Efficient Sensitivity Calculations for Optimization of Power Delivery Network Impedance

This paper presents efficient algorithms for sensitivity calculations of power delivery network (PDN) impedance. The sensitivity algorithm is based on the adjoint system method. Efficient calculation of sensitivity is critical for optimization of complex PDNs. The frequency-domain design of a PDN is a multiobjective optimization problem, which is formulated as a minimax problem in this paper. The design variables are typically the decoupling capacitors (decaps). The objective function is the input impedance of the PDN calculated at relevant frequencies. This paper also presents an efficient algorithm for large-change sensitivity calculations. Based on this method, what-if scenarios can be simulated efficiently, such as the addition, modification, or relocation of a few decaps or a small change in the geometry.