應用時域有限差分法於平行板電容的線性度分析

Linearity analysis of a parallel plate capacitor via the FDTD method

林鼎凱(Ding-Kai Lin)

指導教授 ： 李慶烈

淡江大學/工學院/電機工程學系碩士在職專班/碩士(2006年)

https://doi.org/10.6846/TKU.2006.00886

摘要

在本論文中我們將探討時域有限差分法(Finite Difference Time Domain，FDTD)應用於平行板電容的分析，經由驅動方程式建立準靜電荷的特性來研究平行電容板的結構，由準靜電荷穩定後的電場值來計算出平行金屬板間的電壓，然後再將電荷總量除以電壓即可獲得電容值，並可將平行板電容的特性分析應用於感測器上。
我們設計三種不同結構的電容，來探討線性度的問題，同時利用FR4板金屬以蝕刻方式實際製作電容和FDTD模擬結果做比較；因邊緣效應產生出的非線性問題，會影響到電容式感測器的準確度。我們同時透過實驗法及遺傳演算法( genetic algorithm )進一步求出示波器輸入阻抗及同軸電纜線的輸入電容，再透過電容分壓原理，即可求出未知平行電容板的電容值。電容感測器不僅能做距離的量測，可經由實驗和FDTD模擬來找出不同介電常數的待測物材料。

關鍵字

時域有限差分法 ； 透明源 ； 電容 ； 感測器 ； 遺傳演算法

並列摘要

In this thesis, the application of the finite-difference time-domain (FDTD)method for the parallel-plate capacitor are investigated. Through the use of the transparent current source, the parallel-plates are charged such that the transient and static E fields can be simulated using the FDTD update equation. The static E field is used to calculate the voltage across the parallel-plates. The capacitance is obtained directly by dividing the charge over the voltage. The study of the characteristics for the parallel plate capacitor is make to emphasis on the linearity analysis for the possible sensor application.
There are three capacitor structures investigated for linearity analysis. The capacitors are fabricated by using FR4 board, of which the capacitances are compared with the FDTD simulation results. The non-linearity due to the fringing effect would degrade the performance of a capacitor sensor. The simulated linearity curves of certain structure obtained in this thesis are different from the literature. To confirm the simulated results, the capacitors are fabricated and measured carefully by using a digital oscilloscope. To increase the measurement accuracy we setup a de-embedding procedure for the calibration of the connecting cable and the digital oscilloscope. Furthermore, the genetic algorithm (GA) is employed to find out input impedance of oscilloscope and the capacitance of the probe. Finally, through a simple voltage dividing rule, we can resolve the capacitance for the capacitor under test. On the other hand, the capacitive sensors are also applied to find the dielectric property between the parallel plates.

並列關鍵字

FDTD ； transparent source ； capacitor ； sensor ； genetic algorithm

參考文獻

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