Concise analytical expressions for evaluating time domain potentials in time domain integral equations

New and concise analytical formulae for calculating time domain potentials from Rao-Wilton-Glisson (RWG) type sources are derived in this paper, which can be applied to efficiently evaluate the interaction between two RWG elements in time domain, as is required in methods such as marching-on-in-time (MOT) for time-domain-integral-equations (TDIEs). Compared with previous analytical expressions, formulae in this paper are readily deduced through the RWG coordinates which are very compact to program without finding and paring the intersecting points between the concentric time spheres and the RWG triangles or categorizing the geometric relations of the observation point and the triangles into different occasions. Undifferentiated EFIE, MFIE and CFIE are applied to provide numerical examples that verify the efficacy of these formulae.