Вплив параметрів інтеграторів на нелінійність функції перетворення сигма-дельта модулятора високого порядку

There is developed the simulation model of single-bit high order sigma- delta modulator. Also using this model there are investigated influence of integrator’s nonlinearity on modulator’s nonlinearity for second and third order sigma-delta modulators. There is identified integrator’s decreasing coefficient by sigma-delta modulator of second and third order

Using a Second Order Sigma-Delta Control to Improve the Performance of Metal-Oxide Gas Sensors

Controls of surface potential have been proposed to accelerate the time response of MOX gas sensors. These controls use temperature modulations and a feedback loop based on first-order sigma-delta modulators to keep constant the surface potential. Changes in the surrounding gases, therefore, must be compensated by average temperature produced by the control loop, which is the new output signal. The purpose of this paper is to present a second order sigma-delta control of the surface potential for gas sensors. With this new control strategy, it is possible to obtain a second order zero of the quantization noise in the output signal. This provides a less noisy control of the surface potential, while at the same time some undesired effects of first order modulators, such as the presence of plateaus, are avoided. Experiments proving these performance improvements are presented using a gas sensor made of tungsten oxide nanowires. Plateau avoidance and second order noise shaping is shown with ethanol measurements.Postprint (author's final draft

Stability of sinusoidal responses of marginally stable bandpass sigma delta modulators

In this paper, we analyze the stability of the sinusoidal responses of second order interpolative marginally stable bandpass sigma delta modulators (SDMs) with the sum of the numerator and denominator polynomials equal to one and explore new results on the more general second order interpolative marginally stable bandpass SDMs. These results can be further extended to the high order interpolative marginally stable bandpass SDMs

Force feedback linearization for higher-order electromechanical sigma-delta modulators.

Abstract A higher-order electromechanical sigma–delta modulator can greatly improve the signal-to-noise ratio compared with a second-order loop that only uses the sensing element as a loop filter. However, the electrostatic force feedback on the proof mass is inherently nonlinear, which will produce harmonics in the output spectrum and limits the total signal-to-noise and distortion ratio. High performance inertial sensors, which use sigma–delta modulators as a closed-loop control system, have strict requirements on the output signal distortion. In this paper, nonlinear effects from the force feedback and pick-off circuits are analysed and a strategy for force feedback linearization is put forward which can considerably improve the signal-to-noise and distortion ratio. A PCB prototype of a fifth-order electromechanical modulator with a bulk micromachined accelerometer was used to demonstrate the concept

Design and implementation of generalized topologies of time-interleaved variable bandpass Σ−Δ modulators

In this thesis, novel analog-to-digital and digital-to-analog generalized time-interleaved variable bandpass sigma-delta modulators are designed, analysed, evaluated and implemented that are suitable for high performance data conversion for a broad-spectrum of applications. These generalized time-interleaved variable bandpass sigma-delta modulators can perform noise-shaping for any centre frequency from DC to Nyquist. The proposed topologies are well-suited for Butterworth, Chebyshev, inverse-Chebyshev and elliptical filters, where designers have the flexibility of specifying the centre frequency, bandwidth as well as the passband and stopband attenuation parameters. The application of the time-interleaving approach, in combination with these bandpass loop-filters, not only overcomes the limitations that are associated with conventional and mid-band resonator-based bandpass sigma-delta modulators, but also offers an elegant means to increase the conversion bandwidth, thereby relaxing the need to use faster or higher-order sigma-delta modulators. A step-by-step design technique has been developed for the design of time-interleaved variable bandpass sigma-delta modulators. Using this technique, an assortment of lower- and higher-order single- and multi-path generalized A/D variable bandpass sigma-delta modulators were designed, evaluated and compared in terms of their signal-to-noise ratios, hardware complexity, stability, tonality and sensitivity for ideal and non-ideal topologies. Extensive behavioural-level simulations verified that one of the proposed topologies not only used fewer coefficients but also exhibited greater robustness to non-idealties. Furthermore, second-, fourth- and sixth-order single- and multi-path digital variable bandpass digital sigma-delta modulators are designed using this technique. The mathematical modelling and evaluation of tones caused by the finite wordlengths of these digital multi-path sigmadelta modulators, when excited by sinusoidal input signals, are also derived from first principles and verified using simulation and experimental results. The fourth-order digital variable-band sigma-delta modulator topologies are implemented in VHDL and synthesized on Xilinx® SpartanTM-3 Development Kit using fixed-point arithmetic. Circuit outputs were taken via RS232 connection provided on the FPGA board and evaluated using MATLAB routines developed by the author. These routines included the decimation process as well. The experiments undertaken by the author further validated the design methodology presented in the work. In addition, a novel tunable and reconfigurable second-order variable bandpass sigma-delta modulator has been designed and evaluated at the behavioural-level. This topology offers a flexible set of choices for designers and can operate either in single- or dual-mode enabling multi-band implementations on a single digital variable bandpass sigma-delta modulator. This work is also supported by a novel user-friendly design and evaluation tool that has been developed in MATLAB/Simulink that can speed-up the design, evaluation and comparison of analog and digital single-stage and time-interleaved variable bandpass sigma-delta modulators. This tool enables the user to specify the conversion type, topology, loop-filter type, path number and oversampling ratio

