A semiconductor device includes a first coil that is monolithically integrated in a first portion of a semiconductor body and that includes a first winding wrapping around a first core structure. A second coil is monolithically integrated in a second portion of the semiconductor body and includes a second winding wrapping around the second core structure. The first and second coils are magnetically coupled with each other. An insulator frame in the semiconductor body surrounds the first portion and excludes the second portion. High dielectric strength between the first and the second coils is achieved without patterning a backside metallization for connecting the turns of the windings and without being restricted to thin substrates.