ABSTRACT
This chapter presents two basic mathematical formulations concerning TD modeling of planar circuits. It describes a boundary-value formulation with the corresponding eigen-function expansion and an integral-equation formulation based on the reciprocity theorem of the time-convolution type. The former formulation is useful for validation purposes while the latter serves as the point of departure for TD-CIM. In accordance with the definition given by Okoshi, the planar circuit is defined as a parallel-plane circuit whose thickness is negligible with respect to the spatial support of the excitation pulse. The problem may be formulated as an initial-boundary value problem and solved, when possible, with the help of conventional methods such as the separation of variable technique or the method of images. A somewhat more general boundary condition relating the (non-zero) tangential component of the magnetic field to the vertical component of the electric field.
