Analysis and application of delta sigma modulator using chaos

2016 Fiscal Year Final Research Report

• Project/Area Number: 26820131
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Electron device/Electronic equipment
• Research Institution: Aoyama Gakuin University
• Principal Investigator: Ioka Eri 青山学院大学, 理工学部, 助教 (50583564)
• Co-Investigator(Renkei-kenkyūsha): IOKA Eri 青山学院大学, 理工学部電気電子工学科, 助教 (50583564)
• Research Collaborator: MATSUYA Yasuyuki ; KITAJIMA Hiroyuki ; INAGAKI Youji ; MAKISHIMA Ryo ; WATANABE Nozomi
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: ΔΣ変調器 / カオス変調器 / リアプノフ指数 / ノイズ特性

Outline of Final Research Achievements

The FFT analysis is usually used as evaluation way of the performance of delta sigma modulator. We focused on that the output sequence of the delta sigma modulator becomes chaos when it performs normally. Hence, we studied a new performance analysis method using Lyapunov exponent for the delta sigma modulator. First, we illustrated two-parameter bifurcation diagram on parameter region of integrator leaks, and compered that result with FFT analysis to represent the integrator output sequence can optimize the performance of the modulator. Second, we applied the Lyapunov exponent to output sequence of double loop chaotic delta sigma modulator by using Sano and Sawada's algorithm. This result shows that the Lyapunov exponent becomes positive when the normal performance of the chaotic delta sigma modulator is observed from both the bifurcation diagram and FFT analysis. Moreover, we could confirm unstable period points in the chaos appear as weak tones at the shaping noise.

Free Research Field

非線形システム