Nonlinear Analog Circuits Research Articles

Distortion Analysis and Fault Detection in Weakly Non-linear Analog Circuits Using Simplified Volterra Series Method

In this paper a new method to find the parametric faults in weakly nonlinear analog circuit is proposed. Frequency domain volterra kernels are derived to calculate the test parameters i.e., nonlinear distortions and the cross spectral density. Volterra kernels are sensitive to device parameter and the components used to build the circuit. Device parameter and each component value are varied within the tolerance limit using Monte Carlo simulation. For the fault free circuit maximum and minimum values of the 3rd order harmonic, intermodulation distortion and the cross spectral density are measured. During testing, single and multiple faults are injected and the test parameters are measured. If any one or more test parameters are outside the predetermined bounds the circuit is declared to be faulty. This proposed method offers high fault coverage capability. To validate this method CMOS differential amplifier circuit is taken under consideration.

Analysis of pattern generation in non-periodic clock-driven unidirectionally coupled phase oscillators in a ring

Unidirectionally coupled phase oscillators in a ring are simple structures but unsuitable for application in central pattern generators (CPGs) for six-legged walking due to coexisting stable synchronization patterns. This paper shows that the coupled oscillators can be applied to a CPG by utilizing a non-periodic signal generator as a clock. The non-periodic clock-driven coupled oscillators are implemented by a sequential logic circuit using a field programmable gate array (FPGA) and a nonlinear analog circuit. A laboratory experiment confirms that a hexapod robot mounting the implemented circuits can realize six-legged walking.

INFORM: Inverse Design Methodology for Constrained Multiobjective Optimization

Many system design methods use population-based optimization or a surrogate model for solving constrained multi-objective optimization. When designing a system with multiple objectives and constraints, the designer may first be interested in understanding the trade-offs among different objectives from a small number of simulations. In the next step, the designer may focus on specific regions of interest in the design space near a set of non-dominated solutions to further improve performance on the targeted objectives. This may help make the search process sample-efficient. We propose INFORM: a two-step approach for sample-efficient constrained multi-objective optimization of real-world nonlinear systems. In the first step, we modify a genetic algorithm (GA) to make the design process sample-efficient. We inject candidate solutions into the GA population using inverse design methods instead of determining the candidate solutions for the next generation using only crossover and mutation, as is done in standard GA. We present three types of inverse design techniques based on a (i) neural network verifier, (ii) neural network, and (iii) Gaussian mixture model. The candidate solutions for the next generation are thus a mix of those generated using crossover/mutation and solutions generated using inverse design. At the end of the first step, we obtain a set of non-dominated solutions. In the second step, we choose the regions of interest around the non-dominated solutions to further improve the objective function values using inverse design methods. We demonstrate the efficacy of INFORM through synthesis of nonlinear systems and analog circuits. The experimental results show that INFORM reduces synthesis time by up to 29× and improves the value of the objective function by up to 33% compared to a state-of-the-art baseline design methodology.

Soft Fault Diagnosis of Analog Circuit Based on EEMD and Improved MF-DFA

Aiming at the problems of nonlinearity and serious confusion of fault characteristics in analog circuits, this paper proposed a fault diagnosis method for an analog circuit based on ensemble empirical pattern decomposition (EEMD) and improved multifractal detrended fluctuations analysis (MF-DFA). This method consists of three steps: preprocessing, feature extraction, and fault classification identification. First, the EEMD decomposition preprocesses (denoises) the original signal; then, the appropriate IMF components are selected by correlation analysis; then, the IMF components are processed by the improved MF-DFA, and the fault feature values are extracted by calculating the multifractal spectrum parameters, and then the feature values are input to a support vector machine (SVM) for classification, which enables the diagnosis of soft faults in analog circuits. The experimental results show that the proposed EEMD-improved MF-DFA method effectively extracts the features of soft faults in nonlinear analog circuits and obtains a high diagnosis rate.

