RLC Lattice Transfer Functions

Necessary and sufficient conditions that a real rational function be the transfer function of an RLC symmetric lattice are derived. The range of allowable values of the multiplicative factor (which determines the gain level) in the transfer function is determined and an algorithm for its calculation is given. While the zeros of the transfer function may be anywhere in the complex number plane, the poles must lie in the left-half plane or its boundary excluding the values 0 and ??. However, at a pole of the transfer function on the pure imaginary axis, the function must satisfy certain further properties which are derived. In virtue of these latter conditions, it is found that there are realizable transfer functions which cannot be synthesized (even up to a multiplicative factor) by means of a symmetric lattice. These realizable transfer functions, which lie outside the symmetric lattice structure, always have some pure imaginary poles which do not satisfy our special conditions for lattice realizability. However, when all the conditions are met, a synthesis procedure for obtaining a corresponding lattice is given. The results are illustrated by an example.