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How Well Do You Know James Clerk Maxwell?

There’s no questioning the importance of Maxwell’s equations. But do most engineers still remember them?

What are four of the most influential equations in all of science? One could answer that question by saying “Maxwell’s equations,” which most working RF/microwave engineers should have encountered in an undergraduate course on the road to becoming an engineer. But how many still remember Maxwell’s equations in detail? If someone asked you to sit down and write them, would you be able to do it? I will leave you to go get pencil and paper.

While Maxwell’s equations form the fundamental principles of electromagnetic (EM) theory, do today’s engineers even need to know them? Of course, every person has different responsibilities. But even for those engineers who routinely use EM simulation tools, are Maxwell’s equations necessary?

To come up with an answer, let’s look at a company that’s been in the business of EM simulation for a long time: Sonnet Software. With a history that dates to 1983, Sonnet is no stranger to EM software. On top of that, the company’s founder, James Rautio, has written about James Clerk Maxwell himself (this literature can be found on Sonnet’s website).

So, do Sonnet users need to know Maxwell’s equations? Brian Rautio, VP of operations at Sonnet, responded, “With over 30 years of development effort, ease of use has been a huge priority for Sonnet, and so knowing Maxwell’s equations isn’t really a prerequisite for use. The software discretizes the circuit geometry, casts it into a form of Maxwell’s equations, and solves the problem with relative fluidity. Indeed, in some cases, the user doesn’t even need to enter so much as the permittivity of the material.

“That said,” Rautio added, “there are some concepts that are evasive to software automation—for example, accounting for ground returns, package resonances, and over-moded substrates. As such, we have a dedicated support team with decades of Sonnet experience to answer questions and help our customers make the most effective use of our products.”

Now that we’ve addressed whether or not Sonnet users need to know Maxwell’s equations themselves, another question could be: Should Sonnet users know Maxwell’s equations? Rautio answered with, “I would suggest that knowing Maxwell’s equations covers a broad spectrum. Some of our most dedicated power users are using Maxwell’s equations to derive Green’s functions, Hankel functions, etc. That knowledge can help those users drive the tool to its absolute maximum potential—even going so far as to script new features.”

Rautio continued, “Conversely, we have multidisciplinary users who are interested in validating something specific, and thus have little need to understand the physics beyond successfully extracting a model. In practice, I think there is a “sweet spot,” where the median user of our tool benefits from understanding the general physics of the equations—how waves propagate, types of coupling, resonances, and things of that nature—without having to memorize the underlying equations or be ready to evaluate sets of double integrals. It’s roughly analogous to the hardware we compute on—knowing how the CPU and RAM interact can be quite important to a user but understanding the VLSI architecture of the CPU is extra credit.”

So, there you have some perspective concerning the topic of Maxwell’s equations for today’s engineers. Of course, only you can determine if you really need to know them or not. But perhaps reading this has motivated you to open up that dusty textbook once again in search of those equations.

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