Computation of Carson formulas using piecewise quadratic approximation

Abstract

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.