A volumetric optimization of a low pass filter

The low pass filter is a fundamental component of many power electronic systems, for example the output filters of DC to DC converters. The volume of the two components, that constitute the low pass filter, contribute a majority of the final system's volume, thus effecting the overall power density of the system. To be able to reach the high power densities that are required nowadays, the packaging of these components needs to be addressed. A new packaging approach is considered where the main criteria is to increase the packaging density of the low pass filter. The filter is considered volumetrically and the minimum possible volume is derived. The construction and losses of such a filter are also discussed.