Abstract-In this paper new stability theorems for Yee's FiniteDifference Time-Domain (FDTD) formulation are derived based on the energy method. A numerical energy expression is proposed. This numerical energy is dependent on the FDTD model's E and H field components. It is shown that if the numerical energy is bounded, then all the field components will also be bounded as the simulation proceeds. The theorems in this paper are inspired by similar results in nonlinear dynamical system. The new theorems are used to prove the stability of a FDTD model containing non-homogeneous dielectrics, perfect electric conductor (PEC) boundary, nonlinear dielectric and also linear/nonlinear lumped elements. The theorems are intended to complement the well-known Courant-Friedrich-Lewy (CFL) Criterion. Finally it is shown how the theorems can be used as a test, to determine if the formulation of new lumped element in FDTD is proper or not. A proper formulation will preserve the dynamical stability of the FDTD model. The finding reported in this paper will have implications in the manner stability analysis of FDTD algorithm is carried out in the future.

Abstract-A simple and efficient approximate method to incorporate nonlinear bipolar junction transistor (BJT) into Finite-Difference Time-Domain (FDTD) framework is presented. This method applies Taylor expansion on the nonlinear transport equations of the BJT based on Gummel-Poon model [5]. The results are two coupled one-step explicit finite difference schemes for the electromagnetic fields in the vicinity of the BJT, which can be solved easily. A simulation example is carried out for a power amplifier and the result compares well with the measurement. A two-step simulation scheme is introduced to hasten the process of reaching transient steady state. Finally, brief comments on treating the FDTD framework as a dynamical system is included. This perspective is useful for analyzing the stability of FDTD framework with nonlinear lumped elements.