In this paper we present a novel architecture for phase-locked loop (PLL) based high-speed demodulation of frequency-modulated (FM) atomic force microscopy (AFM) signals. In our approach, we use single-sideband (SSB) frequency upconversion to translate the AFM signal from the position sensitive detector to a fixed intermediate frequency (IF) of 10 MHz. In this way, we fully benefit from the excellent noise performance of PLL-based FM demodulators still avoiding the intrinsic bandwidth limitation of such systems. In addition, the upconversion to a fixed IF renders the PLL demodulator independent of the cantilever's resonance frequency, allowing the system to work with a large range of cantilever frequencies. To investigate if the additional noise introduced by the SSB upconverter degrades the system noise figure we present a model of the AM-to-FM noise conversion in PLLs incorporating a phase-frequency detector. Using this model, we can predict an upper corner frequency for the demodulation bandwidth above which the converted noise from the single-sideband upconverter becomes the dominant noise source and therefore begins to deteriorate the overall system performance. The approach is validated by both electrical and AFM measurements obtained with a PCB-based prototype implementing the proposed demodulator architecture.