First of all, MAX187 does not seem to be a differential input ADC.
Differential Input :
You will need additional interfacing circuitry, mainly a differential
amplifier with enough common-mode range, which should be higher than
the amount by which your differential signal is above your ground. The
differential amplifier will then bring the differential signal to your
ground, which is your ADC's ground. Now your ADC is able to input a
differential signal.
Input Range :
The MAX187 has an internal reference of Vref = 4.096V. Assuming your
are using its internal reference, then the analog input range is from 0
to 4.096V. Your specification of +/- 2.5V would result in a span of 5V,
thus exceeding the analog input with internal reference. Not only this
won't work, but it may exceed the absolute maximums. Read the 'Input
Protection' section in the datasheet.
One possible solution is to incorporate some attenuation in the
differential amplifier we talked about earlier. The differential
amplifier should then bring a differential signal of +/- 2.5V into a
single ended signal in the vicinity of 4V.
Here's an integrated solution :
INA159 ==> MAX187
Look at page 8 of the INA159 Datasheet, and page 7 of MAX187.
The INA159 is used to interface +/- 10V signal to single supply ADCs.
Its gain fairly accurate, but I don't know if its linearity can satisfy
a 12-bit performance.
Instead of this, you can also find differential input ADCs. But this
doesn't mean you won't need any interfacing circuitries. It depends on
what you are interfacing to...
