The Physics of PCB Design


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In this wide-ranging interview, Dr. Eric Bogatin discusses the relationship between physics and electrical theory, and why it’s critical for designers and design engineers to understand the laws of physics. As he points out, the math is important, but designers shouldn’t let the principles of physics “hide behind the math.”

Eric discusses some points of physics that designers need to understand, the physics resources available, and why it’s so important to have some understanding of Maxwell’s equations, even if you don’t have a strong math background. 

Andy Shaughnessy: Eric, we’ve heard a lot lately about how designers need to focus more on physics, not just circuit theory. Since you have two physics degrees and you teach signal integrity, what do you feel are most designers missing in terms of the physics?

Eric Bogatin: First, let me understand the terms that we’re going to use. When you say physics, are you talking about EM fields and Maxwell’s equations? Let’s talk about the terms.

Happy Holden: Other than Newton, James Maxwell helped define modern physics. He didn’t discover magnetic fields, but he certainly showed the relationship. We’re constantly talking about signal integrity problems, and Moore’s Law is driving and challenging Maxwell’s laws. They’re both important. 

Bogatin: Moore’s Law is what drives the ever-finer feature sizes and transistors, the channels. That means shorter rise times and more signal integrity problems, but when it comes to the SI problems and the impact the interconnects have on the signals, there are two ways of thinking about them: the circuit theory approach and the fields approach, which is really a transmission line analysis that’s inherently distributed where the electromagnetic fields are important. 

Barry Matties: When someone says, “PCB design is really just about physics,” is there more to that statement than what you just described?

Bogatin: When they say it’s all physics, it’s the electromagnetic fields described by Maxwell’s equations and electromagnetic fields. They’re all synonymous in this context. It’s correct that the way signals interact with interconnects is all electromagnetic fields and the boundary conditions—all Maxwell’s equations. You don’t have to be a PhD student to learn how to solve Maxwell’s equations, but you must understand a little bit about electromagnetic fields, how they interact, and how they propagate.

I had Professor Walter Lewin as a freshman at MIT, and I still vividly remember his lectures. Now there is a video series from his second semester freshman physics class, and he’s got a million views. I use what I learned in his class almost daily. When I look at the videos, which are recorded 40 years after I took the class, I see he hasn’t changed at all, and the videos are timeless. I always recommend them.

Holden: For people who are interested, are Lewin’s courses suitable for those without electrical engineering degrees, but are interested in understanding the principles?

Bogatin: Yes. They’re offered to freshmen. You don’t need to be enrolled in electrical engineering classes. There’s a little bit of math, but he goes through it slow enough that if you’ve had a little bit of calculus, you’d see it instantly. If you didn’t, that’s okay. It’s only 25% equations. You still get the principles.

Holden: Maxwell is not the easiest subject. Both Nolan and I were in electrical engineering, but because of the difficulty and the flunk-out rate from fields theory, we chose coding and stayed away from the RF and the fields. I just didn’t have the mathematical prowess to handle that.

Bogatin: You’re right. If you go that next step and talk about electromagnetic fields, Maxwell’s equations are differential equations, and you must understand some of that.

What I like about Walter Lewin’s lectures is he emphasizes the principles and the behaviors and doesn’t let the math hide it. My students bring me his videos all the time. Most of the YouTube videos on understanding electromagnetics are bad analogies or they’re not even the right physics. You’re not learning something you can use to leverage other things down the line. 

Just for perspective, at MIT you get mechanics and electromagnetics in your freshman year. It’s some math, but you get the heavy math in your junior and senior years. In my junior year, I took electromagnetics. We used John David Jackson’s Classical Electrodynamics and it’s incredibly heavy in the math. 

Holden: Is the abundance of heavy math instruction the reason why a lot of your focus has been on the rules of thumb and simplification in your books and publications?

Bogatin: Yes. Much of my style comes from what I learned from classes at MIT. Not to say that there isn’t rigor, but my professors emphasized the understanding part first, then the math, and I picked up on that. It is remarkable how far you can go with simple models to understand things. They have the math at their core. Math is the language of engineering and science. You must have that, but you don’t need to have every conversation with math. 

There’s one approach I use called strategic simplification. You want to simplify the problem enough to understand the main points, answer important questions, and get to an answer quickly, but not so simple that you have degraded it, so it doesn’t apply to real problems. How do you take complex problems, describe them in a simple way to get an answer quickly, while still having the core of the problem in the solution in the description with not so much math?

Having said all that, math is important. If you have the opportunity, get as much as you can and apply it. Do it as a student, because when you’re a professional engineer, you don’t always have that time. 

To read this entire conversation, which appeared in the November issue of Design007 Magazine, click here.

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