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A comprehensive study, which is presented in two parts, is performed to assess the radio-frequency (RF) performance potential of array-based carbon-nanotube field-effect transistors (CNFETs). In Part I, which is presented in this paper, the time-dependent Boltzmann transport equation is solved self-consistently with the Poisson equation to study the impact of nanotube phonon scattering on different aspects of intrinsic (single-tube, contact-independent) CNFET operation, including the attainable drive current and transconductance per tube, the intrinsic cutoff frequency, the intrinsic y-parameters, and the small-signal equivalent circuit for the intrinsic transistor. These intrinsic results are used to assess the tube-to-tube distance (pitch) that would be required in a multitube array-based structure to meet the drive current and transconductance requirements of the International Technology Roadmap for Semiconductors for the year 2015, which we use as a benchmark for CNFET technology going forward. In Part II of our paper, we elaborate on the results of Part I by adding the effects of extrinsic (contact-dependent) parasitics, thus providing an overall performance assessment of array-based structures.