Beyond the Spherical Chicken: Rewriting Maxwell for Modern Machines
By Max Maxfield
This is going to be a story in three parts. If we’re lucky, they’ll be related, but I’m not making any promises. Let’s start by discussing one of the things I know nothing about. Yes, I know this is a long (and ever-growing) list, but in this case, I’m thinking about the design and analysis of antennas and radar systems.
The closest I’ve ever come to designing an antenna was when I came into proud possession of a battered old black-and-white vacuum-tube and cathode-ray-tube (CRT) television, circa 1971, when I was about 14 years old. I installed this bodacious beauty in my bedroom, and I used a carefully bent metal clothes hanger as my antenna. The resulting images were noisy and low-resolution, but that wasn’t uncommon in those days of yore.
The point is that I really didn’t know what I was doing or why I was doing what I was doing (a state of affairs that’s as true today as it’s ever been). Happily, I wasn’t alone, because antenna design has historically been as much an art as a science.
Maxwell’s equations—first published in a series of papers between 1861 and 1865 and later unified in his 1873 treatise—form the theoretical foundation of classical electromagnetism, classical optics, and electric and magnetic circuit theory, while simultaneously laying the groundwork for modern antenna analysis. Yet, despite this rigorous mathematical underpinning, practical antenna design and analysis long relied heavily on experience, intuition, empirical tuning, and physical prototyping.
Real-world factors—nearby structures, materials, coupling effects, manufacturing tolerances, and the installation environment—often behaved in ways that were difficult or impossible to predict analytically. As a result, prior to the 1960s, successful antenna designers developed a kind of craft knowledge, blending theory with rules of thumb, measurement, and iterative adjustment.
Engineers have been simulating antennas since at least the 1960s, when numerical techniques like the Method of Moments (formalized for EM applications by Roger Harrington in 1968) enabled Maxwell’s equations to be solved on room-sized computers with less memory than today’s wristwatches.
Of course, simulators have increased in capacity and performance over the decades. Having said this, many of the mathematical foundations behind modern electromagnetic solvers date back 30 to 40 years (or more), when memory was scarce, processors were slow, and simplifying assumptions were a practical necessity, which helps explain why so much classical antenna simulation still treats the devices in splendid isolation. Real aircraft, satellites, and vehicles are inconveniently large and electromagnetically messy, so designers have traditionally analyzed tidy antenna elements hovering in computational nothingness, evoking the physicist’s timeless simplification “…assuming a spherical chicken in a perfect vacuum.”