"Two twenty bit DACs (one per phase) double the resolution for a balanced signal. Double the resolution only adds 6db (one more bit) for a total of 21 bits. In this case, 20+20 equal 21."
Actually, the first sentence isn’t correct. Or at least it is somewhat misleading, depending on what comparison is being implied by the use of the words "for a balanced signal."
As Shadorne correctly indicated earlier, simply using one DAC chip to create one phase (i.e., polarity) of the analog signal and another DAC chip to create the opposite polarity will not increase the resolution beyond what is provided by each of the chips. While it will double the full scale (maximum) output voltage compared to single-ended operation of one DAC chip, it will also double the voltage corresponding to the least significant of the 20 bits. So the number of discrete steps (i.e., possible values) within that doubled voltage range will still be 2^20 (two raised to the 20th power), meaning that resolution will still be 20 bits.
As I described earlier, though, if one DAC chip is used to handle the positive half of the output voltage that is ultimately generated, and the other DAC chip is used to handle the negative half, the resolution would indeed become 21 bits.
Regards,
-- Al
