Limit-cycle oscillations in a log-domain-based filter

A circuit is presented for a class-AB fully differential log-domain parallel resonator based on a capacitively loaded gyrator. It is shown that if floating rather than shunt capacitive loads are used, the circuit is stable for small stimuli, but can be triggered into steady-state limit-cycle oscillations by large enough transient inputs. The nature of the instability is explored and it is shown how SPICE transient analysis can be used to detect the instability and locate the separatrix between stable-equilibrium-point-seeking and limit-cycle-seeking regions of state space. Analysis is also presented to demonstrate that the circuit with floating capacitors does not implement an externally linear transfer function, and therefore, it is not a true log-domain circuit.