The performance of analog circuits is strongly influenced by their layout. Performance specifications are usually translated into physical constraints such as symmetry, common orientation, and distance constraints among certain components. Automatic digital layout tools can be adopted and modified to deal with the imposed performance constraints on the analog layout. The selection and modifications of algorithms to handle the analog constraints became the area of research in analog layout systems. The existing systems are characterized by the use of stochastic optimization techniques based placement, grid based or channel routers, and lack of compaction. In this paper, algorithms for analog circuit placement, routing, and compaction are presented. The proposed algorithms consider the analog oriented constraints, which are important from an analog layout point of view, and reduce the computation cost. The placement algorithm is based on a force directed method and consists of two main phases, each of which includes a tuning procedure. In the first phase, we solve a set of simultaneous linear equations, based upon the attractive forces. These attractive forces represent the interconnection topology of given blocks and some specified constraints. Symmetry constraint is considered throughout the tuning procedure. In the second phase, block overlap resulting from the first phase is resolved iteratively, where each iteration is followed by the symmetry tuning procedure. Routing is performed using a line expansion based gridless router. Routing constraints are taken into account and several routing priorities are imposed on the nets. The compactor part employs a constraint graph based algorithm while considering the analog symmetry constraints. The algorithms are implemented and integrated within an analog layout design system. An experimental result for an OP AMP provided by MCNC benchmark is shown to demonstrate the performance of the algorithms.

This paper advocates the use of linear objective function in analytic analog placement. The role of linear and quadratic objctive functions in the behavior and results of an analog placement algorithm based on the force directed method is discussed. Experimental results for a MCNC benchmark circuit and another one from text books are shown to demonstrate the effect of a linear and a quadratic objective function on the analog constraint satisfaction and CPU time. By introducing linear objective function to the algorithm, we obtain better placements in terms of analog constraint satisfaction and computation cost than in case of conventional quadratic objective function.