Computing Mutual Impedance of Antennas by Spherical Harmonic Transform

The coupling of two antennas can be described with mutual impedance. This paper proposes computing the mutual impedance by reaction theorem, which involves integrating vector products of near fields over a sphere surrounding the second antenna. We express the near fields of both antennas by the vector spherical harmonic transform (SHT), evaluate the near fields of the first antenna on the eccentric sphere by a new fast Fourier transform (FFT)/interpolation method efficiently, and then obtain the mutual impedance by the reaction integrals. This new method has a computation complexity of O(N-3), where N represents the truncation order in SHT. A comparison with the higher order moment method (HOMOM) indicates that the proposed method is a fast, accurate, stable, and universal method to analyze the coupling of any two antennas.