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Despite their use in analog or mixed-signal applications, the high power overheads of traditional linear regulators (both series and shunt) have precluded their successful adoption in regulating the supply of energy-efficient digital circuits. In this paper, we show that linear regulation can in fact reduce the effective supply impedance of digital circuits without increasing their total power dissipation. Achieving this goal requires minimizing the static power dissipation of the regulator, leading to a push-pull topology (similar to the regulators demonstrated by Wu and Sanders, 2001, Poon et al, 1999, and Intersil, 1998) with comparator-based feedback and a switched source-follower output stage. Measured results from a regulator implemented in a 65 nm SOI test-chip verify that by using these techniques, regulation reduces the effective supply noise by ~30% while also enabling a slight decrease (1.4%) in total power dissipation.