Radiofrequency waves in lossy media Inductive effects through a cylindrical body

The electrical and electronics industries are frequently confronted with questions concerning the propagation of radio waves in conductors with cylindrical cross-sections. The article is structured around two problems. The first consists in determining the impedance of a cylinder of infinite length, evaluated by the ratio of the surface electric field to the current flowing through this filiform conductor. The second involves the analytical calculation of current densities induced in a finite-dimensional cylinder subjected to a sinusoidal radio wave. In both cases, the frequencies considered range from 50 Hz to a few GHz.

In terms of practical applications, surface impedance can be used to calculate the attenuation and distortion of signals carried on a transmission line comprising one or two cylindrical conductors of very high electrical conductivity. The calculations reported in the article also concern cylinders of moderate electrical conductivity immersed in an electromagnetic field formed by continuous waves at the frequencies considered above. Under these new assumptions, the cylinder provides an approximate model for predicting the currents induced in a human body exposed to the thermal effects of radio waves.

The article is divided into two main sections detailing the induction mechanisms of a plane wave that, depending on the chosen polarization, gives priority to an electric field oriented parallel to the cylinder or dual polarization determined by a magnetic field parallel to the cylinder.

The first leads to the calculation of surface impedance, illustrated by a few examples, and the determination of current density and power dissipation in a cylinder with conductivity close to the values found in biological media. We'll take this opportunity to see that the cylinder, normally placed on the surface of the ground, resembles a receiving antenna similar to an observer immersed in a high-frequency electromagnetic field.

The second focuses more specifically on the induction of eddy currents generated near the industrial frequency of 50 Hz. We'll see that the calculations undertaken in the article are just as relevant to phenomena induced in the power lines of large electrical equipment, as they are to low-amplitude currents encountered in the human body immersed in a sinusoidally varying magnetic field.

A third part, disjoint from the previous ones, is a mathematical supplement dedicated to setting up and solving the cylindrical wave equation. Although this problem is now dealt with by specific software tools, the analytical approach advocated in the article offers an alternative to the rigor of the all-numerical approach. Admittedly, the use of analytical formulas is subject to a few...