### Abstract

The chaotic delta sigma modulator is a way to suppress the limit cycle oscillation caused by the input of a null or constant signal. By changing integrator gains, the output sequence becomes chaotic and the noise characteristic of the output is changed. This noise characteristic is an important factor for evaluating the performance of delta sigma modulation. The aim of this study is to analyze the noise characteristic of chaotic double loop delta sigma modulation when the null signal is input. We use a bifurcation diagram and FFT analysis to obtain the parameter dependence of the output state and noise characteristic, respectively. The output status of the chaotic double loop delta sigma modulation can be guessed from a bifurcation diagram with the brute force method. We also investigate the noise characteristic of the output signal of the chaotic modulator with FFT analysis and classify the various noise characteristics by changing the integrator gains of the double loop delta sigma modulator. We use FFT and the bifurcation diagram to classify these noise characteristics into three categories: suppressed tone (affected by the chaos), divergence, and the appearance of the limit cycle oscillation. We also confirm the existence of an unusual noise-shaping characteristic caused by the intermittent chaos.

Original language | English |
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Article number | 1650178 |

Journal | International Journal of Bifurcation and Chaos |

Volume | 26 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2016 Oct 1 |

Externally published | Yes |

### Keywords

- bifurcation
- chaotic modulation
- Double loop delta sigma modulation
- FFT analysis
- noise-shaping characteristic

### ASJC Scopus subject areas

- Modelling and Simulation
- Engineering(all)
- General
- Applied Mathematics

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## Cite this

*International Journal of Bifurcation and Chaos*,

*26*(11), [1650178]. https://doi.org/10.1142/S0218127416501789