中文摘要：

建立了双缘调制数字电压型控制Buck变换器的离散迭代映射模型．在该模型的基础上，详细研究了双缘调制数字电压型控制Buck变换器的非线性动力学行为．以输入电压、负载电阻等电路参数作为分岔参数，绘制了输出电压和电感电流的分岔图，并通过分岔图的分析发现了两种相似却又不同的Hopf分岔现象．采用庞加莱截面、时域仿真波形和相轨图，对比分析了两种不同的Hopf分岔和低频振荡现象，并引入离散迭代映射模型的雅克比矩阵的特征值分析方法，从理论上证明了两种Hopf分岔的存在性和差异性．首次观察到基于双缘调制的数字电压型控制Buck变换器出现了奇数倍周期分岔现象，并通过时域仿真波形和相轨图验证了该现象的真实性．为更加接近实际电路，考虑电容和电感的等效串联电阻，使用Psim进行仿真，其结果与理论仿真结果基本一致，验证了理论仿真的正确性．

英文摘要：

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 Poincar6 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 Poincar6 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 tim