A Comparison of Theoretical, Simulated, and Experimental Results Concerning the Stability of Sigma Delta Modulators

Mladenov V, Reiss JD, Tsenov G. A Comparison of Theoretical, Simulated, and Experimental Results Concerning the Stability of Sigma Delta Modulators. In: AES Convention 124. Audio Engineering Society; 2008. Paper 7440. Available from: https://aes.org/publications/elibrary-page/?id=14570

@inproceedings{Mladenov2008_14570,
  author = {Mladenov, Valeri and Reiss, Joshua D. and Tsenov, Georgi},
  title = {{A Comparison of Theoretical, Simulated, and Experimental Results Concerning the Stability of Sigma Delta Modulators}},
  booktitle = {AES Convention 124},
  note = {Paper 7440},
  year = {2008},
  month = may,
  publisher = {Audio Engineering Society},
  url = {https://aes.org/publications/elibrary-page/?id=14570}
}

TY  - CPAPER
TI  - A Comparison of Theoretical, Simulated, and Experimental Results Concerning the Stability of Sigma Delta Modulators
AU  - Mladenov, Valeri
AU  - Reiss, Joshua D.
AU  - Tsenov, Georgi
T2  - AES Convention 124
M1  - Paper 7440
PY  - 2008
DA  - 2008/05/06
UR  - https://aes.org/publications/elibrary-page/?id=14570
PB  - Audio Engineering Society
LA  - en
AB  - Sigma delta modulation is a popular form of audio analogue-to-digital and digital-to-analogue conversion, but suffers from stability problems for many designs and many input signals. A general theory of stability in sigma delta modulators has been developed which predicts the stability of a high order one bit sigma delta modulator (SDM) under a variety of designs. In this paper, the theoretical approach to stability as it applies to boundedness of states is explained. Several low pass SDM designs are developed which are intended for audio analogue to digital conversion, and predicted results for stability of these designs are given. Stability is examined both in terms of the maximum allowable DC input amplitude and the theoretical sufficient conditions for stable behavior. Theoretical results are compared with simulated results, and where possible, with experimental results from a realisation of a third order SDM with adjustable parameters. Practical observations are then made concerning the effect of noiseshaping, pole/zero placement, and cut-off frequency on the stability.
ER  -