Yingyi Yan | Searcharxiv

arXiv2025

Competent Discrete Time Modeling For analogue controlled PWM Converter Considering State-Feedback

Ever since R.D.Middlebrook proposed the state space averaging notion. The small signal model has been widely used as a design tool to tune control parameters. As Moore's law is continuing and the AI chip's high demand for power consumption and dynamic response, the control bandwidth needs to be boosted. However, the average model has two basic assumptions: the low-frequency assumption, the small ripple assumption. In high-bandwidth design, these two assumptions are violated. In order to solve this, various methods have been proposed. This paper gives a comprehensive overview of the existing small signal model for PWM converters from the following perspectives: 1. model fidelity, 2. analytical tractability. 3. complexity of the derivation process and result 4.generality.

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arXiv2025

Foundational Correction of Z-Transform Theory: Restoring Mathematical Completeness in Sampled-Data Systems

This paper revisits the classical formulation of the Z-transform and its relationship to the inverse Laplace transform (L-1), originally developed by Ragazzini in sampled-data theory. It identifies a longstanding mathematical oversight in standard derivations, which typically neglect the contribution from the infinite arc in the complex plane during inverse Laplace evaluation. This omission leads to inconsistencies, especially at discontinuities such as t = 0. By incorporating the full Bromwich contour, including all boundary contributions, we restore internal consistency between L-1 and the Z-transform, aligning the corrected L-1 with results from Discrete-Time Fourier Transform (DTFT) aliasing theory. Consequently, this necessitates a structural revision of the Z-transform, inverse Laplace transform, and the behavior of the Heaviside step function at discontinuities, providing a more accurate foundation for modeling and analysis of sampled-data systems.

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