【摘要】：隨著電子裝備向高頻段、高增益、高密度、小型化方向發(fā)展,結(jié)構(gòu)因素對(duì)其電性能的影響也愈發(fā)凸顯,其中表面粗糙度因其存在的普遍性、分布的隨機(jī)性及其對(duì)電性能影響機(jī)理的復(fù)雜性而備受關(guān)注。本學(xué)位論文在國(guó)家自然科學(xué)基金項(xiàng)目的支持下,以電子裝備腔體結(jié)構(gòu)內(nèi)壁表面粗糙度為具體研究對(duì)象,針對(duì)表面粗糙度的重構(gòu)問(wèn)題,進(jìn)行了深入的研究與探索,主要研究?jī)?nèi)容包括以下三部分:一是應(yīng)用三種典型函數(shù)對(duì)一維表面粗糙度進(jìn)行了建模;二是基于電磁散射理論對(duì)一維表面粗糙度形貌進(jìn)行了重構(gòu);三是進(jìn)行了二維表面粗糙度形貌的重構(gòu)。1、表面粗糙度的建模分別建立了周期函數(shù)、隨機(jī)函數(shù)和分形函數(shù)表面粗糙度模型。采用蒙特卡洛法建立表面粗糙度一維高斯隨機(jī)粗糙度模型,驗(yàn)證了均方根高度、相關(guān)長(zhǎng)度對(duì)粗糙表面形貌的影響關(guān)系;建立了周期函數(shù)粗糙度模型,簡(jiǎn)單討論了其相關(guān)參數(shù)對(duì)粗糙表面形貌的影響關(guān)系;建立了一維W-M分形函數(shù)粗糙度模型,對(duì)其具有的自仿射性、自相似性等性質(zhì)進(jìn)行了驗(yàn)證,并討論了分形函數(shù)的主要參數(shù)對(duì)粗糙表面形貌的影響。2、一維表面粗糙度形貌的重構(gòu)采用矩量法對(duì)一維粗糙表面形貌的電場(chǎng)積分方程進(jìn)行離散,將復(fù)雜的積分方程的求解轉(zhuǎn)換成簡(jiǎn)單的線性方程組求解,從而得到散射數(shù)據(jù);分別仿真驗(yàn)證了一維粗糙表面形貌的源項(xiàng)與入射角度、譜振幅與表面起伏高度之間的關(guān)系,驗(yàn)證了源項(xiàng)與入射場(chǎng)、譜振幅與散射場(chǎng)之間的等價(jià)關(guān)系;采用微擾法-矩量法混合算法對(duì)三種一維小尺度下的粗糙表面形貌進(jìn)行了重構(gòu),包括周期函數(shù)、高斯函數(shù)和分形函數(shù)。由于分形函數(shù)具有處處連續(xù)且處處不可導(dǎo)的特性,使用現(xiàn)有理論出現(xiàn)了散射數(shù)據(jù)無(wú)法準(zhǔn)確計(jì)算,重構(gòu)過(guò)程無(wú)法進(jìn)行的問(wèn)題。本文通過(guò)引入分形幾何領(lǐng)域內(nèi)的分?jǐn)?shù)階微積分理論,解決了分形函數(shù)整數(shù)階不可導(dǎo)問(wèn)題,實(shí)現(xiàn)了分形粗糙表面形貌的準(zhǔn)確重構(gòu)。3、二維粗糙表面形貌的重構(gòu)。針對(duì)二維高斯隨機(jī)粗糙表面,采用蒙特卡洛法建立了二維高斯隨機(jī)粗糙度模型,分析討論了其均方根高度與相關(guān)長(zhǎng)度對(duì)粗糙表面形貌的影響關(guān)系;采用離散化思想將二維高斯隨機(jī)粗糙表面離散成大量可近似為一維粗糙表面形貌的條狀模型,將二維高斯隨機(jī)粗糙表面的電磁散射過(guò)程簡(jiǎn)化為若干一維高斯隨機(jī)粗糙表面的電磁散射過(guò)程,實(shí)現(xiàn)了二維高斯隨機(jī)粗糙表面形貌的準(zhǔn)確重構(gòu)。
[Abstract]:With the development of electronic equipment in the direction of high frequency band, high gain, high density and miniaturization, the influence of structural factors on its electrical performance is becoming more and more prominent. The randomness of distribution and the complexity of its influence mechanism on electrical properties have attracted much attention. Supported by the National Natural Science Foundation of China, this dissertation takes the surface roughness of the inner wall of the cavity structure of electronic equipment as the specific research object, aiming at the problem of surface roughness reconstruction, carries on the thorough research and the exploration. The main research contents include the following three parts: first, using three typical functions to model one-dimensional surface roughness; Secondly, based on the electromagnetic scattering theory, the one-dimensional surface roughness morphology is reconstructed. Firstly, the surface roughness models of periodic function, random function and fractal function are established. The one-dimensional Gao Si random roughness model of surface roughness was established by Monte Carlo method, and the effect of root mean square height and correlation length on rough surface morphology was verified. The periodic function roughness model is established, and the influence of the relative parameters on the rough surface morphology is briefly discussed. The roughness model of one-dimensional W-M fractal function is established and its properties of self-affine and self-similarity are verified. The influence of the main parameters of fractal function on the morphology of rough surface is discussed. The method of moment is used to discretize the electric field integral equation of one-dimensional rough surface topography, and the complex integral equation is transformed into a simple linear equation group to solve the scattering data. The relationship between source term and incident angle, spectral amplitude and surface fluctuation height of one-dimensional rough surface topography is verified by simulation, and the equivalent relationship between source term and incident field, spectral amplitude and scattering field is verified. In this paper, three kinds of rough surface topography at one dimension and small scale are reconstructed by the mixed algorithm of perturbation method and moment method, including periodic function, Gao Si function and fractal function. Because the fractal function is continuous everywhere and can not be differentiable everywhere, using the existing theory, the scattering data can not be accurately calculated, and the reconstruction process can not be carried out. By introducing the fractional calculus theory in the field of fractal geometry, this paper solves the problem of integral order nondifferentiability of fractal functions, and realizes the accurate reconstruction of fractal rough surface topography. 3. The reconstruction of two-dimensional rough surface topography. Aiming at the two-dimensional Gao Si random rough surface, the Monte Carlo method is used to establish the two-dimensional Gao Si random roughness model, and the relationship between the root mean square height and the correlation length on the rough surface morphology is analyzed and discussed. Using the idea of discretization, the two-dimensional Gao Si random rough surface is discretized into a large number of strip models which can be approximated to one-dimensional rough surface morphology. The electromagnetic scattering process of two dimensional Gao Si random rough surface is simplified as that of some one-dimensional Gao Si random rough surface, and the accurate reconstruction of the two-dimensional Gao Si random rough surface morphology is realized.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：TN011

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本文編號(hào)：2419504