A 5MS/s 12-Bit Successive Approximation Analog-to-Digital Converter

With the continuous development of science and technology, digital signal processing is more and more widely used in various fields. Among them, the analog-to-digital converter (ADC) is one of the key components to convert analog signals to digital signals. As a common type of ADC, 12-bit sequential approximation analog-to-digital converter (SAR ADC) has attracted extensive attention for its performance and application. This paper aims to conduct in-depth research and analysis of 12-bit SAR ADC to meet the growing demands of digital signal processing. This article designs a 12-bit, successive approximation analog-to-digital converter (SAR ADC) with a sampling rate of 5 MS/s. The overall circuit adopts a fully differential structure, with key modules including DAC capacitor array, comparator, and control logic. According to the DAC circuit in this paper, a fully differential capacitor DAC array structure is proposed to reduce the area of layout DAC. The comparator uses a digital dynamic comparator to improve the ADC conversion speed. The chip is designed based on the SMIC180 nm CMOS process. The simulation results show that when the sampling rate is 5 MS/s, the effective bit of SAR ADC is 11.92 bit, the SNR is 74.62 dB, and the SFDR is 89.24 dB.

Numerical Study of the Vibrations of Beams with Variable Stiffness under Impulsive or Harmonic Loading

The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation method is a technique for numerical integration of partial differential equations involving both the space and time, with well-known initial conditions on time and boundary conditions on the space. This technique, although having been applied to beams with constant stiffness, is new for the case of beams with variable stiffness, and it aims to use a quadratic parabola (in time) to approximate the solutions of the differential equations of dynamics. The spatial part is studied using the successive approximation method of the partial differential equations obtained, in order to transform them into a system of time-dependent ordinary differential equations. Thus, the integration algorithm using this technique is established and applied to examples of beams with variable stiffness, under variable loading, and with the different cases of supports chosen in the literature. We have thus calculated the cases of beams with constant or variable rigidity with articulated or embedded supports, subjected to the action of an instantaneous impulse and harmonic loads distributed over its entire length. In order to justify the robustness of the successive approximation method considered in this work, an example of an articulated beam with constant stiffness subjected to a distributed harmonic load was calculated analytically, and the results obtained compared to those found numerically for various steps (spatial h and temporal τ ¯ ) of calculus, and the difference between the values obtained by the two methods was small. For example for ( h=1/8 , τ ¯ =1/ 64 ), the difference between these values is 17%.

Capacitor self-calibration technique used in time-interleaved successive approximation ADC

A capacitor self-calibration circuit used in a successive approximation analog-to-digital converter （SA-ADC） is presented. This capacitor self-calibration circuit can calibrate erroneous data and work with the ADC by adding an additional clock period. This circuit is used in a 10 bit 32 Msample/s time-interleaved SA- ADC. The chip is implemented with Chart 0. 25 μm 2. 5 V process and totally occupies an area of 1.4 mm× 1.3 mm. After calibration, the simulated signal-to-noise ratio （SNR） is 59. 586 1 dB and the spurious-free dynamic range （SFDR） is 70. 246 dB at 32 MHz. The measured signal-to-noise and distortion ratio （SINAD） is 44. 82 dB and the SFDR is 63. 760 4 dB when the ADC samples a 5.8 MHz sinusoid wave.

Mismatch Calibration Techniques in Successive Approximation Analog-to-Digital Converters

Comparator offset cancellation and capacitor self-calibration techniques used in a successive approximation analog-to-digital converter （SA-ADC） are described. The calibration circuit works in parallel with the SAADC by adding additional calibration clock cycles to pursue high accuracy and low power consumption, and the calibrated resolution can be up to 14bit. This circuit is used in a 10bit 3Msps successive approximation ADC. This chip is realized with an SMIC 0. 18μm 1.8V process and occupies 0.25mm^2 . It consumes 3. 1mW when operating at 1.8MHz. The measured SINAD is 55. 9068dB, SFDR is 64. 5767dB, and THD is - 74. 8889dB when sampling a 320kHz sine wave.

