Order Continuous-time Research Articles

A Review on Higher Order Continuous-Time Sigma-Delta Modulators for ADC Design

Abstract—In this paper, the concept of adaptive filtering has been proposed. It has been shown that signals often undergo variation in the noise environment encountered. Hence it becomes mandatory to design filters based on noise shaping and adaptive noise cancellation. Such filters are called adaptive filters and are used for applications requiring real time noise cancellation such as speech processing, live video broadcasting etc. The paper presents the structure of Sigma Delta or MASH ADCs which employ recursive encoding. SDM ADCs are also used to convert high bit-count, low- frequency digital signals into lower bit-count, higher-frequency digital signals as part of the process to convert digital signals into analog as part of a digital-to-analog converter (DAC). The paper focuses on the various approaches used thus far for the purpose, citing the pros and cons of each approach. Keywords— Adaptive Filter Design, Noise Filtering, Sigma Delta Modulator (SDM), MASH, Signal to Noise Ratio.

A first order continuous timeVARwith random coefficients

This article considers a first order continuous time vector autoregression with random coefficients. We discuss some difficulties that arise when the exact discrete analogue is used for estimating the continuous time parameters and provide an estimation method based on an approximate discrete model. Some expressions for the estimator of the drift parameter matrix, for its approximated bias and for the covariance matrix of the parameter estimates are derived. The finite sample performance of the proposed method is studied by a Monte Carlo experiment. We also illustrate the advantages of our model in an application on the expectations theory of the term structure of interest rates. Results show that the performance of the proposed methodology is good, and allowing for time variation on coefficients results in large reductions in the root mean square error of the parameter estimates.

Complete design approach of a 3rd order continuous-time sigma-delta ADC with FIR feedback and low-noise low-distortion op-amp achieving 101.8 dB SNDR and −110dB THD

This paper presents a step-by-step design approach of a 3rd order continuous-time sigma-delta modulator with a 4-tap FIR feedback DAC achieving 107 dB DR (A-weighted), −110 dB THD and an SNDR of 101.8 dB. The THD is achieved through a fully differential feed-forward compensated op-amp that maintains high linearity with the aid of a class AB output stage and an optimum bias current through a CMFB loop. The modulator consumes 322.5uW of power while taking an area of 0.2925 mm2.

Design and Implementation of a Second Order Continuous-Time ΣΔ Modulator for ECG Signal Acquisition

The recent developments in biosignal acquisition devices for continuous supervision of cardiovascular signs of high-risk patients require a high-precision and low-power Analog Front End (AFE) circuit. The proposed design adopts Continuous-Time (CT) Sigma-Delta Modulator (ΣΔM) architecture to achieve high resolution and SIgnal-to-Noise And Distortion ratio (SINAD) requirements. The proposed modulator is a second-order CT-ΣΔM with Cascade of Integrators Feed-Forward (CIFF) architecture that consists of a CT loop filter, a single-bit quantizer, and a Digital-to-Analog Converter (DAC). The use of single-bit quantization in the design reduces circuit complexity and power consumption. To use the designed ΣΔM for measuring ECG signals, a bandwidth (Bw) of 150 Hz is considered with a sampling frequency (fs) of 153.6kHz to achieve an oversampling ratio of 512. The design is simulated in a standard Cadence Virtuoso EDA tool at 180nm CMOS technology, operating at 1.8V supply voltage at the block level. The simulation results for the designed modulator show that SINAD is 104.5dB, the Effective Number Of Bits (ENOB) is 17.06bits, with power consumption of 24µW, and achieves Schreier’s Figure-Of-Merit (FOM) equal to 172.45dB.

An arbitrary-order continuous sliding mode control technique for nonlinear PWR-type nuclear power plants

This paper presents an arbitrary order continuous-time sliding mode controller based on the super-twisting algorithm for a nonlinear pressurized water nuclear power plant. A proportional-derivative terminal sliding surface is designed to achieve the finite time convergence and to enhanced the tracking performance. The proposed controller is chattering free, which is always preferable in most of the practical applications and, it is robust against Lipschitz in time uncertainties. The implementation of the proposed controller requires only the information about the system output, and thus, it is most suitable for large scale complex systems, such as nuclear power plants. Superiority of the proposed controller over some conventional control techniques in the presence of uncertainties is shown with the help of simulation results in the MATLAB/Simulink environment.

