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Self-similarity and frequency-mixing phenomena analysis of multi-frequency controlled switching converter

Wu Song-Rong Zhou Guo-Hua Wang Jin-Ping Xu Jian-Ping He Sheng-Zhong

Self-similarity and frequency-mixing phenomena analysis of multi-frequency controlled switching converter

Wu Song-Rong, Zhou Guo-Hua, Wang Jin-Ping, Xu Jian-Ping, He Sheng-Zhong
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  • Based on the operation principle and state equations of multi-frequency (MF) controlled switching converter, the discrete iterative map model is established, the corresponding characteristics equation and Lyapunov exponent of MF controlled switching converter operating in discontinuous conduction mode are derived. According to the discrete iterative map model, its bifurcation behaviors are investigated. It is found that the border-collision bifurcation and the multi-period behaviors occur in converter, when the circuit parameters are varied. When the voltage error boundary is too large, the converter behaves as self-similarity phenomenon, and when the voltage error boundary is too small, the converter behaves as frequency-mixing phenomenon. The converter stability is investigated by Lyapunov exponent, which validates the correctness of bifurcation analysis. Time-domain waveforms and phase portraits of converter with the load varied, are analyzed by circuit simulation, which validates the validity of discrete iterative map model and the correctness of theoretical analysis. Finally, simulation results in this paper are verified by experimental results.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51177140, 61371033), the Sichuan Provincial Youth Science and Technology Fund, China (Grant No. 2013JQ0033), and the Fundamental Research Funds for the Central Universities of China (Grant Nos. 2682013ZT20, SWJTU11CX032).
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    Bao B C, Yang P, Ma Z H, Zhang X 2012 Acta Phys. Sin. 61 220502 (in Chinese) [包伯成, 杨平, 马正华, 张希 2012 物理学报 61 220502]

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    Zhou Y F, Chen J N, Iu H H C, Tse C K 2008 Int. J. Bifurc. Chaos 18 121

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    Zhou Y F, Chen J N, Ke D M 2005 Acta Electron. Sin. 33 915 (in Chinese) [周宇飞, 陈军宁, 柯导明 2005 电子学报 33 915]

    [8]

    Zhou G H, Xu J P, Bao B C 2010 Acta Phys. Sin. 59 2272 (in Chinese) [周国华, 许建平, 包伯成 2010 物理学报 59 2272]

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    Zhou G H, Xu J P, Bao B C 2012 Int. J. Bifurc. Chaos 22 1250008

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    Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508

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    Wang J P, Xu J P, Xu Y J 2011 Acta Phys. Sin. 60 058401 (in Chinese) [王金平, 许建平, 徐扬军 2011 物理学报 60 058401]

    [12]

    Zhang X, Bao B C, Wang J P, Ma Z H, Xu J P 2012 Acta Phys. Sin. 61 160503 (in Chinese) [张希, 包伯成, 王金平, 马正华, 许建平 2012 物理学报 61 160503]

    [13]

    Wang F Q, Zhang H, Ma X K 2008 Acta Phys. Sin. 57 2842 (in Chinese) [王发强, 张浩, 马西奎 2008 物理学报 57 2842]

    [14]

    Wang F Q, Zhang H, Ma X K 2008 Acta Phys. Sin. 57 1522 (in Chinese) [王发强, 张浩, 马西奎 2008 物理学报 57 1522]

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    Xu J P, Wang J P 2011 IEEE Trans. Industr. Electron. 58 3658

    [16]

    Khaligh A, Emadi A 2008 IEEE Trans. Aerosp. Electron. Syst. 44 766

    [17]

    Wang J P, Xu J P, Qin M, Mu Q B 2010 Proc. CSEE 30 1 (in Chinese) [王金平, 许建平, 秦明, 牟清波 2010 中国电机工程学报 30 1]

    [18]

    Wang J P, Xu J P, Zhou G H, Mi C B, Qin M 2011 Acta Phys. Sin. 60 048402 (in Chinese) [王金平, 许建平, 周国华, 米长宝, 秦明 2011 物理学报 60 048402]

    [19]

    Sha J, Bao B C, Xu J P, Gao Y 2012 Acta Phys. Sin. 61 120501 (in Chinese) [沙金, 包伯成, 许建平, 高玉 2012 物理学报 61 120501]

    [20]

    Wu S R, He S Z, Xu J P, Zhou G H, Wang J P 2013 Acta Phys. Sin. 62 218403 (in Chinese) [吴松荣, 何圣仲, 许建平, 周国华, 王金平 2013 物理学报 62 218403]

