There is some confusion with the 1.333 factor given in the data sheet
AD1877.pdf_page2_rev0. What is the applicable value to 2^15 Full Scale?
Vref or Vref x 1.333 ?
The answer to your question is to be found on page 8 of the datasheet in the
section APPLICATIONS ISSUES:Analog Input voltage swing.
Nominally the analog input span is 3.1V, that is, Vref+/- 1.55V. Therefore
there is a little confusion when Vinpp is given as Vref x 1.333 which is 3.0V
(taking Vref at it's nominal value of 2.25V)
However, on page 8 it is explained that the analog input span actually scales
with the reference voltage.
Since the reference voltage is fairly loosely specified in terms of absolute
accuracy (+300mV / - 200mV) there is also a fairly large variation in the input
span. The formula on page 8 shows that the analog input span is in fact
proportional to the reference voltage. If you rearange the formula you get
Yvolts = Xvolts x 1.378
Yvolts is the maximum swing without clipping
Xvolts is the measured reference and 1.378 is the ration between nominal
voltage swing and nominal reference voltage
So, the 1.333 factor given on page 2 is simply being cautious, by stating a
limit for the input signal which will ensure no clipping takes place. In fact,
the "real" number is 1.378, so to calculate the lsb size
1lsb = Vref x 1.378 /2^16 =47.3uV for a nominal reference of 2.25V. The lsb
size will change depending on the actual value of the reference for the
particular device in question.