Deep Neural Network Based Behavioral Model of Nonlinear Circuits

With the rapid growth of complexity and functionality of modern electronic systems, creating precise behavioral models of nonlinear circuits has become an attractive topic. Deep neural networks (DNNs) have been recognized as a powerful tool for nonlinear system modeling. To characterize the behavior of nonlinear circuits, a DNN based modeling approach is proposed in this paper. The procedure is illustrated by modeling a power amplifier (PA), which is a typical nonlinear circuit in electronic systems. The PA model is constructed based on a feedforward neural network with three hidden layers, and then Multisim circuit simulator is applied to generating the raw training data. Training and validation are carried out in Tensorflow deep learning framework. Compared with the commonly used polynomial model, the proposed DNN model exhibits a faster convergence rate and improves the mean squared error by 13 dB. The results demonstrate that the proposed DNN model can accurately depict the input-output characteristics of nonlinear circuits in both training and validation data sets.

AN IMPROVEMENT TO THE HARMONIC-BALANCE TECHNIQUE FOR ANALYZING NONLINEAR CIRCUITS

In this paper,an improved method,which is based on the harmonic-balance tech-nique,for speeding up the convergence iteration procedure is presented.As an example,it isapplied to the nonlinear analysis of microwave mixer,in which a simple time domain to fre-quency domain transformation technique for the mixer diode is firstly introduced.The use of thistechnique saves computing time dramatically.And the analyzed results are in good agreementwith the results published.The improved method can also be extended to the CAA of nonlinearcircuits with multi-devices.

SENSITIVITY ANALYSIS OF NONLINEAR CIRCUITS AND SYSTEMS-NONLINEAR TRANSFER FUNCTION APPROACH

Properties of the nonlinear transfer function are studied in this paper and the n-th order stabili-ty, n-th order frequency response and n-th order sensitivity as well as a novel theory and implementationon the sensitivity of nonlinear transfer system are proposed.

Analysis of Nonlinear Electrical Circuits Using Bernstein Polynomials

In electrical circuit analysis, it is often necessary to find the set of all direct current （d.c.） operating points （either voltages or currents） of nonlinear circuits. In general, these nonlinear equations are often represented as polynomial systems. In this paper, we address the problem of finding the solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n-dimensional box. Branch and Bound algorithms based on interval methods can give guaranteed enclosures for the solution. However, because of repeated evaluations of the function values, these methods tend to become slower. Branch and Bound algorithm based on Bernstein coefficients can be used to solve the systems of polynomial equations. This avoids the repeated evaluation of function values, but maintains more or less the same number of iterations as that of interval branch and bound methods. We propose an algorithm for obtaining the solution of polynomial systems, which includes a pruning step using Bernstein Krawczyk operator and a Bernstein Coefficient Contraction algorithm to obtain Bernstein coefficients of the new domain. We solved three circuit analysis problems using our proposed algorithm. We compared the performance of our proposed algorithm with INTLAB based solver and found that our proposed algorithm is more efficient and fast.

Piezotronic transistors in nonlinear circuit:Model and simulation

For the materials that simultaneously exhibit piezoelectric and semiconductor properties,such as wurtzite Zn O,Ga N and In N,as well as two-dimensional single Mo S2,piezoelectric charges induced by externally applied strain can tune/control carrier transport at a metal-semiconductor contact or semiconductor junction,which is named piezotronic effect.Metal-semiconductor-metal piezotronic transistors are key piezotronic nanodevices for electromechanical applications,and they are typical nonlinear elements.In this paper,a simplified current-voltage analysis solution of piezotronic transistors is developed,which can be used for circuit design and simulation.Furthermore,the typical nonlinear circuit:Chua's circuit based on piezotronic transistors is simulated.We find that the output signal of the piezotronic transistor circuit can be switched and changed asymmetrically by externally applied strain.This study provides insight into the nonlinear properties of the piezotronic transistor,as well as guidance for piezotronic transistor nonlinear circuit application.

Subspace Trajectory Piecewise-Linear Model Order Reduction for Nonlinear Circuits

Despite the efficiency of trajectory piecewise-linear(TPWL)model order re-duction(MOR)for nonlinear circuits,it needs large amount of expansion points forlarge-scale nonlinear circuits.This will inevitably increase the model size as well as the simulation time of the resulting reduced macromodels.In this paper,subspaceTPWL-MOR approach is developed for the model order reduction of nonlinear cir-cuits.By breaking the high-dimensional state space into several subspaces with much lower dimensions,the subspace TPWL-MOR has very promising advantages of re-ducing the number of expansion points as well as increasing the effective region of thereduced-order model in the state space.As a result,the model size and the accuracy of the TWPL model can be greatly improved.The numerical results have shown dra-matic reduction in the model size as well as the improvement in accuracy by using the subspace TPWL-MOR compared with the conventional TPWL-MOR approach.

