The automatic amplitude control (AAC) system is a servo-circuit of voltage-controlled oscillators (VCOs) that proves important for the practical implementation of fully integrated RF front-ends. Nevertheless, the noise contributed by the AAC can degrade the phase noise performance of the oscillator. In this paper, the time-varying noise transfer of the peak detector is analyzed, since it is recognized as the critical noise source in the simple AAC loop taken as reference. A fast rule to predict the noise spectral density at the peak detector output is given that substantially facilitates the estimate of the phase noise degradation on the VCO output. The analysis has been carried out both theoretically and by simulation; experimental validation has also been provided by means of a discrete-components test board. Guidelines for low-noise design of the peak detector of AAC are finally proposed