One can use the standard function "synthesizeNTF" from the Schreier Toolbox to choose an optimal noise transfer function for a delta-sigma modulator. However, many books also mention that one may arbitrarily choose any suitable filter transfer function, especially the Butterworth transfer function (highpass for NTF), and use it after normalization (to fulfill the realizabilty condition).

However, a standard butterworth highpass function comes with all zeros at z=-1, and the out-of-band gain will thus be excessively high (from a few hundreds to tens of thousands), depending on the pole locations. The simulations then show instability even for very small inputs.

Do these texts all assume that one will need to move away the zeros and poles away from the standard Butterworth arrangement and realize kind of a "damped Butterworth" or what is the procedure?

Thanks for comments,

Vivek

Is the sigma-delta using a multi-bit? Is there a difference in stability for 1-bit and multi-bit?