Frequency-Dependent MNL-FDTD Scheme for Wideband Analysis of Printed Circuit Boards With Debye Dispersive Media

A semiimplicit and frequency-dependent 3-D finite-difference time-domain (FDTD) scheme with relaxed numerical stability was presented for wideband analysis of multilayer printed circuit boards (PCBs) with thin conductive and dielectric layers. This new scheme is formulated by directionally and magnetically introducing the Newmark-beta method into the conventional FDTD explicit scheme based on the recursive convolution (RC) approach for the so-called extended Debye model with an effective dc conductivity. No dependence of mesh step in the normal direction to the PCB layers is included in its stable condition. Interestingly, the presented semiimplicit scheme can be reduced to the RC-based explicit FDTD when the Newmark parameter is chosen as zero. The scheme was carefully verified in applications to rectangular power-bus structures, an irregular power-bus structure with decoupling capacitors and multilayer PCBs with planar electromagnetic bandgap structures. It was demonstrated in these test problems that the calculation time was reduced by a factor of 1/4-1/30 in comparison with the explicit scheme, while maintaining the same level of accuracy.