Effects of nonlinear feedback in the frequency domain

A simple methodology to evaluate harmonic distortion in the frequency domain for circuits and systems made up of a nonlinear high-gain path with a nonlinear feedback network is presented. The approach provides compact closed-form expressions which constitute a direct extension of the classic ones valid at dc. The result improve our understanding of nonlinear frequency behavior in general feedback circuits and can even be used in manual design. The accuracy of the equations obtained was evaluated by comparison with computer simulations and measurements on an example circuit. Simulated and experimental data highly agree with the theoretical model.     

Symbolic Steady-State Analysis for Strongly Nonlinear Circuits and Systems

A symbolic method for steady-state analysis of nonlinear circuits and systems is presented. This method is based on the principle of the Equivalent Small Parameter method (the ESP method), which is an improved perturbation technique combined with the harmonic balance method. Using this method, a set of high-order nonlinear differential equations can be solved and the symbolic expressions of the steady-state periodic solutions for the required variables can be obtained. Two examples are given and show that the method is general and can be used for both weakly and strongly nonlinear circuits, and time-variant nonlinear circuits such as switching mode circuits.     

Fast solution of nonlinear equations using parallel analog hardware

Parallel analog circuits are introduced for the solution of systems of nonlinear algebraic equations and the integration of systems of differential equations. Both simulations using HSPICE and a hardware implementation are presented which show how the circuitry can be used to solve: the power flow and transient analysis problems for power systems, and the simulation of a jet engine. In all cases solutions are obtained in better than real time. The results are comparable in accuracy to digital solutions of the same problems.     

基于遗传算法的容差模拟电路故障诊断

给出了用于模拟电路元件参数识别的多频传递函数法的过程,并对故障诊断方程的可解度进行了分析,在此基础上,将诊断方程的求解转化为非线性函数的优化问题,并运用改进的遗传算法来解决这个问题,算法实例表明该方法简化了故障诊断方程的求解过程,加速了容差电路故障元件的定位,有一定的应用价值。     

The time domain solution of the Volterra functional equation: Application to nonlinear circuit analysis

An iterative technique to solve Volterra integral equations based on the Newton-Raphson method is presented which has a wide region of convergence, enabling the analysis of grossly nonlinear circuits. Instead of performing convolution in the frequency domain, the algorithm computes directly in the time domain which is found to be more efficient, if the number of time steps is maintained within a suitable range.     

线性与非线性电路相统一的伴随网络法

把线性电路中的伴随网络法运用到微波非线性电路中,文中给出了对线性与非线性电路都适用的伴随网络法,能快速求解非线性电路中精确的灵敏度.     

A parallel FFT accelerated transient field-circuit simulator

A novel fast electromagnetic field-circuit simulator that permits the full-wave modeling of transients in nonlinear microwave circuits is proposed. This time-domain simulator is composed of two components: 1) a full-wave solver that models interactions of electromagnetic fields with conducting surfaces and finite dielectric volumes by solving time-domain surface and volume electric field integral equations, respectively, and 2) a circuit solver that models field interactions with lumped circuits, which are potentially active and nonlinear, by solving Kirchoff's equations through modified nodal analysis. These field and circuit analysis components are consistently interfaced and the resulting coupled set of nonlinear equations is evolved in time by a multidimensional Newton-Raphson scheme. The solution procedure is accelerated by allocating field- and circuit-related computations across the processors of a distributed-memory cluster, which communicate using the message-passing interface standard. Furthermore, the electromagnetic field solver, whose demand for computational resources far outpaces that of the circuit solver, is accelerated by a fast Fourier transform (FFT)-based algorithm, viz. the time-domain adaptive integral method. The resulting parallel FFT accelerated transient field-circuit simulator is applied to the analysis of various active and nonlinear microwave circuits, including power-combining arrays.     

无源定位观测方程的两类伪线性化方法及渐近最优闭式解

为避免无源定位中的迭代运算,该文针对两类特殊的无源定位(非线性)观测方程,分别提出将其进行伪线性化处理,从而实现目标位置闭式解算的理论分析框架.首先,在不限定具体物理观测量的前提下,归纳总结出两类将非线性观测方程转化为伪线性观测方程的数学模型,并推导出用于目标定位的加权线性最小二乘闭式解.接着,利用一阶误差分析方法定量分析两类闭式解的理论定位方差,并证明其参数估计性能均能够达到相应的克拉美罗界(在门限效应发生前),从而证明闭式解的渐近最优性.最后,文中以AOA/TOA联合定位和AOA/TDOA/FDOA联合定位为算例,分别阐述两类伪线性化无源定位方法的具体应用,并通过仿真实验验证文中理论分析的有效性.     

