Power integrity design has been becoming important in the advanced CMOS digital systems, because power supply noise induces logic instability and electromagnetic radiation. Especially, anti-resonance peaks in power distribution network (PDN) due to the chip-package interaction induce the unwanted power supply fluctuation, and result in large electromagnetic radiation. In this paper, effects of damping condition of the total PDN impedance on power supply noise have been studied by adding variable on-die RC circuit to the intrinsic on-die RC circuit in chip PDN. Two types of test chips were designed with different variable on-die PDN impedances. By varying the values of on-die RC circuit, the simulated waveforms of power supply noises for the two test chips have been changed from oscillatory region to damped regions.