Mutual impedance computation using spherical harmonics between two closely spaced antennas

Öztürk M. A., KOÇ S. S.

AEU - International Journal of Electronics and Communications, vol.168, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 168
  • Publication Date: 2023
  • Doi Number: 10.1016/j.aeue.2023.154711
  • Journal Name: AEU - International Journal of Electronics and Communications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC
  • Keywords: Addition theorem, Mutual coupling, Reaction theorem, Rotation and translation of spherical waves, Vector spherical harmonic expansion
  • Middle East Technical University Affiliated: Yes


Mutual coupling between two identical radiators is computed using vector spherical harmonics and reaction theorem for small element spacing cases. For closely spaced antennas, the minimum spheres that enclose the antennas overlap, and the vector spherical harmonic expansions do not converge on the surface that separates the two antennas. The proposed method mainly uses addition theorems to translate the vector spherical harmonic expansions to a different center. These operations on spherical waves enable to redefine the minimum spheres and convergence regions. The proposed method has been validated by analyzing the coupling between two half-wave dipoles in a side-by-side configuration. The results clearly show excellent agreement with that obtained from induced EMF method. The theory is also tested experimentally. A printed dipole antenna is designed, and its spherical harmonic coefficients are obtained by spherical near field measurement. Mutual impedance between two such dipoles is computed using the proposed method. The computed results for different element spacings in a side-by-side configuration are compared to those obtained from s-parameter measurements.