Localization of critical frequency for simulation of high-speed interconnects

The complexity of electromagnetic simulation of high-speed interconnects drastically rises as frequency moves upwards. Although full wave simulation is with high precision and capable of electromagnetic simulation through dc to hundreds of gigahertz, for consideration of high efficiency the quasi-static-electromagnetic-field-based parameters extraction combined with the circuit simulation still remains the mainstream methodology for large scale integrated circuits and complex packages simulation in practice. With quasi-static simulator, the resistance, inductance, capacitance, and conductance (RLCG) parameters of interconnects are first extracted using the partial element equivalent circuit (PEEC) model or the transmission line model, afterward these extracted parameters are put into the distributed equivalent circuit, and the final simulation result is obtained by performing circuit simulation. In this paper a signal wire differential pair which is widely adopted for high-speed interconnection in RFIC is modeled and simulated from dc to 30 GHz by quasi-static simulator and full wave simulator, respectively. Comparison of the simulation results shows that although quasi-static simulator is not able to simulate some high frequency phenomena such as radiation and eddy current in the conductive substrate, under circumstance of perfectly screening and using low loss substrate (e.g. with loss tangent no more than 0.02) the conventional parameters extraction based on PEEC model and quasi-static approximation performs well up to tens of gigahertz with acceptable accuracy.