Analysis of Nonlinear Behaviors, Design and Control of Sigma Delta Modulators
Abstract
Sigma delta modulators (SDMs) have been widely applied in analogue-to-digital
(A/D) conversion for many years. SDMs are becoming more and more popular in power
electronic circuits because it can be viewed and applied as oversampled A/D converters
with low resolution quantizers. The basic structure of an SDM under analytical
investigation consists of a loop filter and a low bit quantizer connected by a negative
feedback loop.
Although there are numerous advantages of SDMs over other A/D converters, the
application of SDMs is limited by the unboundedness of the system states and their
nonlinear behaviors. It was found that complex dynamical behaviors exist in low bit
SDMs, and for a bandpass SDM, the state space dynamics can be represented by elliptic
fractal patterns confined within two trapezoidal regions. In all, there are three types of
nonlinear behaviors, namely fixed point, limit cycle and chaotic behaviors. Related to the
unboundedness issue, divergent behavior of system states is also a commonly discovered
phenomenon. Consequently, how to design and control the SDM so that the system states
are bounded and the unwanted nonlinear behaviors are avoided is a hot research topic
worthy of investigated.
In our investigation, we perform analysis on such complex behaviors and
determine a control strategy to maintain the boundedness of the system states and avoid
the occurrence of limit cycle behavior. For the design problem, we impose constraints
based on the performance of an SDM and determine an optimal design for the SDM. The
results are significantly better than the existing approaches.
Authors
Ho, Charlotte Y. F.Collections
- Theses [3834]