Nonuniform Multilevel Analog Routing With Matching Constraints

Symmetry, common-centroid, topology-matching, and length-matching constraints are four major routing considerations to improve the performance of an analog circuit. Symmetry constraints are specified to route matched nets symmetrically with respect to some common axes. Common-centroid constraints are also specified to route matched net symmetrically with respect to some common centers. Topology-matching constraints are commonly imposed on critical yet asymmetry nets with the same number of bends, vias, and wirelength. Length-matching constraints are specified to route the nets which have limited resources with the same wirelength. These four constraints can reduce current mismatches and unwanted electrical effects between two critical nets. In this paper, we propose the first work to simultaneously consider the four constraints for analog routing while minimizing total wirelength, bend numbers, via counts, and coupling noise at the same time. We first present a basic integer linear programming (ILP) formulation to simultaneously consider the four constraints for analog routing. Then, a prioritized-constraint-aware routing algorithm is proposed to assist analog designers for assigning the four matching constraints and optimizing routing topologies. Effective reduction techniques are also employed to reduce the numbers of ILP variables and constraints for the two routing algorithms. To further enhance the routing performance, a nonuniform multilevel routing framework is presented and integrated into our routing algorithms. Experimental results show that our approach can obtain better routing results and satisfy all specified routing constraints while optimizing circuit performance.