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Contribution: Two general rules for calculating, in the time domain, step discontinuities of voltages and currents in electric circuits, combining physical principles and basic mathematical treatment. The two general rules, resulting from a formal method of analysis, provide a straightforward way to update the states of a circuit, immediately after the occurrence of switching or impulsive excitation. Among its advantages, they can be used to simplify the numerical simulation of elaborate circuit topologies by avoiding approximate models of impulsive sources or switches. Background: In most engineering undergraduate textbooks, the effects of switching and impulsive sources on higher order electric circuits are usually studied for the particular case of linear time-invariant (LTI) circuits in the Laplace transform domain. This approach, however, can be time consuming and demands little reasoning on the physical principles of circuit operation. Moreover, it is not adequate for linear time-variant or nonlinear circuits. Intended Outcomes: Step discontinuities in electric circuits, caused by switching or impulsive sources, are identified and calculated through the method, allowing complete responses to be obtained afterward. Not only can the method be extended to linear time-variant and nonlinear circuits but it also has interesting consequences in numerical simulation of circuits. Application Design: An application exercise and a set of conceptual questions on the subject were proposed to electrical engineering students. Findings: The analysis of the educational experiment indicates that applying the method presented herein improves the students’ ability to obtain initial conditions of circuits, being a more straightforward and effective approach than using Laplace transform techniques. [ABSTRACT FROM AUTHOR]

A modern challenge in electrical engineering education is to keep the math at a sufficient level, with a goal to find an optimal balance between calculus competence and operative skills needed for real-life technical applications. It is not uncommon that some gaps emerge during this quest, which makes it difficult for undergraduates to entirely understand topics related on prior knowledge. This paper aims to draw attention to several important moments concerning total response of Continuous Linear Time Invariant systems, which are superficially or incorrectly explained in many textbooks, and to offer logical arrangement which can be easily understood and accepted by students. The base of discussion relies on classical calculus background, particularly on Picard's theorem on existence and uniqueness. This theorem is rarely mentioned in signals and systems textbooks. However, mathematical models of many types of signals don't satisfy the condition for continuity, which can easily produce difficulties in the learning process. It is shown that some reported disagreements and issues related to initial conditions, can be easily cleared out by using the smooth transition from classical calculus to mathematics used in system theory. It is also shown that the classical method is always the primary tool, even for determining the impulse response, while the impulse response is unnecessary or sufficient to determine the total system response, regardless of whether the convolution integral is used.

In this article, an analytical concept and hardware verification of the time-varying infinite impulse response narrow multiband-stop filter with nonzero initial conditions are presented. The time variability of the filter parameters and nonzero initial conditions are introduced to the filter structure in order to reduce its transient response. Such a filter can be very useful in various measurement systems. In particular, short transient filters are very desirable for processing signals whose initial part is of great importance. In this article, the algorithm for finding the length of the initial conditions vector is presented. As an example, the proposed IIR multinotch filter is used for removing power-line interferences from the ECG signal. Computer simulations, hardware verification, and performance indices demonstrate that the proposed time-varying IIR multinotch filter with nonzero initial conditions possesses much better properties than the traditional time-invariant filter with zero initial conditions. [ABSTRACT FROM AUTHOR]

The discovery of simple chaotic systems with complex dynamics has always been an interesting research work. This brief aims to construct an extremely simple chaotic system with infinitely many coexisting chaotic attractors. The system consists of five terms with two nonlinearities, and has an infinite number of unstable equilibria owing to its sinusoidal nonlinearity. The most prominent feature of the system is that it coexists infinitely many chaotic attractors for different initial values and fixed system parameters. To our best knowledge, there is no 3-D system with such a simple mathematical model can produce infinitely many coexisting chaotic attractors. The phenomenon of coexisting attractors of the new system is numerically investigated. The circuit and microcontroller-based implementation of the system are presented as well. [ABSTRACT FROM AUTHOR]

