The lower-bound of electromagnetic leakage of 2D wireless power transmission

In two-dimensional communication (2DC), devices put on the surface of a two-dimensional waveguide sheet receive microwave power from the sheet through the couplers. This paper clarifies the condition that a resonant object extracts microwave power from the sheet with significant efficiency. A theoretical analysis presents that the higher intensity of electromagnetic field outside the sheet surface is required for the lower surface reactance. That leads to the fact that power extraction from the lower surface reactance inevitably causes the higher power dissipation by the sheet surface resistance. Considering an inequality between the dissipation and the power flowing out of the sheet, we can determine the lower-bound of the surface reactance for efficient power transmission. The minimal surface reactance determines the minimal power leakage ratio and the maximal transmitted power acceptable in terms of electromagnetic compatibility (EMC). In the case of our typical 2DC systems, the lower-bound of the surface reactance and the corresponding leakage ratio are estimated to be 0.32 Ω/sq. and 1.4 × 10^-5, respectively for the 2DC sheet thickness of 2 mm. In the latter part of the paper we design a sheet with the surface reactance of 1.6 Ω/sq. and show an example of couplers applicable to the low reactance sheet.