一種分析微帶線隨機(jī)參數(shù)敏感性的多項(xiàng)式混沌展開(kāi)方法
發(fā)布時(shí)間：2019-01-04 19:50
【摘要】：針對(duì)傳輸線加工中材料及結(jié)構(gòu)參數(shù)隨機(jī)不確定性對(duì)傳輸性能影響的問(wèn)題,提出了一種計(jì)算隨機(jī)系數(shù)傳輸線電報(bào)方程的多項(xiàng)式混沌(PC)展開(kāi)方法。利用正交多項(xiàng)式混沌基函數(shù),該方法首先將傳輸線電報(bào)方程中的隨機(jī)等效集總參數(shù)、傳輸線電壓及電流響應(yīng)進(jìn)行展開(kāi);其次利用Galerkin法,將隨機(jī)系數(shù)的電報(bào)方程問(wèn)題轉(zhuǎn)化為關(guān)于電壓、電流正交多項(xiàng)式展開(kāi)系數(shù)的確定性擴(kuò)階方程組問(wèn)題,并結(jié)合傳輸線邊界條件可計(jì)算電壓、電流的展開(kāi)系數(shù),進(jìn)而獲得電壓、電流及傳遞函數(shù)的均值、方差和概率密度分布。隨機(jī)參數(shù)微帶傳輸線的仿真結(jié)果表明:低頻時(shí)導(dǎo)帶寬度對(duì)微帶線的傳輸性能影響較大,高頻時(shí)介電常數(shù)對(duì)其傳輸性能影響較大;在滿足計(jì)算精度要求的同時(shí),PC展開(kāi)方法具有比傳統(tǒng)蒙特卡羅(MC)方法更高的計(jì)算效率,計(jì)算耗時(shí)僅約為MC方法的1/500。
[Abstract]:Aiming at the influence of random uncertainty of material and structure parameters on transmission performance in transmission line processing, a polynomial chaotic (PC) expansion method is proposed to calculate the transmission line telegram equation with random coefficients. By using the chaotic basis function of orthogonal polynomials, the random equivalent lumped parameters, transmission line voltage and current responses in the transmission line telegram equation are first expanded. Secondly, by using the Galerkin method, the Telegraph equation problem with random coefficients is transformed into the deterministic expansion equations of the orthogonal polynomial expansion coefficients of voltage and current, and the expansion coefficients of voltage and current can be calculated by combining the boundary conditions of transmission lines. The mean, variance and probability density distributions of voltage, current and transfer function are obtained. The simulation results of random parameter microstrip transmission line show that the transmission performance of the microstrip line is greatly influenced by the width of the conduction band at low frequency and the transmission performance by the dielectric constant at high frequency. At the same time, the PC expansion method has higher computational efficiency than the traditional Monte Carlo (MC) method, and the computational time is only about 1 / 500 of that of the MC method.
【作者單位】： 西安交通大學(xué)電子與信息工程學(xué)院;
【基金】：國(guó)家自然科學(xué)基金資助項(xiàng)目(61471293)
【分類號(hào)】：TN817
[Abstract]:Aiming at the influence of random uncertainty of material and structure parameters on transmission performance in transmission line processing, a polynomial chaotic (PC) expansion method is proposed to calculate the transmission line telegram equation with random coefficients. By using the chaotic basis function of orthogonal polynomials, the random equivalent lumped parameters, transmission line voltage and current responses in the transmission line telegram equation are first expanded. Secondly, by using the Galerkin method, the Telegraph equation problem with random coefficients is transformed into the deterministic expansion equations of the orthogonal polynomial expansion coefficients of voltage and current, and the expansion coefficients of voltage and current can be calculated by combining the boundary conditions of transmission lines. The mean, variance and probability density distributions of voltage, current and transfer function are obtained. The simulation results of random parameter microstrip transmission line show that the transmission performance of the microstrip line is greatly influenced by the width of the conduction band at low frequency and the transmission performance by the dielectric constant at high frequency. At the same time, the PC expansion method has higher computational efficiency than the traditional Monte Carlo (MC) method, and the computational time is only about 1 / 500 of that of the MC method.
【作者單位】： 西安交通大學(xué)電子與信息工程學(xué)院;
【基金】：國(guó)家自然科學(xué)基金資助項(xiàng)目(61471293)
【分類號(hào)】：TN817
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1 B.A.賽雷特;李國(guó)金;;微帶偏置或調(diào)諧電路用的寬帶元件[J];國(guó)外艦船技術(shù).雷達(dá)與對(duì)抗;1982年02期
2 符果行 ,余蓉;類微帶傳，
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