| This is likely not a useful explanation if you do not specifically know what a a Phase-Locked Loop is, but I want to say that it is yet another example of how negative feedback can give you an implementation for the inverse of a component. In this instantiation of the concept, a frequency divider (dividing by a whole number) is something that's easy to build: it's a counter. For example, to divide by 100, count the input clock, when you increment from 49, wrap around to 0, and toggle the output. Putting that divider in a negative feedback loop gives you a multiplier. Another common instantiation: if you put a voltage divider (easy to build with a couple of resistors) in the feedback path of an operational amplifier and you get a voltage multiplier. Another instantiation with op-amps: Put a capacitor in the feedback path, and you "get" an inductor. This one is also a big deal because, practically speaking, it's easier to engineer close-to-ideal capacitors than it is inductors, which are heavy and lossy. And if you really want to take a ride on this conceptual train, consider that it's easy to square a number. Need the square root? Use negative feedback: https://en.wikipedia.org/wiki/Newton%27s_method#Square_root |