COMPLEX HYBRID SYMBOLIC ANALYSIS OF NONLINEAR ANALOG CIRCUITS DRIVEN BY MULTI-TONE SIGNALS

The paper presents a general symbolic method for generating the complex hybrid matrix necessary for computing the periodic or nonperiodic steady-state response of a nonlinear analog circuit driven by multitone signals. This method is remarkable by its great efficiency and generality, and it is very useful in frequency-domain approach based on harmonic balance and least square approximation. For the general case of the nonperiodic steady-state response there are three basic methods: frequency-domain approach based on Voltera series; time-domain approach and a frequency-domain approach based on harmonic balance and least square approximation. The last one is significantly more efficient when the total number of nonlinear resistors, inductors and capacitors is significantly less than the total number of linear inductors and capacitors in the circuit, as is often the case in practice.

A Novel Feature Extraction Method for Soft Faults in Nonlinear Analog Circuits Based on LMD-GFD and KPCA

A Novel Feature Extraction Method for Soft Faults in Nonlinear Analog Circuits Based on LMD-GFD and KPCA

Implementation of Linear and Nonlinear circuits using Operational Transconductance Amplifier

This paper describes implementation of CMOS based linear and non-linear analog circuits using operational trans conductance amplifier as the basic element. These circuits have their applications in communication and signal processing areas. In this work PSPICE is used for the simulation of various analog circuits. The corresponding results are presented.

A Novel Chaotic System with Wide Spectrum, its Synchronization, Circuit Design and Application to Secure Communication

Objective: To investigate a novel chaotic system with unique features, its synchronization using nonlinear active control, analog circuit design and application to secure communication. Methods/Analysis: Dynamical tools such as dissipative analysis, instability of equilibrium points, sensitivity to initial conditions, 0-1 test, recurrence plot, Poincare map, Lyapunov exponents, Lyapunov dimension, frequency spectrum and basin of attraction. Synchronization is achieved using modified nonlinear active control technique and analog circuit design, implementation is done in NI Multisim platform. MATLAB and Multisim results are presented to meet the adequate verification of theoretical approach. Findings: A three-dimensional chaotic system with only two nonlinear terms, three parameters and a total of eight terms are proposed. The proposed system has three saddle focus type equilibria. The proposed system is topologically different from Lorenz’s and Rossler’s, Lu’s, Chen’s, and Liu’s families. Such dynamic systems are very few in the literature as per authors best knowledge. The system has basin of chaotic attractors for which first Lyapunov exponent ranges between 2.5 to 3. Frequency spectrum and large positive Lyapunov exponent result comparatively large bandwidth of the proposed systems against some well-known chaotic systems. Chaos, periodic and stable behaviors are obtained by altering the system parameters. Novelty/Application: The proposed three-dimensional chaotic system has significant chaotic behavior and broader spectrum than the six chaotic systems like Lorenz, Rossler, Lu, Chen, BG and Liu systems. Unlike the conventional active control approach, the proposed nonlinear active control does not result decoupled error dynamics. The system has significantly large bandwidth which is helpful in the masking of message signals and enhances the security of transmitted signals during communication. Keywords: Analog circuit design; Chaos; Chaotic system; Chaosbased communication; Chaos synchronization; Nonlinear active control

Automated abstraction of nonlinear analog circuits to reliable set-valued models with reduced overapproximation

This paper tackles the analog and mixed-signal modeling for verification challenges. It proposes an adjustable automated modeling approach, which provides set-valued models with reduced overapproximation. The models reliably enclose parameter variations and modeling errors. The reduced overapproximation is obtained by computing the intersecting set of models with intervals and affine forms. The nonlinear circuit examples show a reduced overapproximation up to 86%.

Fault Diagnosis of Nonlinear Analog Circuit Based on Generalized Frequency Response Function and LSSVM Classifier Fusion

For fault diagnosis of nonlinear analog circuit, a novel method based on generalized frequency response function (GFRF) and least square support vector machine (LSSVM) classifier fusion is presented. The sinusoidal signal is used as the input of analog circuit, and then, the generalized frequency response functions are estimated directly by the time-domain formulations. The discrete Fourier transform of measurement data is avoided. After obtaining the generalized frequency response functions, the amplitudes of the GFRFs are chosen as the fault feature parameters. A classifier fusion algorithm based on least square support vector machine (LSSVM) is used for fault identification. Two LSSVM multifault classifiers with different kernel functions are constructed as subclassifiers. Fault diagnosis experiments of resistor-capacitance (RC) circuit and Sallen Key filter are carried out, respectively. The results show that the estimated GFRFs of the circuit are accurate, and the fault diagnosis method can get high recognition rate.

