纹波控制直接对DC/DC变换器中的电感电流或输出电压中的开关纹波分量进行控制，具有更快速的动态响应，因此广泛应用于对动态性能有严苛要求的场合。在实际应用中，发现有些不稳定问题无法采用现有建模方法来解释，且针对其性能的分析缺乏坚实的理论依据。为此，本文将针对峰值/谷值电流控制(Peak/Valley Current Mode，PCM/VCM)、峰值/谷值电压控制(Peak/Valley Voltage Mode，PVM/VVM)、固定导通时间控制(Constant On-Time，COT)和固定关断时间控制(Constant Off-Time，COFT)等纹波控制方式，研究其建模方法，以得到准确的数学模型，从而为电路和控制参数的设计及性能分析提供理论指导。 本文首先分析了PCM/VCM方式中调制器的采样特性，指出反馈扰动信号在采样时刻是一个第一类间断点。根据狄利克雷条件，反馈扰动信号的采样值应是采样时刻左右两侧极限值的平均值。据此，可得反馈扰动信号与占空比扰动信号在采样时刻的比值。进而根据采样定理，推导出调制器的数学模型和变换器环路增益的表达式。由于数学模型中存在无穷多的边带频率项，难以直接分析变换器的稳定性。接着，本文通过采用功率级在高频段的近似式并引入无穷项级数恒等式，对调制器的数学模型进行简化。基于简化结果，计算出所需的斜坡补偿系数的选取范围。简化结果同时表明，PCM/VCM型Buck变换器的环路增益的截止频率低于或等于一半开关频率，且在该频段范围内，由于边频分量的影响，调制器呈现出一个左半平面极点的特性。最后，在实验室搭建了一台PCM型Buck变换器原理样机，实验结果验证了理论模型的正确性。 类似地，本文推导了PVM/VVM型DC/DC变换器中调制器的传递函数和环路增益的表达式。本文以Buck变换器为例，针对调制器的数学模型进行了简化。根据简化结果，计算了输出电容的时间常数以及斜坡补偿系数和环路增益相位裕度的关系，并推导出上述参数的可选范围。简化结果同时表明，PCM/VCM型Buck变换器稳定工作时的截止频率低于一半开关频率，且在该频段范围内，由于边频分量的影响，调制器呈现出两个左半平面极点的频域特性。最后，仿真验证了理论模型的正确性。 与PCM/VCM和PVM/VVM方式不同，采用COT/COFT方式时，DC/DC变换器的占空比扰动信号不仅在采样时刻变化，还在开关管关断/开通的时刻变化。为此，本文分别推导了反馈信号与两个占空比扰动信号之间的关系，并结合固定导通/关断时间，得到调制器的模型和环路增益的表达式。接着以Buck变换器为例，通过引入无穷项级数，对其调制器的数学模型进行了简化。基于简化结果，解释了电流型固定导通/关断时间型Buck变换器可以在全占空比范围内稳定工作的现象，同时计算出电压型固定导通/关断时间型Buck变换器中时间常数的可选范围。此外，简化结果表明，在Buck变换器采用电流型固定导通/关断时间方式(Current Mode Constant On-Time/Off-Time，C-COT/C-COFT)时，除接近整数倍开关频率处的微小频段，其他范围内环路增益仅与功率级的参数和固定导通/关断时间值的大小有关，且环路增益的截止频率仅与固定导通/关断时间值的大小有关。最后，仿真验证了理论模型的正确性。 本文进一步深入分析了各类纹波控制方式中调制器的采样特性，指出：只要可以将两个信号列写为与单位周期冲激函数相关的类似采样形式的关系时，就可以利用采样定理推导这两个信号在s域的关系。基于以上思想，本文研究了数字控制DC/DC变换器的建模方法。通过列写数字控制DC/DC变换器中占空比信号与采样前的反馈信号之间的时域关系式，得到了反馈信号到占空比信号在s域的传递函数。最后，仿真验证了理论模型的正确性。 本文最后指出在Boost/Buck-Boost变换器中，在推导由采样建模方法得到的调制器模型的具体表达式时，其中所包含的功率级的传递函数需要采用精确的表达式。利用最终结果，解释了PCM型和AVM(Average Voltage Mode，AVM)型Boost变换器中现有理论模型与实际模型在低频段不匹配的现象，也解释了AVM型Boost变换器采用前沿和后沿调制器方式时出现的稳定性不同的某些现象。

Ripple-based control is widely used in DC/DC converters that have strict requirements on dynamic performance, since it directly controls the switching ripple component of the inductor current or the output voltage in the converter. In practical applications, it is found that the stability performance of ripple-controlled DC/DC converters cannot be analyzed by the existing modeling methods. Therefore, this article will focus on modeling several common ripple-based controls which include peak/valley current control (Peak/Valley Current Mode, PCM/VCM), peak/valley voltage control (Peak/Valley Voltage Mode, PVM/VVM), and constant on-time control (Constant On-Time, COT) and constant off-time control (Constant Off-Time, COFT), to provide theoretical guidance for the design of circuit and control parameters. This article first analyzes the sampling characteristics of the modulator in the PCM/VCM control, and points out that the feedback perturbation signal has a first-type discontinuity at each sampling instant. Therefore, the perturbation value at this instant should be obtained according to the Dirichlet conditions, which is equal to half of the sum of the limit values on the left and right sides of the signal. Accordingly, the ratio of the feedback perturbation signal to the duty cycle perturbation signal at the sampling time can be obtained. Furthermore, according to the sampling theorem, the mathematical model of the modulator and the expression of the loop gain are derived. Due to the infinite sideband components in the mathematical model, it is difficult to directly analyze the converter stability. For this reason, this article approximates the mathematical model of the modulator by introducing the infinite series equality. Based on the approximate results, the sideband effect on