A lot of the notes in Dercuano contain calculations. To take a random example, Lab power supply says:
It could maybe dissipate like 20W, which at 12V would be just 1.7 amps…
Supposing arbitrarily that I were to use a similar ATX power supply capable of 18A on its 12V output, which works out to 216W (a bit over a quarter horsepower), it would be nice to be able to carry that 216W most of the way down the range, say down to 2V — which would mean 108 fucking amperes.…
How much energy do we need to store in the inductor at 62.5kHz? That’s 16 microseconds per cycle. I’m a little unclear on exactly how the math of buck converters works out but I am pretty sure that it will not involve storing more than 16 microseconds’ worth of power in the inductor, which would be three or four millijoules, and I’m pretty sure it’s okay for the inductor current to fluctuate by 10% or so, maybe a lot more. So if ½LI² = 4 mJ and I = 18 A, then L = 2·4 mJ / (18 A)² = 25μH,
Refreshing at 1kHz (again, as suggested in the display datasheet) would require iterating at 11kHz. At the AVR’s internal RC oscillator speed of 8MHz, this gives us 727 clock cycles per display update…
These calculations are unfortunately “dead”, not “live” like the calculations in a spreadsheet, and by the same token, they’re time-consuming to verify — if you want to check to see if my calculations are wrong, you need to enter each number into a spreadsheet or calculator and redo the calculation from scratch. I typically use units(1) to do the calculations (as described in Executable scholarship, or algorithmic scholarly communication) which reduces my chances of accidentally dropping a “milli” or a “kilo” from the calculation, or using the wrong conversion constants, but if you’re using Gnumeric or whatever, you have to check those too.
And the calculations are just individual points, while the underlying formula is a much richer interrelationship. If you’re looking at the ½LI² formula above (see also Dercuano formula display) and you wonder how high the inductance L would need to go to support 20 A of current, you need to think about it for a while. If you’re not used to this kind of thing, the answer may require some square roots and stuff.
Such calculations can be made “live” by generating them from some kind of JS library that does calculations. I’m thinking that something like my prototype RPN editor could be developed into a comfortable way of computing the quantities and displaying how they were derived, although it does require a context switch from editing plain text.