Input Admittance, Directivity and Quality Factor of Biconical Antenna of Arbitrary Cone Angle

TL;DR

This paper derives new analytical formulas and numerical results for the input admittance, directivity, and quality factor of symmetrical biconical antennas with arbitrary cone angles, providing insights into their performance and fundamental limits.

Contribution

It introduces novel analytical expressions for key antenna parameters and evaluates the quality factor using three methods, comparing results with Chu's lower bound.

Findings

Foster's reactance theorem remains invalid for perfectly conducting antennas.

Directivity varies slowly with electrical length and differs from thin dipole behavior.

The ratio of directivity to Q approaches 78% of an ideal omnidirectional antenna for small sizes.

Abstract

New analytical expressions and numerical results for the mode coefficients, the directivity and the quality factor as well as computationally convenient expressions for the input admittance of a symmetrical biconical antenna of arbitrary length $L$ and cone angle $\theta_0$ are presented. The quality factor for a wide-angle biconical antenna is evaluated using three alternative formulations: (i) the evanescent energy stored outside the circumscribing sphere, (ii) the total evanescent energy stored in all space and (iii) by equivalent circuit model, and these are all compared with Chu's lower limit for an ideal antenna. Numerical calculations based on the analytical formula for antenna admittance confirm the conjecture that Foster's reactance theorem remains invalid even for perfectly conducting antennas. Furthermore, the variation of directivity of a wide-angle biconical antenna is a slowly varying function of its electrical length and is shown to depart significantly from that of a thin cylindrical dipole. Lastly, the ratio of directivity to $Q$ of an electrically small biconical antenna is shown to approach 78\% of the value of an ideal omnidirectional antenna.