Placement with symmetry constraints for analog layout design using TCG-S

In order to handle device matching for analog circuits, some pairs of modules need to be placed symmetrically with respect to a common axis. In this paper, we deal with the module placement with symmetry constraints for analog design using the transitive closure graph-sequence (TCG-S) representation. Since the geometric relationships of modules are transparent to TCG-S and its induced operations, TCG-S has better flexibility than previous works in dealing with symmetry constraints. We first propose the necessary and sufficient conditions of TCG-S for symmetry modules. Then, we propose a polynomial-time packing algorithm for a TCG-S with symmetry constraints. Experimental results show that the TCG-S based algorithm results in the best area utilization.