Switched capacitor ADC INL

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yefj

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Hello, I cannot see How they got the expression 10.2-19 bellow:
Why Vout*2C=Vref*(C/2^i-1) there is no 2C feedback loop
Another thing is Why its the worst case?
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The total capacitance in the DAC is 2C. When you only connect the i-th capacitor to Vref, the output of the dac is defined by a capacitive divider and is Vref(Ci/Ctot)=Vref(Ci/2C). It is not the worst case but since you only post a piece of the book, I don't know what they mean by worst-case approach.
 
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