Complete Analytical Calculation of Static Leakage Parameters: A Step Toward HF Transformer Optimization

The predetermination of the leakage inductances of transformers is essential for component designers. Except for special winding disposal, the usual analytical methods of evaluation are ineffective, while the finite-element-method simulation evaluation requires too much time to be suitable for any optimization process. In a previous work, we supplied the analytical expression for vector potential from which we deduced leakage inductance through numerical integration. In this paper, an explicit expression of leakage inductances is given. This expression does not appear as a series, requires shorter computing time, and opens up a lot of future applications relying on optimization software. Moreover, the calculation is not restricted to leakage inductances: It has been extended to all the parameters characterizing the whole leakage behavior of any transformer. The influence of ferrite permeability and thickness is also investigated.