In this paper, a new design for an integrated planar transformer is presented which can provide asymmetric leakage inductance in primary and secondary sides. Therefore, the proposed integrated transformer can be used in bidirectional resonant converters in which the primary and secondary inductors have different values. To achieve a precise, high leakage inductance for the primary and secondary sides, two magnetic shunts are inserted into a planar transformer. In the proposed topology, flexible magnetic sheets which can be cut easily are used as the magnetic shunts, leading the design process to high flexibility. The analysis, design and modelling of the proposed integrated transformer are presented in detail. It is shown that the magnetising inductance can be determined by regulating the length of an inserted air gap inserted between two E-cores. In addition, the leakage inductance of the primary and secondary sides can be regulated separately by the length of air gaps inserted within the magnetic shunts. The theoretical analysis is verified by finite element analysis and the operation of the proposed integrated transformer is demonstrated while it is used in a CLLLC bidirectional converter.