Self-referential abstractions: A quick look at the wacky epistemology of analog circuitry

While you can get a lot more done just focusing on the application and not the theory, sometimes it’s easier to understand and therefore remember what is happening if you look under the covers.

Take, for example, an LED. If you want to power it, common wisdom will indicate you need a resistor to limit the current or else the LED will burn out.

This resistor will depend on the specific LED voltage drop, current rating, and the source voltage.

An equation you may be taught to calculate the resistor needed r for a given source voltage s, a voltage drop d, and a target current i is: r = (s - d) / i

At least when I was learning, it was a little bit difficult to remember such an equation in a vacuum. At some point I realised that at any given instant any circuit component in a circuit (without significant inductance or inductors) will have a set resistance, and given a specific supply voltage through a circuit, you can use V = IR (and a few other rules) to calculate the voltage drop and current through any component. It wasn’t until I realised this that I realised that the calculation for the resistor needed for an LED could be thought of a different way:

An LED (or any diode) can actually be thought of as a dynamic resistor which varies with the current flowing through it to ensure a consistent voltage drop (and yes, this is somewhat a simplification, there is inductance to consider and a number of other complex factors, but when you teach kids electronics, you teach them how to make LEDs light up, not how to design an oscilloscope).

Therefore, I need to form a voltage divider which has one resistor with a resistance u and another resistor with a resistance v. The goal is to pick v given some measurements we have about u. u is dropping d (the LED forward voltage drop from before) and has i amps of current flowing through it. This means that for a supply voltage (to the divider) of s, v has to drop s - d volts and also have i amps of current flowing through it. If we re-arrange V = IR into R = V/I we can now drop in our target voltage s - d and our current i and we get r = (s - d) / i.

Sometimes I really struggle to remember certain formulae, and this is precisely one of the cases where I’ve given up and whenever I need to make a calculation for the resistor for an LED I instead draw upon my more fundamental understanding of electronics to momentarily remind myself how these formulae are derived.

(Apologies for using non-standard variables in these, it’s lobsters, I considered maybe something like Vf and Iled but I wasn’t sure it would be any better.)