I am new to power electronic, power supply design and converting AC(low power-single phase) to DC. My question is that if AC voltage is connected to a transformer with magnetic core as the first part of a SMPS or it is connected to some power semiconductor components first?

I mean core losses of a transformer is proportional to input voltage directly(Vrms^2/Rc), this way we lose lots of active power even if the transformer ratio is 1:1.

 

The mains supply is normally first directly rectified to a high voltage DC value. Conversion to low voltage DC is then done via intermediate switch mode operation at a frequency >> mains frequency with subsequent rectification and smoothing. The transformer can then be physically much smaller & lighter than a "front end" transformer operating at mains frequency.