The comparative analysis of calculating methods for ac impedance of R65 type rails and track 1520 mm gauge in the audio frequency range

Abstract

Knowledge of the exact AC rail impedance in a wide frequency range is necessary for de-signing and modeling audiofrequency track circuits, determining of the traction return current distribution in rails of high-speed railways, testing new types of vehicles on electromagnetic compatibility with track circuits, etc. The aim of the work is to perform a comparative analysis of the methods for calculating of the AC impedance of the R65 type rails of a track 1520 mm gauge in the audiofrequency range. Results of AC rail impedance measurements and theoretical description of frequency dependence of impedance for wires above lossy ground are briefly reviewed. Mathematical formulation of Carson's method and the complex image method proposed by Deri with co-workers for impedance of transmission lines were represented. The impedance of running rails of R65 type and track of 1520 mm gauge have been calculated by using Carson's method and the complex image method. Due to the insufficient amount of literature data concerning AC impedance measurements for rails of type R65 of 1520 mm gauge, the results of calculations for these rails were compared with the measured values for both rails of type R65, 1520 mm gauge, as well as for rails of type UIC 60 with 1435 mm gauge. Calculated frequency dependencies of the AC impedance of R65 type rails are in good qualitative agreement with literature data for rails UIC60 in frequency range Hz. The results for rails of R65 type and 1520 mm gauge calculated according to Carson's method and complex image method differ from reference data presented in literature, and these differences increase with increasing of frequency. Such behavior may be due to error of calculation methods caused by small height of rails above lossy ground and high electrical conductivity between rails and a ground.