Stability Analysis of Limit Cycles in High Order Sigma Delta Modulators

Reiss JD, Sandler M, Reefman D, Janssen E. Stability Analysis of Limit Cycles in High Order Sigma Delta Modulators. In: AES Convention 115. Audio Engineering Society; 2003. Paper 5936. Available from: https://aes.org/publications/elibrary-page/?id=12352

@inproceedings{Reiss2003_12352,
  author = {Reiss, Joshua D. and Sandler, Mark and Reefman, Derk and Janssen, Erwin},
  title = {{Stability Analysis of Limit Cycles in High Order Sigma Delta Modulators}},
  booktitle = {AES Convention 115},
  note = {Paper 5936},
  year = {2003},
  month = oct,
  publisher = {Audio Engineering Society},
  url = {https://aes.org/publications/elibrary-page/?id=12352}
}

TY  - CPAPER
TI  - Stability Analysis of Limit Cycles in High Order Sigma Delta Modulators
AU  - Reiss, Joshua D.
AU  - Sandler, Mark
AU  - Reefman, Derk
AU  - Janssen, Erwin
T2  - AES Convention 115
M1  - Paper 5936
PY  - 2003
DA  - 2003/10/06
UR  - https://aes.org/publications/elibrary-page/?id=12352
PB  - Audio Engineering Society
LA  - en
AB  - We present a mathematical framework, based on state space modelling, for the description of limit cycles of Sigma Delta Modulators (SDMs). Using a dynamical systems approach, the authors treat sigma delta modulators as piecewise linear maps. This enables us to find all possible limit cycles that might exist in an arbitrary sigma delta modulator with predefined input. We then focus on a DC input analyse their stability and show exactly the amount of dither that is necessary to remove any given limit cycle. Using several different SDM designs, we locate and analyse the limit cycles and thus verify the results by simulation.
ER  -