A Single-Opamp Third Order CT ΔΣ Modulator With SAB-ELD-Merged Integrator and Three-Stage Hybrid Compensation Opamp

This paper proposes a 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sup> order continuous-time delta-sigma modulator (CTDSM) with a single amplifier biquad (SAB) and excess loop delay (ELD) merged integrator. The integrator enables a 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order noise-shaping together with ELD compensation with just a single Opamp and feedback DAC. A three-stage Opamp with a hybrid frequency-compensation scheme is presented, which achieves high gain and large unity-gain bandwidth (UGBW) with low power. The circuit secures an extra order noise-shaping through a passive noise-shaping SAR (NS-SAR) quantizer (QTZ) while further incorporating a preliminary sampling and quantization (PSQ) technique, the 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> order NS QTZ can run at 1.5 GHz with 6b. The design, implemented in 28 nm, obtains 74.4 dB SNDR with 50 MHz bandwidth while consuming 10.4 mW from 1.5 V and 1 V power supplies. The prototype attains a dynamic range of 80.6 dB with a Schreier FOM of 171.2 dB. With the presented integrator and Opamp, the loop filter only consumes 14 % of the total DSM power consumption.

64 dB Dynamic-Range 810 μW 90 MHz Fully-Differential Flipped-Source-Follower Analog Filter in 28nm-CMOS

This brief presents a 4 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> -order continuous-time analog filter based on Flipped-Source-Follower stage. Source-Follower (SF) filters typically adopt pseudo-differential topology (critical for matching and bulk/substrate noise rejection) and are realized in not recent CMOS processes (130nm or 180nm) due to the intrinsic voltage headroom required by SF operation. The proposed device solves the above limitations by proposing a fully-differential circuital topology, which improves by 13 dB the power supply rejection with respect to pseudo differential approach, and by operating in 28nm-CMOS process, thanks to a proper level-shifter transistor, which enables optimum biasing point and enhances filter dynamic range. The prototype is composed by the cascade of two biquadratic cells. It features 90 MHz -3 dB bandwidth, and consumes 816 μW power (408 μW per cell) from a 1V supply. Dynamic-Range is 64 dB with 140 μV <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> RMS</sub> output noise, and at 0.32 V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0-PEAK</sub> differential output voltage swing. Figure-of-Merit is 156 dBJ $^{-1}$ .

On the similarity to nonnegative and Metzler Hessenberg forms

Abstract We address the issue of establishing standard forms for nonnegative and Metzler matrices by considering their similarity to nonnegative and Metzler Hessenberg matrices. It is shown that for dimensions n 3, there always exists a subset of nonnegative matrices that are not similar to a nonnegative Hessenberg form, which in case of n = 3 also provides a complete characterization of all such matrices. For Metzler matrices, we further establish that they are similar to Metzler Hessenberg matrices if n 4. In particular, this provides the first standard form for controllable third order continuous-time positive systems via a positive controller-Hessenberg form. Finally, we present an example which illustrates why this result is not easily transferred to discrete-time positive systems. While many of our supplementary results are proven in general, it remains an open question if Metzler matrices of dimensions n 5 remain similar to Metzler Hessenberg matrices.

Second order discrete time-varying and time-invariant linear continuous systems and Kalman type conditions

&lt;p style='text-indent:20px;'&gt;The paper deals with the controllability and observability of second order discrete linear time varying and linear time-invariant continuous systems in matrix form. To this case, we generalize the classical conditions for linear systems of the first order, without reducing them to systems of the first order. Within the framework of Kalman-type criteria, we investigate these concepts for second-order linear systems with discrete / continuous time; we define the initial values and input functions uniquely if and only if the observability and controllability matrices have full rank, respectively. Also a conceptual partner of controllability, that is, reachability of second order discrete time-varying systems is formulated and a necessary and sufficient condition for complete reachability is derived. Also the transfer function of the second order continuous-time linear state-space system is constructed. We have given numerical examples to illustrate the feasibility and effectiveness of the theoretical results obtained.&lt;/p&gt;

Index reduction for second order singular systems of difference equations

This paper is devoted to the analysis of linear second order discrete-time descriptor systems (or singular difference equations (SiDEs) with control). Following the algebraic approach proposed by Kunkel and Mehrmann for pencils of matrix valued functions, first we present a theoretical framework based on a procedure of reduction to analyze solvability of initial value problems for SiDEs, which is followed by the analysis of descriptor systems. We also describe methods to analyze structural properties related to the solvability analysis of these systems. Namely, two numerical algorithms for reduction to the so-called strangeness-free forms are presented. Two associated index notions are also introduced and discussed. This work extends and complements some recent results for high order continuous-time descriptor systems and first order discrete-time descriptor systems.

