Higher order sigma-delta modulator loopfilter paralel form representation in Z and S domain

In this paper we present the conversion of arbitrary high order sigma-delta modulator Z-domain loopfilter transfer function into parallel form low order subsections in both S and Z domains. The benefit of this type filter form representation is the existence of theory that can validate sigma-delta modulator's stability. The S domain filter representation is suitable for analog schematic element value calculation stage done according to the utilized transfer function when direct analogue parallel loopfilter implementation is performed.