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

Abstract

New analytical expressions and numerical results for the mode coefficients, the directivity, and the quality factor and computationally convenient expressions for the input admittance of a symmetrical biconical antenna of arbitrary length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> and cone angle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta _{0}$ </tex-math></inline-formula> are presented. The quality factor for a wide-angle biconical antenna is evaluated using three alternative formulations: 1) the evanescent energy stored outside the circumscribing sphere; 2) the total evanescent energy stored in all space; and 3) 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. Finally, the ratio of directivity to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> of an electrically small biconical antenna is shown to approach 78% of the value of an ideal omnidirectional antenna.