The input impedance of a concentric curved dipole antenna above a spherical conducting surface

Abstract

In this work an analytical expression is determined for the input impedance of a curved concentric dipole antenna located in close proximity to a conducting sphere. A solution to this boundary value problem is facilitated using the spherical vector mode function. The solution is formulated in an infinite series of spherical Bessel functions, spherical Hankel functions, associated Legendre polynomials, and their derivatives. A general current distribution in the antenna is expressed as a Fourier cosine series. In the expression for the input impedance, flexibility is provided so that the impedance as a function of the height above the sphere and as a function of frequency can be determined. For the purpose of numerical calculations two current distribution assumptions were used. They were the sinusoidal and the linear distribution. Calculations were made for two different cases. Case 1 was defined for an antenna whose length and operating frequency were fixed and whose height above the conducting sphere was varied. Case 2 was defined for an antenna whose length and height above the conducting sphere were fixed and whose operating frequency was varied. Results obtained from the numerical calculations indicated that the linear current distribution assumption was good for antennas having a total length less than a quarter wavelength. Laboratory measurements were made to verify the numerical results for Case 1 and Case 2. In most cases the experimental results compared favorably with the predicted values within the range of experimental accuracy.