FAST gradient based yield optimization of nonlinear circuits

A computer program is described that performs a Volterra-series analysis of a weakly nonlinear microwave circuit having an arbitrary topology. The program uses the method of nonlinear currents and a nodal formulation. In this approach, each nonlinear circuit element is described as a linear element in parallel with a set of current sources; each current source represents a single order (greater than one) of the mixing products, and its current is a nonlinear function of the node-voltage components at lower-order mixing frequencies. The weakly nonlinear circuit is reduced to a linear circuit, which contains the linear elements and the linear parts of the nonlinear elements, and a set of excitation sources. The program is intended primarily for use in the design of microwave circuits; its catalog of circuit elements includes the distributed elements necessary for such work. Because the program formulates and solves the circuit equations numerically, the user need not simplify either the circuit or the model of the solid-state device, or make any of the other common simplifying assumptions. >

Reliable yet fast surrogate models are indispensable in the design of contemporary antenna structures. Data-driven models, e.g., based on Gaussian Processes or support-vector regression, offer sufficient flexibility and speed, however, their setup cost is large and grows very quickly with the dimensionality of the design space. In this paper, we propose cost-efficient modeling of antenna structures using Gradient-Enhanced Kriging. In our approach, the training data set contains, apart from the EM-simulation responses of the structure at hand, also derivative data at the respective training locations obtained at little extra cost using adjoint sensitivity techniques. We demonstrate that introduction of the derivative information into the model allows for considerable reduction of the model setup cost (in terms of the number of training points required) without compromising its predictive power. The Gradient-Enhanced Kriging technique is illustrated using a dielectric resonator antenna structure. Comparison with conventional Kriging interpolation is also provided.

An important step of the microwave design process is the adjustment of geometry and material parameters of the structure under consideration to make it meet given performance requirements. Nowadays, it is typically conducted using full-wave electromagnetic (EM) simulations. Because accurate high-fidelity simulations are computationally expensive, automation of this process is quite challenging. In particular, the use of conventional numerical optimization algorithms may be prohibitive as these methods normally require a large number of objective function evaluations (and, consequently, EM simulations) to converge. The adjoint sensitivity technique that recently become available in commercial EM simulation software packages can be utilized to speed up the EM-driven design optimization process either by utilizing the sensitivity information in conventional gradient-based algorithms or by combining it with surrogate-based approaches. Here, several recent methods and algorithms for microwave design optimization using adjoint sensitivity are reviewed. We discuss advantages and disadvantages of these techniques and illustrate them through numerical examples.

This chapter describes some/new artificial neural network (ANN) neuromodeling techniques and natural optimization algorithms for electromagnetic modeling and optimization of nonlinear devices and circuits. Neuromodeling techniques presented are based on single hidden layer feedforward neural network configurations, which are trained by the resilient back-propagation algorithm to solve the modeling learning tasks associated with device or circuit under analysis. Modular configurations of these feedforward networks and optimal neural networks are also presented considering new activation functions for artificial neurons. In addition, some natural optimization algorithms are described, such as continuous genetic algorithm (GA), a proposed improved-GA and particle swarm optimization (PSO). These natural optimization algorithms are blended with multilayer perceptrons (MLP) artificial neural network models for fast and accurate resolution of optimization problems. Some examples of applications are presented and include nonlinear RF/microwave devices and circuits, such as transistors, filters and antennas.

The paper discusses the application of the space-mapping concept to the computer-aided optimisation of nonlinear microwave circuits. This method allows the linear subnetwork to be characterised by electromagnetic (EM) simulation, while the nonlinear analysis and design are based on the piecewise harmonic-balance technique. The map between the EM and the circuit model (CM) parameter spaces is defined implicitly and the search for the optimum EM topology is carried out by a norm-reducing Newton iteration.

