On-die decoupling capacitance: frequency domain analysis of activity radius

On-die capacitances interact with the inductance and resistance of the power distribution network to supply electrical charge. A distributed model is generally required to analyze and design a power distribution network to maintain acceptable levels of supply voltage noise. An approximation method is proposed in this paper for modeling the power distribution system in the frequency domain, defining an effective decoupling capacitance and an effective decoupling radius around each switching element, both of which are frequency dependent. At high frequencies, the supply of decoupling charge is highly localized, and the effective decoupling capacitance is determined primarily by the power grid inductance. Design considerations and guidelines are presented for determining the appropriate density of on-die decoupling capacitances and required power grid parameters, depending upon the density and the frequency characteristics of the switching activity of the circuit