Wavelet neural network based fault diagnosis in nonlinear analog circuits

The theories of diagnosing nonlinear analog circuits by means of the transient response testing are studled. Wavelet analysis is made to extract the transient response signature of nonlinear circuits and compress the signature dada. The best wavelet function is selected based on the between-category total scatter of signature. The fault dictionary of nonlinear circuits is constructed based on improved back-propagation（BP） neural network. Experimental results demonstrate that the method proposed has high diagnostic sensitivity and fast fault identification and deducibility.

A Neural-based L1-Norm Optimization Approach for Fault Diagnosis of Nonlinear Resistive Circuits

This paper deals with fault isolation in nonlinear analog circuits with tolerance under an insufficient number of independent voltage measurements.A neural network-based L1-norm optimization approach is proposed and utilized in locating the most likely faulty elements in nonlinear circuits.The validity of the proposed method is verified by both extensive computer simulations and practical examples.One simulation example is presented in the paper.

Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov expo- nents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k are studied. An effective nonlinear feedback control method is used to suppress hyperchaos to unstable equilibrium. Furthermore, a circuit is designed to realize this new hyperchaotic system by electronic workbench （EWB）. Numerical simulations are presented to show these results.

NEW EFFICIENT ALGORITHM FOR NONLINEAR CIRCUIT SYSTEM

A new efficient algorithm is given for calculation of the steady-state response of non-linear circuit driven by multifrequency signals, which are possibly made up of incommen-surable frequencies. The algorithm is particularly useful when the steady state responseis not periodic. The algorithm is much more efficient than numerical integration methods for circuitscontaining only a few nonlinear elements, compared with the number of inductors andcapacitors. It is based on a combined application of the "harmonic balancen" and "leastsquare approach", and does not require any transient analysis. The algorithm can be usedin a microcomputer.

EQUIVALENT CIRCUIT OF NONLINEAR EFFECT OF SPECTRAL IP

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Mapping equivalent approach to analysis and realization of memristor-based dynamical circuit

A novel mapping equivalent approach is proposed in this paper, which can be used for analyzing and realizing a memristor-based dynamical circuit equivalently by a nonlinear dynamical circuit with the same topologies and circuit parameters. A memristor-based chaotic circuit and the corresponding Chua＇s chaotic circuit with two output differentiators are taken as examples to illustrate this approach. Equivalent dynamical analysis and realization of the memristor-based chaotic circuit are performed by using Chua＇s chaotic circuit. The results indicate that the outputs of memristor-based chaotic circuit and the corresponding outputs of Chua＇s chaotic circuit have identical dynamics. The proposed approach verified by numerical simulations and experimental observations is useful in designing and analyzing memristor-based dynamical circuits.

基于非线性分析的无线通信识别系统优化研究

为了进一步提升插秧机的通信效率及整机作业效率,以无线通信识别模块为研究对象,基于非线性分析控制理论展开优化研究。结合插秧机的作业环境特征和各组件协调作业特点,从通信信号的非线性处理和保证抗干扰能力角度入手,建立通信识别系统的非线性控制器模型,并针对系统的输入输出和接口模块完成电路控制与程序优化布局。同时,进行插秧作业通信监测验证试验,结果表明:此非线性分析应用机理下,插秧机作业的智能性与精准性得到显著提高,通过非线性控制实现了细致有效的数据计算分析,通信传输效率相对提升了5.69%,插秧深度合格率可达96.78%,满足智能插秧设计要求。

Model Reduction by Generalized Falk Method for Efficient Dedicated to Professor Karl Stark Pister for his 95th birthday Field-Circuit Simulations

The Generalized Falk Method(GFM)for coordinate transformation,together with two model-reduction strategies based on this method,are presented for efficient coupled field-circuit simulations.Each model-reduction strategy is based on a decision to retain specific linearly-independent vectors,called trial vectors,to construct a vector basis for coordinate transformation.The reduced-order models are guaranteed to be stable and passive since the GFM is a congruence transformation of originally symmetric positive definite systems.We also show that,unlike the Pade-via-Lanczos(PVL)method,the GFM does not generate unstable positive poles while reducing the order´of circuit problems.Further,the proposed GFM is also faster when compared to methods of the type Lanczos(or Krylov)that are already widely used in circuit simulations for electrothermal and electromagnetic problems.The concept of response participation factors is introduced for the selection of the trial vectors in the proposed model-reduction methods.Further,we present methods to develop simple equivalent circuit networks for the field component of the overall field-circuit system.The implementation of these equivalent circuit networks in circuit simulators is discussed.With the proposed model-reduction strategies,significant improvement on the efficiency of the generalized Falk method is illustrated for coupled field-circuit problems.

