Using Vector Spherical Harmonics to Compute Antenna Mutual Impedance from Measured or Computed Fields

The mutual coupling that exists between the antenna elements in an antenna array can be described with a mutual impedance. The knowledge of this mutual impedance is critical to the successful design of the array. Computing the mutual impedance involves integrating vector products of fields over a surface, but the integrands can oscillate wildly over the integration surface, and are often difficult to integrate accurately. The method proposed and described here relies on the expansion of the fields in terms of vector spherical harmonics. The integrations over the closed surface are performed in closed form, leaving the mutual impedance expressed as a sum of products of expansion coefficients.