Tradeoff core losses against transformer size. Engineering is more than reading theoretical numbers and equations from a physics text book. Pushing Bpeak too high promotes also inrush currents during power switch-on. Transient volt-time product is up to double the periodical peak value.
I have to admit that at this moment I cannot detect the correct unit factor for the above formula, but I've used this for a design I made and it matched exactly with the cross sectional area of most commercial transformers.
Now by a reverse engineering based on my last design ( putting it in S.I. base unit ):
I have to admit that at this moment I cannot detect the correct unit factor for the above formula, but I've used this for a design I made and it matched exactly with the cross sectional area of most commercial transformers
The core heating is the factor that limits the power rating of a transofrmer, and if you want to determine this by some kind of calculation ( estimate, rather ) you should at least have in hands the BxH curve to know the expected amount of losses within the core. In practice we just assume an effective Bsat for which temperature rises acceptably.
you should at least have in hands the BxH curve to know the expected amount of losses within the core. In practice we just assume an effective Bsat for which temperature rises acceptably.
Core loss per cycle due to hysteresis is proportional to the area of the hysteresis loop; hence power lost will be proportional to the area of the hysteresis loop and frequency (Steinmetz theorem)
Core loss per cycle due to hysteresis is proportional to the area of the hysteresis loop; hence power lost will be proportional to the area of the hysteresis loop and frequency (Steinmetz theorem)
Although the hysteresis loop would be the formal way to estimate the core losses on transformer, for the specific case discussed on this thread ( assumed pure 60Hz, Silicon steel lamination ), considering that there is no much variation on the magnetic properties of these materials, a simple formula/chart is the suited method for selecting the core size. We should also keep in mind that the bigger the core, the reduced ability to dissipate generated heat ( "Area/Volume" increases in a ratio smaller than '1' ).
andre_teprom said:
I've used this formula for a design I made and it matched exactly with the cross sectional area of most commercial transformers.
Just a remark on that statement: Equipment which operate with reduced autonomy, such as UPS with limited capacity of the battery bank, some ones are manufactured with smaller transformers than we would expect for the rated load. Manufacturers take advantage of the fact that for a limited time, the core heat profile over time during battery discharge will not reach a critical temperature, and thus saving in material cost ( for power equipments, sometimes the core represents the more expensive part of the BOM ). Therefore, sometimes we cannot infer the transformer capacity of some equipament just by its size, as we usually do.