For the operation of the semiconductor components in medium voltage converter or multilevel converter applications (where the DC bus voltage up to several ten kilovolts), their gate driver systems require very high galvanic insulation voltage capabilities. Hence, this study details a design methodology to optimise a power supply function for insulated gate bipolar transistor gate drivers with high insulated voltage capabilities. To achieve this, a dc-to-dc full-bridge series-series resonant converter with a high air gap pot core planar transformer is selected. This air gap length and the dielectric material define the high insulation voltage capability. The objective of the study is to optimise the geometric elements of the transformer and its associated electrical components in the proposed converter. Magnetic and electrostatic modellings are provided. Maximise the converter efficiency (η con) is the main objective of the proposed optimisation design. Thus, the optimisation results are proposed: the converter efficiency (η con) as function of converter output power (P out). Finally, to validate the authors' proposed methodology, the experimental results are compared with the simulation ones. Then, the results of an improved optimisation design are provided.