Cell biasing and balancing in E-cell based single-ended log filters

Log domain (or instantaneous companding) filtering is a recent appealing paradigm for designing integrable, high-frequency, low-voltage, continuous-time filters. A nonlinear transconductor known as E-cell is the single building block needed for realizing filters of any complexity. Nevertheless, the problem of biasing all the E-cells at proper DC operating points has not yet been systematically solved. Aim of this contribution is to address this topic and to propose a generally applicable mapping which systematically provides proper bias levels. Furthermore, the proposed mapping balances the E-cell branch currents at the DC operating point, allowing overall improved operation.