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you are correct about the offset on the output signalnot sure exactly what you're getting at with the sampling theories. what i'm doing in my project is taking a fixed number of samples where I measure the maximum value of the waveform coming into the MCU. then, using the average value of the max, I calculate the RMS value using max/sqrt(2).
the same way you would calculate the DC current...you just end up getting a sinusoid on the output of the ACS rather than a DC signal. you might have to add some DC bias to the signal so as to make sure you are not feeding negative voltage into the ADC pins of your MCU, though.
yeah definitely don't try powering your arduino with AC!! in addition to the current ratings, each ACS model has a different output voltage proportional to the input current. you need to read the data sheet to get these values.
these ACS modules are actually quite accurate. they don't need a shunt resistor to measure current like you're describing because they use the Hall Effect sensing method to obtain the measurement.
the ACS module can sense AC current quite nicely as well. I'm currently using it in a project where the two input leads are simply connected in series with the live wire from a wall outlet.
these modules output a different mV proportional to the input current. the 5A module gives something like 185mV/A on the output while the 20A gives something like 130mV/A. these values can be found in the datasheet for the ACS712 family.
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