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.

Theoretical analysis method for Howland current source design

The Howland current source(HCS)circuit is commonly used,e.g.in electrical impedance tomography(EIT)systems.It is important to optimise the design parameters,such as the output impedance,bandwidth,current stability and load range.While many people have used this circuit,it has not been systematically analysed.In this paper,a numerical method is proposed to analyse the characteristics of HCS.Based on a non-ideal op-amp model,general formulas and simplified formulas for calculating the output impedance and the close-loop gain of HCS are deduced.From these formulas,the practical formulas are chosen and their effectiveness has been proven by analysis and experiment.The output impendence of two HCS circuits based on μA741 and LM6365 are compared.The magnitude-frequency response and the relationship between the current and the load of HCS are discussed.

ASYMPTOTIC THEORY FOR THE CIRCUIT ENVELOPE ANALYSIS

Asymptotic theory for the circuit envelope analysis is developed in this paper.A typical feature of circuit envelope analysis is the existence of two significantly distinct timescales:one is the fast timescale of carrier wave,and the other is the slow timescale of modulation signal.We first perform pro forma asymptotic analysis for both the driven and autonomous systems.Then resorting to the Floquet theory of periodic operators,we make a rigorous justification for first-order asymptotic approximations.It turns out that these asymptotic results are valid at least on the slow timescale.To speed up the computation of asymptotic approximations,we propose a periodization technique,which renders the possibility of utilizing the NUFFT algorithm.Numerical experiments are presented,and the results validate the theoretical findings.

Predicting stability of integrated circuit test equipment using upper side boundary values of normal distribution

In response to the growing complexity and performance of integrated circuit(IC),there is an urgent need to enhance the testing and stability of IC test equipment.A method was proposed to predict equipment stability using the upper side boundary value of normal distribution.Initially,the K-means clustering algorithm classifies and analyzes sample data.The accuracy of this boundary value is compared under two common confidence levels to select the optimal threshold.A range is then defined to categorize unqualified test data.Through experimental verification,the method achieves the purpose of measuring the stability of qualitative IC equipment through a deterministic threshold value and judging the stability of the equipment by comparing the number of unqualified data with the threshold value,which realizes the goal of long-term operation monitoring and stability analysis of IC test equipment.

Time-domain analysis methodology for large-scale RLC circuits and its applications

With soaring work frequency and decreasing feature sizes, VLSI circuits with RLC parasitic components are more like analog circuits and should be carefully analyzed in physical design. However, the number of extracted RLC components is typically too large to be analyzed efficiently by using present analog circuit simulators like SPICE. In order to speedup the simulations without error penalty, this paper proposes a novel methodology to compress the time-descritized circuits resulted from numerical integration approximation at every time step. The main contribution of the methodology is the efficient structure-level compression of DC circuits containing many current sources, which is an important complement to present circuit analysis theory. The methodology consists of the following parts： 1） An approach is proposed to delete all intermediate nodes of RL branches. 2） An efficient approach is proposed to compress and back-solve parallel and serial branches so that it is error-free and of linear complexity to analyze circuits of tree topology. 3） The Y to πtransformation method is used to error-free reduce and back-solve the intermediate nodes of ladder circuits with the linear complexity. Thus, the whole simulation method is very accurate and of linear complexity to analyze circuits of chain topology. Based on the methodology, we propose several novel algorithms for efficiently solving RLC-model transient power/ground （P/G） networks. Among them, EQU-ADI algorithm of linear-complexity is proposed to solve RLC P/G networks with mesh-tree or mesh-chain topologies. Experimental results show that the proposed method is at least two orders of magnitude faster than SPICE while it can scale linearly in both time- and memory-complexity to solve very large P/G networks.

基于4~20 mA输出的温湿度传感器设计

基于工业现场温湿度信号的测量,为解决温湿度传感器测量信号远距离传输时受噪声干扰、线路阻抗等的影响,利用4~20 mA电流环的抗干扰特性,采用电流进行信号传输,使电路的传输性能大大提高。设计采用SHT15作为测温、测湿的敏感元件,利用C8051F410单片机的IDAC功能,将测得的温湿度数字量转化成模拟量。再经过适当调理转换电路,并通过软件程序设计改善测量信号的线性度,实现4~20 mA的电流输出。最后利用标准温湿度测量设备进行测试试验分析,验证温湿度传感器的4~20 mA电路可以实现高精度的温湿度测量。

Measurement of dynamic resistance in resistance spot welding

The conventional methods of determining the dynamic resistance were mostly done by measuring the voltage and current at secondary side of transformer in resistance welding machines, in which the measuring set-up normally interferes with the movement of electrode, and the measuring precision is influenced by inductive noise caused by the high welding current. In this study, the dynamic resistance is determined by measuring the voltage at primary side and current at secondary side. This increases the accuracy of measurement because of higher signal-noise ratio, and allows to apply to in-process system without any wires connected to electrodes.

