A New Closed Form Field Asymptotic Expansion Applied to Far-field Evaluation of Antenna Arrays at Short Range Lengths

A new general formulation for the asymptotic expansion of electromagnetic fields radiated by an arbitrary antenna is introduced and demonstrated. The presented approach is based on an extended application of the method of stationary phase, updating a methodology proposed by Jones and Kline in 1956. Explicit formulas are derived up to the sixth order (sixth power of the inverse of the distance to a chosen antenna reference point), where coefficients of the spatial field expansion are obtained as linear combinations of even partial-derivatives of the plane-wave spectrum. Provided equations are verified by application to canonical cases of a Hertzian dipole and a 12×4 dipole array. An example how these findings could be leveraged in realistic use cases is delivered, using measured data from the antenna array of a 5G radio base station.