Isotropic versus Anisotropic Dielectric Models in Packaging Substrates
Anisotropic dielectric tensor modeling eliminates up to 8 ohm trace impedance errors and timing skew in high speed package substrates compared to isotropic models.
3d Electromagnetic Solvers
Simulation Engine
Computational software systems model high frequency electromagnetic fields in three dimensional space to extract parasitic parameters of complex printed circuit board structures. Engineers utilize 3d electromagnetic solvers to calculate impedance and crosstalk in transition regions where planar approximations fail. These tools resolve the full vector wave equations across via transitions, connector launches, and complex trace geometries.
S-parameter generation represents the typical output of these calculations, which then guides board design optimization before fabrication.
Mathematical Formulation
Differential and integral equations represent the core formulations that resolve the electromagnetic fields. Computational techniques like the finite element method and the method of moments divide the physical board geometry into a mesh of small elements. The numerical engine computes the electric and magnetic field vectors at every mesh node, accounting for dielectric boundaries and copper surface roughness.
High density boards require dense meshes that increase compute times but deliver precise results.
Extraction Limit
Extraction limits are bounded by the volume of the geometry and the maximum frequency of interest. When frequencies approach forty gigahertz, the physical size of the mesh elements must shrink to resolve the shorter wavelengths. This restriction means that large boards are rarely solved in their entirety, and instead designer focus is restricted to specific transition regions.