SAR ADC offset effect on charge switching equations

[yefj]

Hello,Without offset the calculation is vey simple
First we connect all capacitors on one side we have ground on the V_minus of the opamp and Vin on the other side,so when we disconnect S1 switch
we have -Vin on V_minus of the opamp.
How does this minus voltage is effected if we have V_offset voltage on V_minus instead of Vgnd,What voltage would be after we connect Vin on the first step?
Thanks.

 

[sutapanaki]

During the initial sampling the offset has no effect because S1 switch connects hard the top side of the array to gnd. Offset starts playing when the caps are flipped one way or the other. In a perfect SAR the conversion will end with the (-) side of the comparator close to 0V +/- LSB/2. With offset you have to add to this also the comparator offset and this happens for any input. Thus, comparator offset translates to an offset of the ADC characteristic.

 

[yefj]

Hello Sutapanaki,So When we flip the switch on the MSB as shown bellow, we have a voltage divider as shown bellow,
how this voltage divider is affected?
Given the example bellow i just think that voltage divider of Vfs on MSB not affected so we just get
-Vin+Vfs/2+Voffset
Is it correct that we do everything as before ad just add V_offestto the result without involving it to the voltage divider calculation?
Thanks.

 

[sutapanaki]

The comparator offset doesn't affect the voltage division of the CDAC, so it is as before without the offset. But it affects the decision of the comparator. For example, flipping the MSB cap to Vfs is supposed to compare Vin with Vfs/2. But since the comparator has an offset, it will compare it with something else. Say the offset is 30mV and the input is at 0.52*Vfs. The CDAC produces voltage of Vfs/2. Without offset, the comparator will indicate that the input voltage is higher than the reference Vfs/2. But with the offset comparator will say input is still below. And this is valid for every input voltage.