A Bernoulli Cell-based investigation of the non-linear dynamics in log-domain structures

This paper presents a low-level treatment of the non-linear dynamics encoun tered in log-domain structures, by means of a non-linear circuit element te rmed a Bernoulli Cell. This cell comprises an npn BJT and an emitter-connec ted grounded capacitor, and its dynamic behavior is determined by a differe ntial equation of the Bernoulli form. The identification of the Bernoulli C ell leads to the creation of a system of linear differential equations whic h describe the dynamics of the derived log-domain state-variables. Furtherm ore, it is shown that the Bernoulli Cell has a memristive type dynamic beha vior. The approach aids the analysis of log-domain circuits, and allows the internal non-linear currents to be conveniently expressed in closed analyt ical form. A worked example for a specific topology with confirming simulat ion results in both frequency and time-domain is presented. The celebrated Hodgkin-Huxley nerve axon membrane dynamics are also successfully simulated as a characteristic example of memristive behavior.