Partial-Structure Work-Energy Theorem (PS-WET)-Based Characteristic Mode Theory (CMT) for Yagi–Uda Array Antennas

Partial-structure work-energy theorem (PS-WET) governing the work-energy transformation process of Yagi–Uda array antennas is derived. Partial-structure driving power as the source for sustaining the steady work-energy transformation is formulated in terms of an operator called partial-structure driving power operator (PS-DPO). Using the PS-WET and PSDPO, the essential difference between the working mechanisms of scattering objects and Yagi–Uda array antennas is revealed. The difference exposes that the conventional characteristic mode theory (CMT) for scattering objects cannot be directly applied to Yagi–Uda array antennas. Under the PS-WET framework, this paper proposes a generalized CMT for Yagi–Uda array antennas. By diagonalizing the PS-DPO, the PS-WET-based CMT (PS-WET-CMT) can construct a set of energy-decoupled characteristic modes (CMs) for an objective Yagi–Uda array antenna, and then can provide an effective modal analysis for the antenna. The various orthogonality relationships and the Parseval’s theorem satisfied by the CMs are rigorously proved and physically explained. The physical meanings of the characteristic values and modal significances (MSs) associated to the CMs are also obtained by using the PS-WET-based modal decomposition. Some typical numerical experiments are demonstrated for verifying the validity of the PS-WET-CMT proposed in this paper. In addition, an example using a series of scattering CMs to expand the dominant transmitting CM (for metallic Yagi–Uda structure) is also exhibited.