A state-space formulation for externally linear class AB dynamical circuits

The state-space description of externally linear class AB dynamical systems is explored. Motivated by recent work in the area of log domain filtering, a definition for a generic class AB dynamical system is proposed. Following this, a more useful differential state-space formulation is proposed which is intuitively consistent with the nonlinear electronic circuits that implement class AB systems. A discussion of static and dynamic constraints which imply class AB operation, along with a basic theorem, leads to more practical constraints on the state space formulation which will allow class AB externally linear behavior of a system. Next, the results are used to explain the operation of several already-existing basic class AB log domain and exponential state-space filters. Finally, a new generalization to existing class AB circuit topologies is offered.