Some more off the howto-stuff, I lately started. Sometimes I was mentioning that a frequency should be divided... now, that is strange! So far we had it about multiplication of frequencies by some sort of factors, and now division?!

Yes, rather simple, yes really!

In the digital world, some thing are out there called counters. There are a couple of different counters available. The most primitive of all is the Flip-Flop, which is counting to 2.

Now, how does a Flip-Flop help to divide a frequency? Very simple, have your oscillator's signal on the clock input... .... ah well, it has been written before, check this out.

So, here you got it, cascading Flip-Flops will result in a division by 2^x, as cascading doublers did for multiplication. The cascade of Flip-Flops is known as Ripple-counter.

You may ask yourself, if division by odd numbers would be easily possible, as easily as multiplication was. The answer is NO. One can use hexadecimal or decade counters to divide a frequency, just as it is done with a ripple-counter, however, there is a disadvantage. A ripple counter ensures a 50% duty cycle, i.e. HIGH for half a period and LOW for the other half, which is symmetrical and can be smoothed to a sine-ish waveform by a low-pass filter. Any other counter-divider, however, will result is a duty cycle being off. So, what you really want to do is, ensure that your final division is EVEN and use a Flip-Flop as the last stage. Example: we would like to divide a frequency by 10. We would first use a decade counter, counting to 5. The resulting pulse would be sent to a Flip-Flop, so that the total amount of division would be 10. Always try to have your duty cycle as close as possible to 50%. Assume you need a division by 21. Use a decade counter to divide by 7 and cascade it with a counter to 3. This will give a 33% duty cycle, still relatively symmetrical, compared to a 14% duty cycle in reverse order....