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What is with current sensors?

Hello.

So current sensors’ sensitivity is specified with mV/A but only the mV part is varied. So what is the point then? Am I getting it wrong? Do these all have an A step size? I want my step size to be at least 0.1A.
Can you please explain how these works?

Those numbers are the conversion or sensitivity factors, used to convert the sensor readings into Amperes. They do not imply a measurement step size, which depends instead on the resolution of the ADC used to measure the sensor output voltage.

For example, if you use the ACS724, on the 10A range the sensor will output 4V when 10A is flowing. A 10 bit ADC with 5V reference will divide the range 0-5V into 1024 steps, giving a measurement step size of (4/5)*10A/1024 = 7.8 mA/step.

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Thank you very much!

The actual calculation depends on the ADC and reference voltage you plan to use.