Influence of the gassing materials on the dielectric properties of air

Influence of the gassing materials, such as PA6, PMMA, and POM on the dielectric properties of air are investigated. In this work, the fundamental electron collision cross section data were carefully selected and validated. Then the species compositions of the air–organic vapor mixtures were calculated based on the Gibbs free energy minimization. Finally, the Townsend ionization coefficient, the Townsend electron attachment coefficient and the critical reduced electric field strength were derived from the calculated electron energy distribution function by solving the Boltzmann transport equation. The calculation results indicated that H;O with large attachment cross sections has a great impact on the critical reduced electric field strength of the air–organic vapor mixtures. On the other hand, the vaporization of gassing materials can help to increase the dielectric properties of air circuit breakers to some degree.

Activation of G551D-CFTR by Bicyclooctane Compounds Is cAMP-dependent and Exhibits Low Sensitivity to Thiazolidinone CFTR Inhibitor CFTRinh-172

The G551D-CFTR mutation causing cystic fibrosis(CF) results from a missense mutation at codon 551(G551D) in the gene encoding of the cystic fibrosis transmembrane conductance regulator(CFTR). The G551D mutation in CFTR results in a reduced functional channel but G551D-CFTR is appropriately inserted in the apical membrane. In previous studies we discovered a class of high-affinity bicyclooctane(BCO) G551D-CFTR activators(G551D_ BCOs) with K_d down to 1 μmol/L. In this study, we analyzed the pharmacological activation of G551D-CFTR by the G551D_ BCOs by means of short circuit current analysis and cell-based fluorescence quenching assay. The G551D_ BCOs-induced G551D-CFTR activation is cAMP-dependent and is less sensitive to thiazolidinone CFTR inhibitor CFTRinh-172. These data suggest that (1) the phosphorylation of G551D-CFTR by protein kinase A is required for the activation by G551D_ BCOs; (2) G551D_ BCOs and CFTRinh-172 may act at the same site on the G551D-CFTR molecule.

Robust stability characterizations of active metamaterials with non-Foster loads

Active metamaterials incorporating with non-Foster elements have been considered as one of the means of overcoming inherent limitations of the passive counterparts, thus achieving broadband or gain metamaterials. However, realistic active metamaterials, especially non-Foster loaded medium, would face the challenge of the possibility of instability. Moreover,they normally appear to be time-variant and in unsteady states, which leads to the necessity of a stability method to cope with the stability issue considering the system model uncertainty. In this paper, we propose an immittance-based stability method to design a non-Foster loaded metamaterial ensuring robust stability. First, the principle of this stability method is introduced after comparing different stability criteria. Based on the equivalent system model, the stability characterization is used to give the design specifications to achieve an active metamaterial with robust stability. Finally, it is applied to the practical design of active metamaterial with non-Foster loaded loop arrays. By introducing the disturbance into the nonFoster circuit（NFC）, the worst-case model uncertainty is considered during the design, and the reliability of our proposed method is verified. This method can also be applied to other realistic design of active metamaterials.

Testability Analysis at Switch Level for CMOS Circuits

In this paper we propose a controllability and observability measure at switch level for CMOS circuits based on the cost analysis approach.The complexity of the algorithm is nearly linear.

State Key Laboratory of Power Grid Safety and Energy Conservation,China Electric Power Research Institute,Beijing,China

The power system is experiencing a higher penetration of renewable energy generations(REGs).The short circuit ratio(SCR)and the grid impedance ratio(GIR)are two indices to quantify the system strength of the power system with REGs.In this paper,the critical short circuit ratio(CSCR)is defined as the corresponding SCR when the system voltage is in the critical stable state.Through static voltage stability analysis,the mathematical expression of the CSCR considering the impact of GIR is derived.The maximum value of CSCR is adopted as the critical value to distinguish the weak power system.Based on the static equivalent circuit analysis,it is proved that the CSCR is still effective to evaluate critical system strength considering the interactive impact among REGs.Finally,we find that the GIR can be neglected and the SCR can be used individually to evaluate the system strength when SCR>2 or GIR>5.The correctness and rationality of the CSCR and its critical value are validated on ADPSS.