Impedance and the Power of Analogy

Blog Post created by benz on Apr 20, 2017

  Electrical engineers lead the way

Years ago, a manager of mine seemed to constantly speak in analogies. It was his way of exploring the technical and business (and personal!) issues we faced, and after a while I noticed how often he’d begin a sentence with “It’s like...”

His parallels came in a boundless variety, and he was really creative in tying them to our current topic, whatever it was. He was an excellent manager, with a sense of humor and irony, and his analogies generally improved group discussions.

There were exceptions, of course, and misapplying or overextending qualitative analogies is one way these powerful tools can let us down.

The same is true of quantitative analogies, but many have the vital benefit of being testable in ways that qualitative analogies aren’t. Once validated, they can be used to drive real engineering, especially when we can take advantage of established theory and mathematics in new areas.

The best example I’ve found of an electrical engineering (EE) concept with broad applicability in other areas is impedance. It’s particularly powerful as a quantitative analogy for physical or mechanical phenomena, plus the numerical foundations and sophisticated analytical tools of EE are all available.

Some well-established measurements even use the specific words impedance and its reciprocal—admittance. One example is the tympanogram, which plots admittance versus positive and negative air pressure in the human ear.

Two "tympanograms" are impedance measurements of the human hearing system. These diagrams show admittance (inverse of impedance) to better reveal the response of the system at different pressures, to help diagnose problems.

These tympanograms characterize the impedance of human hearing elements, primarily the eardrum and the middle ear cavity behind it, including the bones that conduct sound. The plot at the left shows a typical maximum at zero pressure, while the uniformly low admittance of the one on the right may indicate a middle ear cavity filled with fluid. (Image from Wikimedia Commons)

Interestingly, those who make immittance* measurements of ears speak of them as describing energy transmission, just like an RF engineer might.

Any discussion of energy transmission naturally leads to impedance matching and transformers of one kind or another. That’s where the analogies become the most interesting to me. Once you see the equivalence outside of EE, you start noticing it everywhere: the transmission in a car, the arm on a catapult, the exponential horn on a midrange speaker. One manufacturer of unconventional room fans has even trademarked the term “air multiplier” to describe the conversion of a small volume of high-speed air to a much larger volume at lower speeds.

All of these things can be quantitatively described with the power of the impedance analogy, leading to effective optimization. It’s typically a matter of maximizing energy transfer, though other tradeoffs are illuminated as well.

Maybe my former manager’s affection for analogies rubbed off on me all those years ago. I certainly have a lot of respect for them, and their ability to deliver real engineering insight in so many fields. We EEs can take some degree of pride in leading the way here, even if we’re the only ones who know the whole story.

*A term coined by our old friend H. W. Bode in 1945.