Modeling of Bipolar Junction Transistor in FDTD Simulation of Printed Circuit Board

Abstract

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.

A Finite-Difference Time-Domain (Fdtd) Software for Simulation of Printed Circuit Board (Pcb) Assembly

“…The discretization of 3D space and associated field components in a Yee's Cell is shown in Fig. 1, following the convention of [7] and [10]. The electric and magnetic field components are updated in discrete time-steps, at an interval of 1 2 ∆t, where ∆t is the time-step.…”

“…Both terms can be dependent on location, orientation and previous field component values. The detailed derivation of the update equations for the field components will not be repeated here, but the reader is referred to the appropriate references [2][3][4][5][6][7][8][9][10][11][12].…”

“…Here ∇ × H n+ 1 2 r(i,j,k) and ∇ × E n r (i,j,k) are shorthand, for instance for x component these are [6,7]:…”

“…FDTD method has been widely used to model interaction of electromagnetic waves in complicated PCB structures [2][3][4][5][6][7]. The classical FDTD approach, which is based on Yee's explicit formulation [1] is adopted for this paper.…”

Nonlinear Characteristics of P-I-N Diode Circuits Analyzed by a Physically Based Simulation Method

“…Their nonlinear characteristics are essential for circuit performances, and thus the accurate modelling of those nonlinear behaviours in circuits is fundamental to the circuit design and application. A number of simulation methods have been proposed, e.g., the equivalent-model based simulation method [3][4][5][6][7]; the analyticalmodel based simulation method [8], etc.. However, the aforementioned approaches suffer from limitations that may preclude their application in some cases.…”