直流-直流轉換器的建模和分析是研究拓撲和控制方法的基礎，通常，轉換器的建模可以分為大信號和小信號。小信號模型是控制器設計的基本工具。目前研擬出的小信號模型多數皆基於狀態時間平均法或採樣數據方法。然而，狀態時間平均法忽略了開關頻率分量，並且僅在低頻範圍內準確。在過去的幾十年中，已經提出了解決這些問題的方法。不過，多數這些方法中，例如延伸採樣數據模型、描述方程式和諧波狀態空間方法，難以推導並且在工業中不被廣泛接受。本文提出了一種基於擴充矩陣方法的小信號模型，將證明基於所提出的模型的頻率響應與基於延伸採樣數據模型的頻率響應完全相同並且與模擬結果匹配。此外，擴充矩陣模型也可以應用於大信號建模，並且可以大大簡化開環和閉環的穩態建模。因此，本文的目的是提出一種基於擴充矩陣的統一小信號和大信號模型。並將介紹與這些模型有關的應用。

The modeling and analysis of DC-DC converters is the basis for studying topology and control methods. Generally,
modeling for converters can be categorized into large-signal
and small-signal. A small-signal model (SSM) is the essential
tool for controller design. Most of the small-signal models
developed are based on time-average(TA) or sampled-data(SD) approaches.
However, the averaged models ignore switching frequency
components and are only accurate at a low frequency range. Over the past decades, methods have
been proposed to remedy these problems. However, most of
these methods, such as extended sampled-data(ESD) model, describing function(DF) and harmonic state
space approaches, are difficult to derive and are not widely
accepted in industry. In this thesis, a small-signal model based on
the augmented matrix (AM) method is proposed. It will be
shown that the frequency responses based on the proposed model
are exactly the same as those based on the ESD
and matches the experimental results. Moreover, it will also be
shown that AM can be applied in large-signal modeling and that
the steady-state modeling for open-loop and closed-loop can be
greatly simplified. Thus, the objective of this thesis is to present
a unified approach based on AM for accurately modeling
both small-signal and large-signal behaviors. Applications pertaining
to these models will also be presented.

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