Implementing the Lorenz oscillator with translinear elements

Nonlinear processing is often more suitable than the traditional linear approach is for analyzing biological signals. Unfortunately, digital nonlinear operations are computationaly expensive. In contrast, a large variety of nonlinear operations can efficiently be implemented in analog electronics, operating at real-time speeds. The low level of accuracy generally associated with analog processing is not a concern in this scenario, as biological signals themselves typically have low signal-to-noise ratios. One challenge of analog processing is in its apparently-ad hoc design, and the fact that there is very little wide-spread knowledge of systematically implementing analog electronics to perform arbitrary nonlinear computations. Another issue is the integrity of the analog components; the analog properties of electronic devices are prone to a large amount of mismatch. In this paper, we examine multiple-input translinear element (MITE) networks, a class of analog circuits that addresses the two concerns of a structured synthesis procedure and component mismatch. We test the ability of these MITE networks for accurately realizing linear and nonlinear systems with prescribed dynamics by attempting to implement the Lorenz equations. We will present the theoretical procedure, address practical implementation issues, and then show experimental results from a version of the circuit fabricated in a 0.5 μm CMOS technology through MOSIS.