Design Equation for Self Resonant Structures of Very Small Normal - Mode Helical Antennas

Recently, normal-mode helical antennas (NMHA) are employed as very small antennas for metal plate proximity uses [1] ~ [3]. In order to obtain efficient radiation, the self resonant condition of a NMHA should be satisfied. In this condition, the inductive reactance and the capacitive reactance of a NMHA are cancelled. As for the inductance, Wheeler presented an equation employing structural parameters [4]. As for capacitance, any useful expression was not found. Therefore, the design equation based on structural parameters is not clarified. How to establish the design equation of self resonance is left questionable. In this paper, authors pay attention to calculated results of the total wire lengths of antennas at self resonances. First, resonant wire lengths are obtained through electromagnetic simulations. Next, an approximate equation for resonant length data are obtained. By utilizing the approximate equation the design equation for self resonances are established. Comparisons of the design equation and simulation results are compared. Moreover, electromagnetic field distributions around the resonance are obtained. Interesting electric field distributions are clarified.