The implementation of extensive optimization capabilities in a general-purpose harmonic-balance simulator is described. Two different optimizers suitable for autonomous and forced circuits, respectively, are discussed in detail, and their merits and limitations are compared. The efficient numerical optimization of nonlinear microwave circuits specified over a finite frequency band is demonstrated. An example is given, showing that the procedure is very efficient, thus opening the way to the straightforward design of some modern monolithic microwave integrated circuit (MMIC) devices such as multioctave distributed mixers and power amplifiers. >

A review of several techniques related to the combination of geometrical decomposition of mixed geometry problems coupled with the inclusion of single and multiple linear and nonlinear circuit elements is addressed for use with the FDTD method. As a demonstrator of the algorithmic aspects related to this problem, a slot loop antenna will be analysed. Several variants of the antenna are described, the simplest variation consisting of a slot loop antenna fed by a CPW line connected via a slotline transition. More elaborate variations include techniques for the inclusion of lumped linear and/or nonlinear elements into the FDTD code. The inclusion of three terminal lumped active devices is demonstrated in order to describe the algorithmic details of the slot loop operated as an active antenna. Where possible, experimental and theoretical predictions are compared in order to validate the methodologies adopted.

This article outlines a novel approach for simulating general nonlinear circuits in the time-domain. The proposed approach can be considered as the generalization of the numerical inversion Laplace transform (NILT). NILT has been used for circuits with only linear elements. The new approach enables the well-known advantages of NILT such as the guaranteed numerical stability and the high-order approximation, to be carried over to the domain of nonlinear circuit simulations. Numerical examples are given to demonstrate the validity and efficiency of the proposed method.

Increasing complexity of actual computer systems has made exact modelling techniques prohibitively expensive, and the need for approximation techniques for performance evaluation is well-recognized. A new approximation technique is given for product-form queueing networks with constant-rate servers. It estimates the shift in mean queue lengths rather than the fractional deviations used in the Chandy-Neuse linearizer. Experimental results are reported which show that the new approximation 92% of the times has superior accuracy to linearizer. As population grows, the superior accuracy over linearizer increases. In 58% of the test cases, the new approximation technique gave errors of zero (at least 6 digits) while linearizer achieves such accuracy in less than 2.5% of cases. In some of the stress cases described, the new approximation technique has roughly five orders of magnitude less error than linearizer.KeywordsApproximation TechniqueQueue LengthPoint ProblemGenerate Test CaseFractional DeviationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The optimization of the operating bias condition and input harmonic termination is investigated for the practical circuit design of high efficiency inverse class-F amplifiers. It is found that inverse class-F amplifiers exhibit a high efficiency at the quiescent current of larger than 10% Idss, which cannot be achieved by class-F amplifiers. It is also revealed that the efficiency of inverse class-F amplifiers can be effectively improved by the open or high impedance of the input 2nd harmonic termination. These results have been explained by the behavior of the amplitude and phase relationship between the input and output harmonics.

This paper presents pseudo-coevolutionary genetic algorithms (GA's) for power electronic circuit (PEC) optimization. Circuit parameters are optimized through two parallel co-adapted GA-based optimization processes for power conversion stage and feedback network, respectively. Each process has tunable and untunable parametric vectors. The best candidate of the tunable vector in one process is migrated into the other process as untunable vector through a migration controller, in which the migration strategy is adaptively controlled by a first-order projection of the maximum and minimum bounds of the fitness value in each generation. Implementation of this method is suitable for systems with parallel computation capacity, resulting in considerable improvement of the training speed. Optimization of a buck regulator for meeting requirements under large-signal changes and at steady state is illustrated. Simulation predictions are verified with experimental results.

Self-contained long-lasting energy sources are rapidly increasing in importance as portable electronics and inaccessible devices such as wireless sensors are finding wider and more varied applications. However, in many circumstances replacing power supplies, such as conventional batteries, becomes impractical and the development of a self-renewing source of energy is paramount to the continued development of such devices. The ability to convert ambient mechanical energy to usable electrical energy fills these requirements and one aspect of current research seeks to increase the efficiency and performance of these energy harvesting systems. However, to achieve acceptable performance conventional vibration-based energy harvesting devices based on linear elements must be specifically tuned to match environmental conditions such as the frequency and amplitude of the external vibration. As the environmental conditions vary under ambient conditions the performance of these linear devices is dramatically decreased. The strategy to efficiently harvest energy from low-level, intermittent ambient vibration, proposed herein, relies on the unique properties of a particular class of strongly nonlinear vibrating systems that are referred to as “essentially” nonlinear.