Optimal control of higher order differential inclusions with functional constraints

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

Techniques for Sigma Delta ADC Design using CMOS Technology for CODEC

This paper presents the careful study of sigma-delta analog to digital convertor. The operations, characterizing parameters and totally different structures projected square measure conferred in basic type. the varied techniques and strategies for the design of a CMOS 3rd order Continuous Time (CT) Sigma Delta (SD) Modulator, where in to enhance the gain of the loop filter and to avoid the loading effect of the succeeding stage, facile differential pairs square measure enclosed between the passive RC integrators. then the ADC are optimized victimization Genetic Algorithms so as to realize the nice exchange between RC variations and loop stability.This makes SD-ADC more advantageous compared to conventional converters, that makes possible to use this SD-ADC in bio-medical applications

Numerical analysis of Volterra integro-differential equations for viscoelastic rods and membranes

We consider the initial boundary value problems for a homogeneous Volterra integro-differential equations for viscoelastic rods and membranes in a bounded smooth domain Ω. The memory kernel of the equation is made up in a complicated way from the (distinct) moduli of stress relaxation for compression and shear, which is challenging to approximate. The literature reported on the numerical solution of this model is extremely sparse. In this paper, we will study the second order continuous time Galerkin approximation for its space discretization and propose a fully discrete scheme employing the Crank–Nicolson method for the time discretization. Then we derive the uniform long time error estimates in the norm Lt1(0,∞;Lx2) for the finite element solutions. Some numerical results are presented to illustrate our theoretical error bounds.

Stability analysis of fractional Quaternion-Valued Leaky Integrator Echo State Neural Networks with multiple time-varying delays

This paper studies the stability problem of fractional order continuous-time Quaternion-Valued Leaky Integrator Echo State Neural Networks (NN) with multiple time-varying delays. The NN is decomposed into four real-valued systems without considering the non-commutativity of quaternion multiplication resulting in Hamilton rules. Then, the delay-independent stability analysis of the NN equilibrium point with Lipschitz continuous activation function is derived in the real space. The existence and uniqueness of the equilibrium point are also given using the contraction map in the real space. Simulations results show the feasibility of the method.

An explicit numerical scheme for solving fractional order compartment models from the master equations of a stochastic process

We derive the generalized master equations for a stochastic process representing populations entering, leaving, or waiting in compartments at discrete times. This discrete time compartment model limits to a fractional order continuous time compartment model for a particular choice of waiting time distribution and the appropriate limiting process. We demonstrate that the discrete time master equations can be used to provide an explicit numerical method that can be employed for solving the fractional order compartment equations. The advantage of this approach is that the numerical scheme has a physical interpretation, it is stable, and it is easy to implement. The method can be applied to a wide class of fractional order compartment model equations that arise in a broad range of applications.

A Wireless Fiber Photometry System Based on a High-Precision CMOS Biosensor With Embedded Continuous-Time Modulation.

Fluorescence biophotometry measurements require wide dynamic range (DR) and high-sensitivity laboratory apparatus. Indeed, it is often very challenging to accurately resolve the small fluorescence variations in presence of noise and high-background tissue autofluorescence. There is a great need for smaller detectors combining high linearity, high sensitivity, and high-energy efficiency. This paper presents a new biophotometry sensor merging two individual building blocks, namely a low-noise sensing front-end and a order continuous-time modulator (CTSDM), into a single module for enabling high-sensitivity and high energy-efficiency photo-sensing. In particular, a differential CMOS photodetector associated with a differential capacitive transimpedance amplifier-based sensing front-end is merged with an incremental order 1-bit CTSDM to achieve a large DR, low hardware complexity, and high-energy efficiency. The sensor leverages a hardware sharing strategy to simplify the implementation and reduce power consumption. The proposed CMOS biosensor is integrated within a miniature wireless head mountable prototype for enabling biophotometry with a single implantable fiber in the brain of live mice. The proposed biophotometry sensor is implemented in a 0.18- CMOS technology, consuming from a 1.8- supply voltage, while achieving a peak dynamic range of over a 50- input bandwidth, a sensitivity of 24 mV/nW, and a minimum detectable current of 2.46- at a 20- sampling rate.

