Planar transformer and active circuit

An active circuit comprising:

• a planar transformer comprising a winding structure and a magnetic core structure,
• the winding structure comprises primary-side, primary-side parallel, and secondary-side windings,
• the magnetic core structure comprises a plurality of magnetic cylinders,
• wherein the primary-side winding is wound in series and parallel around M magnetic cylinders in the plurality of magnetic cylinders and the secondary-side winding is wound around one of the plurality of magnetic cylinders,
• wherein M is a positive integer and M≥3,
• wherein a cross-sectional area of at least one of the M magnetic cylinders is different from a cross-sectional area (Ae) of another magnetic cylinder,
• wherein each of a quantity P of the primary-side parallel windings is wound around one of the M magnetic cylinders and connected in parallel with the primary-side winding,
• wherein P is a positive integer and P is ≥2,
• wherein the quantity P of primary-side parallel windings is wound around P magnetic cylinders in series or in parallel, and
• wherein a ratio of (i) a sum of cross-sectional areas of the P magnetic cylinders and (ii) a sum of cross-sectional areas of the M magnetic cylinders is from 80% to 120%.