Optimum design of printed circuit board to reduce deformation in reflow process by a global optimization method

Abstract

A printed circuit board (PCB) is a laminated composite made of circuit and insulator layers. The PCB is heated in a furnace in order to mount electronic devices. This process is called a reflow process. The PCB deforms in the reflow process by gravity and thermal expansion difference of materials. The mechanical properties of the layers of the PCB are modeled based on the micro mechanics of composites. In addition, the relationship between stress and strain of the PCB is modeled by using the laminated composite theory in order to estimate deformation of the PCB. A design optimization problem is defined so that the area ratios of copper in the circuit layers and the ratios of thickness increase in the insulator layers are determined to decrease the PCB deformation. A penalty is introduced into the objective function so that the cost of design change is minimized. Because the consideration of the less design change results in some sets of local optimum values of design variables, a global optimization method is adopted. Several optimization examples clarify features of the optimum PCB designs with small deformation and less design change. The validity of the optimum design is verified by an experiment.