Are the calculations same for all type of transformers? If no, then what is it for Ring or Toroid Transformers?
I think maximum power capacity of core will directly proportional to the area of core. the bigger the area of core , much amount of power it can transfer without getting saturate. however it is my basic understanding. you can refer given link for the more details.
http://engineerexperiences.com/design-calculations.html
With modern CRGO materials, size could be considerably reduced due to higher working flux density, though inrush would increased, refer my papers....
Maximum power capacity of core is directly proportional to the product core area and core vindow (space for winding). For detals see Tranzistor power converters book, or Prekidačka napajanja by Radojle Radetić.
The volt-ampère (VA) rating is directly proportional to the product of core area and the area occupied by the wires (copper areas). Even though the complications of temperature rise resulting from wires and core losses have been disregarded, we are able to confirm an important qualitative observation: the higher the VA rating, the greater area product.
The AP (area product) is the most common method to rate the transformer core. It is given in every datasheet. But every core or transformer should be cooled... and the material parameters (Steinmetz) is also different from core to core. The best "Recipe" to get the power-capability is given in --> Transformer Design. W. G. Hurley1 and; W. H. Wölfle2
You are usually trying to design a system that does not saturate the flux in the core. Hence this is the limiting factor on power. Noting that increasing the frequency is one way of increasing the power through the core. This is the approach taken in Switch mode power supplies. Aircraft use a 400Hz power system for this reason. Because you spend less time going up and down the B-H curve you do not get to saturation area.
or as pointed out you can change the size/type of material.
As stated which parameters of transformers get affected when the frequency is changed to 400Hz from 50Hz? Is it only the leakage reactances as they are proportional to frequency or some other parameters also?