中文摘要：

作为直流变换器中重要的非线性环节，PWM比较器是研究和分析直流变换电路首先需要考虑的问题。将PWM比较器等效为线性比例环节是一种常用的方法，该模型虽然简单，但是只适用于低频段。基于描述函数的方法可以获取准确的理论模型，但其计算量大、物理意义不明确并且结果的描述形式不够简洁。为了建立准确的PWM比较器模型，同时避免描述函数法的各种缺点，本文提出了PWM比较器的采样模型及其矩阵形式的描述。该模型采用采样等效的方法求取PWM比较器输出各频率成分的数值，大大减小了计算量；之后根据线性空间的概念建立了模型的矩阵形式，从而将非线性的PWM比较器转化为由向量和矩阵描述的线性模型。本文所提的模型具有准确、简洁且物理意义明确等优点，仿真和实验结果表明模型的正确性和有效性。

英文摘要：

When analyzing DC-DC converters, the PWM comparator should be taken into account firstly because it is one of the most importantnonlinear parts. In traditional, PWM comparators are considered as a linear amplifier, which is simple but questionable when approaching half of the switching frequency. The describing function method can obtain accurate model for PWM comparator, however, it takes a large amount of calculations and lacks of physical insight. To make the modeling accurate to describe the PWM comparator and avoid the complexity of describing function method, this paper proposes a sampling-based model and gives its matrix description. The PWM is calculated by an impulse-train sampling equivalent method to reduce the computation and a linear space concept is established to simplify the nonlinear PWM comparator as a linear model described by vectors and matrix. The proposed model has some advantages such as high accuracy, simple formula and definite physical meaning, the simulation and experimental results validate its accuracy and effectiveness.