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I'm trying to use a MAX471 module (no brand) with arduino (5V) following this tutorial.

I measure the current with my multimeter of a motor with a 200Ω resistor and i get ~14.84mA. The sensor displays ~13.8mA and some times it drops to ~8.6mA

I power the motor with Arduino as power supply via the module.

When I connect instead of a motor a LED via a 1k resistor, i get 2.80mA in the multimeter the sensor displays 0. Does it have a minimum range and can this be fixed so to get current sensing for low current?

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According to the Datasheet on the IC, the accuracy drops to 15% at 1% full scale current. Full scale is 3A, 1% is 30mA. So you definitely need a better current sensor.

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    \$\begingroup\$ The fact that the module is an Ebay cheapie based on an obsolete part from a prolifically faked manufacturer adds weight to your advice! \$\endgroup\$ – replete Apr 25 '17 at 2:24

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