A mathematical investigation of a normal mode helical antenna (NMHA) is presented to provide an equivalent model. The vector potential of a single-turn NMHA using a developed helix line is first derived. To avoid complexity in the vector potential, a useful relationship between the source point and the helix line is established. Employing this relationship, the integral of the vector potential can be calculated as that of a linear current antenna, and the result leads to an equivalent model that is a combination of the electric dipole and the magnetic dipole, i.e., exactly the same as assumed in previous work. A helix line of several turns can be regarded as a combination of the turns. Thus a general NMHA can be analysed as the sum of the vector potentials of the turns in the helix. To verify the obtained formulas, the calculated radiation characteristics are compared with the results of the commercial simulation, showing good agreement.
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