### Crystal oscillator and dividing it’s frequency to make something useful

Last time I was messing with crystals, I managed to get a stable 0.5Hz timebase for my nixie clock and frequency counter projects. After some investigation through data sheets, I thought I’d take a moment and de-mystify a very useful IC called the 4521 24-stage frequency divider. Not that it is much of a mystery to those who know electronics, but for an amateur like myself who is figuring this all out for the first time, it can be a bit annoying to build something and not know why it works. I won’t go into the details of the crystal oscillator part, but focus on the 4521 IC.

Basically what this little beastie does is take the frequency pulses from a pulse generator (in this case, a crystal oscillator) and performs some math on them to divide the frequency down from the megahertz range to the hertz range which is more suitable for clocks and things that humans actually will see.

Consider the schematic on the right.

Pretty simple huh? The crystal’s frequency (printed on the can) is 4.194304MHz. That’s 4,194,304 cycles per second. You might think that is a weird number to pick but as usual, math comes to the rescue. Stick with me. The 4521 frequency divider exponentially divides the frequency generated by the crystal oscilator by powers of 2. You can see outputs labelled Q18-24. These are the exponents of 2. So Q18 is 2^{18}. What it does is divide the frequency from its input by this number and out pops the result on the appropriate pin of the IC. So in the case of Q18: 4,194,304/2^{18} = 16Hz. Get it? Not hard at all. For my 0.5Hz timebase, I used the Q23 pin so: 4,194,304/2^{23} = 0.5Hz. I’ve helpfully labelled the outputs on the schematic for you to show the various output frequencies.

Of course, if you substitute a crystal with a different frequency, you will get different results using the math above proportional to that frequency.