Unified matrix method for systematic synthesis of log-domain ladder filters

A matrix-based method of synthesising log-domain ladder filters is described. The nodal matrix equations characterising a LCR prototype are made directly realisable, facilitating the design of high-order filters. Different structures with a range of characteristics can be generated by a variety of matrix decompositions. The problem of floating capacitors normally required to realise transmission zeros in the log-domain is solved by matrix transformations. This avoids externally-LTV dynamics and hence distortion. Simulated results of different designs derived by various matrix decompositions validate the proposed procedures, which have been formalised in the CAD filter package XFILTER.