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Recently, optical phase modulation has been widely used in microwave photonics (MWP) systems, such as radio over fiber systems, photonic microwave filters, optical microwave and millimeter-wave signal generators, and optical subcarrier frequency up-converters. An optical phase-modulated signal can be converted to an intensity-modulated signal in a dispersive optical fiber. Due to the intrinsic nonlinearity of optical phase modulation, for linear applications such as microwave signal distribution and filtering, the modulation index should be kept small to minimize the unwanted modulation nonlinearity. However, for nonlinear applications such as microwave frequency multiplication and subcarrier frequency upconversion, the modulation index should be large to maximize the frequency multiplication and upconversion efficiency. In this paper, for the first time to our knowledge, we develop a thorough theoretical framework for the characterization of phase-modulation-based MWP systems, in which the phase modulation to intensity modulation conversion is realized using a dispersive fiber. Analytical models for the distributions of single-tone and two-tone microwave signals and for microwave frequency multiplication and subcarrier frequency upconversion are developed, which are verified by numerical simulations. The analytical models for single-tone and two-tone transmissions are further confirmed by experiments. The developed analytical models provide an accurate mathematical tool in designing phase-modulation-based MWP systems.