Modeling the effects of BJT base currents on the dynamics of a log-domain filter

Floating-capacitor implementations of differential-output log-domain circuits exhibit externally nonlinear behavior. However, the cause of these dynamics may differ from case to case. In a floating-capacitor class AB log-domain parallel resonator it was the finite forward-current gain of a pair of cross-coupled transistors that played a crucial role in the emergence of the nonlinearities. On the other hand, it was recently proved that in floating-capacitor log-domain LC-ladders the BJT parasitic capacitances considerably affect the dynamics and must be taken into account for modeling purposes, no matter how small they are with respect to the floating capacitors. This work proves that, as was the case for the parallel resonator, the base currents of a number of transistors are responsible for the nonlinear dynamics of a class AB log-domain exponential state-space filter. This is achieved by presenting and validating the simplest mathematical model able to capture the nonlinear behavior of the circuit in both the autonomous and non-autonomous cases