Radiation Impedance of a Thin Straight Antenna Derived from Hallen's Equation by the Circuit-Theoretical Method

摘要

Extending the domain of the vector potential in the so-called Hallen's equation, four unknown constants are determined to satisfy the boundary conditions in the same way as the circuit theory, where the vector potential plays the leading role, from which the current density and the current itself are derived. Vanishing of the current density just outside the ends of the antenna is required. For a tube-shaped antenna with walls of infinitesimal thickness, further the current just inside the ends of the antenna should vanish, as a result, the current distribution becomes sinusoidal. Adoption of either the surface current distribution or axial current distribution incurs a crucial effect on the value of the currents calculated from the vector potential. The numerical results of the radiation impedance of a hslf-wave antenna show a tendency of consistency with that relatively newly obtained by employing the exact kernel. The problem on the non-solvability of Hallen's equation is cleared up. Comments are given on the moment method in relation to the boundary value problems to recommend to add two more undecided constants to Hallen's equation.