    [21]

    Xu J P, Wang J P, Zhou G H, Qin M, Wu S R, Mu Q B 2010 Chinese Patent ZL 2009 2 0079219.X [2010-01-13] (in Chinese) [许建平, 王金平, 周国华, 秦明, 吴松荣, 牟清波 2010 中国专利 ZL2009 2 0079219.X[2010-01-13]]

  • [1]

    Maity S, Tripathy D, Bhattacharya T K, Banerjee S 2007 IEEE Trans. Circ. Syst.-I 54 1120

    [2]

    Yang P, Bao B C, Sha J, Xu J P 2013 Acta Phys. Sin. 62 010504 (in Chinese) [杨平, 包伯成, 沙金, 许建平 2013 物理学报 62 010504]

    [3]

    Bao B C, Yang P, Ma Z H, Zhang X 2012 Acta Phys. Sin. 61 220502 (in Chinese) [包伯成, 杨平, 马正华, 张希 2012 物理学报 61 220502]

    [4]

    Wang F Q, Zhang H, Ma X K 2012 Chin. Phys. B 21 020505

    [5]

    Zhou G H, Bao B C, Xu J P, Jin Y Y 2010 Chin. Phys. B 19 050509

    [6]

    Zhou Y F, Chen J N, Iu H H C, Tse C K 2008 Int. J. Bifurc. Chaos 18 121

    [7]

    Zhou Y F, Chen J N, Ke D M 2005 Acta Electron. Sin. 33 915 (in Chinese) [周宇飞, 陈军宁, 柯导明 2005 电子学报 33 915]

    [8]

    Zhou G H, Xu J P, Bao B C 2010 Acta Phys. Sin. 59 2272 (in Chinese) [周国华, 许建平, 包伯成 2010 物理学报 59 2272]

    [9]

    Zhou G H, Xu J P, Bao B C 2012 Int. J. Bifurc. Chaos 22 1250008

    [10]

    Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508

    [11]

    Wang J P, Xu J P, Xu Y J 2011 Acta Phys. Sin. 60 058401 (in Chinese) [王金平, 许建平, 徐扬军 2011 物理学报 60 058401]

    [12]

    Zhang X, Bao B C, Wang J P, Ma Z H, Xu J P 2012 Acta Phys. Sin. 61 160503 (in Chinese) [张希, 包伯成, 王金平, 马正华, 许建平 2012 物理学报 61 160503]

    [13]

    Wang F Q, Zhang H, Ma X K 2008 Acta Phys. Sin. 57 2842 (in Chinese) [王发强, 张浩, 马西奎 2008 物理学报 57 2842]

    [14]

    Wang F Q, Zhang H, Ma X K 2008 Acta Phys. Sin. 57 1522 (in Chinese) [王发强, 张浩, 马西奎 2008 物理学报 57 1522]

    [15]

    Xu J P, Wang J P 2011 IEEE Trans. Industr. Electron. 58 3658

    [16]

    Khaligh A, Emadi A 2008 IEEE Trans. Aerosp. Electron. Syst. 44 766

    [17]

    Wang J P, Xu J P, Qin M, Mu Q B 2010 Proc. CSEE 30 1 (in Chinese) [王金平, 许建平, 秦明, 牟清波 2010 中国电机工程学报 30 1]

    [18]

    Wang J P, Xu J P, Zhou G H, Mi C B, Qin M 2011 Acta Phys. Sin. 60 048402 (in Chinese) [王金平, 许建平, 周国华, 米长宝, 秦明 2011 物理学报 60 048402]

    [19]

    Sha J, Bao B C, Xu J P, Gao Y 2012 Acta Phys. Sin. 61 120501 (in Chinese) [沙金, 包伯成, 许建平, 高玉 2012 物理学报 61 120501]

    [20]

    Wu S R, He S Z, Xu J P, Zhou G H, Wang J P 2013 Acta Phys. Sin. 62 218403 (in Chinese) [吴松荣, 何圣仲, 许建平, 周国华, 王金平 2013 物理学报 62 218403]

    [21]

    Xu J P, Wang J P, Zhou G H, Qin M, Wu S R, Mu Q B 2010 Chinese Patent ZL 2009 2 0079219.X [2010-01-13] (in Chinese) [许建平, 王金平, 周国华, 秦明, 吴松荣, 牟清波 2010 中国专利 ZL2009 2 0079219.X[2010-01-13]]

