What are the components of a hybrid solver in PowerSI

A Hybrid solver is a specialized solver developed by Cadence for SI/PI applications. The hybrid solver uses transmission line theory (telegrapher’s equations) to represent distributed transmission lines (traces), followed by using closed-form SPICE models to represent vias, pads, and so on. However, unlike SPICE, it uses finite element and boundary element field solvers instead of SPICE RLC models to model critical structures, such as planes and wire bonds. The tool combines all models for the different parts into a single matrix (impedance matrix) to solve and obtain the current distribution on the structure.

The Hybrid solver is the core field solver used by PowerSI. This is the same engine used in other Sigrity tools, such as OptimizePI. The solver comprises of three different solvers that run independently but communicate with each other at each time step or frequency point. This results in maximum efficiency with balanced accuracy.

1. Plane/EM Solver takes into account coupling between vias, reflection from edges, resonances, power and ground voltage fluctuations, and metal/dielectric losses.
2. Circuit Solver handles linear and nonlinear circuit components, including IBIS models and HSPICE transistor models.
3. Transmission Line Solver includes trace coupling, skin-effect loss, dielectric loss, and frequency dependent dielectrics.