Can the customer use it as output current Iol=11mA by setting the pull-up resistor to 430Ω?
The reason why the customer wants to use 11mA is because he wants to use a MOS FET Relay.
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Thanks for reaching out on the forum. For some of our pins we have a 5mA limit due thermal dissipation which can damage the part. The VOL spec shows a test condition of 3mA which could just mark the beginning or the internal mosfet's saturation region or it could be the max sinking current value we suggest. I need to verify with one of our design engineers and I will try to have that response for you on the next business day.
Based on my discussion with one of the design engineers, your customer may be able to use a 430Ω. If they do so, then the device Vol will likely be outside of the max range listed in the electrical characteristics section. Based off the device VOL specification, the internal mosfet worst case resistance looks like 100Ω. That value in series with 430Ω leads to the INA381 sinking 9.4mA. That much current across 100Ω is 940mV. If you have a microcontroller connected to this, it may violate the specification for a status low level signal.