The problem of maximum range calculation for an electromagnetic system in a lossy media leads to a transcendental implicit equation. There were few suggestions to deal with that problem, beginning with an iterative method offered by L.V. Blake back in 1969, to some non realistic remarks found in few other texts. This work presents a simple method for taking atmospheric losses into account in maximum range evaluations. This consideration gains more significance as operating frequency goes higher towards mm-waves and beyond. The method presented is based on a single solution of a generic equation, and use this solution to solve a specific problem. The generic equation is a generalization of almost all electromagnetic systems' range equations, including communication links, radiometric sensors, monostatic radar and some EW scenarios. The work deals with both homogeneous and exponential atmospheres.
Abner Ephrath, Abner Ephrath,
"Evaluation of transmission range in a lossy media", Proc. SPIE 3699, Targets and Backgrounds: Characterization and Representation V, (14 July 1999); doi: 10.1117/12.352955; https://doi.org/10.1117/12.352955