In this paper, the resonance behavior of graphene plates with different shapes, rectangular, circular and triangular in the terahertz frequency range is analyzed with a new approach using the characteristic mode analysis. Studying the modal behavior of graphene plates leads to provide a systematic method for analyzing and designing graphene-based patch terahertz antennas, also, the parameters of graphene antennas can be obtained with simpler analyzes and better physical view. At first the effect of graphene parameters, such as chemical potential and relaxation time is studied especially on the first and second modes of the graphene plate with constant dimension. Then the effect of plate dimensions and the presence of a metal ground plane under the graphene plate on the behavior of characteristic modes is investigated. Finally, functions to calculate the resonance frequency of the plate in terms of effective parameters of the plate are presented. These functions can be used to calculate the resonance frequency in the analysis and design of graphene antennas.