the frequency response of the modulator and the loop gain is analyzed, and the required range for the slope compensation is calculated. The simplified results also show that the cut-off frequency of the loop gain is lower than or equal to half the switching frequency, and in this frequency range, the modulator behaves as a left half-plane pole due to the sideband effect. Finally, a PCM-type Buck converter prototype was built in the laboratory, and the experimental results verified the correctness of the theoretical models. Similarly, the expressions of the transfer function of the modulator and the loop gain in the PVM/VVM controlled DC/DC converter are derived. What is different from PCM/VCM control is that the influence of the time constant of the output filter capacitor on the modulator gain factor is needed to consider. Then, the Buck converter is taken as an example to approximate the mathematical model of the modulator. Based on the approximate results, the relationship among the time constant of the output capacitor, the slope compensation, and the phase margin of the loop gain is derived, and the optional range of the above parameters are derived. The simplified results also show that the cut-off frequency of the loop gain is lower than half the switching frequency, and in this frequency range, the modulator behaves as two left half-plane poles due to the sideband effect. Finally, the correctness of the theoretical model is verified by simulation. Different from the PCM/VCM and PVM/VVM controls, when the COT/COFT control is adopted in the DC/DC converter, the duty cycle perturbation signal not only changes at each sampling instant, but also changes at the moment when the switch tube is turned off/on. For this reason, this paper derives the relationship between the feedback perturbation signal and the two sets of narrow pulse width signals in the duty cycle perturbation signal, from which the transfer function of the modulator and the loop gain are obtained. Then, the Buck converter is taken as an example to approximate these expressions. According to the approximate results, the influence of the time constant of the output capacitor on the distribution of the poles of the closed-loop transfer function is analyzed, from which the selectable range of the time constant is derived. Also, the phenomenon that Buck converter with the C-COT/C-COFT control can work stably in the full duty cycle range is explained. In addition, the simplified results show that in the C-COT/C-COFT controlled Buck converter, the cut-off frequency of the loop gain is only related to the value of the contonstant on/off time. Finally, the correctness of the theoretical model is verified by simulation. Besides, through the in-depth observation of the sampling characteristics of the modulator in various basic controls, it is found that the relationship of the two signals in the s-domain can be obtained, as long as the relationship of these two signals in the time-domain can be written as that of the sampling form. Based on this idea, the proposed modeling method is extended to the digital control, and the corresponding derivation process is introduced with the example of a current-mode digitally controlled buck converter. Simulation results verify the effectiveness of the obtained method. Finally, it is pointed out that in the Boost/Buck-Boost converter, the modulator model should be derived base on the accurate transfer function of the power stage. Based on the accurate results, the instability phenomenon in the AVM controlled Boost converter is explained.