A meta-heuristic cuckoo search and eigen permutation approach for model order reduction

In this paper, a new model order reduction technique is presented by combining the benefits of the meta-heuristic cuckoo search optimization and Eigen permutation methods for order reduction of higher order continuous-time systems. In the proposed approach, the numerator and the denominator polynomials of reduced order model are determined by Cuckoo search and Eigen permutation approaches, respectively. The proposed approach preserves the stability of the original system into the lower order model as the Eigen permutation retains the dominant pole with simultaneous cluster formation of the remaining real and complex poles. The effectiveness of the proposed method is validated by single-input single-output and multiple-inputs multiple-outputs numerical examples.

Low Power Continuous-Time Delta-Sigma Modulators Using the Three Stage OTA and Dynamic Comparator

A second-order sigma delta modulator that uses an operational transconductance amplifier as integrator and latch comparator as quantizer. The proposed technique where a low power high gain OTA is used as integrator and another circuit called dynamic latch comparator with two tail transistors and two controlling switches are used to achieve high speed, low power and high resolution in second order delta sigma modulator. It enhances the power efficiency and compactness of the modulator by implementing these blocks as sub modules. A second order modulator has been designed to justify the effectiveness of the proposed design. Technology 180nm CMOS process is used to implement complete second order continuous time sigma delta modulator. We introduce the sub threshold three stage OTA, which is a way of achieving low distortion operation with input referred noise at 1 KHz is equal to the 2.2647pV/ and with low power consumption of 296.72nW. A high-speed, low-voltage and a low-power Double-Tail dynamic comparator is also proposed. The proposed structure is contrasted with past dynamic comparators. In this paper, the comparator’s delay will be investigated and systematic analysis are inferred. a novel comparator using two tail transistor is proposed, here circuitry of a customized comparator having two tail is changed for low power dissipation and also it operates fast at little supply voltages. By maintaining the outline and by including couple of transistors, during the regeneration strengthening of positive feedback can be maintained, this results in amazingly diminished delay parameter. It is investigated that in proposed design structure of comparator using two tail transistors, power consumption is reduced and delay time is also diminished to a great extent. The proposed comparator is having maximum clock frequency that is possibly expanded up to 1GHz at voltages of 1 V whereas it is dissipating 10.99 µW of power, individually. By using sub threshold three stage OTA and dynamic standard two tail latch comparator, designed second order sigma delta ADC will consume 29.95µW of power.

Moment method estimation of first-order continuous-time bilinear processes

ABSTRACTIn the present paper, we propose an estimation method of the first order continuous-time bilinear (COBL) process based on Euler-Maruyama discretization of the Itô solution asociated with the stochastic differerential equation (SDE) defining the process, and we suggest a standard moment method (MM) estimates of the unknown parameters involving in COBL process. So, some relationships linking the parameters and the theoretical moments of the process and its quadratic version are given. These relationships we allow to construct two algorithms to estimate the parameters based on MM. Using the fact that the incremented processes are strongly mixing with exponential rate whenever certain conditions are fulfilled, we show that the resulting estimators are strongly consistent and asymptotically normal. The theory can be applied to the COGARCH(1, 1), Gaussian Ornstein-Uhlenbeck (OU) models and among other specifications. Finite sample properties are also considered throught Monte-Carlo experimencts. In end, this algorithm is then used to model the exchanges rate of the Algerian Dinar against the US-dollar and against the single European currency.

Optimal design of fractional order low pass Butterworth filter with accurate magnitude response

The design of (1+α) order, 0<α<1, low pass Butterworth filter approximated in terms of an integer order continuous-time transfer function using a nature-inspired optimization technique called Gravitational Search Algorithm (GSA) is presented in this paper. While approximations of the non-integer order Laplacian operator sα in terms of second order rational function using the continued fraction expansion method for the design of fractional order low pass Butterworth filters (FOLBFs) is recently reported in literature, however, such a design technique is non-optimal. In this work, the metaheuristic global search process of GSA efficiently explores and intensely exploits the nonlinear, non-uniform, multidimensional, and multimodal FOLBF design problem error landscape. At the end of the iterative search routine of GSA, the optimal values of the coefficients in terms of the third order rational approximations are achieved which accurately approximate the magnitude response of the ideal FOLBF. The proposed GSA based FOLBFs consistently achieve the best solution quality with the fastest convergence rate as compared with the designs based on Real coded Genetic Algorithm (RGA) and Particle Swarm Optimization (PSO). Comparison with the recent literature also demonstrates the superiority of the proposed designs. SPICE simulations justify the design feasibility of the proposed FOLBF models.