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To decrease power consumption without affecting circuit speed, several power supply voltages are used in modern high performance ICs such as microprocessors. To maintain the impedance of a power distribution system below a specified level, multiple decoupling capacitors are placed at different levels of the power grid hierarchy. The system of decoupling capacitors used in power distribution systems with multiple power supplies is the focus of this paper. The dependence of the impedance on the power distribution system parameters is investigated. Design techniques to cancel and shift the antiresonant spikes out of range of the operating frequencies are presented.