i'm not sure what the problem is here, the math is easy.
You can't use the empirical formula when stacking cores!
you doubled the core, but not the window area. however, because the copper wasn't doubled in lenght, only increased by say 75%, you can get more power out if % regulation was the limiting factor, but not if temp rise was the limiting factor.. see the discrepancy here?
those imperical formulas assumed that the core cross section ratio was less than 1.5:1 or approximatly square, and that by doubling the core area, you also doubled the window area; because you selected the next larger core size, not stacked more laminations up!
The difference between today and 100 years ago is the ratio between iron and copper. at $7 a pound/cu and iron losses of 1 watt per KG at 1.7T/60Hz, i can afford to spend more on iron, or cheap out and use aluminum wire at $1.5/lb
this is why most microwave oven transformers and sub 500Kva transformers are now wound with Al wire.. because the iron loss is so low.
You can't use the empirical formula when stacking cores!
you doubled the core, but not the window area. however, because the copper wasn't doubled in lenght, only increased by say 75%, you can get more power out if % regulation was the limiting factor, but not if temp rise was the limiting factor.. see the discrepancy here?
those imperical formulas assumed that the core cross section ratio was less than 1.5:1 or approximatly square, and that by doubling the core area, you also doubled the window area; because you selected the next larger core size, not stacked more laminations up!
The difference between today and 100 years ago is the ratio between iron and copper. at $7 a pound/cu and iron losses of 1 watt per KG at 1.7T/60Hz, i can afford to spend more on iron, or cheap out and use aluminum wire at $1.5/lb
this is why most microwave oven transformers and sub 500Kva transformers are now wound with Al wire.. because the iron loss is so low.
AndrewT,
Equation 5-1 of this document provides an expression for the area product (Ap=Wa*Ac) as a function of power and other parameters.
Transformer and Inductor Design Handbook - Google Books
Wa is the winding area.
Rick
Equation 5-1 of this document provides an expression for the area product (Ap=Wa*Ac) as a function of power and other parameters.
Transformer and Inductor Design Handbook - Google Books
Wa is the winding area.
Rick
Tony,
What are you trying to tell us? The flux density is independent of the core cross sectional area. However, flux is flux density times core area or F=B*Ac. Regarding current density and winding area, it is the other way around. The current density is the independent variable and a function of temperature rise. Therefore, Aw is determined by current and the number of turns. Aw=Kw*J*N where Kw is a factor related to the utilization of the winding area.
Finally, L=uo*N^2*Ac/(lg+lm/ur). So the magnetizing current is dependent on Ac, lg and lm.
What else do you want to know?
Rick
What are you trying to tell us? The flux density is independent of the core cross sectional area. However, flux is flux density times core area or F=B*Ac. Regarding current density and winding area, it is the other way around. The current density is the independent variable and a function of temperature rise. Therefore, Aw is determined by current and the number of turns. Aw=Kw*J*N where Kw is a factor related to the utilization of the winding area.
Finally, L=uo*N^2*Ac/(lg+lm/ur). So the magnetizing current is dependent on Ac, lg and lm.
What else do you want to know?
Rick
sure, but we don't really care about magnetising current, unless it gets above about 5% full load current, which it won't do with reasonable air gaps and unsaturated cores.
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