Design And Implementation Of Fractional-order Sigma-delta Modulator

MEMS(Micro-Electromechanical System)accelerometers have an important role in military,technology and commercial fields due to their low power consumption,small size,high sensitivity,large dynamic range,mass production and immunity from electromagnetic fields.Therefore,it is of strategic importance to develop MEMS accelerometers.The mechanical sensing element and detective circuit are combined to work as a Sigma-Delta modulator in MEMS accelerometer system,and through cascading electronic integrators after the mechanical sensing element to improve the performance of MEMS accelerometer.Sigma-Delta modulator is a key component in MEMS accelerometer system,and the dynamic range,bandwidth,precision,sensitivity,system stability and noise-shaping capability of Sigma-Delta modulator play a key role in the performance of MEMS accelerometer.Sigma-Delta modulator can be divided into 2nd-order and high-order Sigma-Delta modulator.A 2nd-order Sigma-Delta modulator uses the mechanical sensitive structure as a 2nd-order mechanical loop integrator,which has the advantages of absolute stability,fewer parameters to be designed,but the signal-to-noise ratio(SNR),noise-shaping capability,dynamic range,etc.are failed to meet the standards of high precision MEMS accelerometer.High-order Sigma-Delta modulator is obtained by cascading high-order electronic integrator with the sensitive structure.High-order Sigma-Delta modulator has ideal noise-shaping performance,higher SNR,wider dynamic range,etc.,but the parameters are complicated to be designed and the stability are not guaranteed.Therefore,it is of practical significance to study the parameter design method and improve the stability for the high-order Sigma-Delta modulator.In this paper,a fractional-order electronic loop integrator is used to replace the integer-order electronic loop integrator to construct a fractional-order Sigma-Delta modulator based on traditional Sigma-Delta modulator.The fractional-order loop integrator contains several phase lead and phase lag parts,and through changing the orders and coefficients of the fractional-order loop integrator to improve stability in the placement of the fractional-type poles and zeros.Thus,the fractional-order loop integrator extends the stability domain of the entire closed-loop Sigma-Delta modulator system.With respect to the proposed fractional-order Sigma-Delta modulato,chaotic particle swarm optimization(CPSO)algorithm is used to optimize the system parameters in a wider fractional stability domain,which simplifies the design complexity of high-order Sigma-Delta modulator,and also creates more room for further improving system performance.The research content of this paper mainly focuses on the structural design,parameter optimization,performance improvement and hardware implementation of the proposed fractional-order Sigma-Delta modulator.At the same time,the noise-shaping ability,SNR,system stability of the optimized fractional Sigma-Delta modulator is analyzed,respectively.The specific work of this paper can be summarized as:Firstly,the overall structure and the simulation model of the proposed fractional-order Sigma-Delta modulator are constructed,respectively,and the parameter selection mechanism for the proposed system is proposed.The simulation model of the proposed fractional-order Sigma-Delta modulator system is built on Matlab/Simulink platform.We consider the high SNR as the objective function of CPSO algorithm,and the overall system parameters are the position vector of CPSO algorithm.Then the parameter optimization results are brought back to the system model to do the analysis of system SNR,stability,and noise floor,etc.The advantages of the proposed system in terms of stability,noise floor and SNR are verified by comparing with the traditional integer-order Sigma-Delta modulator.The fractional-order zero-phase integrator is applied to improve the noise-shaping ability without causing the phase lag based on the proposed fractional-order Sigma-Delta modulator.The nonlinearity problem of the 1-bit quantizer of Sigma-Delta modulator is analyzed by the sliding mode variable structure control theory,which verify that the peoposed fractional-order Sigma-Delta modulator shows the robustness to system nonlinearity.Secondly,this paper proposes a novel disturbance observer to estimate the system noises and eliminate the effect of these noises for Sigma-Delta modulator to improve the ant-disturbance ability and robust stability for MEMS accelerometer.In this paper,the proposed disturbance observer is introduced in which a bode ideal cut-off(BICO)filter is used for the traditional Q-filter,and the order of BICO filter is extended from the integer-order domain to the real-number domain to further improve immunity performance,and the order of BICO filter of the proposed fractional-order Sigma-Delta modulator is optimized by CPSO algorithm.Finally,the parameters and structure of the proposed fractional-order Sigma-Delta modulator are further optimized.The numerical implementation algorithm of the fractional integrator is designed.The design and implementation of the fractional-order integrator by FPGA is carried out based on the fixed-point coefficiencies and optimized system structure.The proposed fractional-order Sigma-Delta modulator system is implemented by hardware,where integrates an ADC module,a fractional-order loop integrator module,a 1-bit comparator,and a synchronous clock generation unit on a FPGA chip,then a MEMS sensing element chip and an analog-digital hybrid ASIC are systematically integrated on the printed circuit board(PCB)to jointly debug.Finally,a test verification platform for the fractional-order Sigma-Delta modulator system is established.Installing the designed PCB on the isolation platform of the ultra-quiet room for the self noise floor test.The digital card is used to collect the 1-bitstream from the PCB,and the noise power spectrum analysis is performed on the MATLAB software to verify the performance of the proposed fractional-order Sigma-Delta modulator.This study can promote the development of high performance of MEMS accelerometer,and also provide a scientific and technical supports for the application of fractional-order theory to practical system.