Hi,
to destinguish 50Hz from 60Hz you need some accuracy ... no matter which way you chose.
But:
* here (Europe) we have 50Hz. There are not much times in a year where it is outside 50Hz +/- 0.2Hz, which is just +/- 0.4%. If outside, then there will be a more global reason. Actual measurement:
https://www.netzfrequenzmessung.de/
* 5% seems to be huge.
* for nominal 60Hz you get 8.333ms (not 8.77 ms)
Sqrt(10ms * 8.333ms) = 9.129ms (I simplified it to 9ms). This gives 8.7% to 50Hz and 8.7% to 60Hz
It´s on you to chose the right one shot according your requirements.
You can buy one, you can build your own using a comparator .. or build one using an XTAL and a counter. (Like 1MHz XTAL, reset at rising zero cross mains, trigger the DFF at count 9129)
If you build one with comparator you can chose resistors, capacitors and comparators according the expected accuracy.
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The given solution updates the result
every full wave. You did not specify how fast / how often you need an update.
For sure if you need an update every 1s you can just count full waves for one second ... and decide at which threshold(s) you show 50Hz and 60Hz respectively.
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Also you gave no information why no microcontroller. (Is it a school project?) For me it is the most obvious solution: accurate, adjustable, reliable, small, low power, low part count, no drift / aging, optional filtering .... Even an 8 pin microcontroller will do the job. I´d use an XTAL.
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Regarding FvM´s phase detector:
I guess he wants to use the fact that the signal phase changes a lot around "resonance frequency" of the band pass filter. So the phase tells you whether your input signal is below or above the "resonance frequency". Ouptut of phase detector = below / above 55Hz.
Klaus