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

  • Authors:

  • E. M. Drakakis;A. J. Payne

  • Affiliations:

  • Department of Electrical and Electronic Engineering, Imperial College, SW7 2BT e.drakakis&commat/ic.ac.uk/ a.j.payne&commat/ic.ac.uk;Department of Electrical and Electronic Engineering, Imperial College, SW7 2BT

  • Venue:
  • Analog Integrated Circuits and Signal Processing - Special issue on dynamic translinear and log-domain circuits
  • Year:
  • 2000

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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.