Mapping duality as a means to allow finite βF compensation in bipolar log filters

Log-domain filters are a promising design paradigm for analog signal processing. They achieve tunability and operation up to high frequencies, with voltage and power requirements typically better than those of conventional filtering architectures. Implementation can be based only on capacitors, current sources and an exponential, differential V/I converter referred to as the E-cell. Non-idealities in the E-cell, like the presence of non-negligible input currents due to finite βF, can reduce system performance. The aim of this paper is to investigate E-cell-based design strategies and to introduce a duality principle whose exploitation can allow finite βF compensation. As a validation, HSPICE simulation results are illustrated for a second-order bandpass filter.