Low profile transformer

A method for providing a low profile transformer of predetermined operational and material specifications adaptable into a receiving housing, wherein the transformer comprises a core unit having a pair of core members, each core member having a base portion, an inserting portion, and a pair of lateral portions, the method comprising:

• providing the receiving housing having a first cross section, defining a first available area in the first cross section for receiving the transformer;
• determining an actual effective cross-sectional area (Ae—act) of the inserting portion, wherein (Ae—act) is less than the first available area;
• selecting an available coil winding width (W) of the transformer not greater than the distance between the inserting portion and either one of the lateral portions;
• applying the predetermined operational and material specifications to a characteristic equation to selectively provide a characteristic effective area function Ae(Np, N) and a characteristic magnetic flux variation function ΔB(Np, N), the characteristic equation being defined as
• A
• e
• =
• V
• in_min
• 
• D
• 
• (
• V
• in_min
• ,
• N
• ,
• V
• o
• )
• N
• p
• 
• Δ
• 
• 
• B
• ·
• fre
• wherein
• Ae denotes an effective cross-sectional area of an inserting portion,
• Vin—min denotes minimum AC (alternating current) input voltage in [V],
• N denotes winding ratio between primary and secondary windings,
• Vo denotes DC output voltage in [V],
• D(Vin—min, N, Vo) denotes duty cycle, wherein
• D
• 1
• -
• D
• =
• N
• 
• V
• 0
• V
• in_min
• ,
• Np denotes primary winding number,
• ΔB denotes change in magnetic flux density in [Tesla],
• fre denotes operating frequency in [KHz];
• selecting a suitable solution pair (Np, N) from the solution space of the characteristic effective area function Ae(Np, N) or the characteristic magnetic flux variation function ΔB(Np, N);
• obtaining a secondary coil winding number (Ns) from the solution pair (Np, N) for determining a total required coil winding area (Atotal) through the selected Np and the corresponding Ns;
• and
• obtaining an available coil winding length (L) of the transformer by dividing the total required coil winding area (Atotal) by the available coil winding width (W).