A Barrier Function Method for Optimal Placement of Decoupling Capacitors on Resonant Plane Pairs

A constrained optimization algorithm is proposed for the optimal placement of decoupling capacitors on power delivery networks (PDN) of high-speed digital circuits. The algorithm is based on barrier methods and calls for the first and second order partial derivatives of optimization variables for gradient search. In the analysis, the PDN is modeled as a resonant planar circuit. In the calculation of derivatives, mutual coupling among multiple ports and discrete components of the problem domain is accounted for with matrix calculus techniques. An analytical representation of the plane impedance is utilized for accurate calculation of the derivatives. The proposed method is tested on a practical example and the results are observed in good agreement with those obtained from a numerical electromagnetic (EM) simulator.