Unusual method for impedance evaluation of short dipole with arbitrarily mutual arms location and the implications for dc field sensors

Abstract

A relatively unknown analytical method is developed further in order to evaluate the capacitance between two long cylinders of equal length and diameter. The main approximation associated with the relatively unknown method was in assuming that the cylinders are uniformly charged no matter what is their length and diameter and no matter what is their mutual location and orientation. The cylinders in our treatment are long in terms of length to diameter ratio, but they are much shorter than a wavelength. One of the presently treated cases is due to two gapped collinear cylinders of equal diameters and lengths. Such a structure (when the gap between the cylinders is small) is similar to that of a short dipole antenna. There have been several analytical methods mentioned in the literature for estimating the short dipole impedance. It is interesting that the present method of evaluation, which is completely independent, compliments some of the previous methods. It is also known relatively well that evaluating the inductance of iron cored coils bears direct relationship (through EM duality theory) to the short electric dipole capacitance evaluation. It means that the present work is helpful for inductors design and also for evaluating cored search coil magnetometers. The work contributes to better understanding of fieldmills and fluxgates that are employed for sensing electric and magnetic dc fields, respectively. Furthermore, a new type of an electric dc field sensor has been developed by us recently. Its structure is that of a short dipole, where the length of the gap between the dipole cylindrical arms is modulated periodically. Its operation is somewhat similar to that of a fieldmill, and is also due to the periodic variation of the structure antenna-capacitance. The presently developed analytical method serves also for evaluating the variable capacitance of the new sensor, and is in particular helpful for the interpretation of its operation. Generally speaking, the work is helpful in demonstrating that dc field sensors should be regarded as being related to antennas and should not be treated as if they were separate entities.