功率平衡与基波分析法

含有非线性放大器件g(u)的网络N，如果建立由n个谐波组成的周期振荡，则可以将该网络划分成基波与非基波两部分，非基波成份的存在依赖于基源的激励，而基波成分保持自激，依靠本身的反馈，因此用基波分部网络去替换非线性网络，其稳定性的判断结果是一致的，而基波分部网络的稳定性可以采用线性正弦量的分析方法。     

基本电子电路

TN7,()462 2004010479磁过滤阴极真空弧沉积装置研究中的等效电路方法/王广甫,张荟星(北京师范大学)11真空科学与技术学报一2003,23(1).12一18提出了模拟磁过滤阴极真空弧放电等离子体沉积装置阴极弧放电过程的等效电路,并用该电路定性研究了各参数对弧放电的影响,结果同实验符合的很好图2参12(刚)划分成基波与非基波两部分.非基波成份的存在依赖于基波,而基波成份保持自激,依靠本身的反馈,用基波分部网络去替换非线性网络,尽管两者建立的振荡波形不同,但关于稳定性的判断结果是一致的,而基波成份的稳定性可以采用线性正弦量的分析方法。图…     

用基波平衡原理分析非线性振荡与混沌

用"基波平衡原理"求得注入网络的基波电流Isl.它的流向代表网络在脱离激励源以后,为维持自激振荡关于实功与虚功的盈亏情况,是判断网络稳定性和振荡性状的有力依据.当实功与虚功同时取得平衡时,能求得基波解的振荡频率ωs和幅值Um,网络必然存在有对应的周期解.结论的普遍性可推广到三阶非线性微分方程.并阐明微分方程存在有多个周期解是产生混沌振荡的重要原因.其正确性可以用SIMULINK仿真验证.     

功率平衡基础上的基波分析法

在非线性网络的适当端口施加正弦电压源U_s.用基波平衡原理求得注入网络的基波电流i_s1.当i_s1=0时,正弦电压源的频率和幅值被称为基波解.如果能求出n个基波解,则原网络必然也对应的存在有n个周期解.如果基波解不存在,则原网络的周期解也不存在.以考比兹电路为例,说明虚功平衡和周期振荡的密切关系,以蔡氏电路为例,用基波平衡原理说明混沌振荡的性状.结论的普遍性可以推广到三阶非线性微分方程.其正确性可以用SIMULINK仿真验证.     

用基波平衡原理分析非线性电子网络的稳定性

对于一个非线性非保守的电子网络,根据等效推力理论,可以求出变阻尼力在一周期中贡献能量的等效平均值Df.文中在等效推力的基础上,提出基波平衡原理.若在适当端口施加正弦电压源,则网络的稳定性取决于进入端口基波电流的实功与虚功成份的符号值.这种原理适用于含几个非线性器件的三阶电子网络.     

基波平衡原理的推广

注入网络的基波电流iS1=0。则可由Gi(Um,ωS)=0和Bi(Um,ωS)=0求出基波解的频率和幅值(ωS,Um)。如果有n对合理的正实数(ωSi,Umi,i=1,2,3….n≠∞),同时满足式Gi=0和Bi=0,则原网络会对应地建立n个周期振荡。以上情况被称为基波解严格存在。若由式Gi≤0,Bi≤0解出的频率和幅值有无限多组解(ωS,Um),分布在一定连续较广范围内,这表明基波解不但在更加广泛的范围内存在,且有向负载送出实功与虚功的能力。含多个平衡点的非线性网络,能够在相空间建立多个座标体系分析网络的全局稳定性。不同的参考体系,应得出相同的结论。但用多个不同的座标体系能够发现相图性状的变化规律。     

各类自激振荡的基波分析法

为了消除寄生振荡 ,必须分析电子网络的稳定性 ,对于判定非线性网络在小信号下的稳定性 ,可以采用微变等效线性模型 ,对于在大信号情况下的稳定性 ,文中以几种类型的振荡为例证 ,提出适用于各种不同情况的基波分析法 ,得出比较简单而充分准确的结论。     

用微变模型分析非线性网络的稳定性

含有非线性放大器件 g(u)的网络 N,如果能够建立周期振荡 ,它由 n个谐波组成 ,每一谐波又可分成 m个微分量 (n→∞ ,m→∞ ) ,这说明存在一个等效模型 ,该模型是 n× m个微量成份的迭加 ,每一微量成份都是线性微变模型 Njk,每一个 Njk吸收的功率为 Pjk+ j Qjk,网络 N功率平衡的条件是 P =∑nj=1∑mk=1Pjk=0 ,Q =∑nj=1∑mk=1Qjk=0 ,因而起码有一个微量成份满足 Pjk≤ 0和 Qjk≤ 0 ;如果对于任意微量成份都是 Pjk>0或 Qjk>0 ,则说明这个网络无法寄生任何形式的周期振荡     

高次谐波的产生和光混频

为了在紫外区产生相干光，除用激光振荡的方法外，也有利用各种介质的非线性效应所产生的高次谐波和光混频的方法。此种方法最显著的特点是改变入射光的波长，使输出波长能够连续变化，再用此变化的输出作为基波，同样会产生激光的相干特性。     