A specific class of nonlinear systems, admitting finite-duration attractors (FDAs), is introduced in this paper, and used for consensus of multiagent systems (MASs). The advantage is that one can obtain a closed-form solution for the settling time function of the presented nonlinear systems. Such a system exhibits a two-phase convergence process, and its settling time function takes values over a finite duration. However, the duration width changes with respect to the initial condition. The FDA-based consensus protocol is shown to make the MAS undertaken achieve finite-duration convergence. With illustrative examples, the perfect consensus property is verified for MASs with or without a leader agent. [ABSTRACT FROM AUTHOR]

An experiment was performed to study the effect of a magnetic field on the initial radius of a metallic gas-puff Z-pinch with a power-law density profile. The IMRI-5 generator (450 kA and 450 ns) was used as a driver. The preembedded axial magnetic field $B_{z0}$ was varied from 0 to 1.5 T. To determine the initial pinch radius $r_{0}$ , the function $r(t)$ was used that was derived from the time dependence of the pinch inductance $L(t)$. The time-dependent inductance $L(t)$ , in turn, was determined as a function of load voltage $V_{\mathrm{ load}}(t)$ and pinch current $I(t)$. The function $r(t)$ was verified using time-gated optical imaging. Measurements have shown that the initial radius of the metallic gas-puff Z-pinch decreased from 7 to 8 cm at $B_{z0} = 0$ to 2.1–1.7 cm at $B_{z0} = 1.5$ T. The decrease in initial radius $r_{0}$ was accounted for by the effect of the magnetic field on the ion gyroradius. [ABSTRACT FROM AUTHOR]

In this paper, a new method is presented to calculate the exact analytical solution of distributed RC, LC, and RLC interconnects with a random input at an arbitrary point through the line. The proposed method, based on a modified Duhamel theorem, is used to calculate the time-domain transient response of the initially conditioned interconnects. This method is applied to a line driven by ramp and exponential inputs. The new analytical solutions are expressed as an infinite summation of sinusoidal terms. However, a negligible worst case error of <1% is observed for the expressions compared with HSPICE simulations for Fourier series with tens of terms. In addition, from these results a new model for transient response of a line considering the driver output resistance and capacitance is presented. Good accuracy is observed between the model and HSPICE simulations for various distributed interconnects and drivers. Furthermore, the developed solution is extended to include signal transient and crosstalk noise in multicoupled inductive-effect-prominent lines. In addition, arbitrary switching patterns for identical and nonidentical lines are investigated employing the new method and evaluated with HSPICE simulations. [ABSTRACT FROM AUTHOR]

With Fourier series and Fourier integrals, a new and systematic approach, called the Amir and Nasser (AMN) method, is proposed to derive exact analytical expressions for step input response of distributed resistance capacitance (RC), inductance-capacitance (LC), and resistance-inductance-capacitance (RLC) models of interconnects. These solutions are obtained for time-domain responses of any arbitrary point on a finite interconnect line, considering initial voltage through the line. This method is appropriate for both on-chip and printed circuit board wires without any limitations in their length or characteristic parameters. The developed solutions are expressed as infinite summation of sinusoidal terms. An accuracy of over 99.5% is observed for the expressions compared with the HSPICE simulations for at most a number of several tens of sinusoidal terms for Fourier series. It is shown that ignoring the initial voltage through the line leads to considerable error as high as 33% at the far end voltage in global interconnects for 65-nm technology node. The AMN method is extended to semi-infinite distributed $RC$ and $RLC$ interconnects for which exact closed-form expressions are achieved. [ABSTRACT FROM AUTHOR]

