LDI z-domain images of lossless LC ladders

Discrete-time images of lossless LC one-port ladder networks are presented. Such images are obtained by expanding discrete-time reactance functions into continued fractions to obtain the discrete-time counterparts of Cauer-1, Cauer-2, and mixed-Cauer expansions. The existence of these expansions is proven and a methodology for synthesis of these expansions is given similar to the one known for synthesis of the continuous-time reactance function. The type of reactance functions used is related to the continuous-time counterpart by the lossless discrete integrator (LDI) s-to-z transform. Simple first and second order discrete-time reactance networks are proposed and used in a step-by-step procedure to realize higher-order networks. The resulting discrete networks are considered images of LC one-port ladders in the z-domain