FM demodulation can be done with phase locked loop (PLL), and this method is  common in high-end communication system. This system uses TC9400 that has high linearity. Using TC9400, the performance of phase-locked loop will increases greatly. That will give very precise tracking of Vout with respect to Fin. Here is the block diagram of the FM demodulation with a phase-locked loop:

FM DEMODULATION WITH A PHASE LOCKED LOOP circuit schematic

The operation principle is very simple, since the feedback system force the V/F converter (VFC) to follow the FIN by manipulating the control input of VFC,  as the result, the control input of VFC will follow the the variation  of  FIN. This control signal is then tapped for the output of this circuit. [System’s block diagram source: Microchip Application note]