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Title: | 部分元素等效電路法輻射阻抗、時域模擬、及穩定性之研究 On the Radiation Resistance, Transient Simulation, and Stability of the Partial Element Equivalent Circuit Method |
Authors: | Chiu-Chih Chou 周求致 |
Advisor: | 吳宗霖 |
Keyword: | 部分元素等效電路,數值方法,穩定性,被動性, partial element equivalent circuit,numerical method,stability,passivity, |
Publication Year : | 2019 |
Degree: | 博士 |
Abstract: | 本論文針對部分元素等效電路法(partial element equivalent circuit,以下簡稱 PEEC)的三個面向進行探討。第一個面向為全波(full-wave) PEEC所具有的複數電感與複數電位係數之物理意義。經由理論推導,本論文嚴格的證明了此複數電感電位所引生的功率損耗,完全對應到該結構的總輻射功率;若該結構本身沒有電源,而是受入射波的激發,則此功率損耗對應該結構的總散射功率。因此,此複數電感電位,其虛部具有該結構之輻射電阻(radiation resistance)的物理意義。
第二個面向為全波PEEC之時域模擬方法。由於全波模型中,互感與互容的耦合皆帶有時間延遲(time delay),而一般的電路模擬軟體並不支援帶時延之互感,故傳統上必須自行撰寫程式來解全波模型之時延微分方程,因而限縮了全波PEEC與其他電路之整合性。本論文提出一種方法,利用電路模擬軟體中受控電源(controlled source)之時延功能,將全波PEEC模型實現成電路模擬軟體支援的形式,進而可用一般商用軟體來模擬時域響應。此法使得全波PEEC之模擬困難度大幅降低。又,透過此方法,我們得以模擬許多不同的模型,從中觀察到全波PEEC在時域上經常會出現不穩定的響應,因而啟發了本論文第三部分的研究。 第三個面向即為全波PEEC之穩定性(stability)分析。此穩定性問題又可分為三個部分:一、如何判斷一個模型穩定與否。二、若不穩定,是何原因導致其不穩定。三、如何改善其穩定性。對於第一個問題,本論文提出一套演算法,能將電路模型一部分的自然頻率(natural frequency)找出來,作為判斷穩定性的必要條件。第二個問題,本論文從被動性(passivity)的角度來分析,證明了標準的PEEC模型,其電感與電位矩陣,不具備被動性;相反的,其可產生大量的能量,以供應電路的發散響應。第三個問題,本論文先將文獻中的各種阻尼電路彙整,並做系統性的分析,再利用前述自然頻率的檢測,提出一個系統性的阻尼設計方法。最後,本論文再探討如何從被動性的角度來進行阻尼的設計。 This dissertation studies three aspects of the partial element equivalent circuit (PEEC) method. The first one is the physical meaning of the complex inductance and potential coefficient occurred in full-wave (FW) PEEC model. Through rigorous derivation, we prove that the total power consumed in these complex coupling networks corresponds to the total radiated power of the circuit. If the circuit is not excited internally, but illuminated by an incident wave, then this power consumption corresponds to the total scattered power. Consequently, the imaginary parts of these complex couplings have the physical meaning of radiation resistance of the structure. The second part deals with the time domain simulation method of FW PEEC. Due to the presence of time delay, the inductive and potential couplings are not supported by typical circuit simulators such as SPICE. Traditionally, researchers had to write their own differential equation solver in order to conduct transient simulation. In this dissertation, we exploit the time delay function of the controlled sources in typical SPICE and propose a method to cast the FW PEEC model into a fully SPICE-compatible form, which greatly eases the effort of conducting time domain simulation as well as the co-simulation with external linear or nonlinear lumped circuit. Also, from several simulation results, we observe that the time domain response of FW PEEC often suffers from unstable resonance. This then motivates the study of the third part. The third part of the dissertation focuses on the stability properties of FW PEEC. The stability problem can be further divided into three subparts: (a) how do we test if a given model is stable or not; (b) if it is unstable, what is the reason for its instability; and (c) what are the methods that we can apply to improve the stability. In part (a), we propose an algorithm that can efficiently obtain some of the natural frequencies of the circuit. Such information serves as a necessary-condition test for stability. In part (b), we show that the inductive and potential coupling matrices of general FW PEEC models are far from being passive. They are thus the energy sources that support the unstable resonances of the circuit. In part (c), we first summarize existing damping method in the literature. And then we present systematic analysis of various damping structures, and propose two design approaches based on stability and passivity. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/7235 |
DOI: | 10.6342/NTU201902629 |
Fulltext Rights: | 同意授權(全球公開) |
Appears in Collections: | 電信工程學研究所 |
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ntu-108-1.pdf | 9.07 MB | Adobe PDF | View/Open |
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