Ratio of the Worst Case Noise and the Impedance of Power Distribution Network

Abstract

The classical method of designing power distribution networks (PDNs) is to control the target impedance across a broad frequency range. This methodology is based on the assumption that there is an upper bound for the ratio of the time-domain maximum output voltage noise to the product of target impedance and time-domain maximum input current. In this paper, we analyze the mathematical relation between the time-domain voltage response and the frequency-domain impedance of PDN. We present the closed-form expressions of the maximum ratio for the series RL/RC circuit and LC tank cases in PDN structures. We observe that the maximum ratio for LC tank case is 1.5. Our results show that the worst case noise is not only determined by target impedance, but also depended on the shape of the output impedance profile. A complete PDN path is demonstrated with the worst case ratio of greater than one. We further propose a method to predict the worst case noise of the complete PDN path. The average prediction error of the proposed method is 7% under different PDN cases.