Optimum Design of Printed Circuit Board to Reduce Deformation after Reflow Process

概要

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A printed circuit board (PCB) is a laminated composite made of circuit and insulator layers. The PCB is heated in a furnace 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 deformation does not disappear after the process by the viscoelastic property of the resin in the circuit and insulator layers. The viscoelastic property is measured and the deformation of the PCB after the reflow process is modeled by the micro mechanics of composites, the laminated composite theory and the viscoelastic model. 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 after the process. 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. The validity of the optimum design is verified by an experiment.