A dual phase velocity boundary method for simulation of broadband microwave and millimeter applications

The “Magic Tool Suite” is a Finite-Difference, Time-Domain Particle-in-Cell (FDTD-PIC) software suite employed in the modeling of vacuum electronics devices. The methods of FDTD-PIC are well known and the literature contains the basic equations and descriptions for the solution of Maxwell´s equations. Because of its computational efficiency and relative ease of implementation this approach is very attractive and widely used. Simulation of broadband response to circuits is challenging. The bandwidths of interest begin relatively close to the cutoff frequency of the output waveguides and span sufficient frequency spectrum that the phase velocity can vary by as much as a factor of 2 or 3. This provides some difficulties in ensuring that the simulation model does not introduce too high a level of spurious reflections far from the band edges to lead to oscillations. The Dual Phase Velocity method (DPV) is an approach that diminishes such effects.