Global stability, limit cycles and chaotic behaviors of second order interpolative sigma delta modulators

It is well known that second order lowpass interpolative sigma delta modulators (SDMs) may suffer from instability and limit cycle problems when the magnitudes of the input signals are at large and at intermediate levels, respectively. In order to solve these problems, we propose to replace the second order lowpass interpolative SDMs to a specific class of second order bandpass interpolative SDMs with the natural frequencies of the loop filters very close to zero. The global stability property of this class of second order bandpass interpolative SDMs is characterized and some interesting phenomena are discussed. Besides, conditions for the occurrence of limit cycle and fractal behaviors are also derived, so that these unwanted behaviors will not happen or can be avoided. Moreover, it is found that these bandpass SDMs may exhibit irregular and conical-like chaotic patterns on the phase plane. By utilizing these chaotic behaviors, these bandpass SDMs can achieve higher signal-to-noise ratio (SNR) and tonal suppression than those of the original lowpass SDMs

Limit cycles in embedded high-order, lowpass sigma-delta modulators with distinct NTF zeros

In a related work by the authors, high-order sigma-delta (/spl Sigma//spl Delta/) modulators with distinct noise transfer function (NTF) zeros are decomposed into second-order and first-order subsystems, whose state-trajectories are then investigated by continuous-time embedding. This paper, based on the properties of these subsystems, furthers the study by introducing a scalable numerical method to locate the fixed-points on the generalized Poincare sections. A closed-form tangent linear manifold matrix for an arbitrary order modulator is derived, enabling the stability determination of the fixed-points and the accompanying limit cycles. Numerical examples show that the estimated DC input bound based on the boundary transition flow assumption cannot be relied on for modulators of order greater than fourlpublished_or_final_versio

Difference between irregular chaotic patterns of second-order double-loop ΣΔ modulators and second-order interpolative bandpass ΣΔ modulators

In this paper, we find that, by computing the difference between two consecutive state vectors of second-order double-loop sigma-delta modulators (SDMs) and plotting one component of the subtracted vectors against the other component, irregular chaotic patterns will become two vertical lines. By multiplying a matrix on the subtracted vectors, it can be further transformed to two fixed points. However, second-order interpolative bandpass SDMs still exhibit chaotic behaviors after applying the same transformations. Moreover, it is found that the Lyapunov exponent of state vectors of second-order double-loop SDMs is higher than that of second-order interpolative bandpass SDMs, whereas the Lyapunov exponent of transformed vectors becomes negative infinity for second-order double-loop SDMs and increases for second-order interpolative bandpass SDMs. Hence, by examining the occurrence of chaotic behaviors of the transformed vectors of these two SDMs, these two SDMs can be distinguished from their state vectors and their transformed vectors without solving the state equations and knowing the information of input signals

Multi-bit sigma-delta modulators with enhanced dynamic-range using non-linear DAC for hearing aids

15th IEEE International Conference on Electronics, Circuits and Systems, MaltaThis paper presents the possibility of employing nonlinear low-resolution DACs in the feedback paths of multi-bit second-order Sigma-Delta modulators. The proposed technique is particularly attractive in applications such as hearing aids, requiring a very large dynamic range and medium signal-tonoise-plus-distortion-ratio. As demonstrated through simulated results in which noise and mismatch effects are included, for the same over-sampling ratio, improvements in the order of 6-to-9 dB in the dynamic range can be achieved when comparing with the same topology employing linear-DACs