Systematic derivation of explicit design formulae for log-domain: A 3rd-order lowpass example

The operational simulation of passive prototypes in log-domain is feasible either by means of state-space-based techniques or by transforming the SFG corresponding to the linear prototype. However, the correlation of the prototype element values with circuit parameter (i.e. capacitor and biasing current) values constitutes a synthesis step, which is not explained in detail by the available literature and usually entails a considerable amount of expertise. This paper aims at elaborating one possible way of such an explicit correlation by means of the concept of the Intermediate Transfer Function. An exemplary 3rd-order LP ladder Chebychev response is synthesised and analytic design relations are systematically derived.The resulting general formulae allow the engineer to explore several possible design freedom parameters as far as the filter topology selection and its performance are concerned. HSPICE simulation results are provided.