The Successive Approximation Broyden-like Algorithm for Nonlinear Complementarity Problems

In this paper, we present a new form of successive approximation Broyden-like algorithm for nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we get the global convergence on the algorithms. Some numerical results are also reported.

An Energy-Efficient 12b 2.56 MS/s SAR ADC Using Successive Scaling of Reference Voltages

This paper presents an energy efficient architecture for successive approximation register(SAR)analog to digital converter(ADC).SAR ADCs with a capacitor array structure have been widely used because of its simple architecture and relatively high speed.However,conventional SAR ADCs consume relatively high energy due to the large number of capacitors used in the capacitor array and their sizes scaled up along with the number of bits.The proposed architecture reduces the energy consumption as well as the capacitor size by employing a new array architecture that scales down the reference voltages instead of scaling up the capacitor sizes.The proposed 12-bit SAR ADC is implemented in Complementary Metal Oxide Semiconductor(CMOS)0.13 um library using Cadence Virtuoso design tool.Simulation results and mathematical model demonstrate the overall energy savings of up to 97.3%compared with conventional SAR ADC,67%compared with the SAR ADC with split capacitor,and 35%compared with the resistor and capacitor(R&C)Hybrid SAR ADC.The ADC achieves an effective number of bits(ENOB)of 11.27 bits and consumes 61.7 uW at sampling rate of 2.56 MS/s,offering an energy consumption of 9.8 fJ per conversion step.The proposed SAR ADC offers 95.5%reduction in chip core area compared to conventional architecture,while occupying an active area of 0.088 mm2.

User scheduling and power allocation for downlink multi-cell multi-carrier NOMA systems

In Non-Orthogonal Multiple Access(NOMA),the best way to fully exploit the benefits of the system is the efficient resource allocation.For the NOMA power domain,the allocation of power and spectrum require solving the mixed-integer nonlinear programming NP-hard problem.In this paper,we investigate user scheduling and power allocation in Multi-Cell Multi-Carrier NOMA(MCMC-NOMA)networks.To achieve that,we consider Weighted Sum Rate Maximization(WSRM)and Weighted Sum Energy Efficiency Maximization(WSEEM)problems.First,we tackle the problem of user scheduling for fixed power using Fractional Programming(FP),the Lagrange dual method,and the decomposition method.Then,we consider Successive Pseudo-Convex Approximation(SPCA)to deal with the WSRM problem.Finally,for the WSEEM problem,SPCA is utilized to convert the problem into separable scalar problems,which can be parallelly solved.Thus,the Dinkelbach algorithm and constraints relaxation are used to characterize the closed-form solution for power allocation.Extensive simulations have been implemented to show the efficiency of the proposed framework and its superiority over other existing schemes.

Coalitional game based resource allocation in D2D-enabled V2V communication

The joint resource block(RB)allocation and power optimization problem is studied to maximize the sum-rate of the vehicle-to-vehicle(V2V)links in the device-to-device(D2D)-enabled V2V communication system,where one feasible cellular user(FCU)can share its RB with multiple V2V pairs.The problem is first formulated as a nonconvex mixed-integer nonlinear programming(MINLP)problem with constraint of the maximum interference power in the FCU links.Using the game theory,two coalition formation algorithms are proposed to accomplish V2V link partitioning and FCU selection,where the transferable utility functions are introduced to minimize the interference among the V2V links and the FCU links for the optimal RB allocation.The successive convex approximation(SCA)is used to transform the original problem into a convex one and the Lagrangian dual method is further applied to obtain the optimal transmit power of the V2V links.Finally,numerical results demonstrate the efficiency of the proposed resource allocation algorithm in terms of the system sum-rate.

