Semidefinite Programming-Based Decoupling Capacitor Placement for Power Distribution Network Optimization

Power distribution networks (PDNs) are designed to deliver sufficient and stable power to circuit components. For high-speed printed circuit boards (PCBs), transient current pulses increasingly affect the power integrity in PDNs, potentially leading to circuit malfunction or component damage. Decoupling capacitors (decaps) are placed on a PDN to ensure power stability. Minimizing the number of decaps becomes critical and has been extensively studied. Traditional heuristic methods often search for unnecessary spaces or get stuck in local minima. To overcome these limitations, we propose an analytical approach that reformulates the nonlinear decap placement problem as an equivalent integer semidefinite programming model. We adopt techniques like integer relaxation and port reduction to improve scalability and minimize the usage of decaps by an adaptive optimization scheme. Experimental results on industrial benchmarks demonstrate that our analytical decap placer achieves better results than the state-of-the-art non-deterministic methods and even significantly outperforms the commercial tool in solution quality and runtime.