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Considering that the variation of nonlinear characteristics of DC-DC converter with parameter k and the fact that entropy can reflect the statistical characteristic of numerical sequence, in this paper we propose a new method to estimate the nonlinear characteristics of DC-DC converter based on the information about entropy. In this study, taking one-order DCM Buck and Boost converter for example, the distributions of numerical sequences and entropies are analysed under different values of feedback gain k and initial values of x0. The results prove that the entropy of DC-DC converter is determined by feedback gain k and irrelevant to initial value x0, and its final value is smaller than the theoretical maximum value log2N (N is the number of partition), and that entropy can discriminate the period-doubling bifurcation and chaos. So a quantifiable nonlinear dynamical behavior index is obtained which can provide theoretical basis for understanding chaos characteristic and chaos control, and perfect the theoretical analysis method in DC-DC converters.
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Keywords:
- DC-DC converters /
- entropy /
- chaos /
- feedback gain k
[1] Wu C H, Chen C L 2009 IEEE Trans. Circuits Syst. II 56 763
[2] Hsieh C Y, Chen K H 2009 IEEE J. Solid-State Circuits 44 2568
[3] Liu X, Guo S X, Chang Y C, Zhu S D, Wang S 2009 J. Chin. Univ. Posts Telecommun. 16 98
[4] Ma Y, Kawakami H, Tse C K 2004 IEEE Trans. Circuit Syst. I 51 1184
[5] Zou Y L, Luo X S, Chen G R 2006 Chin. Phys. 15 1719
[6] De S, Dutta P S, Banerjee S 2012 Phys. Lett. A 376 400
[7] Zhou Y F, Chen J N, Tse C K, Ke D M, Shi L X, Sun W F 2004 Acta Phys. Sin. 53 3676 (in Chinese) [周宇飞, 陈军宁, 谢智刚, 柯导明, 时龙兴, 孙伟锋 2004 物理学报 53 3676]
[8] Toribio E, El Aroudi A, Olivar G, Benadero L 2000 IEEE Trans. Power Electron 15 1163
[9] Zhusubaliyev Z T, Mosekilde E, De S, Banerjee S 2008 Phys. Rev. E 77 026206
[10] Wang F Q, Zhang H, Ma X K 2012 Chin. Phys. B 21 020505
[11] Lu W G, Zhou L W, Luo Q M, Du X 2007 Acta Phys. Sin. 56 6275 (in Chinese) [卢伟国, 周雒维, 罗全明, 杜雄 2007 物理学报 56 6275]
[12] Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508
[13] Chen X, Qiu S S 2010 Acta Phys. Sin. 59 7630 (in Chinese) [陈旭, 丘水生 2010 物理学报 59 7630]
[14] Ren H P, Liu D 2005 Chin. Phys. 14 1352
[15] Wang F Q, Ma X K, Yan Y 2011 Acta Phys. Sin. 60 060510 (in Chinese) [王发强, 马西奎, 闫晔2011 物理学报 60 060510]
[16] Xie L L, Gong R X, Zhuo H Z, Ma X H 2012 Acta Phys. Sin. 61 058401 (in Chinese) [谢玲玲, 龚仁喜, 卓浩泽, 马献花 2012 物理学报 61 058401]
[17] Zhusubaliyev Z T, Mosekilde E, Yanochkina O O 2011 IEEE Trans. Power Electron. 26 1270
[18] Zhou Y F, Chen J N, Tse C K, Qiu S S, Ke D M, Shi L X, Sun W F 2004 Acta Elec. Sin. 32 264 (in Chinese) [周宇飞, 陈军宁, 谢智刚, 丘水生, 柯导明, 时龙兴, 孙伟锋 2004 电子学报 32 264]
