Design optimization of L-C filters

L-C filters are commonly used to reduce the output ripple of DC power supplies. They can be a significant factor in the size, weight or cost of equipment. When high values of attenuation are required, several series L-C sections may be used. The question arises for a given performance in terms of attenuation: what should the number of sections be and what relation should they have to each other such that the over-all size, weight or cost is optimum? The energy storage in the inductor, L, and capacitor, C, in an L-C section can be related to the attenuation performance characteristics. It is also possible to relate the size, weight or cost of the L and C component to the energy storage and thereby obtain the size, weight or cost of a given section in terms of the attenuation. The attenuation of a given section is determined in relation to the break frequency of the section. An equation for the total size, weight, or cost of a section can be expressed in terms of the break frequency and the respective specific size, weight or cost of the component L and C. This equation can be used to determine the optimum relation between L and C to achieve minimum size, weight or cost. Similarly it is possible to mathematically express the size, weight or cost of a series of L-C sections when given the required total attenuation at a given frequency. Using this equation it is possible to determine analytically the optimum number of sections and the optimum relation between the sections. Curves, tables and equations are given to aid in optimizing a design using size, weight or cost as the basis criterion.