The Designer's Guide Community Forum

The Designer's Guide Community Forum
https://designers-guide.org/forum/YaBB.pl
Design >> Mixed-Signal Design >> choosing stable butterworth noise transfer functions for delta-sigma modulators
https://designers-guide.org/forum/YaBB.pl?num=1221550298

Message started by vivkr on Sep 16^th, 2008, 12:31am

Title: choosing stable butterworth noise transfer functions for delta-sigma modulators
Post by vivkr on Sep 16^th, 2008, 12:31am

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

Title: Re: choosing stable butterworth noise transfer functions for delta-sigma modulators
Post by vivkr on Sep 17^th, 2008, 7:14am

For anyone who is interested, I found a solution to this problem.

I simply redesign the Butterworth filter of choice with lower and lower cutoff frequency (but keeping the same order) until the out-of-band gain of the NTF (H_inf) is within reasonable limits. This yields satisfactory results, and I now have stable NTFs.

This method is advocated in the "cookbook" design procedure in Chapter 5 of the yellow book by Norsworthy, Schreier & Temes.

Regards,

Vivek

Title: Re: choosing stable butterworth noise transfer functions for delta-sigma modulators
Post by rf-design on Sep 22^nd, 2008, 3:24pm

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

Title: Re: choosing stable butterworth noise transfer functions for delta-sigma modulators
Post by vivkr on Sep 22^nd, 2008, 10:56pm

rf-design wrote on Sep 22^nd, 2008, 3:24pm:

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

The sigma-delta is multi-bit but that is not really relevant here except in the sense that the final choice of the NTF should give a much lower H_inf for the single-bit case. In either case, the butterworth transfer function needs to be adjusted until a certain level of H_inf is reached.

Regards,

Vivek