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Article by Douglas Brooks (Note: This article is adopted from my new publication, "The Physics of Electrical Engineer- ing for PCB Designers," available soon.) 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 elec- trons along the trace 1 . In fact, the definition of an amp of current on a copper conductor is 6.25*10 18 electrons crossing a surface in one second 2 . 18 DESIGN007 MAGAZINE I DECEMBER 2022 But this new breed of engineers came along and many of them started saying things like 3 : • "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 say 4 . e following discussion heavily paraphrases these principles and simplifies them for issues relative to this article. No, calculus will not be necessary.

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