Volumetric limits of planar integrated resonant transformers: a 1 MHz case study

The integrated planar resonant/transformer structures analyzed are constructed from planar ferrites, conductive layers, leakage layers and ceramic dielectric substrates. The minimum dimensions for these electromagnetically integrated structures are determined based on electromagnetic and technological limits respectively. Thus to answer the question as to what is the minimum required volume that can be theoretically achieved, the electromagnetic material limits are analyzed. These material limits are expressed in terms of the permeabilities, permittivities and conductivities, skin effect and breakdown field of the different materials. A design based solely on these electromagnetic limits is developed and compared to the present constructional limitations. This is conducted for an example of a particular integrated resonant/transformer structure, the L-L-C-T, to illustrate the analysis. This analysis indicates that design based on the electromagnetic limits results in volumes two orders of magnitude smaller than the present prototypes, illustrating that the power density is at present only limited by constructional technology. The thermal limit, however, is expected to be the next barrier within one order of magnitude.