Accuracy of Approximate Formulas for Internal Impedance of Tubular Cylindrical Conductors for Large Parameters

Exact formulas for internal impedance per unit length of tubular cylindrical conductors energized by time-harmonic current involve Bessel functions. These functions are deflned by inflnite series, which yield unstable and often erroneous results for complex arguments of large magnitudes. Although it is well known how to evaluate Bessel functions numerically and many routines are now available to perform the actual computation, the available software routines often fail when computing equations that consist of a product and a quotient of Bessel functions under large complex or real arguments. For such cases, difierent approximate formulas can be used. In this paper, three types of approximate formulas for internal impedance of tubular cylindrical conductors are compared with respect to numerical stability and accuracy.