A Bernoulli Cell-Based Investigation of the Non-Linear Dynamics in Log-Domain Structures

Abstract

This paper presents a low-level treatment of the non-linear dynamics encountered in log-domain structures, by means of a non-linear circuit element termed a Bernoulli Cell. This cell comprises an npn BJT and an emitter-connected grounded capacitor, and its dynamic behavior is determined by a differential equation of the Bernoulli form. The identification of the Bernoulli Cell leads to the creation of a system of linear differential equations which describe the dynamics of the derived log-domain state-variables. Furthermore, it is shown that the Bernoulli Cell has a memristive type dynamic behavior. The approach aids the analysis of log-domain circuits, and allows the internal non-linear currents to be conveniently expressed in closed analytical form. A worked example for a specific topology with confirming simulation 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.