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.

Hierarchical Symbolic Analysis of Large Analog Circuits with Totally Coded Method

Symbolic analysis has many applications in the design of analog circuits. Existing approaches rely on two forms of symbolic-expression representation: expanded sum-of-product form and arbitrarily nested form. Expanded form suffers the problem that the number of product terms grows exponentially with the size of a circuit. Nested form is neither canonical nor amenable to symbolic manipulation. In this paper, we present a new approach to exact and canonical symbolic analysis by exploiting the sparsity and sharing of product terms. This algorithm, called totally coded method (TCM), consists of representing the symbolic determinant of a circuit matrix by code series and performing symbolic analysis by code manipulation. We describe an efficient code-ordering heuristic and prove that it is optimum for ladder-structured circuits. For practical analog circuits, TCM not only covers all advantages of the algorithm via determinant decision diagrams (DDD) but is more simple and efficient than DDD method.

An Analysis on the Mechanism Governing the Effect of Bomb Length upon the Sensitivity of Detection of a Capacitance Fuze

For a detector in a capacitanee fuze working in an electrostatic field, the bomblength (effective length of the conductor part) is an important factor affecting the sensitivityof detection. For the two different kinds of detecting circuit models in general use (the frequency-sensitive and the amplitude-coupling ), mechanism of the effect of bomblength on the sensitvity of detection is analyzed. Through the analysis a conclusion in fullagreement with experimental results has been drawn, that is. the longer the bomb length,the higher the sensitivity, on the condition that the sizes and the sites of the detecting electrodes and bomb diameter remain unchanged.

A Signal-Flow Driven Automatic Physical Synthesis Methodology for Analog Circuits

This paper introduces a novel automatic physical synthesis methodology for analog circuits based on the signal-flow analysis.Circuit analysis sub-system adopts the newly advanced methodology,circuit topology analysis,and circuit sensitivity analysis to generate layout constraints and control performance degradations.Considering the heuristic information about signal-flow,complexity of the methodology is less than the pure performance-driven methodology.And then these constraints are implemented in device generation,placement,and routing sub-systems separately,which makes the different constraints be satisfied at most easily implemented stages.Excellent circuit performance obtained by the methodology is demonstrated by practical circuit examples.

AN ANALYSIS METHOD FOR HIGH-SPEED CIRCUIT SYSTEMS

A new method for analyzing high-speed circuit systems is presented. The method adds transmission line end currents to the circuit variables of the classical modified nodal approach. Then the matrix equation describing high-speed circuit system can be formulated directly and analyzed conveniently for its normative form. A time-domain analysis method for transmission lines is also introduced. The two methods are combined together to efficiently analyze high-speed circuit systems having general transmission lines. Numerical experiment is presented and the results are compared with that calculated by Hspice.

Theoretical analysis method for Howland current source design

The Howland current source （HCS） circuit is commonly used, e.g. in electrical impedance tomography （EIT） sys tems. 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 nonideal opamp model, general formulas and simplified for mulas for calculating the output impedance and the closeloop 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 t^A741 and LM6365 are compared. The magnitudefrequency response and the relationship between the cur rent and the load of HCS are discussed.

Filling the Teaching Gap between Electromagnetics and Circuits

Electrical engineers normally are taught electromagnetism in an electromagnetics course （e.g. in [ 1-2]）, and circuit analysis in an independent course （e.g. in [4-6]）. Circuits are dominated by Kirchhoff s laws, while electromagnetics is dominated by Maxwell＇s equations. However, the correspondence between two sets of equations is not immediately perceived and this creates some uncertainty in the young electrical or electronic engineer, which may grow with the doubt that KirchhotTs laws may be somewhat laws of the nature independent of the laws of electromagnetism. This paper has the purpose of supplying teaching material that may be used to fill the gap, and therefore be taught either at the end of an electromagnetics or at the beginning of a circuit course. It exploits large parts of the paper published in a conference [8], but also contains significant enhancements. The paper first shows simple distributed parameter systems, whose behaviour follows Maxwell＇s equations, and then shows that they, under given assumptions, can be modelled as circuits, whose behaviour is governed by Kirchhoff＇s laws.

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.

A Temperature-Autocompensated Detecting Circuit for the Capacitance Fuze

In view of drastic possible changes in fuze environment tempera- ture,a kind of temperature autocompensated detecting circuit for the capaci- tance fuze is proposed.It provides a steady detected output when the envi- ronment temperature varies from-50℃ to 65℃ and keeps a stable detecting sensitivity.Based on an analysis of the circuit,influence of the major param- eters of the oscillating circuit on the amplitude are explored.A few impor- tant controllable parameters affecting the circuit feature are found out.A parameter-control method is given in order to improve the circuit perfor- mance.

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.

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.

Calculating magnetic shielding effectiveness for high-power dc comparator by magnetic circuit method

Magnetic shielding is very important in the design of a high-power dc comparator. This paper addressed the application of magnetic circuit method to calculate the magnetic shielding effectiveness of high-power dc comparators when an external radial magnetic field is added. The mathematical relationship between the magnetic shielding effectiveness and the parameters of the magnetic shielding body were obtained. To verify the validity of the calculation method, we developped a procedure to measure the magnetic shielding effectiveness of the magnetic body by measuring the induction voltage of the detection winding instead of the magnetic intensity at a point in the magnetic shielding body, making the manipulation much easier. The result calculated with the magnetic circuit method turns out to be closer to the measured one compared with that calculated with a conventional algorithm proposed by Ren, suggesting that the magnetic circuit method is an applicable tool for estimating the toroidal cavity magnetic shielding effectiveness of a heavy current comparator when a radial magnetic field is added.

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.

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.

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.

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.

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.