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I have two similar questions regarding the PGA of the ADS1115.

Datasheet

Say I have the PGA set to 2, so the max voltage read is 2.048V. If I apply 3V to AIN0, I assume it will give me the max voltage reading. But will it fry my board?

Also, say I have 4V connected to AIN0 and 3.8V connected to AIN1. Say I wish to take a differential measurement, the answer being 0.2V. To get a precise measurement, should I set the PGA to 1 = 4.096V max, or to 16 = 0.256V max? I do not know if setting it to 16 will give me any result because the individual measurements are much higher than 0.256V, or if it will fry my board.

Thank you very much!

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The board will not fry if all analogue input voltages are within the range 0.3v below ground to 0.3v above Vdd, regardless of the PGA setting.

If the measurement voltage is outside the maximum voltage range according to the PGA setting, the digital code will be clipped at the maximum (or minimum).

If the differential input voltage is 0.2v, regardless of the common mode, which can be anywhere from gnd to vdd, fir example your 3.8 and 4.0v, with a vdd >= 4v, the most sensitive range for measurement will be gain 16, +/- 256mV full scale.

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As long as you keep within the supply voltages (plus or minus a few hundred mV as specified in the datasheet) you will not damage the part. The reading may not be correct (it will probably saturate at full count in either direction) if the gain is too high.

You do, however, have to ensure that the input voltage to the ADC does not exceed the supply voltage of the ADC. When you are using an external amplifier (as you must) that means clamping the voltage to the rails by some method or another.

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