The complex envelope (CE) ADI-FDTD method

Abstract

To efficiently simulate modulated electromagnetic fields, the complex envelope (CE) concept has been adapted into the FDTD method. However, such formulated CE FDTD has been found inferior to the conventional FDTD method and of little practical values due to the CFL stability condition. Therefore, attempts have been made to adapt the CE concept to the unconditionally stable ADI-FDTD method. In this paper, the full-wave CE ADI-FDTD formulations are presented with the unconditional stability. Numerical dispersion analysis and numerical experiments are performed, showing that the CE-ADI-FDTD is superior to the ADI- FDTD and is comparable to the conventional FDTD in terms of accuracy. Therefore, it offers an alternative time- domain modeling technique for RF/microwave structures especially for modulated signals. Index Terms — ADI-FDTD, Complex envelope (CE), modulated signals, unconditional stability. method. Further numerical studies were carried out again in two-dimensional cases in (6) and similar conclusions were reached. More comprehensive and rigorous theoretical poof of the unconditional stability and numerical dispersion analyses can be found in (7). In this paper, the full-wave CE ADI-FDTD formulations in three dimensions are first described. Then, the results from the numerical analyses are presented. Finally, numerical examples are shown to demonstrate the advantages and limitations of the CE ADI-FDTD method.