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Distribution of natural frequencies in electrical ladder networks

The evolution of the distribution of natural frequencies in electrical ladder networks composed by the iteration of the same elemental structure, as the number of sections increase, is analyzed. These networks are seen as a large-scale many-body system. Several collective properties of the spectrum; namely, the eight first moments of the density of natural frequencies, the skewness, and the excess; are explicitly calculated. Different cases of transmission lines represented by ladder networks are considered.