Equivalent circuit (EC) FDTD method for dispersive materials : derivation stability criteria and application examples
Although many computational methods are currently available to analyze electromagnetic problems of high complexity, further progress is necessary to unify the different approaches and to improve the robustness of some algorithms. This chapter aims at reaching these two goals. It presents an equivalent circuit (EC) finite difference time domain (FDTD) method which both represents a complete circuital formulation of conventional FDTD based on the electric and magnetic fields Yee scheme and provides guaranteed stability criteria for dispersive media. A circuital formulation of FDTD offers several benefits. Since its update values are voltages and currents (as opposed to electric and magnetic fields), it facilitates the integration of electronic components, such as for instance diodes and transistors,into the simulation. In addition, it provides increased computational speed thanks to a reduced number of multiplications in the update equations. Finally, it may be easily generalized to arbitrary dispersive media via simple manipulations of the mesh immittances. While no convenient explicit guaranteed stability criterion for dispersive media is available in the framework of the conventional FDTD technique, the EC FDTD provides such a criterion. This is a distinct advantage for both emerging metamaterials, which are inherently dispersive, and for various natural materials, such as metals at the optical frequencies, ferrimagnetic and ferromagnetic materials and biological tissues, which exhibit various types of more or less complex dispersion responses.
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