Synthesis of MITE log-domain filters with unique operating points

Practical log-domain filter circuits might have multiple operating points in regions in which the translinear element does not obey the exponential law. In this paper, a method is proposed to implement any filter by a log-domain circuit that necessarily has a unique operating point. Any state-space description of the filter is shown to have an equivalent description that can be implemented by such a circuit. This methodology is applied to the synthesis of multiple-input translinear element (MITE) filters. As an example, shifted-companion-form (SCF) filters are synthesized. Further, it is proved that the resulting filters have a unique operating point.