A Hybrid Algorithm for Computation of Rectangular Conductor Internal Impedance

The accurate and fast computation of the per unit length (pul) internal impedance of rectangular conductors is required in electromagnetic analysis of various engineering and scientific problems where high current frequencies are involved [1, 2]. This pul internal impedance of a rectangular conductor can also be used in more complicated conductor structures where the shape of the conductor is approximated by a number of rectangular conductors [3]. Methods for computing the rectangular conductor pul internal impedance are based on different theoretical assumptions. The most often used numerical methods are those that employ a subdivision of the rectangular conductor into smaller segments [4÷8]. More accurate methods are analytical one-dimensional (1D) and twodimensional (2D) algorithms. The 2D analytical algorithms [9,10] are the most accurate ones but they are characterized by infinite sums in the expression for pul internal impedance. The Rong formula [9] has an infinite double sum in the expression for pul internal impedance, which significantly prolongs the computational time needed to acquire accurate results. On the other hand, the Giacoletto formula [10] only has a single infinite sum and produces results of similar accuracy faster. An analysis of the impact of the term numbers in the Giacoletto algorithm on accuracy and computational speed will be investigated. In this paper, it will be shown that for high frequencies when the skin effect is well developed, the rectangular conductor can be accurately approximated by a cylindrical conductor. Then the formulas developed for the pul internal impedance of solid cylindrical conductor can be used [11 12]. A hybrid algorithm which combines two formulas is developed. In the first part the Giacoletto formula with a truncated infinite sum is used, whereas in the second part the cylindrical conductor formula is used [11]. The hybrid algorithm developed yields highly accurate results in a shorter computational time. ,