A study on the stability of bipolar-junction-transistor formulation in finite-difference time-domain framework

Recently, a new stability result has been put forward for three-dimensional finite-difference time-domain (FDTD) framework by deriving a discrete energy relation similar to the Poynting Theorem in electromagnetism. In this paper, the result is used to show how stability analysis of an FDTD model containing three-terminal nonlinear components can be performed. Here the bipolar junction transistor (BJT) is used to illustrate the idea. It is shown that instability can be due to the BJT contributing numerical energy to the system during simulation, thus causing the E- and H-field components to blow up. This paper also shows how we can prevent instability by identifying the operating region of the device where it is contributing numerical energy. By preventing the device from contributing numerical energy to the system, dynamical stability can be maintained. Formulation, which can source and sink numerical energy, is called conditionally proper. The BJT formulation in FDTD is such an example.