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This paper addresses the high-frequency performance limitations of graphene field-effect transistors (GFETs) caused by material imperfections. To understand these limitations, we performed a comprehensive study of the relationship between the quality of graphene and surrounding materials and the high-frequency performance of GFETs fabricated on a silicon chip. We measured the transit frequency (f_T) and the maximum frequency of oscillation (f_max) for a set of GFETs across the chip, and as a measure of the material quality, we chose low-field carrier mobility. The low-field mobility varied across the chip from 600 cm²/Vs to 2000 cm²/Vs, while the f_T and f_max frequencies varied from 20 GHz to 37 GHz. The relationship between these frequencies and the low-field mobility was observed experimentally and explained using a methodology based on a small-signal equivalent circuit model with parameters extracted from the drain resistance model and the charge-carrier velocity saturation model. Sensitivity analysis clarified the effects of equivalent-circuit parameters on the f_T and f_max frequencies. To improve the GFET high-frequency performance, the transconductance was the most critical parameter, which could be improved by increasing the charge-carrier saturation velocity by selecting adjacent dielectric materials with optical phonon energies higher than that of SiO₂.