Dynamical analysis and circuit simulation of a new three-dimensional chaotic system

This paper reports a new three-dimensional autonomous chaotic system. It contains six control parameters and three nonlinear terms. Two cross-product terms are respectively in two equations. And one square term is in the third equation. Basic dynamic properties of the new system are investigated by means of theoretical analysis, numerical simulation, sensitivity to initial, power spectrum, Lyapunov exponent, and Poincar~ diagrams. The dynamic properties affected by variable parameters are also analysed. Finally, the chaotic system is simulated by circuit. The results verify the existence and implementation of the system.

A monolithic distributed phase shifter based on right-handed nonlinear transmission lines at 30 GHz

The epitaxial material, device structure, and corresponding equivalent large signal circuit model of GaAs planar Schottky varactor diode are successfully developed to design and fabricate a monolithic phase shifter, which is based on right-handed nonlinear transmission lines and consists of a coplanar waveguide transmission line and periodically distributed GaAs planar Schottky varactor diode. The distributed-Schottky transmission-line-type phase shifter at a bias voltage greater than 1.5 V presents a continuous 0°–360° differential phase shift over a frequency range from 0 to 33 GHz. It is demonstrated that the minimum insertion loss is about 0.5 dB and that the return loss is less than-10 dB over the frequency band of 0–33 GHz at a reverse bias voltage less than 4.5 V. These excellent characteristics, such as broad differential phase shift, low insertion loss, and return loss, indicate that the proposed phase shifter can entirely be integrated into a phased array radar circuit.

Synchronization of the fractional-order generalized augmented L u¨system and its circuit implementation

In this paper, the synchronization of the fractional-order generalized augmented Lti system is investigated. Based on the predictor--corrector method, we obtain phase portraits, bifurcation diagrams, Lyapunov exponent spectra, and Poincar6 maps of the fractional-order system and find that a four-wing chaotic attractor exists in the system when the system pa- rameters change within certain ranges. Further, by varying the system parameters, rich dynamical behaviors occur in the 2.7-order system. According to the stability theory of a fractional-order linear system, and adopting the linearization by feedback method, we have designed a nonlinear feedback controller in our theoretical analysis to implement the synchro- nization of the drive system with the response system. In addition, the synchronization is also shown by an electronic circuit implementation for the 2.7-order system. The obtained experiment results accord with the theoretical analyses, which further demonstrate the feasibility and effectiveness of the proposed synchronization scheme.

Stability of operation versus temperature of a three-phase clock-driven chaotic circuit

We evaluate the influence of temperature on the behavior of a three-phase clock-driven metal–oxide–semiconductor （MOS） chaotic circuit. The chaotic circuit consists of two nonlinear functions, a level shifter, and three sample and hold blocks. It is necessary to analyze a CMOS-based chaotic circuit with respect to variation in temperature for stability because the circuit is sensitive to the behavior of the circuit design parameters. The temperature dependence of the proposed chaotic circuit is investigated via the simulation program with integrated circuit emphasis （SPICE） using 0.6-μm CMOS process technology with a 5-V power supply and a 20-kHz clock frequency. The simulation results demonstrate the effects of temperature on the chaotic dynamics of the proposed chaotic circuit. The time series, frequency spectra, bifurcation phenomena, and Lyapunov exponent results are provided.

三阶三次幂非线性混沌电路的自适应反馈控制和H_(∞)控制

针对三阶三次幂非线性混沌电路,研究其控制问题.首先,给出系统的Lyapunov指数和混沌吸引子,验证系统存在复杂的混沌现象;其次,用自适应反馈控制方法和H_(∞)状态反馈控制方法,设计参数已知和参数未知的自适应反馈控制器以及H_(∞)状态反馈控制器,将混沌系统状态稳定到平衡点上;最后,通过MATLAB软件进行数值仿真验证控制器的有效性,并对两种控制器的控制效果进行比较.

考虑精确磁通的电磁加载装置等效磁路建模

为提高电磁加载装置在控制应用时的模型预测快速性与精确性,考虑电磁加载装置硅钢片表面涡流磁场生成因素与不同轴偏心下有效气隙长度,采用非线性方程拟合硅钢片磁化曲线,建立包含磁极边缘效应、磁极铁心、转子硅钢片动态磁阻与涡流磁场的电磁加载装置非线性等效磁路模型。研究了硅钢片表面涡流磁场生成因素与气隙磁场分布,并与有限元仿真结果比较分析。应用该模型在水润滑轴承试验台上进行电磁加载力测试试验。研究结果表明:等效磁路法对磁场分布的表征与有限元法一致,且对气隙的计算更为精确;电磁加载力稳态误差小于4%,响应时间低于0.55 s。