Theory of the frequency responses of uniform and quasi-taper helical antennas

A theory is presented for the frequency responses of uniform and quasi-taper helical antennas radiating in the axial mode. Based on a model assuming a single traveling wave of current, expressions for the far-zone electric field are obtained by summing the contributions of the current elements from one end of the helix to another. These expressions are used to study the variation of the axial electric field with frequency, first assuming the Hansen-Woodyard (HW) condition and then assuming Sensiper´s solution for the phase velocity. It is found that the HW condition leads to the result that the electric field increases monotonically with frequency over the entire axial mode range, which is in violation with the recent experimental measurements of King and Wong. On the other hand Sensiper´s phase velocity yields frequency response curves that are consistent with King and Wong´s measurements. Numerical results are given for uniform helices and quasi-taper helices consisting of two uniform sections of different diameters.