An evaluation of leakage inductance for a flat cable transformer with a circular cross–sectional core

We have derived the relationship between the leakage inductance and the winding structure for an electronic transformer with a flat cable wound around a circular cross-sectional core. It is found that: (1) the leakage inductance of a flat cable transformer with a circular cross-sectional core is approximately identical to one with a square core cross-sectional core. Next, the winding configuration of a multilayer winding flat cable transformer is classified into lap winding, turn-up lap winding and twisted lap winding; (2) the leakage inductance is higher for the lap winding and the turn-up lap winding than for the one layer winding, but the increase of the equivalent capacitance is minimal for the lap winding; (3) the leakage inductance is even smaller in the twisted lap winding than in the one layer winding; and (4) the leakage inductance per winding length does not increase in the flat cable transformer even if insulators are inserted between layers. Further, based on the leakage coefficient, the unit leakage constant is defined. It is found that: (5) the circular cross-section core is superior to the square cross-sectional core for a wider relative bandwidth and a restricted range of unit leakage constant; and (6) a wider relative bandwidth is more difficult to obtain as the core becomes smaller. These results agree well with experimental findings.