Question for SC integrator

[gmcfilter]

sc integrator

Hi everyone

I study the sigma delta modulator

What is different delay free SC integrator and delaying SC integrator ??


The transfer function is different

delay free SC integrator Z/(Z-1)

delaying SC integrator 1/(Z-1)

what is different ??

I don`t know exatly???

 

[LvW]

1 / (z-1) integrator

1.) H(z)=z/(z-1) is called "Euler-backward" approximation. It deviates from the ideal integrator function for higher frequencies (in the vicinity of the sampling frequency) and has a POSITIVE phase error.

2.) The other function H(z)=1(z-1) is the "Euler-forward" approximation and causes a NEGATIVE phase error at higher frequencies.

3.) Therefore, in many S/C circuits both types are combined with the aim to compensate the phase error. Tthat is the secret of the so called LDI integrator, which does not exist in reality, but can be defined as the result of the mentioned combination.