Impedance measurement techniques based on small-signal injections in ac power system have been well developed but a gap in the analysis is that the selection of an injection amplitude is based only on experience. This letter develops an analytical process to analyze the noise existing in power systems and thereby determines the minimum injection amplitude according to an allowable error. The process is based on knowledge of stochastic processes and statistics, where the Monte Carlo method is also employed to simplify the process. A power hardware-in-the-loop system with a grid-following inverter is employed in experimental verification of the results.