Design of digital filters from LC ladder networks

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Abstract
A design procedure is given which enables digital filters to be derived directly from ladder LC filters. The erivation is based on an element-by-element transfer of the ladder components to the digital domain. The manner in which such a transfer is achieved is dependent on linear voltage-current transformations, a special case of which is that relying on scattering parameters which has already been described by this author and by others elsewhere. A specific set of constraints are imposed on the transformations in this paper so as to satisfy the readability condition and also to ensure that the digital filters thus derived have transfer functions which are identical to the original ladder transfer function, generally modified by a constant multiplier, as viewed through the bilinear complex frequency transformation. Two special cases of the general approach presented in this paper show that the digital filter structures so derived have a low attenuation sensitivity to multiplier variation, which is consistent with the expectation for the low sensitivity properties of the doubly-terminated lossless ladder filters.

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