Analytic structure of phase-locked loops in complex time

Hisa Aki Tanaka, Toshiya Matsuda, Shinichi Oishi, Kazuo Horiuchi

    研究成果: Article

    抄録

    The analytic structure of the governing equation for a 2nd order Phase-Locked Loops (PLL) is studied in the complex time plane. By a local reduction of the PLL equation to the Riccati equation, the PLL equation is analytically shown to have singularities which form a fractal structure in the complex time plane. Such a fractal structure of complex time singularities is known to be characteristic for nonintegrable, especially chaotic systems. On the other hand, a direct numerical detection of the complex time singularities is performed to verify the fractal structure. The numerical results show the reality of complex time singularities and the fractal structure of singularities on a curve.

    元の言語English
    ページ(範囲)1777-1782
    ページ数6
    ジャーナルIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    E77-A
    発行部数11
    出版物ステータスPublished - 1994 11

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    Phase-locked Loop
    Phase locked loops
    Fractal Structure
    Fractals
    Singularity
    Riccati equations
    Chaotic systems
    Riccati Equation
    Chaotic System
    Governing equation
    Verify
    Numerical Results
    Curve

    ASJC Scopus subject areas

    • Hardware and Architecture
    • Information Systems
    • Electrical and Electronic Engineering

    これを引用

    Analytic structure of phase-locked loops in complex time. / Tanaka, Hisa Aki; Matsuda, Toshiya; Oishi, Shinichi; Horiuchi, Kazuo.

    :: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 巻 E77-A, 番号 11, 11.1994, p. 1777-1782.

    研究成果: Article

    Tanaka, Hisa Aki ; Matsuda, Toshiya ; Oishi, Shinichi ; Horiuchi, Kazuo. / Analytic structure of phase-locked loops in complex time. :: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences. 1994 ; 巻 E77-A, 番号 11. pp. 1777-1782.
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