This paper presents a method for creating a wideband PLL-based phase shifter, which yields maximum phase resolution over its entire range of output frequencies. Furthermore, by generating the phase shifts at low frequency and upconverting the phase information with the PLL, this system can generate phase shifts of resolution comparable with state of the art phase modulators without the need for complex matching or calibration techniques. A rigorous proof of the necessary and sufficient conditions for maximum phase resolution in integer-N synthesizers is presented. A 0.64-2.7 GHz, 7-bit phase modulator system is designed and simulated in a 1V 65nm CMOS process, and the results prove the efficacy of the presented modulation method. The presented design shows finer phase resolution than is achievable using current-starved inverter based delays in the 65nm process.