Diagnosis of Incipient Faults in Nonlinear Analog Circuits Based on High Order Moment Fractional Transform

Considering the problem to diagnose incipient faults in nonlinear analog circuits, a novel approach of fault feature-extracting based on HMFT (high order moment fractional transform) of the component parameter change is proposed. Firstly, the equivalence circuit model is established according to the topological structure and the voltage sensitivity of the circuit under test (CUT). Then the HMFT of component parameter changes are derived, which are used as fault features. Finally, using the extracted features, incipient fault diagnosis is accomplished. The simulations illustrate the proposed method and show its effectiveness in the incipient fault recognition capability.

Nonlinear Soft Fault Diagnosis of Analog Circuits Based on RCCA-SVM

In the soft fault diagnosis of nonlinear analog filter circuits, the single feature can't maximally reveal the behaviors hidden in signals. In order to overcome such shortcomings, a fusion algorithm weighted feature from multi-group is proposed. This method use reliefF algorithm to optimize canonical correlation analysis combines support vector machine(RCCA-SVM) for diagnosis. The fault characteristics used in this method are extracted from the time-domain, statistical features and frequency-domain by wavelet packet transform (WPT). And then the CCA algorithm is used to improve the correlation of features according to the weights of the features. Finally, the fusion features are dimension reduced by principal component analysis(PCA), support vector machine(SVM) is the classifier of the diagnosis. The simulations show that the proposed method has a good diagnostic effect on circuit fault diagnosis of non-linear analog circuits.

A Method for Fault Diagnosis Based on Multidimensional Scaling (MDS) in Analog Circuits

Considering different fault state of the circuit in the nonlinear analog circuit fault diagnosis, the output response of the circuit varies. A Method for Fault Diagnosis of Nonlinear Analog Circuits on the basis of Multidimensional Scaling (MDS) was put forward according to the variable output response. This method can transform the difference of output response under different fault states into a low-dimensional fitting composition and then distinguish the different fault types. Under the condition of single fault of the circuit, the simulation result proves that the method presented in this paper enjoys high accuracy in effectively classifying the different fault types, locating the faulty components and observing the difference among variable faults intuitively in the low-dimensional coordinate system.

Modeling and sizing of non-linear CMOS analog circuits used in mixed signal systems

In this paper, modeling of performance parameters and time efficient yet accurate sizing methodology of CMOS analog non-linear circuits have been proposed. The proposed modeling methodology generates empirical models of the non-linear circuit performance parameters in monomial or posynomial form, which is geometric programming (GP) compatible, as a function of the final design variables of the circuit (i.e. the width and length of the transistors). The proposed non-linear circuit sizing methodology, referred to as iterative geometric programming utilizes a correction factor for each of the GP compatible performance parameter models. These correction factors are updated using SPICE simulation after every iteration of the GP optimization. The proposed methodology takes advantage of GP optimization and at the same time it uses SPICE simulation to improve the design point by rectifying inaccuracies that may exists in the GP compatible performance models. Both the proposed methodologies have been validated in a 0.18 μm CMOS technology. The dynamic comparator and the bootstrap switch which are commonly used non-linear circuits in analog-mixed signal systems, have been used as the example circuits. It has been observed that the proposed sizing algorithm converges rapidly and give final design point with SPICE level accuracy higher than 99 %. The efficiency and the accuracy of the proposed algorithm has been numerically compared w.r.t. the sizing algorithm using evolutionary algorithm. It has been observed that the proposed algorithm gives much better results. Moreover, the proposed algorithm is hundreds times faster than that of the evolutionary algorithm.

