. For the high speed edges (with the greatest spectral content) of the signal where dI/dT is a maximum the signal returns along the path of least inductance - i.e. the ground core nearest to it, this minimises the H field generated. It is this inductance that is the major cause of ground bounce and crosstalk on multi-core cables.

Screened cables are not perfect. Very high frequency cables are constructed literally like copper pipe - the outer conductor is a solid tube. This is obviously very expensive and difficult to work with. For lower frequencies and less demanding applications braided cable is often used. A measure of the quality of the braid is the % optical coverage - how much light the braid lets through. Because of the regularity of the braid it can coincide with specific wavelengths and be much less effective at their corresponding frequencies. For this reason double braids or braid and foil constructions are often used. Foil screens on their own are not ideal because they are too thin to be effective at low frequencies (skin depth is inversely proportional to frequency), they are easily damaged and good contact can not be guaranteed along the seem in the foil wrap.

Ground planes work by allowing every trace on a circuit board to have an idealised return path adjacent to it - i.e. the loop area is minimised. Any track near to its edge of its ground plane ought to have a minimum of three track widths of ground plane beyond it. If you imagine the field lines they need to terminate on the plane below - if it is not there then we get what are known as fringing fields firing out from the edge of the PCB.

Decoupling capacitors work well by providing local stores of energy for their electronic devices to draw power from. By being located close to the devices they are decoupling inductance is minimised along with the loop areas that the high frequencies encircle. They literally ’decouple’ the device from its power supply at high frequencies.

Filters work by limiting the bandwidth of a signal to the frequency range of concern. Higher frequencies that require much smaller loop area or cable lengths to radiate to freespace are excluded.

Minimise loop area. By doing this you are keeping inductance as low as possible. This is particularly important on screen terminations. Ground planes and multiple grounds, distributed in ribbon connectors, are both good ways of minimising loop area. By doing this you also minimise cross talk and ground bounce effects. The return current prefers to follow the path of lowest inductance.

EM fields are a two way street. In digital products if you have poor emissions then you very likely have poor immunity and vice versa. In most analogue products this does not necessarily follow since many analogue circuits, by their very nature, should not emit RF (although unstable op-amps can make good, unintentional, oscillators). They can of course suffer from poor immunity. In this sense it can be easier to fix digital EMC problems than analogue ones.

Emissions from PCB’s tend to be dominated by the near field magnetic component, this is because of the physical sizes of the boards. The current loops must be controlled carefully to minimise these. Emissions from signal cables tend to be dominated by the electric field component.

EMC has much in common with Quality. It must be designed in to a product. You can not apply it in a separate process just before you ship the product out of the factory doors. Much of it is intangible and you can easily lose sight of the benefits when cost cutting or re-engineering. You won’t necessarily realise the benefits until you get things badly wrong, at which point your customers will be calling your service department and your companies reputation (or worse) will be suffering.

If you are the company "EMC guru" then ensure that you are in a position where you can review and veto all EMC critical design decisions and changes. Controls should be set up on your company stock system identifying EMC critical parts so that alternatives can not be purchased without your involvement. Every design ought to be reviewed before any prototypes are made. It is very difficult finding the more esoteric problems in a product that has fundamental EMC errors included in its design.

References and Further Reading

"Electrotechnology", M.G.Say, Butterworth, 1974, ISBN 0 408 00123 2.
"Electromagnetics", John D.Kraus, McGraw Hill, 1999, ISBN 0 071 16429 4.
"Design Techniques For EMC" series - In Particular:- "Part2, Cables and Connectors", "Part4, Filtering and Shielding". Available electronically from the magazine archive at www.compliance-club.com.
"EMC for systems and installations", Tim Williams and Keith Armstrong, Newnes, 2000, ISBN 0 7506 4167 3.
"Why Digital Engineers Don’t Believe in EMC", Dr. Howard Johnson. Available electronically from the magazine archive at www.compliance-club.com.

John Haughton, BSc, MIEE is a self employed electronics engineer and consultant. He has twenty years experience in professional audio and EMC.
Email: jlh@jlhsystems.co.uk
Phone: +44 (0)7963 501929 Copyright: JLH Systems Limited. December 2005.


Reprinted by kind permission of The EMC Journal
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