Sigma delta MOD1 quantizer expression

[yefj]

Hello, I amh having trouble to deside the quantizer i am not sure about the expression for Vref and Vo,int regarding the time inside.

I dont know if these two expressions are true:
Why Vo,n=Vo,int+en
e_n is the noise of the quantizer
Vo,int is the signal before the quantizer
if its before the quantizer then they should be N-1 time , Vo,n=Vo,int_n-1+e_n-1
Why its on the same time??I cant see the logic in this.

 

[FvM]

SD implements a unit delay between the quantizer input and the modulator. If the quantized output is delayed or not doesn't affect the feedback loop.

 

[yefj]

Ok So if i understand you correctly from the diagram shown bellow
Vo_n=V_int(n-1)+err(n-1 )
Vref remains the problem how should i define it ?
is there some similar developed implementation i could read?
Thank.

 

[yefj]

Hello,I am trying to figure out the development shown bellow of the SIGMA DELTA ADC transfer function. However the definition of Vref, and Vint are the same except the time if n-1 instead of n. very non imtuitive explanation. I cant find anywhere in the internet a similar switch capacitance implementation. Is there some anternative source of switch capacitor i can follow its development?
Thanks.