Though commonly used to calculate Q-factor and fractional bandwidth, the energy stored by radiating systems (antennas) is a subtle and challenging concept that has perplexed researchers for over half a century. Here, the obstacles in defining and calculating stored energy in general electromagnetic systems are presented from first principles as well as using demonstrative examples from electrostatics, circuits, and radiating systems. Along the way, the concept of unobservable energy is introduced to formalize such challenges. Existing methods of defining stored energy in radiating systems are then reviewed in a framework based on technical commonalities rather than chronological order. Equivalences between some methods under common assumptions are highlighted, along with the strengths, weaknesses, and unique applications of certain techniques. Numerical examples are provided to compare the relative margin between methods on several radiating structures.

Design of small antennas is challenging because fundamental physics limits the performance. Physical bounds provide basic restrictions on the antenna performance solely expressed in the available antenna design space. These limits offer antenna designers a-priori information about the feasibility of antenna designs and a figure of merit for different designs. Here, an overview of physical bounds on antennas and the development from circumscribing spheres to arbitrary shaped regions and embedded antennas are presented. The underlying assumptions for the methods based on circuit models, mode expansions, forward scattering, and current optimization are illustrated and their pros and cons are discussed. The physical bounds are compared with numerical data for several antennas.

A new method to improve the accuracy and efficiency of characteristic mode (CM) decomposition for perfectly conducting bodies is presented. The method uses the expansion of the Green dyadic in spherical vector waves. This expansion is utilized in the method of moments (MoM) solution of the electric field integral equation (EFIE) to factorize the real part of the impedance matrix. The factorization is then employed in the computation of CMs, which improves the accuracy as well as the computational speed. An additional benefit is a rapid computation of far fields. The method can easily be integrated into existing MoM solvers. Several structures are investigated illustrating the improved accuracy and performance of the new method.