Fast PCB Stack-Up Optimization Using Integer Programming

Abstract

This paper presents a flexible and efficient methodology to optimize stack-up for multi-layer printed circuit boards (PCBs) with enormous search space and various design constraints. PCB stack-up optimization is crucial in high-speed system design to achieve the desired electrical performance while reducing system costs. The stack-up optimization process is labor-intensive and time-consuming for a large number of layers. Moreover, after the optimization process, the electrical performance of a real design, such as the impedance and loss, may deviate from the target design due to manufacturing variations. Estimating the worst cases due to the manufacturing variations, referred to as “corner cases” in this paper, is essential for a confident PCB design but challenging since the number of related parameters is large. In this paper, PCB stack-up optimization and corner-case searching are addressed and greatly accelerated using the integer programming technique. All constraints are converted to mathematical equalities and inequalities that can be solved rapidly by an integer programming solver to obtain feasible stack-up solutions. After the cross-sections of the transmission lines are optimized based on the stack-up design to achieve a target electrical performance, the upper and lower bound of impedance and loss are acquired using integer programming when the design parameters vary in a particular range. The proposed method is verified using multi-layer PCB designs with practical constraints and demonstrates its effectiveness and high efficiency.