While searching about power factor correction topologies, the topology I came across almost all the time was the Boost PFC topology, and I'd like to know why? why is it the most widely used one, in comparaison to say, buck PFC or flyback PFC.
Active power factor correction (PFC) is all about controlling the circuit's input current waveform and making it as close to input voltage waveform as possible (Sinusoidal in the case of AC mains).
Converter topologies such as Buck (Shown in next image) and Flyback work by quickly connecting and disconnecting themselves from supply source in order to modify their output voltage while keeping it continuous with stored energy from capacitors and inductors. Since they are completely disconnecting from power source while switching, input current is inherently discontinuous which is not desired if we are attempting to control it.
On the other hand, converters such as Boost (Shown in next image) and SEPIC don't directly disconnect themselves from power source. This causes input current to be continuous. Furthermore, its value can be smoothly controlled from the converter's switching components, making these topologies ideal for active PFC.
Active PFC methods for Buck-type topologies exist but tend to be less effective than Boost-type topologies. That said, this paper proposes a 2-stage Boost-Buck converter topology (as opposed to one-stage Boost-Buck), in order to control input current with the first stage and to reduce output voltage with the last one (Which could not be done with a Boost converter alone). Disclaimer: I'm one of the authors of this work.