This paper addresses a fundamental question on wireless power transfer between antennas: how the recently developed coupling quality factor, or kQ, theory relates to the classical Friis transmission formula. The Friis formula has long been used to describe far-field wireless propagation, whereas kQ theory has emerged as a powerful framework for evaluating maximum power transfer efficiency in near-field coupled systems. Clarifying the relationship between these two theories is crucial for building a unified understanding of wireless power transfer over a wide range of distance.

The awarded paper shows, both analytically and numerically, that these two approaches agree in the far-field region while holding the coupling efficiency not to exceed 100% even in the immediate vicinity. Starting from a pair of Hertzian dipoles, the authors derive a far-field expression of kQ and demonstrate that it leads to the same maximum power transfer efficiency as predicted by the Friis formula. They then extend the study to practical dipole antennas of three practical lengths and perform electromagnetic simulations over distances from 1 mm to 10 m at 3 GHz, covering both near-field and far-field regions. The results reveal that the efficiency predicted by the kQ theory changes smoothly with distance and asymptotically approaches the line given by the Friis formula in the far field.

This work is valuable because it clarifies the relationship between two theories that had often been treated separately and presents them in a single coherent framework for wireless power transfer. The paper provides not only a clear theoretical contribution, but also gives a practical insight into antenna propagation and wireless power system design across near-field and far-field regimes. For these reasons, it is acknowledged to be a highly significant contribution to the field of antennas and electromagnetic-wave propagation and thus deserves the IEICE Paper Award.