This paper presents a new mathematical approach to design an asynchronous pulse width modulation (APWM) for the switched mode power supply (SMPS). Unlike the conventional APWM that utilises a Hysteretic comparator based Asynchronous Pulse Width Modulation (HAPWM) to provide the self-oscillating property, the proposed APWM is based on a Binary comparator based Asynchronous Pulse Width Modulation (BAPWM) and a delay cell. This way, compared to the HAPWM, the mathematical analysis of the modulator is significantly simplified. This was achieved by replacing the describing function (DF) -based graphical method with a ?linearised mathematical model. The introduced mathematical approach is extended to study the behaviour of the higher order self-oscillating modulators in terms of the harmonic distortion. To confirm the effectiveness of the analytical derivations, the BAPWMs are employed in a classic DC–DC buck converter and the system-level simulation results are provided. It is concluded that there is an acceptable degree of similarity between the simulation results and the deployed analytical calculations for different orders of the modulators. Finally, to validate these analytical and simulation results and also to compare the BAPWM performance with its HAPWM counterpart, both modulators are implemented using off-the-shelf components and their measurement results are presented.

中文翻译：

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开关电源异步脉冲宽度调制技术的分析与设计

本文提出了一种新的数学方法来为开关电源（SMPS）设计异步脉宽调制（APWM）。与利用基于迟滞比较器的异步脉冲宽度调制（HAPWM）来提供自激特性的常规APWM不同，所提出的APWM基于基于二进制比较器的异步脉冲宽度调制（BAPWM）和延迟单元。这样，与HAPWM相比，可以大大简化调制器的数学分析。这是通过用线性化数学模型代替基于描述函数（DF）的图形方法来实现的。引入的数学方法已扩展为研究高阶自振荡调制器在谐波失真方面的行为。为了确认分析推导的有效性，在经典的DC-DC降压转换器中采用了BAPWM，并提供了系统级的仿真结果。结论是，对于不同阶数的调制器，仿真结果与部署的分析计算之间存在可接受的相似度。最后，为了验证这些分析和仿真结果，并比较BAPWM性能和其HAPWM对应产品，两个调制器均使用现成的组件实现，并给出了它们的测量结果。结论是，对于不同阶数的调制器，仿真结果与已部署的分析计算之间存在可接受的相似度。最后，为验证这些分析和仿真结果，并与BAPWM性能和其HAPWM对应产品进行比较，两个调制器均采用现成的组件实现，并给出了其测量结果。结论是，对于不同阶数的调制器，仿真结果与已部署的分析计算之间存在可接受的相似度。最后，为验证这些分析和仿真结果，并与BAPWM性能和其HAPWM对应产品进行比较，两个调制器均采用现成的组件实现，并给出了其测量结果。