I have analyzed on the effect on leakage inductance for the planar transformer, therefore came across the research paper and found the below formula for leakage inductance calculation: Also, i have attached the research paper of it for reference:
Leakage Inductance, L = u0. N1.N1.T.(a+b+3c)/3.W Henry
Where u0=permeability of air N1=No of turns on the primary T =Mean length of turn W=Window width / winding width a=Height of primary turns b=Height of secondary turns c=Gap of insulation layer
QNS1: From the above formula, The leakage inductance values does not depend upon the core material. Is it so? If not, what will be the impact on the leakage inductance with respect to core material used?
QNS2: In the attached paper, they provide the method for alter the leakage inductance of the transformer. Since flux is leaking in winding area and insulation area, shall i assume ur(relative permeability) as 1for calculating flux density?and what should be the effective magnetic path need to be considered while calculating flux density of leakage inductance?
Transformer leakage inductance (designated L' in the past) is, in effect, an inductance in series with the transformer, and is modeled as such. Traditionally, the leakage inductance energy was divided equally between inductances in series with the primary and secondary, but either can be completely moved to the other winding by the square of the turns ratio.
Leakage inductance is a measure of the energy stored in the magnetic field produced by a power input, or "primary" winding, that is not coupled to the output (secondary) winding. For well coupled (low L') windings, this energy islargleh in the magnetic field in the windings and the space between the windings, with a smaller contribution in fringe fields just outside the windings. Thus the permeability of the core, or even its presence, has a minimal effect on the leakage inductance.
Your formula neglects the effects of multiple primary-secondary 'pairs' or 'sections'. This "interleaving" of primary and secondary windings dramatically reduces the leakage inductance, at the expense of increased interwinding capacitance coupling. Alternative formulas for L' (in the CGS system) which include interleaving effects are in the attached extract (page HFM-17) from my "High Frequency Magnetics" seminar notes, which are also attached.
Again, I must emphasize that these formulas apply only to well or tightly coupled windings. If much or most of the coupling is through the flux in the core, such as is done by placing the windings on separate legs of a core to increase leakage inductance, that is a completely different situation. (This also tends to result in a very large external magnetic field, whose energy provides the high leakage inductance, but which can also become a major source of EMI problems.)
I suggest you should also read my paper on the leakage inductance of planar transformers [48], available on ResearchGate, but also attached for your convenience.
In general, most of the leakage flux lines travel through the air instead of the transformer core, thus, there is no saturation or hysteresis effect, and the calculation therefore can be done using only the permeability of the vacuum mu_0.
For an accurate flux leakage calculation, threedimensional finite element analysis is a powerful tool and still the best method for the analysis of this type of problem.
The leakage flux value is proportional to the load applied to the transformer. this flux is negligible when the transformer operates at no load. however, leakage fluxes are increased when both windings carry significant current.
An important thing to bear in mind is that the transformer coils resistance is usually negligible and the percentage value of the impedance is calculated by the ratio between the total magnitude of the leakage flux and the main flux in the core. Load loss is present only when the transformer is loaded.
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