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

Authors: Drakakis E.M.¹; Payne A.J.²

Source: Analog Integrated Circuits and Signal Processing, Volume 22, Numbers 2-3, March 2000 , pp. 127-146(20)

Publisher: Springer

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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.

Keywords: log-domain circuits; active filters; analog integrated circuits; circuit theory

Language: English

Document Type: Regular paper

Affiliations: 1: Department of Electrical and Electronic Engineering, Imperial College, SW7 2BT e.drakakis@ic.ac.uk; a.j.payne@ic.ac.uk 2: Department of Electrical and Electronic Engineering, Imperial College, SW7 2BT

Publication date: 2000-03-01