Application of thin-wire integral representations of the electromagnetic field to the electrodynamic analysis of vibrator antennas with a large cross-section

Abstract

The article considers the construction of mathematical models of vibrator antennas with a large cross-section on the basis of thin-wire integral representations of the electromagnetic field. A mathematical model of a thin-wire vibrator is obtained, equivalent to the model of a tubular vibrator. It is shown that taking into account the rotational symmetry of the structure in the fine-wire integral representations of the electromagnetic field when solving the internal electrodynamic problem leads to the Fredholm integral equation of the first kind, and not to the singular integral equation, which takes place when using the tubular model. The results of calculation of current distributions on thin conductors forming a vibrator are presented, as well as the dependence of their input resistance on the electrical length of the vibrator.

Keywords

• broadband electric vibrator
• fine-wire approximation
• integral fredholm equation of the first kind
• ill-posed problem
• rotation symmetry
• pocklington equation
• hallen equation
• integral representation of the electromagnetic field