Separatrices in high-dimensional state space: System-theoretical tangent computation and application to SRAM dynamic stability analysis

Shrinking access cycle times and the employment of dynamic read/write assist circuits have made the use of standard static noise margins increasingly problematic for scaled SRAM designs. Recently proposed dynamic noise margins precisely characterize dynamic stability using the concept of stability boundaries, or separatrices, and provide elegant separatrix tracing algorithm. However, the present separatrix characterization method is only efficient in the two-dimensional state space and hence not practically applicable to fully extracted SRAM designs with additional parasitics. We present a rigorous system-theoretical approach for computing the tangent approximation to the separatrix in the high-dimensional space. Using this as a basis, we develop fast method based on tangent approximation and exact iterative-refinement method for analyzing SRAM dynamic stability. The proposed algorithms have been implemented as a SPICE-like CAD tool and are broadly applicable to efficient computation of dynamic noise margins.