基於極點數估計的快速向量擬合及透過改變參考阻抗改善巨觀建模的高低頻準確度;Quick Vector Fitting based on Pole Number Estimation and a New Method of Improving the Accuracy of Macromodeling at High and Low Frequencies by Using Complex Reference Impedance

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Title:	基於極點數估計的快速向量擬合及透過改變參考阻抗改善巨觀建模的高低頻準確度;Quick Vector Fitting based on Pole Number Estimation and a New Method of Improving the Accuracy of Macromodeling at High and Low Frequencies by Using Complex Reference Impedance
Authors:	方子源;Fang, Tzu-Yuan
Contributors:	電機工程學系
Keywords:	向量擬合;巨觀建模;Vector Fitting;Macromodeling
Date:	2025-07-15
Issue Date:	2025-10-17 12:40:56 (UTC+8)
Publisher:	國立中央大學
Abstract:	近年來數位信號傳輸速度越來越快，同時也讓更多的因素影響信號完整度，為了確認信號的品質，人們常用眼圖來當作一種參考的依據，然而眼圖是將時域的訊號疊圖而成，而模擬或量測所得的資料卻是頻域的，這時就需要工具有效的把資料從頻域轉成時域，本文所提到的巨觀建模即為一種常用於將頻域的散射參數轉換為時域波形以進行訊號完整性分析的方法，此外，在巨觀建模中常配合使用向量擬合來進行數值上的近似。本篇論文旨在探討如何加速向量擬合及改善巨觀建模在高低頻的準確度，因此分別提出兩種辦法，分別是快速向量擬合方法及提升高低頻準確度的巨觀建模方法。向量擬合是一種常見的理性函數逼近方法，但需預先設定極點數，對大型或多埠系統而言，選錯極點數會大幅增加運算時間。因此，本文提出一種基於相位展開與誤差調整策略的新方法，用以快速估計合適的極點數，並自動調整以收斂至目標誤差。實驗證明該方法於不同測量與模擬案例中，比商業工具（如ADS）更有效率，且多數情況下能以更少的極點數達成相似精度。傳統巨觀建模使用固定參考阻抗（如50歐姆）進行轉換，可能在電源完整性應用的低頻段造成誤差。本文針對此問題，提出以頻率依賴的複數參考阻抗進行散射參數重新正規化，使其更貼近實際阻抗，進而減少轉換至阻抗或導納參數時的誤差放大。該方法確保新參考阻抗具因果性與穩定性，並於SPICE實作中提出等效電路轉換方式，使其可在模擬工具中使用。 ;In recent years, with the continuous increase in digital signal transmission speeds, more factors have emerged that affect signal integrity. To assess signal quality, eye diagrams are commonly used as a reference tool. However, eye diagrams are formed by superimposing time-domain signals, while the data obtained from simulations or measurements are typically in the frequency domain. Therefore, effective tools are needed to convert frequency-domain data into the time domain. The macromodeling method discussed in this thesis is a widely used approach for converting frequency-domain scattering parameters into time-domain waveforms for signal integrity analysis. Moreover, Vector Fitting is often employed in macromodeling to achieve numerical approximation. This thesis aims to accelerate Vector Fitting and improve the accuracy of macromodeling at both high and low frequencies. Accordingly, two approaches are proposed: a Quick Vector Fitting method and a macromodeling technique to enhance accuracy across the frequency range. Vector Fitting is a common rational function approximation technique but requires predefining the number of poles. For large-scale or multi-port systems, an incorrect choice of poles can significantly increase computation time. To address this, a novel method based on phase unwrapping and error adjustment is proposed to rapidly estimate the appropriate number of poles and automatically refine it to meet the target error. Experiments demonstrate that the proposed method is more efficient than commercial tools (e.g., ADS) across various measurement and simulation cases, often achieving comparable accuracy with fewer poles. Traditional macromodeling uses a fixed reference impedance (e.g., 50 Ω) for conversion, which can cause errors at low frequencies in power integrity applications. To mitigate this, the paper introduces a frequency-dependent complex reference impedance to renormalize the scattering parameters, making them closer to the actual impedance and reducing error amplification when converting to impedance or admittance parameters. This approach ensures that the new reference impedance is causal and stable. An equivalent circuit transformation is also proposed for SPICE implementation, allowing the method to be used within simulation tools.
Appears in Collections:	[Graduate Institute of Electrical Engineering] Electronic Thesis & Dissertation

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