  • [1] Qin Ming, Xu Jian-Ping. Study of multilevel pulse train control technique for switching converters. Acta Physica Sinica, 2009, 58(11): 7603-7612. doi: 10.7498/aps.58.7603
    [2] Wu Song-Rong, He Sheng-Zhong, Xu Jian-Ping, Zhou Guo-Hua, Wang Jin-Ping. Dynamical modeling and multi-period behavior analysis of voltage-mode bi-frequency controlled switching converter. Acta Physica Sinica, 2013, 62(21): 218403. doi: 10.7498/aps.62.218403
    [3] Liu Zhong, Bao Bo-Cheng, Zhou Guo-Hua, Xu Jian-Ping. Dynamical modeling and analysis of current mode controlled switching converter with ramp compensation. Acta Physica Sinica, 2010, 59(6): 3769-3777. doi: 10.7498/aps.59.3769
    [4] Qin Ming, Xu Jian-Ping, Gao Yu, Wang Jin-Ping. Current referenced pulse train control technique applied to switching converter. Acta Physica Sinica, 2012, 61(3): 030204. doi: 10.7498/aps.61.030204
    [5] Bao Bo-Cheng, Yang Ping, Ma Zheng-Hua, Zhang Xi. Dynamics of current controlled switching converters under wide circuit parameter variation. Acta Physica Sinica, 2012, 61(22): 220502. doi: 10.7498/aps.61.220502
    [6] Sha Jin, Xu Jian-Ping, Liu Shu-Han, Zhong Shu. Valley current mode pulse train control switching converter and its energy model analysis. Acta Physica Sinica, 2014, 63(9): 098401. doi: 10.7498/aps.63.098401
    [7] Bao Bo-Cheng, Zhou Guo-Hua, Xu Jian-Ping. Analysis of symmetrical dynamic phenomenon of peak and valley current-mode controlled switching DC-DC converters. Acta Physica Sinica, 2010, 59(4): 2272-2280. doi: 10.7498/aps.59.2272
    [8] He Sheng-Zhong, Zhou Guo-Hua, Xu Jian-Ping, Wu Song-Rong, Chen Li. Effect of output capacitance time-constant on dynamic characteristics of V2-controlled buck converter. Acta Physica Sinica, 2014, 63(13): 130501. doi: 10.7498/aps.63.130501
    [9] Liu Xiao-Tian, Zhou Guo-Hua, Li Zhen-Hua, Chen Xing. Discrete iterative-map modeling and dynamical analysis of digital voltage-mode controlled buck converter with dual-edge modulation. Acta Physica Sinica, 2015, 64(22): 228401. doi: 10.7498/aps.64.228401
    [10] Lai Xiao-Ming, Bian Bao-Min, Yang Ling, Yang Juan, Bian Niu, Li Zhen-Hua, He An-Zhi. Self-similarity model of nonsingular perfect gas universe. Acta Physica Sinica, 2008, 57(12): 7955-7962. doi: 10.7498/aps.57.7955
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  • Received Date:  30 September 2013
  • Accepted Date:  16 October 2013
  • Published Online:  20 January 2014

Self-similarity and frequency-mixing phenomena analysis of multi-frequency controlled switching converter

  • 1. Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China;
  • 2. School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 51177140, 61371033), the Sichuan Provincial Youth Science and Technology Fund, China (Grant No. 2013JQ0033), and the Fundamental Research Funds for the Central Universities of China (Grant Nos. 2682013ZT20, SWJTU11CX032).

Abstract: Based on the operation principle and state equations of multi-frequency (MF) controlled switching converter, the discrete iterative map model is established, the corresponding characteristics equation and Lyapunov exponent of MF controlled switching converter operating in discontinuous conduction mode are derived. According to the discrete iterative map model, its bifurcation behaviors are investigated. It is found that the border-collision bifurcation and the multi-period behaviors occur in converter, when the circuit parameters are varied. When the voltage error boundary is too large, the converter behaves as self-similarity phenomenon, and when the voltage error boundary is too small, the converter behaves as frequency-mixing phenomenon. The converter stability is investigated by Lyapunov exponent, which validates the correctness of bifurcation analysis. Time-domain waveforms and phase portraits of converter with the load varied, are analyzed by circuit simulation, which validates the validity of discrete iterative map model and the correctness of theoretical analysis. Finally, simulation results in this paper are verified by experimental results.

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