移相式谐波失真度测量

采用移相的原理,将无谐波失真的标准信号移相后与被测的失真信号相叠加,同时使标准信号的相位与被测的失真信号中的基波的相位相反,而两者的幅度值相等,结果将基波成份抵消而保留了谐波成份,由此而测出谐波失真度。     

Nonlinear design of multiple-cavity switchable dielectric-resonator oscillators

The application of nonlinear CAD techniques to the design of multiple-cavity dielectric-resonator oscillators is demonstrated. The circuit topology consists of an FET oscillator which can be coupled to one of several dielectric resonators by means of a diode switching network. The circuit is numerically designed as a whole making use of a novel broadband optimisation technique especially devised for autonomous nonlinear circuits. At each fundamental frequency of interest the steady state of oscillation is determined by harmonic-balance analysis and at the same time the oscillator is tuned to the prescribed frequency by changing a parameter of the corresponding resonator. The electrical performance is simultaneously specified at all the fundamentals, and the optimisation is carried out with respect to the circuit parameters of the frequency-invariant part of the network.<>     

Whirling‐Folded Triboelectric Nanogenerator with High Average Power for Water Wave Energy Harvesting

Ocean wave energy, as one of the most abundant resources on the earth, is a promising energy source for large‐scale applications. Triboelectric nanogenerators (TENGs) provide a new strategy for water wave energy harvesting; however, its average performance in realistic water wave conditions is still not high. In this work, a whirling‐folded TENG (WF‐TENG) with maximized space utilization and minimized electrostatic shielding is constructed by 3D printing and printed circuit board technologies. The flexible vortex structure responds easily to multiform wave excitation with improved oscillation frequency. A standard water wave tank is established to generate controllable water waves to characterize the device performance. It is found to be determined by wave conditions and internal structure, which is also revealed by a theoretical dynamical analysis. The WF‐TENG can produce a maximum peak power of 6.5 mW and average power of 0.28 mW, which can power a digital thermometer to operate constantly and realize self‐powered monitoring on the TENG network to prevent possible damage in severe environments. Moreover, a self‐charge‐supplement WF‐TENG network is proposed to improve the output performance and stability. This study provides an effective strategy for improving the average power and characterizing the performance of spherical TENG towards large‐scale blue energy.     

Numerical Stability Verification of a Two-Dimensional Time-Dependent Nonlinear Shallow Water System Using Multidimensional Wave Digital Filtering Network

This paper aims to study the stability effects of a two-dimensional time-dependent nonlinear shallow water (NLSW) system based on the concordance analysis of necessary and sufficient conditions derived from a multidimensional wave digital filtering (MDWDF) network. Approximating the differential equations used to describe elements of a MD passive electrical circuit by grid-based difference equations, the satisfactory Courant–Friedrichs–Levy condition usually known to be necessary are derived with various initial conditions to provide theoretical support for the existence of a MD passive dynamical system and thus stability of the discrete equivalent. Together with the evaluation of the system’s energy and hence solution error propagation that both arise directly and sufficiently to the stability of MDWDF networks, the numerical convergence of the network can be fully established. As a consequence, all instability related aspects in relation to computational errors and overflow corrections are fully excluded leading to uniquely a high degree of robustness of MDWDF architecture. Feasible comparisons are made with a finite element method implemented in the COMSOL Multiphysics to confirm the verification process.     

相对论返波振荡器的非线性理论

本文建立起分析相对论返波管注波互作用过程的自洽非线性工作方程组,理论模型中计及了正向波基波与电子注的异步互作用效应、电子注的空间电荷效应.运用四阶龙格一库塔法编制了数值求解工作方程组的Fortran程序,对均匀耦合阻抗型器件和耦合阻抗单阶跃变型器件的效率进行了仿真和优化.数值模拟结果表明正向波基波与同步波在慢波结构起始处的相差,正向波基波与电子注的异步互作用效应能显著地影响相对论返波管效率,均匀阻抗器件运行于最佳状态时,效率可达到27%,耦合阻抗单阶跃变型器件最优化效率可达到50%.     

Absolute stability of analytic neural networks: an approach based on finite trajectory length

A neural network (NN) is said to be convergent (or completely stable) when each trajectory tends to an equilibrium point (a stationary state). A stronger property is that of absolute stability, which means that convergence holds for any choice of the neural network parameters, and any choice of the nonlinear functions, within specified and well characterized sets. In particular, the property of absolute stability requires that the NN be convergent also when, for some parameter values, it possesses nonisolated equilibrium points (e.g., a manifold of equilibria). Such a property, which is really well suited for solving several classes of signal processing tasks in real time, cannot be in general established via the classical LaSalle approach, due to its inherent limitations to study convergence in situations where the NN has nonisolated equilibrium points. A method to address absolute stability is developed, based on proving that the total length of the NN trajectories is finite. A fundamental result on absolute stability is given, under the hypothesis that the NN possesses a Lyapunov function, and the nonlinearities involved (neuron activations, inhibitions, etc.) are modeled by analytic functions. At the core of the proof of finiteness of trajectory length is the use of some basic inequalities for analytic functions due to Lojasiewicz. The result is applicable to a large class of neural networks, which includes the networks proposed by Vidyasagar, the Hopfield neural networks, and the standard cellular NN introduced by Chua and Yang.