Implement the 3-D FDTD method for a cubical cavity resonator that is 10 cm on a side. Use the PEC…

Implement the 3-D FDTD method for a cubical cavity resonator that is 10 cm on a side. Use the PEC boundary condition on the cavity walls. To make the boundary condition easy to implement, set up the grids so that the outermost face of each Yee cell on all six sides of the cube has normal magnetic fields and tangential electric fields (this will lead to different size arrays for the six field components). To excite the cavity, impress a pulse source at some point in the domain not on a plane of symmetry and away from the cavity walls. To avoid a DC component in the field solution, it is

»Implement the 3-D FDTD method for a cubical cavity resonator that is 10 cm on a side. Use the PEC boundary condition on the cavity walls. To make the boundary condition easy to implement, set up the grids so that the outermost face of each Yee cell on all six sides of the cube has normal magnetic fields and tangential electric fields (this will lead to different size arrays for the six field components). To excite the cavity, impress a pulse source at some point in the domain not on a plane of symmetry and away from the cavity walls. To avoid a DC component in the field solution, it is convenient to use the derivative of a Gaussian as the pulse shape, so that where t 0 = 80 ps. (What is the bandwidth of this pulse?) The interior of the PEC cube forms a resonant cavity that will “ring” at its resonance frequencies, while other frequency components excited by the source will die out as the source decays to zero. As the simulation runs, store one component of the fields at another point in the domain, also not on a plane of symmetry. Run the simulation for about Ntt = 20 ns. (What determines the required simulation time?) In postprocessing, compute the FFT of the stored field. Plot the magnitude of the FFT versus frequency in GHz. Compare the result with the exact resonance frequencies of the PEC cavity by marking the exact resonances as vertical lines on the plot. The simulation should take only a minute or so with a reasonably fast processor and with the grid step sizes chosen so that the computational domain is about 25 × 25 × 25 grid cells. Fields in the cavity can be conveniently visualized using the MATLAB slice command.

»