Comparison of currents in differential log-domain filters with common-mode feedback

Applying high-gain common-mode feedback (CMFB) at both ports of a differential second-order log-domain filter allows all of the currents within the filter to be calculated in simple closed form. This is very useful for design, as it greatly simplifies choosing transistor geometries to avoid clipping. It also makes it easier to compare filter topologies. Considering the possibility of not using CMFB at one or both ports, or adding geometric-mean CMFB or harmonic-mean CMFB at one or both ports in a second-order filter yields nine unique log-domain filter circuits. Closed-form solutions are derived for the maximum currents in eight of these cases. For one of the combinations with no added CMFB at one of the ports, simulations verify that the filter performs almost as well as the best combination using CMFB at both ports.