The Upper Bound on Antenna Gain and Its Feasibility as a Sum of Characteristic Gains

The upper bound on antenna gain is expressed as a sum of lossy characteristic modes, specifically, as a sum of characteristic far fields squared. The procedure combines the favorable properties of Harrington’s classical approach to maximum directivity and current-density-based approaches. The upper bound is valid for any antenna or array designed in a given design region for which optimal performance is determined. The decomposition into modes makes it possible to study the degrees of freedom of an obstacle, classify its radiation into normal or super-directive currents, and determine their compatibility with a given excitation. The bound considers an arbitrary shape of the design region and specific material distribution. The cost in
$Q$
-factor and radiation efficiency is studied. The extra constraint of a self-resonance current is imposed for an electrically small antenna. The examples verify the developed theory, demonstrate the procedure’s utility, and provide helpful insight to antenna designers. The feasibility of the optimal gain is studied in detail on an example of endfire arrays using the aforementioned decomposition of optimal current density into lossy characteristic modes.