Analysis of Nonlinear Behaviors, Design and Control of Sigma Delta Modulators

M PhilSigma 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

Bandpass electromechanical sigma-delta modulator

Ph.DDOCTOR OF PHILOSOPH

Multi-band Oversampled Noise Shaping Analog to Digital Conversion

Oversampled noise shaping analog to digital (A/D) converters, which are commonly known as delta-sigma (ΔΣ) converters, have the ability to convert relatively low bandwidth signals with very high resolution. Such converters achieve their high resolution by oversampling, as well as processing the signal and quantization noise with different transfer functions. The signal transfer function (STF) is typically a delay over the signal band while the noise transfer function (NTF) is designed to attenuate quantization noise in the signal band. A side effect of the NTF is an amplification of the noise outside the signal band. Thus, a digital filter subsequently attenuates the out-of-band quantization noise. The focus of this thesis is the investigation of ΔΣ architectures that increase the bandwidth where high resolution conversion can be achieved. It uses parallel architectures exploiting frequency or time slicing to meet this objective. Frequency slicing involves quantizing different portions of the signal frequency spectrum using several quantizers in parallel and then combining the results of the quantizers to form an overall result. Time slicing involves quantizing various groups of time domain signal samples with different quantizers in parallel and then combining the results of the quantizers to form an overall output. Several interesting observations can be made from this general perspective of frequency and time slicing. Although the representation of a signal are completely equivalent in time or frequency, the thesis shows that this is not the case for known frequency and time sliced A/D architectures. The performance of such systems under ideal conditions are compared for PCM as well as for ΔΣ A/D converters. A multi-band frequency sliced architecture for delta-sigma conversion is proposed and its performance is included in the above comparison. The architecture uses modulators which realize different NTFs for different portions of the signal band. Each band is converted in parallel. A bank of FIR filters attenuates the out of-band noise for each band and achieves perfect reconstruction of the signal component. A design procedure is provided for the design of the filter bank with reduced computational complexity. The use of complex NTFs in the multi-band ΔΣ architecture is also proposed. The peformance of real and complex NTFs is compared. Performance evaluations are made for ideal systems as well as systems suffering from circuit implementation imperfections such as finite opamp gain and mismatched capacitor ratios

1-Bit processing based model predictive control for fractionated satellite missions

In this thesis, a 1-bit processing based Model Predictive Control (OBMPC) structure is proposed for a fractionated satellite attitude control mission. Despite the appealing advantages of the MPC algorithm towards constrained MIMO control applications, implementing the MPC algorithm onboard a small satellite is certainly challenging due to the limited onboard resources. The proposed design is based on the 1-bit processing concept, which takes advantage of the affine relation between the 1-bit state feedback and multi-bit parameters to implement a multiplier free MPC controller. As multipliers are the major power consumer in online optimization, the OBMPC structure is proven to be more efficient in comparison to the conventional MPC implementation in term of power and circuit complexity. The system is in digital control nature, affected by quantization noise introduced by Δ∑ modulators. The stability issues and practical design criteria are also discussed in this work. Some other aspects are considered in this work to complete the control system. Firstly, the implementation of the OBMPC system relies on the 1-bit state feedbacks. Hence, 1-bit sensing components are needed to implement the OBMPC system. While the ∆∑ modulator based Microelectromechanical systems (MEMS) gyroscope is considered in this work, it is possible to implement this concept into other sensing components. Secondly, as the proposed attitude mission is based on the wireless inter-satellite link (ISL), a state estimator is required. However, conventional state estimators will once again introduce multi-bit signals, and compromise the simple, direct implementation of the OBMPC controller. Therefore, the 1-bit state estimator is also designed in this work to satisfy the requirements of the proposed fractionated attitude control mission. The simulation for the OBMPC is based on a 2U CubeSat model in a fractionated satellite structure, in which the payload and actuators are separated from the controller and controlled via the ISL. Matlab simulations and FPGA implementation based performance analysis shows that the OBMPC is feasible for fractionated satellite missions and is advantageous over the conventional MPC controllers

1-Bit processing based model predictive control for fractionated satellite missions

In this thesis, a 1-bit processing based Model Predictive Control (OBMPC) structure is proposed for a fractionated satellite attitude control mission. Despite the appealing advantages of the MPC algorithm towards constrained MIMO control applications, implementing the MPC algorithm onboard a small satellite is certainly challenging due to the limited onboard resources. The proposed design is based on the 1-bit processing concept, which takes advantage of the affine relation between the 1-bit state feedback and multi-bit parameters to implement a multiplier free MPC controller. As multipliers are the major power consumer in online optimization, the OBMPC structure is proven to be more efficient in comparison to the conventional MPC implementation in term of power and circuit complexity. The system is in digital control nature, affected by quantization noise introduced by Δ∑ modulators. The stability issues and practical design criteria are also discussed in this work. Some other aspects are considered in this work to complete the control system. Firstly, the implementation of the OBMPC system relies on the 1-bit state feedbacks. Hence, 1-bit sensing components are needed to implement the OBMPC system. While the ∆∑ modulator based Microelectromechanical systems (MEMS) gyroscope is considered in this work, it is possible to implement this concept into other sensing components. Secondly, as the proposed attitude mission is based on the wireless inter-satellite link (ISL), a state estimator is required. However, conventional state estimators will once again introduce multi-bit signals, and compromise the simple, direct implementation of the OBMPC controller. Therefore, the 1-bit state estimator is also designed in this work to satisfy the requirements of the proposed fractionated attitude control mission. The simulation for the OBMPC is based on a 2U CubeSat model in a fractionated satellite structure, in which the payload and actuators are separated from the controller and controlled via the ISL. Matlab simulations and FPGA implementation based performance analysis shows that the OBMPC is feasible for fractionated satellite missions and is advantageous over the conventional MPC controllers

The design of a 250MHz CMOS bandpass sigma-delta A/D modulator with continuous-time circuitry

Master'sMASTER OF ENGINEERIN

Analogue filter networks: developments in theory, design and analyses

Not availabl