This paper presents the following: (1) a method for evaluating weather forecasts using satellite passive millimeter-wave observations and (2) tropical weather forecast evaluation for a weather forecasting system composed of the fifth-generation NCAR/Penn State Mesoscale Model employing its best physics options and gridded analyses and forecasts from the NCEP Global Forecast System used for initial and boundary conditions. Forecasts at 5-km resolution between 8 and 10 h after the initial time for 79 storm systems that are distributed over Thailand and nearby regions and span a year are evaluated using brightness temperatures (TBs) and precipitation parameters coincidentally observed by the passive millimeter-wave spectrometer Advanced Microwave Sounding Unit (AMSU) aboard the NOAA-16 satellite. The precipitation parameters including surface precipitation rate, peak vertical wind, and water paths for rainwater, snow, and graupel; the sum of rainwater, snow, and graupel; cloud liquid water; and cloud ice are from the AMSU MIT Precipitation (AMP) retrieval products. Despite the difficulty of weather forecasting in the tropics, results are encouraging. Forecasted TBs and precipitation parameters statistically agree with AMSU observations. The forecasted storm location, morphology, intensity, and area are generally similar to AMSU observations. The main forecast errors include storm location offsets and overforecasting of large ice particles. The weather forecasting system can provide useful high-resolution forecasts for the tropics 8-10 h in advance. Weather forecasts in the tropics will be substantially improved if storm locations can be accurately corrected by employing satellite passive millimeter-wave observations. [ABSTRACT FROM AUTHOR]

Negative bias temperature instability (NBTI) has evolved into one of the most serious reliability concerns for highly scaled pMOSFETs. It is most commonly interpreted by some form of reaction-diffusion model, which assumes that some hydrogen species is first released from previously passivated interface defects and then diffuses into the oxide. It has been argued, however, that hydrogen motion in the oxide is trap-controlled, resulting in dispersive transport behavior. This defect-controlled transport modifies the characteristic exponent in the power law that describes the threshold-voltage shift. So far, a number of NBTI models based on dispersive transport have been published. Interestingly, although seemingly based on similar physical assumptions, these models result in different predictions. Most notably, both an increase and a decrease in the power-law time exponent with increasing dispersion have been reported. Also, different functional dependences on the dispersion parameter have been given in addition to differences in the prefactors and the saturation behavior. We clarify these discrepancies by identifying the boundary and initial conditions which couple the transport equations to the electro-chemical reaction at the interface as the crucial component. We proceed by deriving a generalized reaction (dispersive) diffusion formalism and provide the missing link between the various published models by demonstrating how each of them can be derived from this generalized model. [ABSTRACT FROM PUBLISHER]

System identification problems often arise where the only modeling records available consist of multiple short-time-duration signals. This motivates the development of a modeling approach that is tailored for this situation. An identification algorithm is presented here for parameter estimation based on minimizing the simulated prediction error, across multiple signals. The additional complexity of estimating the initial states corresponding to each signal is removed from the estimation algorithm. A numerical simulation demonstrates that the proposed algorithm performs well in comparison to the often-used least squares method (which leads to biased estimates when identifying systems from measurement noise corrupted signals). The approach is applied to the identification of the passive oculomotor plant; parameters are estimated that describe the dynamics of the plant, which represent the time constants of the visco-elastic elements that characterize the plant connective tissue. [ABSTRACT FROM AUTHOR]

The magnetic hysteresis phenomenon plays an important role in the ferroresonance behavior of a transformer. however, most existing transformer models for the analysis of the ferroresonance phenomenon either ignore the hysteresis effects or represent it based on the hysteresis major loop and scale it for lower current levels. Such a modeling approach does not reflect the actual physical behavior of the magnetic core with respect to the ferroresonance phenomenon. This paper, based on Preisach theory, introduces an accurate model of hysteretic inductor to represent a single-phase transformer for the investigation of the ferroresonance phenomenon. Based on the developed model, time-domain simulation studies show that even in the case of a single-phase transformer where no magnetic coupling exists between the three-phases, all known types of ferroresonance, including fundamental, sub-harmonic, quasi-periodic and chaotic modes, may occur. The effects of hysteresis and its initial conditions, grading capacitors and transformer winding capacitance on occurrence of ferroresonance and its change of mode are also discussed. [ABSTRACT FROM AUTHOR]

Synchronization between two identical chaotic systems (drive and response) with different initial conditions can be achieved provided that the conditional Lyapunov exponents are all negative. Adding an AM signal to the drive system, the two systems become asymptotically synchronized. The AM signal can be recovered by utilizing the property of the asymptotic synchronization. Chaotic AM noise is present as a direct result of the chaotic AM demodulation. Signal-to-chaotic-AM-noise ratio is calculated as a function of the signal amplitude [ABSTRACT FROM PUBLISHER]