Nonlinear Analog Research Articles

Nonlocal and strain gradient based model for electrostatically actuated silicon nano-beams

Conventional continuum theory does not account for contributions from length scale effects which are important in modeling of nano-beams. Failure to include size-dependent contributions can lead to underestimates of deflection, stresses, and pull-in voltage of electrostatic actuated micro and nano-beams. This research aims to use nonlocal and strain gradient elasticity theories to study the static behavior of electrically actuated micro- and nano-beams. To solve the boundary value nonlinear differential equations, analogue equation and Gauss---Seidel iteration methods are used. Both clamped-free and clamped---clamped micro- and nano-beams under electrostatical actuation are considered where mid-plane stretching, axial residual stress and fringing field effect are taken into account for clamped---clamped cases. The accuracy of solution is evaluated by comparison of the pull-in voltages of different micro-electro-mechanical systems with those results previously published in the literature. A main drawback of the previous theoretical researches using nonlocal or strain gradient methods was that they don't account for effects of the size on the Young modulus of the beam and merely they adjust the length scale parameters for small sizes to fit data with experimental results. In the present study, the experimental voltages for static pull-in of different micro- and nano-beams are used to estimate the silicon Young's modulus, nonlocal and length scale parameters. Using the estimated parameters, pull-in voltages of silicon micro- and nano-beams based on strain gradient and nonlocal theories are compared with respect to each other and also with the experimental and previous theoretical results. The conducted results demonstrate that the predicted pull-in voltages using proposed strain gradient theory will give the best fit with experimental observations.

Auxiliary Model-Based Forgetting Factor Stochastic Gradient Algorithm for Dual-Rate Nonlinear Systems and its Application to a Nonlinear Analog Circuit

This paper studies the identification problem of dual-rate Hammerstein nonlinear systems. By means of the key-term separation principle, we develop a regression identification model with different input and output sampling rates. In order to promote the convergence rate of the stochastic gradient (SG) algorithm, an auxiliary model-based forgetting factor SG algorithm is derived. Finally, the proposed algorithm is applied to model a nonlinear analog circuit with dual-rate sampling and the simulation result shows the effectiveness of the algorithm.

Sine-cosine Method for a Class of Nonlinear Fourth Order Variant of a generalized Camassa-holm equation

In this paper we study a class of nonlinear fourth order analogue of a generalized Camassa-Holm equation by using sine-cosine method. The compactons, solitary wave, solitary patterns, periodic wave and solitary patterns solutions of a class of nonlinear fourth order analogue of a generalized Camassa-Holm equation are successfully obtained. It is shown that the sine-cosine provides a powerful mathematical tool for solving a great many nonlinear partial differential equations in mathematical physics.

Bifurcations of Travelling Wave Solutions for the B(m,n) Equation

Using the bifurcation theory of dynamical systems to a class of nonlinear fourth order analogue of the B(m,n) equation, the existence of solitary wave solutions, periodic cusp wave solutions, compactons solutions, and uncountably infinite many smooth wave solutions are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of the above waves are determined.

Harmonic Balance Surrogate-Based Immunity Modeling of a Nonlinear Analog Circuit

A novel harmonic balance surrogate-based technique to create fast and accurate behavioral models predicting, in the early design stage, the performance of nonlinear analog devices during immunity tests is presented. The obtained immunity model hides the real netlist, reduces the simulation time, and avoids expensive and time-consuming measurements after tape-out, while still providing high accuracy. The model can easily be integrated into a circuit simulator together with additional subcircuits, e.g., board and package models, as such allowing to efficiently reproduce complete immunity test setups during the early design stage and without disclosing any intellectual property. The novel method is validated by means of application to an industrial case study, being an automotive voltage regulator, clearly showing the technique's capabilities and practical advantages.

On one class of dynamic transportation models

A model is studied that describes the process of good transportation occurring in some technologies. Transportation regimes satisfying a given management system are examined. Such regimes are described by traveling-wave solutions to a nonlinear finite-difference analogue of a parabolic equation. Possible transportation regimes are described, and the stability of stationary regimes is analyzed.

Fault Modeling on Complex Plane and Tolerance Handling Methods for Analog Circuits

Due to the lack of a feasible fault modeling method, soft fault diagnosis and tolerance are two challenging problems in analog circuit fault diagnosis. This paper proposes approaches to solve these two problems. First, a new fault modeling method and its theoretical proof are presented. In analog circuits, either the real part (“Ur”) or the imaginary part (“Ui”) of output voltage is the function of fault component parameter “ z,” viz., Ur=f1(z) and Ui=f2(z). By eliminating “ z,” equation F(Ur,Ui)=0 is achieved, where function “ F()” is independent from the value of “ z” and uniquely determined by the location of “ z” and the other fault free component in the circuit under test (CUT). Hence, the function “ F()” can be used as the fault model, which is applicable to both hard (open or short) and soft (parametric) faults. It is also applicable to either linear or nonlinear analog circuits. On a complex plane, the equation “ F(Ur, Ui)=0” represents a curve which is determined by the fault free output voltage and the shape of “ F().” Then, the parameter tolerance is taken into consideration. The tolerance influences the fault diagnosis by shifting the fault free output voltage and distorting the shape of “ F().” These influences can be mitigated in two ways: 1) The free output voltage is measured when an actual circuit is under steady state and free of fault, and 2) the minimal distance approach is used to find the fault component. The effectiveness of the proposed approaches is verified by both simulated and experimental results.

