Exploring Multiple Analog Placements with Partial-Monotonic Current Paths and Symmetry Constraints Using PCP-SP

Modern analog placement techniques require consideration of current path and symmetry constraints. The symmetry pairs can be efficiently packed using the symmetry island configurations, but not all these configurations result in minimum gate interconnection, which can impact the overall circuit routing and performance. This article proposes the first work that reformulates this problem considering all of them together in the form of parallel current path (PCP) constraints. PCP constraints, in addition to monotonic current paths, also consider partial-monotonic current paths to generate a more compact placement. We use a novel two-step approach to detect symmetry-feasible sequence-pairs (SFSPs) without doing placement construction by using representative sequence-pair (RSP). Then a placement algorithm satisfying these constraints is formulated to reduce a vast search space via efficient sequence pair manipulation. The experimental results show that this formulation and algorithm can generate multiple placement solutions that satisfy all the constraints in a more tightly packed configuration, resulting in smaller wirelength, reduced parasitics, and thus better post-layout performance.