Sigma-delta modulator integrator question

[ljy4468]

Hi all~
I've a question about SDM's intgrator.
when we model integrator as a z-domain(see attatched)

some book (analog integrated circuit design: Martin) explain as (b)

but some book(richard schreier) explain integrator as (a)

what is correct??
I'm so confused.
Somebody gives me help please

Thanks in advance

 

[safwatonline]

actually the second one has v/u= (Z^-1)/((Z^-1)-1)
i think the second is the used one as it has a delay in the forward path

 

[lijianheng]

(a) seems to be a noise shaping function

 

[ljy4468]

Thanks, safwatonline!
what's the difference that a delay in forward-path??
explain me more detail please

 

[noiseless]

just second one has a delay compared to first one

 

[ieropsaltic]

Both are integrators i.e both will provide you with the required NTF (1-z^-1) .The only difference is that the STf of the first one = 1 while for the second one is z^-1 which is simply delay (i.e the output is same as input but with a delay) .

Sometimes when you implement a digital SDM (as in PLLs ir DACs) ,you need registers to be placed at the forward path not the feedback one to reduce your critical path and enalle higher clock speeds (same idea as pipelining) .Also, for high order single loops, this may affect stability (but I'm not sure about that) .