Non-Convex Optimization of Resource Allocation in Fog Computing Using Successive Approximation

Fog computing can deliver low delay and advanced IT services to end users with substantially reduced energy consumption.Nevertheless,with soaring demands for resource service and the limited capability of fog nodes,how to allocate and manage fog computing resources properly and stably has become the bottleneck.Therefore,the paper investigates the utility optimization-based resource allocation problem between fog nodes and end users in fog computing.The authors first introduce four types of utility functions due to the diverse tasks executed by end users and build the resource allocation model aiming at utility maximization.Then,for only the elastic tasks,the convex optimization method is applied to obtain the optimal results;for the elastic and inelastic tasks,with the assistance of Jensen’s inequality,the primal non-convex model is approximated to a sequence of equivalent convex optimization problems using successive approximation method.Moreover,a two-layer algorithm is proposed that globally converges to an optimal solution of the original problem.Finally,numerical simulation results demonstrate its superior performance and effectiveness.Comparing with other works,the authors emphasize the analysis for non-convex optimization problems and the diversity of tasks in fog computing resource allocation.

SOLITARY WAVES IN STRATIFIED FLUIDS AND THEIR INTERACTION

A systematic procedure is proposed for obtaining solutions for soli- tary waves in stratified fluids. The stratification of the fluid is assumed to be expo- nential or linear. Its comparison with existing results for an exponentially stratified fluid shows agreement, and it is found that for the odd series of solutions the direc- tion of displacement of the streamlines from their asymptotic levels is reversed when the stratification is changed from exponential to linear. Finally the interaction of solitary waves is considered, and the Korteweg-de Vries equation and the Boussinesq equation are derived. Thus the known solutions of these equations can be rehed upon to provide the answers to the interaction problem.

On The Cauchy Problem For Some Parabolic Fractional Partial Differential Equations With Time Delays

The Cauchy problem for some parabolic fractional partial differential equation of higher orders and with time delays is considered. The existence and unique solution of this problem is studied. Some smoothness properties with respect to the parameters of these delay fractional differential equations are considered.

ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR GENERALIZED BURGERS EQUATION

This paper is concerned with the stability of the rarefaction wave for the Burgers equationwhere 0 ≤ a < 1/4p (q is determined by (2.2)). Roughly speaking, under the assumption that u_ < u+, the authors prove the existence of the global smooth solution to the Cauchy problem (I), also find the solution u(x, t) to the Cauchy problem (I) satisfying sup |u(x, t) -uR(x/t)| → 0 as t → ∞, where uR(x/t) is the rarefaction wave of the non-viscous Burgersequation ut + f(u)x = 0 with Riemann initial data u(x, 0) =

Joint Task Scheduling, Resource Allocation, and UAV Trajectory under Clustering for FANETs

This paper establishes a new layered flying ad hoc networks(FANETs) system of mobile edge computing(MEC) supported by multiple UAVs,where the first layer of user UAVs can perform tasks such as area coverage, and the second layer of MEC UAVs are deployed as flying MEC sever for user UAVs with computing-intensive tasks. In this system, we first divide the user UAVs into multiple clusters, and transmit the tasks of the cluster members(CMs) within a cluster to its cluster head(CH). Then, we need to determine whether each CH’ tasks are executed locally or offloaded to one of the MEC UAVs for remote execution(i.e., task scheduling), and how much resources should be allocated to each CH(i.e., resource allocation), as well as the trajectories of all MEC UAVs.We formulate an optimization problem with the aim of minimizing the overall energy consumption of all user UAVs, under the constraints of task completion deadline and computing resource, which is a mixed integer non-convex problem and hard to solve. We propose an iterative algorithm by applying block coordinate descent methods. To be specific, the task scheduling between CH UAVs and MEC UAVs, computing resource allocation, and MEC UAV trajectory are alternately optimized in each iteration. For the joint task scheduling and computing resource allocation subproblem and MEC UAV trajectory subproblem, we employ branch and bound method and continuous convex approximation technique to solve them,respectively. Extensive simulation results validate the superiority of our proposed approach to several benchmarks.

EXISTENCE OF GLOBAL SMOOTH SOLUTION FOR SCALAR CONSERVATION LAWS WITH DEGENERATE VISCOSITY IN 2-DIMENSIONAL SPACE

This article concerns the existence of global smooth solution for scalar conservation laws with degenerate viscosity in 2-dimensional space. The analysis is based on successive approximation and maximum principle.

