Exploiting device nonlinearity in analog circuit design
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This dissertation presents analog circuit analysis and design from a nonlinear dynamics perspective. An introduction to fundamental concepts of nonlinear dynamical systems theory is given. The procedure of nondimensionalization is used in order to derive the state space representation of circuits. Geometric tools are used to analyze nonlinear phenomena in circuits, and also to develop intuition about how to evoke certain desired behavior in the circuits. To predict and quantify non-ideal behavior, bifurcation analysis, stability analysis and perturbation methods are applied to the circuits. Experimental results from a reconfigurable analog integrated circuit chip are presented to illustrate the nonlinear dynamical systems theory concepts. Tools from nonlinear dynamical systems theory are used to develop a systematic method for designing a particular class of integrated circuit sinusoidal oscillators. This class of sinusoidal oscillators is power- and area-efficient, as it uses the inherent nonlinearity of circuit components to limit the oscillators' output signal amplitude. The novel design method that is presented is based on nonlinear systems analysis, which results in high-spectral purity oscillators. This design methodology is useful for applications that require integrated sinusoidal oscillators that have oscillation frequencies in the mid- to high- MHz range. A second circuit design example is presented, namely a bandpass filter for front end auditory processing. The bandpass filter mimics the nonlinear gain compression that the healthy cochlea performs on input sounds. The cochlea's gain compression is analyzed from a nonlinear dynamics perspective and the theoretical characteristics of the dynamical system that would yield such behavior are identified. The appropriate circuit for achieving the desired nonlinear characteristics are designed, and it is incorporated into a bandpass filter. The resulting nonlinear bandpass filter performs the gain compression as desired, while minimizing the amount of harmonic distortion. It is a practical component of an advanced auditory processor.