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The operation principle of digital voltage-mode controlled buck converter with dual-edge modulation is analyzed in this paper. Based on the state equation of buck converter and six possible evolutions in one switching cycle, the discrete iterative-map model of digital voltage-mode controlled buck converter with dual-edge modulation is established. Ignoring the quantization error of analog-digital converter and on the basis of its discrete iterative-map model, the nonlinear dynamical behavior of digital voltage-mode controlled buck converter with dual-edge modulation is investigated in detail. Taking the input voltage and the load resistance as bifurcation parameters, the output voltage bifurcation diagram and the inductor current bifurcation diagram are plotted. Through analyzing the bifurcation diagrams, it is indicated that there are two kinds of similar but different Hopf bifurcation phenomena. By use of Poincar section, time-domain simulation waveforms and phase portraits, two different Hopf bifurcations and low-frequency oscillation phenomena are compared and studied. Observing the inductor current and capacitor voltage waveforms respectively, it is obviously found that their oscillation frequencies and amplitudes are different, the shapes of two Poincar$ sections and phase portraits are also different. In order to verify the correctness of the simulation and theoretical analysis, the eigenvalues of Jacobian matrix of the discrete iterative map model are introduced and solved in two kinds of stable evolutions. Through analyzing variation of eigenvalues of Jacobi matrix with input voltage, the existence and difference of two kinds of Hopf bifurcation phenomena are proved theoretically. Moreover, it is observed in this paper that the odd period-doubling bifurcation phenomenon exists in digital voltage-mode controlled buck converter with dual-edge modulation for the first time, where the operation state of the buck converter turns from period-one into period-three. Its authenticity is verified by using the time-domain simulation waveforms and phase portraits. In order to approach to the actual circuit, the equivalent series resistances of capacitor and inductor are considered. The actual circuit is simulated by using the software Psim. A comparison shows that there are little differences between the theoretical simulation and the actual circuit simulation. So the theoretical simulation can be used to analyze the performances of the actual circuit. The research results in this paper have guiding significance and practical value for designing the digital voltage-mode controlled buck converter with dual-edge modulation.
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Keywords:
- switching converter /
- dual-edge modulation /
- digital control /
- odd period-doubling bifurcation
[1] 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 59 2272]
[2] Maity S, Tripathy D, Bhattacharya T K, Banerjee S 2007 IEEE Trans. Circuit Syst. I 54 1120
[3] Zhou G H, Bao B C, Xu J P, Jin Y Y 2010 Chin. Phys. B 19 050509
[4] Deivasundari P, Uma G, Poovizhi R 2013 IET Power Electr. 6 763
[5] Xie F, Yang R, Zhang B 2011 IEEE Trans. Circuit Syst. I 58 2269
[6] 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 57 2842]
[7] Dai D, Li S N, Zhang B, Ma X K 2008 Proc. CSEE 28 1 (in Chinese) [戴栋, 李胜男, 张波, 马西奎 2008 中国电机工程学报 28 1]
[8] Aroudi A E, Benadero L, Toribio E, Olivar G 1999 IEEE Trans. Circuit Syst. I 46 1374
[9] Aroudi A E, Benadero L, Toribio E, Machiche S 2000 Int. J. Bifurcat. Chaos 10 359
[10] Zhang X T, Ma X K, Zhang H 2008 Acta Phys. Sin. 57 6174 (in Chinese) [张笑天, 马西奎, 张浩 2008 57 6174]
[11] Huang M, Wong S C, Tse C K, Ruan X B 2013 IEEE Trans. Circuit Syst. I 60 1062
[12] Aroudi A E, Leyva R 2001 IEEE Trans. Circuit Syst. I 48 967
[13] Zhou G H, Bao B C, Xu J P 2013 Int. J. Bifurcat. Chaos 23 1350062
[14] Zhou Y F, Tse C K, Qiu S S, Chen J N 2005 Chin. Phys. 14 0061
[15] Yang N N, Liu C X, Wu C J 2012 Chin. Phys. B 21 080503
[16] Wang F Q, Zhang H, Ma X K 2012 Chin. Phys. B 21 020505
[17] He S Z, Xu J P, Zhou G H, Bao B C, Yan T S 2015 Chin. J. Electron. 24 295
[18] Xie F, Zhang B, Yang R 2013 IEEE Tran. Ind. Electron. 60 3145
[19] Zhao Y B, Feng J C, Chen Y F 2013 Int. J. Bifurcat. Chaos 23 1350113
[20] Zhou G H 2011 Ph. D. Dissertation (Chengdu: Southwest Jiaotong University) (in Chinese) [周国华 2011 博士学位论文 (成都: 西南交通大学)]
[21] Tse C K 2004 CRC Press Data pp96-132
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[1] 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 59 2272]
[2] Maity S, Tripathy D, Bhattacharya T K, Banerjee S 2007 IEEE Trans. Circuit Syst. I 54 1120
[3] Zhou G H, Bao B C, Xu J P, Jin Y Y 2010 Chin. Phys. B 19 050509
[4] Deivasundari P, Uma G, Poovizhi R 2013 IET Power Electr. 6 763
[5] Xie F, Yang R, Zhang B 2011 IEEE Trans. Circuit Syst. I 58 2269
[6] 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 57 2842]
[7] Dai D, Li S N, Zhang B, Ma X K 2008 Proc. CSEE 28 1 (in Chinese) [戴栋, 李胜男, 张波, 马西奎 2008 中国电机工程学报 28 1]
[8] Aroudi A E, Benadero L, Toribio E, Olivar G 1999 IEEE Trans. Circuit Syst. I 46 1374
[9] Aroudi A E, Benadero L, Toribio E, Machiche S 2000 Int. J. Bifurcat. Chaos 10 359
[10] Zhang X T, Ma X K, Zhang H 2008 Acta Phys. Sin. 57 6174 (in Chinese) [张笑天, 马西奎, 张浩 2008 57 6174]
[11] Huang M, Wong S C, Tse C K, Ruan X B 2013 IEEE Trans. Circuit Syst. I 60 1062
[12] Aroudi A E, Leyva R 2001 IEEE Trans. Circuit Syst. I 48 967
[13] Zhou G H, Bao B C, Xu J P 2013 Int. J. Bifurcat. Chaos 23 1350062
[14] Zhou Y F, Tse C K, Qiu S S, Chen J N 2005 Chin. Phys. 14 0061
[15] Yang N N, Liu C X, Wu C J 2012 Chin. Phys. B 21 080503
[16] Wang F Q, Zhang H, Ma X K 2012 Chin. Phys. B 21 020505
[17] He S Z, Xu J P, Zhou G H, Bao B C, Yan T S 2015 Chin. J. Electron. 24 295
[18] Xie F, Zhang B, Yang R 2013 IEEE Tran. Ind. Electron. 60 3145
[19] Zhao Y B, Feng J C, Chen Y F 2013 Int. J. Bifurcat. Chaos 23 1350113
[20] Zhou G H 2011 Ph. D. Dissertation (Chengdu: Southwest Jiaotong University) (in Chinese) [周国华 2011 博士学位论文 (成都: 西南交通大学)]
[21] Tse C K 2004 CRC Press Data pp96-132
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