Energy Efficiency Optimization for D2D Communications Based on SCA and GP Method

In this paper, we propose an energy-efficient power control scheme for device-to-device(D2D) communications underlaying cellular networks, where multiple D2D pairs reuse the same resource blocks allocated to one cellular user. Taking the maximum allowed transmit power and the minimum data rate requirement into consideration, we formulate the energy efficiency maximization problem as a non-concave fractional programming(FP) problem and then develop a two-loop iterative algorithm to solve it. In the outer loop, we adopt Dinkelbach method to equivalently transform the FP problem into a series of parametric subtractive-form problems, and in the inner loop we solve the parametric subtractive problems based on successive convex approximation and geometric programming method to obtain the solutions satisfying the KarushKuhn-Tucker conditions. Simulation results demonstrate the validity and efficiency of the proposed scheme, and illustrate the impact of different parameters on system performance.

Successive MISOCP Algorithm for Islanded Distribution Networks with Soft Open Points

An optimal operation scheme is of great significance in islanded distribution networks to restore critical loads and has recently attracted considerable attention.In this paper,an optimal power flow(OPF)model for islanded distribution networks equipped with soft open points(SOPs)is proposed.Unlike in the grid-connected mode,the adequacy of local power generation in distribution networks is critical for islanded systems.The proposed approach utilizes the power output of local distributed generations(DGs)and the benefits of reactive power compensation provided by SOPs to allow maximum loadability.To exploit the available resources,an optimal secondary droop control strategy is introduced for the islanded distribution networks,thereby minimizing load shedding.The formulated OPF problem is essentially a mixed-integer nonlinear programming(MINLP)model.To guarantee the computation efficiency and accuracy.A successive mixed-integer second-order cone programming(SMISOCP)algorithm is proposed for handling the nonlinear islanded power flow formulations.Two case studies,incorporating a modified IEEE 33-bus system and IEEE 123-bus system,are performed to test the effectiveness of the proposed approach.

An SQP algorithm for mathematical programs with nonlinear complementarity constraints

In this paper, we describe a successive approximation and smooth sequential quadratic programming （SQP） method for mathematical programs with nonlinear complementarity constraints （MPCC）. We introduce a class of smooth programs to approximate the MPCC. Using an 11 penalty function, the line search assures global convergence, while the superlinear convergence rate is shown under the strictly complementary and second-order sufficient conditions. Moreover, we prove that the current iterated point is an exact stationary point of the mathematical programs with equilibrium constraints （MPEC） when the algorithm terminates finitely.

A statistical RCL interconnect delay model taking account of process variations

As the feature size of the CMOS integrated circuit continues to shrink, process variations have become a key factor affecting the interconnect performance. Based on the equivalent Elmore model and the use of the polynomial chaos theory and the Galerkin method, we propose a linear statistical RCL interconnect delay model, taking into account process variations by successive application of the linear approximation method. Based on a variety of nano-CMOS process parameters, HSPICE simulation results show that the maximum error of the proposed model is less than 3.5%. The proposed model is simple, of high precision, and can be used in the analysis and design of nanometer integrated circuit interconnect systems.

APPROXIMATION OF SOLUTION OF LINEAR DIFFERENTIAL EQUATION WITH ALMOST PERIOD FUNCTION COEFFICIENTS

This paper is devoted to the study of approximation of the solution for the differential equation whose coefficients are almost period functions. To this end the authors establish the estimation of the solution of general linear differential equation for infinite interval case. For finite interval case, this equation was investigated by G. Tamarkin([1]) applying the Picard method of successive approximation.

Optimal disturbances rejection control for singularly perturbed systems with time-delay

The optimal control design for singularly perturbed time-delay systems affected by external distur-bances is considered.Based on the decomposition theory of singular perturbation,the system is decom-posed into a fast subsystem without time-delay and a slow time-delay subsystem with disturbances.Theoptimal disturbances rejection control law of the slow subsystem is obtained by using the successive ap-proximation approach(SAA)and feedforward compensation method.Further,the feedforward and feed-back composite control(FFCC)law for the original problem is developed.The FFCC law consists of lin-ear analytic terms and a time-delay compensation term which is the limit of the solution sequence of theadjoint vector equations.A disturbance observer is introduced to make the FFCC law physically realiz-able.Numerical examples show that the proposed algorithm is effective.