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.

Double patterning lithography (DPL) is one of the most promising solutions for the 28nm technology node and beyond. The main idea of DPL is to decompose the layout into two sub-patterns and manufacture the layout by two masks. In addition to traditional analog design constraints, the pre-coloring constraint should also be considered, in which patterns of critical or sensitive modules have predefined masks before layout decomposition to reduce mismatches. In this paper, we present the first work that considers DPL during analog placement and simultaneously minimizes area, wirelength, and DPL conflicts. We first propose an extended conflict graph (ECG) to represent the relation between patterns of analog modules and apply an integer linear programming (ILP) formulation to determine the orientation of each module and the color of each pattern for conflict minimization. ILP reduction schemes are proposed to further reduce the runtime. Finally, we present a three-stage flow and DPL-aware perturbations to obtain desired solutions. Experimental results show that the proposed flow can effectively and efficiently reduce area, wirelength, and DPL conflicts.

Current-flow and current-density are two major considerations for placement and routing of analog layout synthesis. The current-flow constraints are specified to the critical nets with monotonic current/signal paths to reduce parasitic impacts. The current-density constraints are usually specified on the nets with variable wire widths to avoid the IR-drop and electromigration problems. In this paper, we propose the first work to simultaneously consider current-flow and current-density constraints while placing and routing the analog circuits with minimized chip area, routed wirelength, bend numbers, via counts, and coupling noise at the same time. We first present an enhanced B*-tree representation to simultaneously model modules and interconnects for an analog circuit. Then a simultaneous placement and routing algorithm is presented to generate a layout while satisfying the current-flow and current-density constraints with minimized chip area, routed wire-length, bend numbers, via counts, and coupling noise. Experimental results show that our approach can obtain better layout results and satisfy all specified constraints while optimizing circuit performance.

Symmetry, topology-matching, and length-matching constraints are three 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. 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 three 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 three constraints for analog routing while minimizing total wirelength, bend numbers, via counts, and coupling noise at the same time. We first present an integer linear programming (ILP) formulation to simultaneously consider the three constraints for analog routing, and employ effective reduction techniques to further reduce the numbers of ILP variables and constraints. Then, a non-uniform multilevel routing framework is presented to enhance the performance of our routing algorithm. Experimental results show that our approach can obtain better routing results and satisfy all specified routing constraints while optimizing circuit performance.