XFdtd^® provides a wide variety of excitations, including both voltage and current sources and series/parallel RLC circuits. In this example a parallel plate capacitor is charged, first by a current source, then by a LaPlace static potential solver.

The capacitor consists of a pair of 20mm x 20mm conducting plates separated by 2mm.

Figure 1 is the geometry. The metal plates are connected to the ideal current source by a pair of wires. The small green rectangle in the left-hand portion of the geometry represents the current source.  The green rectangles in the upper and lower wires are 50 ohm resistors, used to dissipate the transient fields induced when the current source is used.

In the next 3 figures, the current source is excited by a Gaussian pulse. Once the pulse ends, the ideal current source is an open circuit. The pulse contains a spectrum of frequency components. As time goes by, some of this energy is radiated and some is dissipated in the two resistors. The steady state solution is thus the static fields due to the charges on the capacitor plates and the wires. Figures 2 and 3 are false-color magnitude and vector sequences of the Electric field during the first 3500 time steps of the problem computation, about 6.7 nano seconds, during which time most of the transients dissipate. Figure 4 shows the electric field vectors after 5000 time steps, when the transients are essentially dissipated leaving the steady state solution.

Figure 2 Animation

Figure 3 Animation

In the next figure, instead of current source charging, the upper plate is preset to +10V, the lower plate preset to -10V, and the steady state electric fields are found by solving LaPlace's equation at each FDTD mesh edge in the problem space. Compare Figure 4 with Figure 5, which is a vector display of the electric field after just one time step showing the LaPlace solution. Of course, transient energy may then be applied in the usual ways with the static solution representing the starting point of the FDTD computation.