一種分析微帶線隨機參數(shù)敏感性的多項式混沌展開方法
發(fā)布時間：2019-01-04 19:50
【摘要】：針對傳輸線加工中材料及結(jié)構(gòu)參數(shù)隨機不確定性對傳輸性能影響的問題,提出了一種計算隨機系數(shù)傳輸線電報方程的多項式混沌(PC)展開方法。利用正交多項式混沌基函數(shù),該方法首先將傳輸線電報方程中的隨機等效集總參數(shù)、傳輸線電壓及電流響應(yīng)進行展開;其次利用Galerkin法,將隨機系數(shù)的電報方程問題轉(zhuǎn)化為關(guān)于電壓、電流正交多項式展開系數(shù)的確定性擴階方程組問題,并結(jié)合傳輸線邊界條件可計算電壓、電流的展開系數(shù),進而獲得電壓、電流及傳遞函數(shù)的均值、方差和概率密度分布。隨機參數(shù)微帶傳輸線的仿真結(jié)果表明:低頻時導帶寬度對微帶線的傳輸性能影響較大,高頻時介電常數(shù)對其傳輸性能影響較大;在滿足計算精度要求的同時,PC展開方法具有比傳統(tǒng)蒙特卡羅(MC)方法更高的計算效率,計算耗時僅約為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】： 西安交通大學電子與信息工程學院;
【基金】：國家自然科學基金資助項目(61471293)
【分類號】：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】： 西安交通大學電子與信息工程學院;
【基金】：國家自然科學基金資助項目(61471293)
【分類號】：TN817
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1 B.A.賽雷特;李國金;;微帶偏置或調(diào)諧電路用的寬帶元件[J];國外艦船技術(shù).雷達與對抗;1982年02期
2 符果行 ,余蓉;類微帶傳，
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