Analytic Approximation of Free-Space Path Loss for Implanted Antennas

Implantable wireless bioelectronic devices enable communication and/or power transfer through <PRE_TAG>RF wireless connections</POST_TAG> with external nodes. These devices encounter notable design challenges due to the <PRE_TAG>lossy nature of the host body</POST_TAG>, which significantly diminishes the radiation efficiency of the implanted antenna and tightens the <PRE_TAG>wireless link budget</POST_TAG>. Prior research has yielded <PRE_TAG>closed-form approximate expressions</POST_TAG> for estimating losses occurring within the lossy host body, known as the <PRE_TAG>in-body path loss</POST_TAG>. To assess the total path loss between the implanted transmitter and external receiver, this paper focuses on the <PRE_TAG>free-space path loss</POST_TAG> of the implanted antenna, from the body-air interface to the external node. This is not trivial, as in addition to the inherent radial spreading of <PRE_TAG>spherical electromagnetic waves</POST_TAG> common to all antennas, implanted antennas confront additional losses arising from electromagnetic scattering at the interface between the host body and air. Employing analytical modeling, we propose <PRE_TAG>closed-form approximate expressions</POST_TAG> for estimating this <PRE_TAG>free-space path loss</POST_TAG>. The approximation is formulated as a function of the <PRE_TAG>free-space distance</POST_TAG>, the <PRE_TAG>curvature radius of the body-air interface</POST_TAG>, and the <PRE_TAG>permittivity of the lossy medium</POST_TAG>. This proposed method undergoes thorough validation through <PRE_TAG>numerical calculations</POST_TAG>, <PRE_TAG>simulations</POST_TAG>, and <PRE_TAG>measurements</POST_TAG> for different implanted antenna scenarios. This study contributes to a comprehensive understanding of the path loss in implanted antennas and provides a reliable analytical framework for their efficient design and performance evaluation.