Where Exactly is the Signal?

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(Note: This article is adopted from my new publication, “The Physics of Electrical Engineering for PCB Designers,” soon to be available on Amazon and for download on the UltraCAD Website.)

When I first got involved in printed circuit board design in the early 1990s, fast rise/fall times were just starting to become an issue. Prior to that we had been pretty much a “connect-the-dots” kind of technology. But as rise times got faster, it became necessary to worry about (electromagnetic) fields. One manifestation of that was EMI, and the increasing need to pass FTC compliance testing.

So, a new type of engineer came on the scene: the electromagnetic compliance/compatibility engineer. Until that time, we understood that electrical current on a copper trace was the “flow” (movement) of electrons along the trace¹. In fact, the definition of an amp of current on a copper conductor is 6.25*10¹⁸ electrons crossing a surface in one second².

But this new breed of engineers came along and many of them started saying things like³:

• “No, current isn’t electron flow. Electrons can’t flow at the same speed signals flow.” (My response: But they can transfer energy between themselves at the speed of light, which is how they “flow.”)
• “Maxwell and Maxwell’s equations tell us that the signal is in the field around the trace, not on the trace itself.”
• Stop worrying about traces; ignore them. Just control the fields and you will be fine.”

So, before we answer the questions about where the current and signal truly are, let’s look at the fundamental principles behind Maxwell’s equations and see what they say⁴. The following discussion heavily paraphrases these principles and simplifies them for issues relative to this article. No, calculus will not be necessary.

The Principles

Charles-Augustin de Coulomb (1736–1806) was a French physicist. He is best known (at least to us) for developing a couple of laws in the 1700s. One was:

“There are two types of charge, positive and negative. ‘Unlike’ charges attract and ‘like’ charges repel each other (Figure 1) with a force that is proportional to the product of their charge and inversely proportional to the square of the distance between them.”

Coulomb also gave us another law related to magnetism: Every magnetic pole is a dipole with an equal and opposite pole. That is the same thing as saying that a magnetic “north” pole cannot exist without there also being a magnetic “south” pole. Even if you cut a magnet in half (see Figure 2) the individual poles would not be preserved; new poles would appear to preserve the dipole nature of the magnet.

 

To read this entire article, which appeared in the December 2022 issue of Design007 Magazine, click here.

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