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SAR ADC with Selectable Input Range

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I am in the middle of designing 8-bit SAR ADC and believe I have mostly understood this architecture.

However, I can only design it for Vin range from 0V to Vmax (where Vmax < Vdd and is a separate input).

The issue is how to design SAR ADC with arbitrary input range from Vin_min to Vin_max (both < Vdd).

Example: Vdd=800mV, Vin_min=250mV, Vin_max=550mV
Vin <= 250mV = 00000000
Vin = 325mV = 01000000
Vin = 400mV = 10000000
Vin = 475mV = 11000000
Vin>= 550mV = 11111111
(something like that)

How can I design SAR ADC to work with an somewhat arbitary Vin range (as opposed to 0V to Vmax)?
 

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