Multiple operating points in a CMOS log-domain filter

A second-order bandpass filter was designed by converting a conventional BJT-based log-domain filter circuit to its weak-inversion CMOS equivalent. When biased as designed, the filter performed as expected, but the integrated circuit at times self-biased to an unintended operating point, rendering the circuit useless. This behavior is related to the positive feedback loops used in log-domain (and many other) circuits. Such situations cannot in general be predicted by inspection of the circuit topology. A method is presented for predicting and analyzing multiple operating points in SPICE circuit simulation. Of course, the predictions apply only to the circuit as modeled in the simulator. Detailed analysis illustrates that the number of predicted operating points can depend on the modeling of effects (in this case, well-substrate leakage currents) that are often modeled carelessly, if at all.