The standard Finite-difference Time-domain (FDTD) method requires extremely small time-step sizes when modelling electrically-small regions (much smaller than a wavelength): the method can thus become impractical due to the unaffordable computation times required. This problem can be solved by implementing a quasi-static approximate version of FDTD. This approach is based on transferring the working frequency to a higher frequency, to reduce the number of time steps required. Then, the generated internal field at the higher frequency can be scaled back to the frequency of interest [1,2]. It should be noted that this approach is only valid if the size of the interacting structure in the problem space is 10 times or more smaller than the wavelength and |σ + jωε| ωε{sub}0 [2], where a and e are the conductivity and permittivity of the medium respectively, ω is the radian frequency, and ε{sub}0 is the permittivity of free space. In order to prove the validity of this quasi-static approach, a three-dimensional FDTD program was used to directly model a single homogeneous or multi-layered sphere inside a lossless or lossy problem space: this represented a biological cell under microwave irradiation, a topic of substantial current interest. The sphere was excited by a plane wave, which is replaced by an equivalent surface. The edge of the problem space was truncated by Berenger's perfectly matched layer (PML) absorbing boundary condition (ABC), with matching impedance condition (σ/ε = σ{sup}*/u, for lossless or lossy media, whereas σ/ε{sub}0 = σ{sup}*/μ{sub}0 for free space). This was solved at the interface layer for an optimum value of the g (grading) factor.
展开▼
