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Leakage power is becoming the dominant component of chip power consumption with continued CMOS scaling. An important but commonly unnoticed fact is that leaky transistors act as resistors that help dampen the mid-frequency power supply noise. This paper focuses on the damping effect of various on-chip current components including the leakage current which becomes significant in scaled technologies. By developing physics-based damping models for active and leakage currents, we show that leakage, particularly gate tunneling leakage, provides more damping than strong-inversion current. The proposed models were validated in a 32-nm predictive CMOS technology under process-voltage-temperature (PVT) variations. Examples on large circuits such as SRAM caches are shown to illustrate the application of the proposed model. Simulation results show that the leakage induced damping effect can compensate the speed degradation at high temperatures by 7% or offer 61% saving in decap area and leakage power.