Reliability assessment of CMOS differential cross-coupled LC oscillators and a novel on chip self-healing approach against aging phenomena

In this paper, reliability of CMOS differential cross-coupled LC oscillators is examined, and a novel on chip aging detection and healing technique is developed to increase the lifetime of oscillator circuits. Aging causes degradation in several transistor parameters, such as threshold voltage, mobility, and transconductance. While these changes cause irregular timing characteristics and increased power consumption in digital circuits, the case is quite different for their analog counterparts. Analog circuits, especially nonlinear ones, show more deviations at the output due to parameter changes. In order to evaluate the aging effects on nonlinear analog circuits, two different oscillator structures (n-type and p-type) with 5GHz oscillation frequency were designed using 0.13μm technology. The phase noise analysis of fresh and aged oscillators was performed analytically and through simulations. Based on these analyses the robustness of oscillators was discussed. Finally, an on chip aging sensor and self recovery mechanism are proposed to increase the robustness of the CMOS LC oscillators.

An MTL-Based Configurable Block for Current-Mode Nonlinear Analog Computation

A configurable analog block (CAB) architecture based upon the MOS translinear (MTL) principle is proposed. It is programmed to implement some current-mode nonlinear analog computational functions. The proposed CAB architecture consists of one cascoded MTL cell, a local switch network, and a pMOS array. The cascoded MTL cell implements one MTL loop that is reconfigurable and programmable using the switch network and the pMOS array. This CAB architecture is capable of implementing various frequently used nonlinear functions, such as squaring/inverse function, rectifying (absolute value), and square-rooting/geometric mean functions. The CAB has been fabricated in a 0.5- μm CMOS technology and verifies the concept. High capability and flexibility of the proposed CAB makes it suitable for current-mode analog computational and signal processing applications.

Analytic investigations on the susceptibility of nonlinear analog circuits to substrate noise

Abstract. This work deals with the conducted susceptibility of nonlinear analog circuits with respect to substrate noise. The substrate coupling mechanism is modeled by a passive three-terminal network that is obtained by means of the finite element method with a subsequently performed model order reduction. Applying this substrate model to the bulk terminal of MOS transistors in integrated analog circuits, it is possible to examine the influence of substrate noise on the circuit's functionality. By means of a block-oriented approach, analytic expressions for the output behavior of the circuits are found. The utilized multi-input Wiener model separates the linear dynamic from the nonlinear static circuit properties. Due to this separation the frequency response of both signals, i.e.,input signal and substrate noise, respectively, can be identified, and hence, the frequency range in which the circuit is most susceptible to substrate noise. Since the nonlinear static behavior of each MOS transistor depends on two signals, truncated multivariate Taylor series expansions of the nonlinear elements are performed on the basis of the EKV model description (Enz et al., 1995). The proposed modeling is illustrated by a simple example.

Analog Circuit Fault Diagnosis Based on Volterra Series

The Volterra series are a functional series.Its kernals both in time domain and frequency domain have definite physical significance and are independent with the system input. Thus the kernals can reflect intrinsic nature of the system. Thus the Volterra series can be used to analyze the nonlinear analog circuit.The fault feature can be extracted based on the direct analysis on the frequency response of nonlinear analog circuit so as to detect the fault in nonlinear analog circuit.

The zero dynamics of a nonlinear system: From the origin to the latest progresses of a long successful story

The concept of zero dynamics of a nonlinear system was introduced about thirty years ago as nonlinear analogue of the concept of transmission zero of the transfer function of a system. This paper reviews a few historical landmarks in the development of this concept and then addresses some current challenging issues, such as the development of global and coordinate free version of a standard output-feedback design paradigm, the analysis of problems of stabilization and tracking in the presence of unstable zero dynamics, and extensions to multivariable systems.

An anisotropic eigenvalue problem of Stekloff type and weighted Wulff inequalities

We study the Stekloff eigenvalue problem for the so-called pseudo p-Laplacian operator. After proving the existence of an unbounded sequence of eigenvalues, we focus on the first nontrivial eigenvalue σ2,p, providing various equivalent characterizations for it. We also prove an upper bound for σ2,p in terms of geometric quantities. The latter can be seen as the nonlinear analogue of the Brock–Weinstock inequality for the first nontrivial Stekloff eigenvalue of the (standard) Laplacian. Such an estimate is obtained by exploiting a family of sharp weighted Wulff inequalities, which are here derived and appear to be interesting in themselves.

