The concept of Electromagnetic Fields in a PCB

One of the most important concepts in designing printed circuit boards (PCBs) for low electromagnetic interference (EMI) is the concept of fields. Specifically, as engineers, we need to focus on containing these fields. 

Electromagnetic field distribution around a signal trace, illustrating electric and magnetic fields across a dielectric material and a return reference plane.

EMI, or electromagnetic interference, is fundamentally about field containment and controlling where the fields need to be strong and where they need to be weakened.

When we talk about fields, we are referring to both electric and magnetic fields.  Therefore, if our goal is to design PCBs with low EMI, we must understand how these fields behave and how to control them. 

By doing so, we can not only achieve a high-performing circuit but also ensure that the design passes electromagnetic compatibility (EMC) tests, which are essential before the product can be sold in the marketplace.

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One of the things I found most useful for understanding electromagnetic (EM) fields is to actually visualize them. While these phenomena can be very complex, having a simplified visual representation can significantly help us grasp the fundamentals. This understanding is essential when designing or debugging products for low EMI.

The first image we need to have in mind when discussing fields is how these fields surround a conductor.

Figure 1 - Electric Field of Conductor.

[ Φ magnetic flux; Ψ dielectric flux; from Steinmetz (1911, p.10) ]

In this scenario, the circle in the center represents the conductor, viewed in cross-section. Surrounding this conductor are the magnetic and electric fields, which together form the electromagnetic field.

The magnetic field is quantified by the number of lines of magnetic force, denoted by the symbol Φ (PHI). These magnetic field lines encircle the conductor, forming closed loops that represent the magnetic flux generated by the current flowing through the conductor.

For the electric field, these are represented by dashed lines in the picture.

These lines originate from the conductor and are measured by the number of lines of electric force, denoted by the symbol Ψ (PSI). In the case of a single conductor, the electric field lines radiate outward as straight lines from the conductor.

However, when a return conductor is introduced, the behavior of the fields changes, as illustrated in Figure 2.  In this scenario, the magnetic field lines become concentrated between the two conductors, forming stronger, more focused loops in the space between them. Outside of this space, the magnetic field lines spread out more broadly.

For the electric fields, when we have the return conductor, the lines of force change their behavior as well. Instead of radiating outward from a single conductor, the electric field lines now start from one conductor and terminate at the other.

Figure 2 - Electric and magnetic fields around the conductors in a circuit.

[ Φ magnetic flux; Ψ electric flux; from Steinmetz (1911, p.11) ]

The key takeaway from these visualizations is that magnetic field lines always form closed loops, while electric field lines terminate at conductors.

This distinction leads us to describe the magnetic field as a "magnetic circuit," where the field lines loop continuously. In contrast, the electric field can be described as an "electric circuit," where the field lines originate and terminate at specific points.

Another way to represent electromagnetic fields is through the concept of polarities:

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