1. THREAD — On understanding the fundamentals. When I was at university, I took a three-semester course on radio-frequency (RF) engineering, which taught me the profound importance of understanding things from first principles.
  2. When two electrical systems are interfaced, each one, looking towards the other, sees a certain “impedance”, or resistance. Only when the two impedances are “matched” can the combined system be stable.
  3. An important activity in RF engineering is, therefore, the design of a third electrical system that sits in the middle, and matches the impedance seen by the two interfacing systems, thereby providing overall system stability.
  4. So the first semester of the course was spent learning how to design matching circuits, using a procedure involving the drawing of “stability regions” on intricate circular graphs, called a Smith Charts, printed on paper.
  5. Once you had properly drawn a stability region, you could then be sure that as long as your matching circuit’s characteristic parameters fell inside that region, the resulting electrical system is guaranteed to be inherently stable.
  6. The notion of bounded inherent stability struck me as elegant, similar to the Shannon Sampling Theorem, which guarantees the reconstructability of an analog system, as long as you’ve digitally sampled at twice the highest frequency.
  7. (As an aside: Only those who understand the Shannon Sampling Theorem will understand the incredible scam that selling “oversampled” compact disk players was, back in the day.)
  8. Back to the story, the second semester opened with a surprise, when Dr. Hertling told us that having spent three months learning to design circuits with Smith Charts, we would never use them again! In the real world, we’ll use software!
  9. So why was one third of the three-semester course spent learning a technique we’d never use in practice?
  10. Because it taught us the first principles. It taught us that there’s boundaries to design values, if we want a stable system. It gave us the intuitive understanding of RF design to recognize when software output is likely to be wrong.
  11. The importance of understanding things from first principles was one of the most valuable lessons I took away from university, and that course in particular, and which has proven transferrable to so many areas of life, including investing.