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# Remembering Circuit Theory

`December 27, 2018         `

For those of you who studied electrical engineering in college, remember the circuit theory course?

It has been almost half a century since I took that class, and my memories of it are vague. But I find electronics fun and fascinating, so thought it might be worthwhile to revisit that material. Lord knows what happened to most of my college textbooks, so I ordered Circuit Analysis, Theory and Practice (by Robbins and Miller) from Abebooks. It's a thousand-page tome that must weigh in at over five pounds. The price (used): \$3.70, with free shipping. What a deal! I can't imagine how they make any money on it.

I'm 600 pages in at the moment and have been surprised and gratified to find I remember most of the material. Norton's and Thevenin's Theorems, Kirchhoff's Laws, and more still lurked in these decaying gray cells.

Yet in 45 years of being a practicing EE I've never once used these fundamental principles. They're good to know, and foundational to analyzing circuit networks. It's like knowing how to integrate a simple differential equation to get the formula for an RC time constant… but in practice, in the real world, one only uses the resultant formula:

Then, in AC circuits, there are phasors. No, not the kind Captain Kirk uses against the Klingons (and which are spelled "phaser"), but the rotating vectors used to represent phase and magnitude of a sine wave. A rotating vector? Doesn't that sort of break the rules of vectors, which are entities that have magnitude and direction? Well, at any point in time a phasor does have those properties. I don't think I really understood them while struggling through that class. Now they make sense, but still seem quite cumbersome compared to the trig:

I have to convert a phasor expression to the trig to solve real-world problems, but that could be a flaw in my understanding.

Though I've used the trig formulation thousands of time in my career, I've never used the phasor representation.

Then there are the problems students need to solve. Every chapter ends with a lot of these, some of which are incredibly convoluted. THAT I remember: for instance, reducing some absurd network of resistors to one equivalent value. Jeez, the profs made us burn some serious brain cells doing this. Here's an example problem from the book:

Perhaps young, malleable minds need to struggle through the contortions needed to reduce this to a single equivalent resistor. Perhaps doing so drives the basic ideas of series and parallel resistors indelibly into a budding engineer's psyche.

In the real world I've used the classic formula for two resistors in parallel a zillion times:

And the more generalized one for many resistors a few times:

But to solve for a nasty resistor network like the one above? Never. Need a resistor? Calculate the required value, check the Digi-Key site, and buy one with the closest value to that required. Problem solved.

Then there was that statics class. That was tough. The next semester things got so much worse in dynamics where everything was moving! Ironically, I do use statics a lot, but for computing loads on my sailboat or moving logs around the yard. Never in electrical engineering.

I was an electronics nerd long before starting at the University of Maryland and found that the formal education gave a theoretical grounding to the practical knowledge gleaned from years of messing about with circuits. I do appreciate those years suffering under the tutelage of the academics.

One of the best books on electronics is The Art of Electronics by Horowitz and Hill. It's very practical and written to appeal to people who design things. It's short on theory; you won't find a complex number anywhere. So I'm tremendously enjoying Circuit Theory which is the philosophical conjugate to of the H&H book, sort of existing on the j axis while H&H are in the real domain.

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