Wireless power transfer efficiency formula applicable in near and far fields

Abstract

Microwave-based wireless power transfer in the near field (up to about 10 m) is now drawing much interest since the transfer range when using current magnetic induction or magnetic resonance methods is limited in current industry. The Friis efficiency formula is valid only in the far field, so this paper proposes a new efficiency formula for use in the near field as well as in the far field. The proposed formula is derived under the assumption that the fields generated from transmitting-antenna elements are coherently (or constructively) added at a receiving antenna. The proposed formula is validated by EM-simulations and measurements using a 1 × 8 phased array antenna. The proposed efficiency formula is shown to be accurate in the near field and converge to the Friis formula in the far field.