1887

## Directives Concerning the Protection of Telecommunication Lines Against Harmful Effects from Electric Power and Electrified Railway Lines. Volume II

### Calculating Induced Voltages and Currents in Practical Cases The Directives provide a comprehensive description of electromagnetic effects due to the close proximity of telecommunication lines to power and electrified railway systems. Such effects may result in danger to personnel, damage to telecommunication equipment, deterioration of telecommunication transmission quality or to disturbance of signalling. Volume II - Calculating induced voltages and currents in practical cases - describes the methods for evaluating voltages and currents resulting from capacitive, inductive and conductive coupling in a variety of commonly-encountered situations.

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## Calculation of Inductive Coupling

This study of inductive coupling concerns the self-impedance of a conductor with earth return and the mutual impedance between two single conductors both with earth return. The theoretical background for evaluation of these impedances is presented in Volume III. In the present section, formulas, curves and tables are given which can be used to calculate the results of inductive coupling in practical cases. In each case the value of inductance is used and given instead of, or together with, the value of impedance. The relationship between impedance Z and inductance M, in the case of alternating currents of frequency f (angular frequency ω = 2 πf) is: Z = jωM. The expressions of impedances include real and imaginary components, the magnitudes of which vary greatly with the distance between the lines. In the neighbourhood of the inducing line the imaginary component of Z (the real component of M) predominates. The electric field induced along a parallel conductor in this area and the current density at ground level are almost in 90° phase shift to the inducing current. At large distances from the inducing line the real component of Z (imaginary component of M) is predominant: the electric field induced along a parallel conductor and the current flow at ground level are almost in phase opposition to the inducing current. The variation with distance of the phase difference between the magnitudes of both currents is continuous and fairly uniform. The imaginary components of M have negative values throughout the whole range, consequently when multiplying them by jω the calculated real component of Z will be positive.

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