Dissipation Factors of Spherical Current Modes on Multiple Spherical Layers

Radiation efficiencies of modal current densities distributed on a spherical shell are evaluated in terms of dissipation factor. The presented approach is rigorous, yet simple and straightforward, leading to closed-form expressions. The same approach is utilized for a two-layered shell and the results are compared with other models existing in the literature. Discrepancies in this comparison are reported and reasons are analyzed. Finally, it is demonstrated that radiation efficiency potentially benefits from the use of internal volume, which contrasts with the case of the radiation <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>-factor.