This instructable shows a reciprocal frequency counter capable of measuring frequencies fast and with reasonable precision. It is made with standard components and can be made in a weekend (it took me a bit longer :-) )

The old school way to measure the frequency of a signal is to use a logic AND-gate, feed the signal to be measured into one port and a signal with an exactly 1 second high time to the other port and count the output. This works quite well for signals of a few kHz well into the GHz. But what if you want to measure a low frequency signal with good resolution? Say you want to measure the frequency of mains (here 50 Hz). With the old school method you will see a constant 50 on your display if you are lucky, but more likely you will see the display switch from 49 to 50 or 50 to 51. The resolution is 1 Hz, and that’s it. You will never see 50.002 Hz unless you are willing to increase the gate time to a 1000 seconds. That’s more than 16 minutes, for a single measurement!

A better way to measure low frequency signals is to measure the period of it. Taking mains as an example again, has a period of 20 millisecond. Take the same logic AND-gate, feed it with, say 10 MHz (0.1 us pulses) and your signal on the other port and out come 200000 pulses, so the period time is 20000.0 uS and that translates back into 50Hz. When you measure just 199650 pulses the frequency is 50.087 Hz, that’s a lot better, and it is in just one second measuring time.
Unfortunately this does not work well with higher frequencies. Take for example, we now want to measure 40 kHz. With the same 10 MHz input frequency as the reference we now measure just 250 pulses. When we count just 249 pulses the calculation gives 40161 Hz and with 251 the result is 39840 Hz. That’s not an acceptable resolution. Of course increasing the reference frequency improves the results but there is a limit to what you can use in a micro controller.”

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