Beside Henri comment I would like to add that look to the application for this high frequency transformer. A large value of maximum flux density Bm of the transformer allows (ΔB)max to be large and results in a small Ac and hence in a smaller core size. Also, it is worth mention that (ΔB)max is limited by Bm.
I think 1 Khz is still in the range of iron. Laminated iron, reduce Bmax, and take the
iron as thin as possible to reduce eddy current loss. Beforehand, calculate eddy current loss (from conductivity and lamination thickness) and make sure its OK.
Beside Henri comment I would like to add that look to the application for this high frequency transformer. A large value of maximum flux density Bm of the transformer allows (ΔB)max to be large and results in a small Ac and hence in a smaller core size. Also, it is worth mention that (ΔB)max is limited by Bm.
Ironloss should be minimum as possible, and as frequency is 1k or below iron core would work. Hence by keeping v/f constant , find A and B constant for the given core, as Wi=Wh+We=Af+B(f)(f). Find accurate hysteresis loss and eddy current loss for given frequencies range, would be more accurate....