Log-domain filtering by simulating the topology of passive prototypes

A systematic method for designing log-domain filter structures that simulate the topology of the corresponding passive prototypes is introduced in this paper. This has been achieved by transposing the i-υ characteristic equation of each passive element in the linear domain, to the corresponding one in the log domain. The transposition has been done in such a way that, the current that flows through the terminals of the passive element in the linear domain sustains its value in the corresponding log-domain configuration. In this way the linear operation of the whole filter is preserved. With regard to the voltage at each terminal of the passive prototype, this is logarithmically compressed in order to achieve filtering in the log domain. Following the above considerations, the log-domain equivalents of all passive elements of the prototype filter were derived. Having established the equivalents, the procedure for designing high-order log-domain filters is quite facilitated. The validity of the proposed technique is demonstrated through simulation results for a fifth-order elliptic low-pass filter.