Fundamental Limits for Implanted Antennas: Maximum Power Density Reaching Free Space

Fundamental limits on antenna performances are of key interest to the antenna designer, as they allow fast assessment of the feasibility of specific antenna requirements. These limits are defined by the key performance indicators (KPI) of specific antennas, such as the directivity for large aperture antennas or the achievable bandwidth on electrically small antennas. These limits have been obtained considering that the antenna radiates into free space. In this contribution, we develop the fundamental limits for implanted antennas, which thus radiate first into a lossy medium. KPIs assessing the quality of a specific antenna radiating into lossy medium are the total radiated power reaching free space (out of the lossy host medium) and the maximum power density obtained at the surface of the lossy host medium. The fundamental limits for implanted antennas proposed in this paper yield upper bounds for both KPIs and have been obtained considering elementary sources radiating into a spherical phantom. The spherical wave expansion of the electromagnetic fields was used to determine all the fields, and the limits obtained yield a useful upper bound for more complex scenarios.