Decoupling Capacitor Placement Optimization With Lagrange Multiplier Method

This paper proposes a decoupling capacitor placement optimization method based on the cavity model and Lagrange multiplier. The variable conditions associating with coordinates (x,y) of input impedance expression based on the cavity model are combined with the Lagrange multiplier method. The decoupling capacitor optimum placement within a defined area of the board can be found through the proposed analytical method. The example of finding an optimum location of the decoupling capacitor within a defined area of the power delivery network is exposed, the results are compared to the brute-force method to prove the effectiveness of the proposed method.