Flux density in a transformer core is inversely proportional to supply frequency and inversely proportional to the cross-sectional area of the core for given voltage supply. Less number of turns and smaller core cross-sectional area can be used at the same voltage, so the frequency of transformer operates will increases. This can be concluded that at the same power rating, the high frequency transformers are smaller than low frequency transformer.
Hysteresis loss in the core increases with frequency when the flux densities are kept constant is one of problems while transformer operates at the high frequency. So to solve the problems, high frequency transformers can operate at frequency more than 500Hz, laminated iron core is discards and ferrite material are used. Transformer need to operate at the lower flux density than iron but however this could exhibit zero the hysteresis loss.