Abstract: The requirements to envelope a target power spectral density（PSD） function compatible with the design response spectra are usually prescribed by seismic codes for generating artificial time series as seismic input. This paper contrasts several methodologies which are most widely used in engineering seismology for defining spectrum compatible PSD. Parameters of these methodologies were analyzed using the RG1.60 and AP1000 design response spectra of safe shutdown earthquake. The emphasis was then placed on the method proposed by Kaul and its applicability was illustrated. Artificial time histories, whose response spectra were in agreement with 2%-damped design response spectrum, were generated and their average PSD would be the minimum PSD requirements compatible with the spectrum. Numerical examples show the accuracy and applicability of those approaches.