An analysis of gain-switched semiconductor lasers generating pulse-code-modulated light with a high bit rate

A theoretical analysis of gain-switched semiconductor lasers is described. Results of the numerical solution of the coupled rate equations for photon and electron densities are presented, along with analytical expressions which have been derived by using certain approximations to solve these nonlinear differential equations. The two sets of results are seen to be in good agreement. The design requirements to be met in order to use the pulse-code-modulated output in an optical communications system are discussed. It is shown theoretically that bit rates, of the order of 7 Gbits/s without time-division multiplexing, and 35 Gbits/s with multiplexing can be obtained.     

使用遗传算法进行微波非线性电路包络仿真

介绍用于分析任意调制信号激励的微波非线性电路包络仿真技术,相应给出了线性器件的伴随模型,并将该方法发展为分析多载波调制信号激励的强非线性电路。此外,本文给出了一种求解非线性谐波平衡方程组或交调波平衡方程组的非数值方法———基于十进制编码的混沌遗传算法(DCGA),融合设计了相应的交叉和变异操作,并将混沌过程引入其中以避免陷入早熟状态,可有效地产生更优解,并加速种群的收敛。最后,给出了运用这种方法的两个计算实例。     

Modeling of discrete semiconductor devices

Numerical modeling established itself as a powerful tool for the analysis and design of discrete semiconductor devices and integrated circuits. The paper reviews the basic semiconductor equations, the physical internal mechanisms implemented in the present simulation programs and the numerical methods used to solve the nonlinear semiconductor equations. Selected results of numerical simulation of high frequency and high power discrete devices are given. The exemples comprise bipolar and FET devices made on Si or GaAs, operating in steady state or transient conditions and modeled in one or two dimensions.     

A Multi-Band Transformer for Two Arbitrary Complex Frequency-Dependent Impedances

A multi-frequencies transformer for two arbitrary complex frequency-dependent impedances is presented. Design equations of the proposed transformer are derived, and particle swarm algorithm can be used to solve the resulting nonlinear equations. Some numerical examples for two-, three-, and four-section transmission line transformer were presented to verify the validity of the proposed design.     

Time-domain analysis of lossy multiconductor transmission lines based on the Lax–Wendroff technique

Taking advantage of the hyperbolic characteristics of the telegrapher equations, this paper applies the Lax–Wendroff technique, usually used in fluid dynamics, to transmission line analysis. A second-order-accurate Lax–Wendroff difference scheme for the telegrapher equations for both uniform and nonuniform transmission lines is derived. Based on this scheme, a new method for analyzing lossy multiconductor transmission lines which do not need to be decoupled is presented by combining with matrix operations. Using numerical experiments, the proposed method is compared with the characteristic method, the fast Fourier transform (FFT) approach, and the Lax–Friedrichs technique. With the presented method, a circuit including lossy multiconductor transmission lines is analyzed and the results are consistent with those of PSPICE. The nonlinear circuit including nonuniform lossy multiconductor transmission lines is also computed and the results are verified by HSPICE. The proposed method can be conveniently applied to either linear or nonlinear circuits which include general transmission lines, and is proved to be efficient.     

The finite-difference time-domain solution of lossy MTL networkswith nonlinear junctions

We describe a numerical technique to solve lossy multiconductor transmission line (MTL) networks, also known as tube/junction networks, which contain nonlinear lumped circuits in the junctions. The method is based on using a finite-difference technique to solve the time-domain MTL equations on the tubes, as well as the modified nodal analysis (MNA) formulation of the nonlinear lumped circuits in the junctions. The important consideration is the interface between the MTL and MNA regimes. This interface is accomplished via the first and last finite-difference current/voltage pair on each MTL of the network and, except for this, the two regimes are solved independently of each other. The advantage of the FDTD method is that the MTL equations may contain distributed source terms representing the coupling with an external field. We apply the method to previously published examples of multiconductor networks solved by other numerical methods, and the results agree exceptionally well. The case of an externally coupled field is also considered     