Recent works have introduced an effective technique to analyze nonlinear dynamics of a class LM of circuits containing ideal flux– or charge–controlled memristors and linear lossless elements (i.e. ideal capacitors and inductors). The technique, named Flux–Charge Analysis Method (FCAM), is based on analyzing the circuits in the flux–charge domain instead of the traditional voltage–current domain. Goal of this paper is to extend the FCAM to a larger class N of circuits containing also nonlinear capacitors and inductors. Nonlinear circuits with memristors and nonlinear lossless elements are widely used to several real nanoscale devices including the well-known Josephson junction. After deriving the constitutive relation in the flux–charge domain of each two–terminal element in N, the work focuses on a relevant subclass of N for which a state equation description can be obtained. State Equations (SE) formulation provides the fundamental basis for studying the chief features of the nonlinear dynamics: presence of invariant manifolds in autonomous circuits; coexistence of infinitely many different reduced–order dynamics on the manifolds; bifurcations due to changing of initial conditions for a fixed set of parameters, a.k.a. bifurcations without parameters.

Multimedia applications usually have throughput constraints. An implementation must meet these constraints, while it minimizes resource usage and energy consumption. The compute intensive kernels of these applications are often specified as cyclo-static or synchronous dataflow graphs. Communication between nodes in these graphs requires storage space which influences throughput. We present an exact technique to chart the Pareto space of throughput and storage trade-offs, which can be used to determine the minimal buffer space needed to execute a graph under a given throughput constraint. The feasibility of the exact technique is demonstrated with experiments on a set of realistic DSP and multimedia applications. To increase scalability of the approach, a fast approximation technique is developed that guarantees both throughput and a, tight, bound on the maximal overestimation of buffer requirements. The approximation technique allows to trade off worst-case overestimation versus run-time.

Purpose. To work out the methodology and computer program for calculation of processes of the commercial frequency electromagnetic field penetration into steel body taking into account non-linearity of magnetizing steel characteristics. Research methods. The method of magnetoelectric equivalent circuits is used to calculate electromagnetic fields in a ferromagnetic medium. A feature of the method is the use of so-called "magnetic current" - the derivative of the magnetic flux. This made it possible to introduce “magnetic capacitors” into the circuit, which significantly simplified the equations of state, which are compiled on the basis of Kirchhoff's laws for electric and magnetic circuits, the law of electromagnetic induction, and the law of total current. Methods of numerical integration of differential equations are taken in the form of additional equations, which are attached to the state equations. The result is a system of linear algebraic equations, which at each step of integration has a unique solution. The magnetization curve of steel is approximated by splines, which allows to refine variable coefficients of the system of equations at each integration step.. The results. The developed methodology and algorithm allowed developing the computer program for calculating the dynamics of penetration of an electromagnetic field into a steel body. Calculations for this program allowed us to calculate the depth of penetration of the electromagnetic field into the steel body. The proposed method allows a coil with a ferromagnetic core to be considered as a linear element in the intervals of the applied voltage determined in this method, to calculate the equivalent magnetic permeability of the core, as well as the inductance of the coil. Originality. For the first time, the method of using nonlinear magnetoelectric equivalent circuits was used to analyze the transient processes of penetration of an electromagnetic field into a steel body, which made it possible to reduce the calculation time by more than two. Practical value. Based on the research, the limits of magnetic field strength values are determined, in which linear methods of analysis can be applied. This allows the use of linear analysis methods for modeling electromagnetic fields in the structural elements of transformers using the finite element.