Fundamental Bound on Maximum Gain as a Sum of Lossy Characteristic Modes and Its Feasibility

The fundamental bound on maximum 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 gain and current-density-based approaches. 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 also studied. The extra constraint of a self-resonance current is imposed for an electrically small antenna. The example verifies the developed theory, demonstrates the procedure's utility, and provides helpful insight to antenna designers.