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Per the Seeeduino specifications here, it says:

DC Jack & Vin Input Voltage

7V to 12V (lower is preferred). Maximum is 20V. If input lower than 7V and switch set to 5V, then VCC at AVR is about 2V below the input.

So two contradictory statements back to back. Input voltage is 7-12V, and maximum is 20V. What should I make of that? I have a 16 volt power source that I'd like to power it from. Will that work? Would a higher input voltage limit my current draw since the voltage regulator has to burn off the extra power? Any other limitations?

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That’s not so contradictory but quite an usual specification.

The max. rating (20V) is where your device will get damaged with high probability.

The nominal input range 7-12V is where it operates without restriction.

The range in-between, i.e. 12-20V is not recommended because it has some (internal?) restrictions. In the present case I assume there is an internal regulator that produces a lot of heat with higher voltages. So you might be able to operate it at 19V, but it would get very hot and this will limit the lifetime of the device.

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