Diagnosis of Incipient Faults in Weak Nonlinear Analog Circuits

Aiming at the problem to diagnose incipient faults in weak nonlinear analog circuits, an approach is presented in this paper. The approach calculates the fractional Volterra correlation functions beforehand. The next step is to use the fractional Volterra correlation functions and different angle parameters of the fractional wavelet packet transform (FRWPT) to extract the fault signatures. Meanwhile, the computational complexity is analyzed. Then the variables of the fault signatures are constructed, which are used to form the observation sequences of the hidden Markov model (HMM). HMM is used to accomplish the fault diagnosis. The simulations show that the presented method can significantly improve the incipient fault diagnosis capability.

Global and local parametric diagnosis of analog short‐channel CMOS circuits using homotopy‐simplicial algorithm

SUMMARYThe paper offers an algorithm for local and global parametric diagnosis in nonlinear analog circuits, including both identification of the faulty parameters and determination their values. The algorithm exploits a nonlinear algebraic type test equations which may possess multiple solutions, corresponding to different sets of the parameters values which meet the test. To find the solutions, the homotopy concept is applied. Since the test equation is not given in explicit analytical form, the simplicial method is used to trace the homotopy path. The proposed approach can be applied to a broad class of analog circuits, including the complementary metal–oxide–semiconductor circuits fabricated in nanometer technology. The developed diagnostic procedure has been implemented in DELPHI, whereas the required by the algorithm repeated circuit analyses are carried out using IsSPICE 4 and both environments have been joined together. For illustration, two numerical examples are given. Copyright © 2013 John Wiley & Sons, Ltd.

Thermodynamic measure of the magnetoelectric coupling in a three-dimensional topological insulator

We show that the magneto-electric coupling in 3D (strong) topological insulators is related to a second derivative of the bulk magnetization. The formula we derive is the non-linear response analog of the Streda formula for Hall conductivity (P. Streda, J. Phys. C: Solid State Physics, 15, 22 (1982)), which relates the Hall conductivity to the derivative of the magnetization with respect to chemical potential. Our finding allows one to extract the magneto-electric coefficient by measuring the magnetization, while varying the chemical potential and one more perturbing field. Such an experimental setup could circumvent many of the current difficulties with measuring the magneto-electric response in 3D topological insulators. The relation we find also makes transparent the effect of disorder on the magneto-electric response, which occurs only through the density of states, and has no effect when the system is gapped.

Nonlinear Analog Circuit Fault Diagnosis Based on MFDFA Method

This paper presents a fault diagnosis method for nonlinear analog circuit based on multifractal detrended fluctuation analysis (MFDFA) method. The MFDFA method is applied to analysis fault signal and extracts the multifractal features from the raw signal. The selected features are given to SVM classifier for further classification. The data required to develop the classifier are generated by simulating various faults using Pspice software. The simulation results show that the proposed method provides a robust and accurate method for nonlinear circuit fault diagnosis.

Modified current differencing transconductance amplifier – new versatile active element

Abstract This paper introduces a new current mode component called Modified Current Differencing Transconductance Amplifier (MCDTA). Important parameters of the circuit i.e. input resistance, z terminal resistance and transconductance of the output stage can be tuned electrically. The circuit can be implemented in linear and non-linear analog signal processing. The paper presents an example of the MCDTA application - a complete quadrature oscillator with the amplitude regulation. The functionality of the example circuit and its tuning capability were proved by the SPICE simulation results.

Research of Automatic Tracing Control for Infrared Intelligent Lunar Vehicle

In intelligent lunar vehicle’s infrared tracing automatic control, reflective infrared sensor array is adopted for detecting the path. By processing the sensor data and relative error through the detection of nonlinear analog A/D sampling, real-time processing and non-linearizing the control parameters in the PID variable scale incremental control algorithm, closed-loop control would be realized. In addition, incremental PD formula can be derived by fuzzy control technology, while the sensitivity and stability of the vehicle tracing can be improved by adjusting parameters in programming. It proved that this method can effectively shorten response time, reduce random interference, optimize the tracing line, eliminate oscillation and improve the mobility.

On the Hong–Krahn–Szego inequality for the p-Laplace operator

Given an open set Ω, we consider the problem of providing sharp lower bounds for λ 2(Ω), i.e. its second Dirichlet eigenvalue of the p-Laplace operator. After presenting the nonlinear analogue of the Hong–Krahn–Szego inequality, asserting that the disjoint unions of two equal balls minimize λ 2 among open sets of given measure, we improve this spectral inequality by means of a quantitative stability estimate. The extremal cases p = 1 and p = ∞ are considered as well.