[19] Li M, Ma X K, Dai D, Zhang H 2005 Acta Phys. Sin. 54 1084 (in Chinese) [李明, 马西奎, 戴栋, 张浩 2005 物理学报 54 1084]
[20] Wang X M, Zhang B, Qiu D Y 2011 IEEE Trans. Power Electron. 26 2101
[21] Xie F, Yang R, Zhang B 2012 Acta Phys. Sin. 61 110504 (in Chinese) [谢帆, 杨汝, 张波 2012 物理学报 61 110504]
[22] Fu Z Y 2001 Information Theory (Beijing: Electronics Industry Press) p24 (in Chinese) [傅祖芸2001信息论(北京: 电子工业出版社) 第24页]
[23] Tse C K 1994 Int. J. Circuit Theory Appl. 22 263
[24] Tse C K 1994 IEEE Trans. Circuit Syst. I 42 16
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[1] Wu C H, Chen C L 2009 IEEE Trans. Circuits Syst. II 56 763
[2] Hsieh C Y, Chen K H 2009 IEEE J. Solid-State Circuits 44 2568
[3] Liu X, Guo S X, Chang Y C, Zhu S D, Wang S 2009 J. Chin. Univ. Posts Telecommun. 16 98
[4] Ma Y, Kawakami H, Tse C K 2004 IEEE Trans. Circuit Syst. I 51 1184
[5] Zou Y L, Luo X S, Chen G R 2006 Chin. Phys. 15 1719
[6] De S, Dutta P S, Banerjee S 2012 Phys. Lett. A 376 400
[7] Zhou Y F, Chen J N, Tse C K, Ke D M, Shi L X, Sun W F 2004 Acta Phys. Sin. 53 3676 (in Chinese) [周宇飞, 陈军宁, 谢智刚, 柯导明, 时龙兴, 孙伟锋 2004 物理学报 53 3676]
[8] Toribio E, El Aroudi A, Olivar G, Benadero L 2000 IEEE Trans. Power Electron 15 1163
[9] Zhusubaliyev Z T, Mosekilde E, De S, Banerjee S 2008 Phys. Rev. E 77 026206
[10] Wang F Q, Zhang H, Ma X K 2012 Chin. Phys. B 21 020505
[11] Lu W G, Zhou L W, Luo Q M, Du X 2007 Acta Phys. Sin. 56 6275 (in Chinese) [卢伟国, 周雒维, 罗全明, 杜雄 2007 物理学报 56 6275]
[12] Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508
[13] Chen X, Qiu S S 2010 Acta Phys. Sin. 59 7630 (in Chinese) [陈旭, 丘水生 2010 物理学报 59 7630]
[14] Ren H P, Liu D 2005 Chin. Phys. 14 1352
[15] Wang F Q, Ma X K, Yan Y 2011 Acta Phys. Sin. 60 060510 (in Chinese) [王发强, 马西奎, 闫晔2011 物理学报 60 060510]
[16] Xie L L, Gong R X, Zhuo H Z, Ma X H 2012 Acta Phys. Sin. 61 058401 (in Chinese) [谢玲玲, 龚仁喜, 卓浩泽, 马献花 2012 物理学报 61 058401]
[17] Zhusubaliyev Z T, Mosekilde E, Yanochkina O O 2011 IEEE Trans. Power Electron. 26 1270
[18] Zhou Y F, Chen J N, Tse C K, Qiu S S, Ke D M, Shi L X, Sun W F 2004 Acta Elec. Sin. 32 264 (in Chinese) [周宇飞, 陈军宁, 谢智刚, 丘水生, 柯导明, 时龙兴, 孙伟锋 2004 电子学报 32 264]
[19] Li M, Ma X K, Dai D, Zhang H 2005 Acta Phys. Sin. 54 1084 (in Chinese) [李明, 马西奎, 戴栋, 张浩 2005 物理学报 54 1084]
[20] Wang X M, Zhang B, Qiu D Y 2011 IEEE Trans. Power Electron. 26 2101
[21] Xie F, Yang R, Zhang B 2012 Acta Phys. Sin. 61 110504 (in Chinese) [谢帆, 杨汝, 张波 2012 物理学报 61 110504]
[22] Fu Z Y 2001 Information Theory (Beijing: Electronics Industry Press) p24 (in Chinese) [傅祖芸2001信息论(北京: 电子工业出版社) 第24页]
[23] Tse C K 1994 Int. J. Circuit Theory Appl. 22 263
[24] Tse C K 1994 IEEE Trans. Circuit Syst. I 42 16
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