A forced directed component placement procedure for printed circuit boards

This paper deals with the problem of placing components on a carrier, such as a printed circuit board (PCB). We present a new mathematical formulation of the concept of force directed placement, and describe an efficient computational procedure for solving the resulting system of equations. The placement procedure is broken down into two phases, Phase I being the "relative location phase," and Phase II being the "slot assignment or component overlap resolution phase." In Phase I of the procedure, we solve a set of simultaneous equations, based upon the interconnection topology of the system of components, in an endeavor to determine the optimum relative location of every component with respect to every other component. The equations are set up such that there are attractive forces between components sharing a common signal, and repulsive forces between components having no signals in common. The results of Phase I are often unacceptable from a physical standpoint because there is a great deal of overlap among the components. Phase II eliminates component overlap by either of two methods, depending upon the physical properties of the carrier. If the carrier is subdivided into slots, then the components are assigned to these slots using a criteria which minimiZes the total distance that all components need be moved. We perform this assignment by using the linear assignment algorithm. If the carrier is such that components are allowed to reside anywhere, then a different technique to resolve component overlap is used. A parametric analysis of the procedure is given based upon 12 different PCB's. These results show comparisons of this method to the work of others, and provide some insight into the method's absolute merits.