A New Adaptive Chaotic Key Generator

The chaotic generation is of great interest in Encryption/Decryption process. It is increasingly applied in Key generation that is used for encryption/decryption of plain text data before transmission to the required destination. The chaos pattern is first generated as phenomena of nonlinear unstable analog circuit. The problem is limited word length size of the key generated (small key space) which has low brittle force and it is susceptible to key estimation and as a result weak security. In this paper a new algorithm of adaptive digital chaotic generator is proposed and keys blocks of different length are produced. The randomness of the generated key sequences is tested and evaluated for different initial conditions and different learning periods. The results are encouraged.

Verifying nonlinear analog and mixed-signal circuits with inputs

We present a new technique for verifying nonlinear and hybrid models with inputs. We observe that once an input signal is fixed, the sensitivity analysis of the model can be computed much more precisely. Based on this result, we propose a new simulation-driven verification algorithm and apply it to a suite of nonlinear and hybrid models of CMOS digital circuits under different input signals. The models are low-dimensional but with highly nonlinear ODEs, with nearly hundreds of logarithmic and exponential terms. Some of our experiments analyze the metastability of bistable circuits with very sensitive ODEs and rigorously establish the connection between metastability recovery time and sensitivity.

Synthesis Procedure of Configurable Building Block-Based Linear and Nonlinear Analog Circuits

Synthesis and design methodology suitable for computer-aided design tools are now emerging as major challenge for analog system designers. This paper proposes a systematic synthesis procedure which provides reusability and programmability, for linear and nonlinear analog circuits using configurable building block (CBB) and analog cell (AC). Operational transconductance amplifier-based ACs are synthesized in terms of CBBs. Reusability and programmability of the synthesis methodology have been demonstrated by realizing different types of linear and nonlinear circuits and mapping those circuits in field programmable analog array. Finally, the proposed methodology has been integrated as an electronic design automation tool AnaSyn1.0. Performance of all the proposed circuits has been verified by SPICE simulation.

Parametric fault detection of analog circuits based on Bhattacharyya measure

This paper presents a fault detection algorithm to detect parametric fault in linear and weakly non-linear analog circuits by Bhattacharyya measure, a statistical metric. Linear feedback shift register (LFSR) generated pseudo-random bit sequences are fed to digital-to-analog converter (DAC) to obtain random analog input stimuli for the circuit under test (CUT). Bhattacharyya coefficient is measured from the probability density function (PDF) of the output. The non-Gaussian auto-regressive model is used to estimate the PDF. Component tolerance is mapped into statistical space by Monte Carlo simulation. The proposed methodology is validated through three benchmark circuits: continuous-time low pass state variable filter circuit, fourth order low pass Chebyshev filter circuit and cascade amplifier. All the circuits are simulated with CADENCE Virtuoso using UMC-180nm technology. Defect screening is also measured with linear regression analysis. Detectability of the proposed method for parametric fault is reasonably large in comparison to functional test method.

Research on fractal method for soft fault diagnosis of nonlinear analog circuits

Research on fractal method for soft fault diagnosis of nonlinear analog circuits

Generalized Multi-fractal Method for Soft Fault Feature Extraction of Non-linear Analog Circuits Based on EMD

The soft fault signal of non-linear analog circuits is non-linear and unstable. Its inherent characteristics cannot be analyzed by the traditional linear method. Therefore, a new method based on the empirical mode decomposition (EMD) and a generalized multi-fractal dimension algorithm is proposed for soft fault signal feature extraction of non-linear analog circuits. The EMD decomposed the circuits soft fault signal into several intrinsic mode functions (IMF). The EMD then modified a traditional G-P correlation dimension algorithm to simply and reliably use it for calculating the generalized multi-fractal dimensions of the fault signals. According to fractal theory, the generalized fractal dimensions of the original fault signals and IMF can be obtained for an appropriate weight factor q. The principle IMF component can then be filtered using the cross-correlation coefficient criterion. The obtained generalized multi-fractal dimension of the principle IMF component was continually input in the supporting vector machine as a characteristic vector to diagnose the soft fault of the non-linear analog circuits. The feasibility and validity of this proposed method were demonstrated by experiments.