用时域-谱平衡法分析 FDMA 数字调制信号激励的微波非线性电路

本文提出一种用于微波非线笥电路分析的时域－谱平衡算法,这种算法可以用于各种数字调制信号激励的微波非线性电路的分析,尤其适用于频分多址的数字调制信号的分析。利用算法,分析了ＱＰＳＫ信号激励的微波放大器,所得模拟结果与理论分析吻合。     

基于FDTD的约瑟夫森结与超导传输线协同分析方法

为实现高性能处理器,超导RSFQ（快速单磁通量子）电路被提出.该电路主要由超导约瑟夫森结和超导无源传输线组成,对其建模分析是超导RSFQ电路设计的基础.本文提出了基于FDTD（时域有限差分）的约瑟夫森结与超导传输线的协同分析方法.该方法采用FDTD数值方法求解超导传输线的电报方程.在超导传输线与约瑟夫森结交界处的非线性边界条件上,采用了Newton-Raphson迭代算法.数值结果表明,本文提出的约瑟夫森结和超导传输线的协同分析方法与WRspice仿真软件相比具有相同精度,且运算效率显著提高.     

Integrated physics-oriented statistical modeling, simulation, andoptimization [MESFETs]

Physics-based modeling of MESFETs is addressed from the point of view of efficient simulation, accurate behavior prediction and robust parameter extraction. A novel integration of a large-signal physics-based model into the harmonic balance equations for simulation of nonlinear circuits, involving an efficient Newton update, is presented and exploited in a gradient-based FAST (feasible adjoint sensitivity technique) circuit optimization technique. For yield-driven MMIC design a relevant physics-based statistical modeling methodology is presented. Quadratic approximation of responses and gradients suitable for yield optimization is discussed. The authors verify their theoretical contributions and exemplify their computational results using built-in and user-programmable modeling capabilities of the CAE systems OSA90/hope and HarPE. Results of device modeling using a field-theoretic nonlinear device simulator are reported     

Analysis of the annular-ring-loaded circular-disk microstripantenna

A rigorous analysis of the natural resonance frequencies and input impedance characteristics of an annular-ring-loaded (ARL) circular-disk microstrip antenna is presented. Using vector Hankel transforms, the problem is formulated in terms of vector dual-integral equations. Galerkin's method is then used to solve the equations to obtain the resonance frequencies and the current distribution on the conductive patches arising from a probe excitation. Due to the singular nature of the current distribution, the singularity subtraction method has been used to accelerate the convergence of basis function expansions. Experiments for determining resonance frequencies and input impedance characteristics of an ARL circular-disk microstrip antenna with various substrate thicknesses have been made. The theoretical results are in good agreement with the experimental data even when the thickness of the substrate is 0.1 substrate wavelength. It is shown that this theory can be used to analyze some microstrip antennas with an electrically thick substrate, including the analysis of mutual coupling between conductive patches or between the path and the feed of a microstrip antenna     

Plane-wave theory of self-doubling optical parametric oscillators

This paper presents a theoretical analysis of self-doubling optical parametric oscillators (OPOs) where a single nonlinear crystal is used for both parametric generation and frequency doubling. In these devices, the parametric generation and frequency-doubling processes are both phase matched for the same direction of propagation inside the crystal. Different polarization geometries for which this simultaneous phase-matching condition can potentially be satisfied are identified and categorized. Plane-wave coupled-mode equations are presented for each of these categories. Numerical solutions of these coupled-mode equations and calculation of the single-pass saturated signal gain are outlined. Intracavity signal photon flux calculations based on these numerical solutions are presented. The dependence of performance measures such as the photon conversion efficiency on various design parameters are investigated     

Analysis and design of class E amplifier with shunt capacitance composed of nonlinear and linear capacitances

The Class E amplifier requires exact shunt capacitance to achieve optimum operation. Most Class E amplifiers are usually constructed by adding an external capacitor to the output capacitance of the power transistor in order to obtain the total required shunt capacitance. The output capacitance of the power transistor is nonlinear and the external capacitance is linear. Therefore, neither design equations for linear shunt capacitance nor the design equations for nonlinear shunt capacitance can be used in most designs, especially when the two are comparable. This paper presents an analysis and a design procedure for the Class E amplifier with a shunt capacitance composed of both a transistor nonlinear output capacitance and a linear external capacitance for the duty cycle D=0.5. Because the design equations do not have analytical forms, this paper provides a table and figures, which show results of numerical analysis. The Class E amplifier can be designed using these table and figures. A design example is given to illustrate the design procedure. Simulation results of the example circuit with PSpice and experimental results are presented to verify the theoretical results.