Calculation of the total Q-factor for electrically small antennas with metamaterials using characteristic modes

In this paper, we address the problem of the analysis and evaluating metamaterial-based antennas through the use of characteristic modes. We propose a new expression for the total Q factor, independently from the excitation and based on the eigenvalues of the structure. The proposed expression is utilized to compute the Q factor of an arbitrary shaped antenna and metamaterial-based antenna and shown excellent agreements with other expressions from the literature.