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The 1.65 V bias is generated by dividing 3.3 V supply with 1k + 1k voltage divider, see ADDA card schematic. It's usual to bias differential input ADC at the center of analog supply voltage for best linearity.
That's not possible, you need to consider ADC input voltage range. 0 V (or may be -0.2 or -0.3 V) is the most negative voltage that can be processed by an ADC input pin.
If you read the datasheet thoroughly, you'll notice that single ended operation gives reduced performance anyway. For DC capable operation of a differential input ADC, you preferably use a fully differential amplifier, see e.g. AD9248 evaluation board schematic.
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Thanks for the explanation. Do you know what is the original input range of the Terasic board? The manual only says 2Vpp span. Do you have an idea what simple circuit can be used to make the board suitable for 0-2V DC signaling? Even if the performance is not perfect? I would like to leave the ADC on the board like it is, but I could completely change the circuit to VINp and VINn. I searched a lot for available boards with DC coupling and a suitable interface, but without luck. I know decided to modify the board, but I'm not sure about all the voltage levels etc.