PIER M | |

Progress In Electromagnetics Research M | ISSN: 1937-8726 |

Home > Vol. 16 > pp. 171-184
## ACCURACY OF APPROXIMATE FORMULAS FOR INTERNAL IMPEDANCE OF TUBULAR CYLINDRICAL CONDUCTORS FOR LARGE PARAMETERSBy D. Lovric, V. Boras, and S. Vujevic
Abstract:
Exact formulas for internal impedance per unit length of tubular cylindrical conductors energized by time-harmonic current involve Bessel functions. These functions are defined by infinite 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, different 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.
2. Saraj·cev, P. and S. Vujevie, "Grounding grid analysis: Historical background and classification of methods," 3. Dommel, H. W., 4. Dawalibi, F. P. and R. D. Southey, "Analysis of electrical interference from power lines to gas pipelines --- Part I: Computation methods," 5. Moore, J. and R. Pizer, 6. Stevenson, W. D., 7. Spiegel, M. R. and J. Liu, "Mathematical Handbook of Formulas and Tables,", Schaum's Outlines Series, 150-159, McGraw-Hill, New York, 1999. 8. Jeffrey, A. and H.-H. Dai, "Handbook of Mathematical Formulas and Integrals," 9. Abramowitz, M. and I. A. Stegun, "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables," 10. Paul, C. R., "Analysis of Multiconductor Transmission Lines," 11. Wang, Y. J. and S. J. Liu, "A review of methods for calculation of frequency-dependent impedance of overhead power transmission lines," 12. Amos, D. E., "A subroutine package for Bessel functions of a complex argument and nonnegative order,", SAND85-1018, Sandia National Laboratories, Albuquerque, NM., 1985. 13. Amos, D. E., "Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order," 14. Nahman, N. S. and D. R. Holt, "Transient analysis of coaxial cables using the skin effect approximation A + Bs," 15. Semlyen, A. and A. Deri, "Time domain modeling of frequency dependent three phase transmission line impedance," 16. Wedepohl, L. M. and D. J. Wilcox, "Transient analysis of underground power transmission systems: System-model and wave propagation characteristics," 17. Vujevic , S., V. Boras, and P. Saraj·cev, "A novel algorithm for internal impedance computation of solid and tubular cylindrical conductors," 18. Mingli, W. and F. Yu, "Numerical calculations of internal impedance of solid and tubular cylindrical conductors under large parameters," 19. Knight, D. W., "Practical continuous functions and formulae for the internal impedance of cylindrical conductors,", March 2010, http://www.g3ynh.info/zdocs/comps/Zint.pdf. 20. Schelkunoff, S. A., "The electromagnetic theory of coaxial transmission lines and cylindrical shields," |

© Copyright 2010 EMW Publishing. All Rights Reserved