以時域有限差分法分析近遠場轉換之電磁場共點與非共點排列

Abstract

本研究使用時域有限差分法（Finite-Difference Time-Domain, FDTD）探討近遠場轉換（Near-to-Far-Field, NTFF）中電磁場之共點與非共點排列方式對模擬準確度之影響，並透過向量勢推導二維近遠場轉換公式，再搭配空間幾何平均與時間插值法建立場值共點排列策略，以有效解決電場與磁場錯位所造成的積分誤差問題。研究設計兩種模擬架構進行交叉驗證，結果顯示未經共點處理之模擬，於主瓣以外的高角度區域產生明顯誤差。而透過本研究提出之場值共點處理方法，模擬誤差在所有角度範圍內皆顯著下降，最大誤差值可從3.4 dB左右降低至0.0357 dB，並具備邊界條件獨立性與模擬重現性。本研究提出之方法已成功驗證可有效提升近遠場轉換之模擬準確度與穩定性。

This study examines how collocated and non-collocated electromagnetic field sampling methods affect the accuracy of near-to-far-field (NTFF) transformations in finite-difference time-domain (FDTD) simulations. A two-dimensional NTFF formulation based on vector potentials was developed, along with a field-collocation strategy that employs spatial geometric averaging and temporal interpolation to minimize numerical integration errors caused by spatial and temporal misalignments between electric and magnetic fields. Two independent simulation frameworks were implemented for cross-validation. The results show that the non-collocated approach introduces significant errors, especially at high-angle regions outside the main lobe, while the proposed collocated method reduces the maximum error dramatically—from approximately 3.4 dB to just 0.0357 dB. Additionally, the collocated method maintains consistent accuracy regardless of boundary dimensions and demonstrates strong reproducibility across different simulation setups. The numerical approach presented in this study not only improves the precision and stability of NTFF simulations but also offers reliable applicability for practical electromagnetic analysis.