Power Transmission Determined by the Mutual Impedance and the Transducer Power Gain in the Near Field Region

Abstract

This paper describes the role of mutual impedance and the transducer power gain which comes from key parameters to determine the amount of wireless power especially in a near-field environment. These two key parameters are applied to the two configurations; one is a dipole-dipole, and the other is a dipole-metal plate-loop configuration. Discussions are given on the achievable maximum power transfer between the sender and the receiver affected by the matching and the pass blockage. Ⅰ. IntroductionDepending on the relative wavelength distance between a sender and a receiver, wave regions are classified as near field and far field regions [1]. When a pair of antenna operates in the far field region, mutual impedance becomes so negligible that each transmitting and receiving antenna could be treated independently and so little attention might be paid on their mutual impedance. However, for antennas operated in the near field, mutual impedance could no longer be ignored since the antenna pair becomes very dependent on each other. This fact is equally applied to recent wireless power transmissions since most of this system operates in a near field region. RFID (Radio Frequency Identification) is one of example operating in near field zone with the principle of magnetic induction [2]. Many papers are published about these topics [3], [4], including some domestic papers about wireless power transmissions [5], [6].The main concern of this paper is to show parameters simple and accurate enough to determine the amount of received power from the sender under the near field circumstances. This task is accomplished by introducing the mutual impedance and the transducer power gain. Once the mutual impedance is known either by analytical formula or by simulated value, the transducer power gain can be determined based on the "black box" approach. The resulting transducer gain enables us to calculate the power arrived at the receiving antenna, a key quantity in wireless power transmission.As an illustration, configurations of {dipole-dipole} and {dipole-metal plate-loop} are considered. The configuration of {dipole-dipole} is included here because its formula of mutual impedance is already known. Therefore one can estimate the errors involved in numerical calculation. A second configuration having no analytic solution is also studied because we can still calculate the receiving power using the transducer power gain formula even in this situation. In addition, the achievable power transfer is discussed with respect to 50 ohm reference resistance and the conjugate matched load. We focus on the moderate level of analytic approach not on the elaborate experimental study to provide the stepping stones between academic interest and industrial practice. Ⅱ. Formulation of the Problem 2-1 Mutual Impedance of Dipole-Dipole StructureMutual impedance dictates the determination of wireless power, particularly, on systems operating in a near field region. Fig. 1 shows a pair of half wavelength dipoles of radius a, length l and distan...