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Computation of Carson formulas using piecewise quadratic approximation

机译：使用分段二次逼近计算卡森公式

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In this paper, an existing numerical algorithm for high-accurate computation of exact Carson formulas based on piecewise linear approximation is improved. Carson formulas are used for computing of per-unit-length (pul) self and mutual impedances of infinitely long parallel conductors. The proposed algorithm is based on piecewise quadratic approximation of kernel function and analytical integrations of approximated kernel function multiplied by the rest of two integrands. Using proposed algorithm, high-accurate results with desired computer machine n-digit accuracy can be easily obtained. Total number of sample points is significantly decreased with proposed algorithm in comparison with piecewise linear approximation. Results computed by two approximation methods are compared with high-accurate results computed by proposed numerical algorithm for large frequency range.
机译：本文改进了一种基于分段线性逼近的高精度计算精确卡森公式的数值算法。卡森公式用于计算无限长的平行导体的每单位长度（pul）自阻抗和互阻抗。所提出的算法基于核函数的分段二次逼近，以及近似核函数的解析积分乘以其余两个被积数的结果。使用所提出的算法，可以容易地获得具有所需计算机机n位精度的高精度结果。与分段线性逼近相比，所提出的算法大大减少了采样点的总数。将两种近似方法计算出的结果与拟议数值算法在大频率范围内计算出的高精度结果进行比较。

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