Leakage Inductance in a Transformer

Good electromagnetic coupling between the primary and secondary windings is normally achieved when the core has a high permeability. However, some leakage inductance is always present, related to transformer characteristics such as short circuit performance.
This Demonstration shows how the leakage inductance and the concomitant magnetic field are influenced by the winding configuration. A simple transformer structure with two windings around a cylindrical core is considered. A simplified field calculation technique from [1] is implemented for determining the leakage inductance. For convenience, the primary and secondary windings have the same number of turns, , with a fixed core radius (), conductor size () and winding turn-pitch ().
You can select the winding type: "stacked solenoids", "separated solenoids" or "separated disk windings." You can change the number of turns and the separation distance of the windings. The magnitude of the magnetic field is indicated by the color, and its direction is shown by white arrows.
Although the field is calculated with a relatively fast image method, computation may become slower as the number of turns increases. The primary and secondary currents producing the field are set with the same number of ampere turns, oppositely oriented.


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Snapshot 1: one-turn concentric windings separated by 100 mm
Snapshot 2: two solenoids separated by 60 mm
Snapshot 3: two disk windings separated by 80 mm
In the approximation we use, the winding ring current is accompanied by another ring current (i.e., image current) inside the core, due to its infinitely large core permeability. This approximation is by no means perfect, since the magnetic field does not intersect the core surface at right angles everywhere. Because the discrepancy occurs on the periphery, it may have a limited effect on the calculated leakage inductance.
By definition, the leakage inductance is proportional to the magnetic flux between two windings and the square of the number of turns. Calculations with a different number of turns and separation distances verify these relations.
[1] F. de Leon and A. Semlyen, "Efficient Calculation of Elementary Parameters of Transformers," IEEE Transactions on Power Delivery, 7(1), 1992 pp. 376–383. doi:10.1109/61.108931.
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