Quasi-Static Antenna Design Algorithm: A scientific approach to designing electrically small antennas.

The quasi-static antenna design algorithm is a scientific approach to designing electrically small antennas. The radiation resistance is computed from the electrostatic dipole potential. The capacitance is computed from the electrostatic potential on the enclosed sphere. The Q-factor is calculated from the radiation resistance and capacitance. The general thick-disk-cap monopole, enclosed by a sphere, is modeled with electrostatic multipole basis functions on the disk. A sequence of solutions is computed with one to five electrostatic multipole basis functions. The sequence of solutions converges in shape and Q-factor. Chu´s [1] theoretical limit Q_Chu for an antenna enclosed by a sphere is used to calculate the Q-factor ratio (Q/Q_Chu). At low frequencies, the Q-factor ratio for the thick-disk-cap monopole is 1.825. This is almost the same as the spherical-cap monopole Q-factor ratio of 1.75. The thick-disk-cap and spherical-cap monopole were modeled with Computer Simulation Technology (CST) Microwave Studio. At resonance, the thick-disk-cap monopole´s Q-factor is 22.5. This is much smaller than the spherical-cap monopole´s Q-factor of 46.1. Above the resonant frequency, the thick-disk-cap monopole had a 37% lower Q-factor. Stuart´s equivalent circuit is fit to the CST impedance near the resonant frequency. The simplest circuit is the dipole eigenmode (a series LC and a resistor parallel to the L). The dipole eigenmode circuit gives the ω² radiation resistance. The CST radiation resistance includes a ω⁴ term. A capacitor approximation of the higher-order eigenmodes explains the ω⁴ term in the CST radiation resistance. The capacitor is parallel to the dipole eigenmode-circuit. Stuart´s equivalent circuit is used to compute the dc capacitance, inductance, effective height, Q-factor, and Q-factor ratio at low frequencies. The circuit model and CST impedance are almost identical. The agreem- nt between the CST impedance and the dc quasistatic values is reasonable. The circuit model impedance is expressed in an easy-to-understand format.