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The purpose of this paper is to propose a novel nonlocal fractal calculus scheme dedicated to the analysis of fractal electrical circuit, namely, the generalized nonlocal fractal calculus.

For being generalized, an arbitrary kernel function has been adopted. The condition on order has been derived so that it is not related to the γ-dimension of the fractal set. The fractal Laplace transforms of our operators have been derived.

Unlike the traditional power law kernel-based nonlocal fractal calculus operators, ours are generalized, consistent with the local fractal derivative and use higher degree of freedom. As intended, the proposed nonlocal fractal calculus is applicable to any kind of fractal electrical circuit. Thus, it has been found to be a more efficient tool for the fractal electrical circuit analysis than any previous fractal set dedicated calculus scheme.

A fractal calculus scheme that is more efficient for the fractal electrical circuit analysis than any previous ones has been proposed in this work.

Power consumption is a top priority in high-performance asynchronous circuit design today. The purpose of this study is to provide a spatial correlation-aware statistical dual-threshold voltage design method for low-power design of template-based asynchronous circuits.

In this paper, the authors proposed a statistical dual-threshold voltage design of template-based asynchronous circuits considering process variations with spatial correlation. The utilized circuit model is an extended Timed Petri-Net which captures the dynamic behavior of the asynchronous circuit with statistical delay and power values. To have a more comprehensive framework, the authors model the spatial correlation information of the circuit. The authors applied a genetic optimization algorithm that uses a two-dimensional graph to calculate the power and performance of each threshold voltage assignment.

Experimental results show that using this statistically aware optimization, leakage power of asynchronous circuits can be reduced up to 3X. The authors also show that the spatial correlation may lead to large errors if not being considered in the design of dual-threshold-voltage asynchronous circuits.

The proposed framework is the scheme giving a low-power design of asynchronous circuits compared to other schemes. The comparison exhibits that the proposed method has better results in terms of performance and power. To consider the process variations with spatial correlation, the authors apply the principle component analysis method to transform the correlated variables into uncorrelated ones.

The purpose of this paper is to introduce an innovative theoretical, numerical and experimental investigations on the HP NGD function. The identified HP NGD topology under study is constituted by first order passive RC-network. The simulations and measurements confirm in very good agreement the HP NGD behaviors of the tested circuits. NGD responses with optimal values of about -1 ns and cut-off frequencies of about 20 MHz are obtained.

The identified HP NGD topology understudy is constituted by a first-order passive Resistor-capacitor RC network. An innovative approach to HP NGD analysis is developed. The analytical investigation from the voltage transfer function showing the meaning of HP properties is established.

This paper introduces innovative theoretical, numerical and experimental investigations on the HP NGD function.

The NGD characterization as a function of the resistance and capacitance parameters is investigated. The feasibility of the HP NGD function is verified with proofs of concept constituted of lumped surface mounted components on printed circuit boards. The simulations and measurements confirm in very good agreement the HP NGD behaviors of the tested circuits. NGD responses with optimal values of about −1 ns and cut-off frequencies of about 20 MHz are obtained.

The purpose of this paper is to investigate the circuit analysis differential equations, which play an important role in the field of electrical and electronic engineering, and it was necessary to propose a very simple and direct method to obtain approximate solutions for the linear or non-linear differential equations, which should be simple for engineers to understand.

This paper introduces a simple novel Maclaurin series method (MSM) to propose an approximate novel solution in the area of circuit analysis for linear and non-linear differential equations. These equations describe the alternating current circuit of the resistor–capacitor, which evaluates the effect of non-linear current resistance. Linear and non-linear differential equations are evaluated as a computational analysis to assist the research, which reveals that the MSM is incredibly simple and effective.

Simulation findings indicate that the achieved proposed solution using the novel suggested approach is identical to the exact solutions mentioned in the literature. As the Maclaurin series is available to all non-mathematicians, this paper reflects mostly on theoretical implementations of the numerous circuit problems that occur in the field of electrical engineering.

A very simple and efficient method has been proposed in this paper, which is very easy to understand for even non-mathematicians such as engineers. The paper introduced a method of the Maclaurin series to solve non-linear differential equations resulting from the study of the circuits. The MSM mentioned here will be a useful tool in areas of physical and engineering anywhere the problem of the circuits is studied.

This work is intended to historically commemorate the one hundredth anniversary of the invention of a new type of electronic circuit, referred to in 1919 by Abraham and Bloch as a multivibrator and by Eccles and Jordan as a trigger relay (later known as a flip-flop).

The author also considers the circuit-technical side of this new type of circuit, considering the technological change as well as the mathematical concepts developed in the context of the analysis of the circuit.

The multivibrator resulted in a “circuit shape” which became one of the most applied nonlinear circuits in electronics. It is shown that at the beginning the multivibrator as well as the flip-flop circuits were used because their interesting properties in the frequency domain.

Therefore, it is a very interesting subject to consider the history of the multivibrator as electronic circuits in different technologies including tube, transistors and integrated circuits as well as the mathematical theory based on the concept from electrical circuit theory.

With continuous scaling of digital circuit CMOS technology, the vulnerability of these circuits are significantly increasing against the soft errors. On the other hand, the effects of process variation in the electrical properties of nano-scale circuits, have introduced the statistical methods as an unavoidable choice for the soft error rate (SER) estimation. The purpose of this paper is to provide a statistical soft error rate (SSER) estimation approach for combinational circuits in the presence of process variation.

In this paper a new method is proposed for the SSER estimation of combinational circuits based on the Bayesian networks (BNs). This allows to factor the joint probability distributions over variables in a circuit graph. The distribution of the initial transient fault pulse is estimated by the pre-characterization tables. Timing signals are propagated by BN theory and the probability distribution of electrical and timing masking are calculated.

Simulation results for some benchmark circuits show that the proposed method is accurate with 3.7 percent difference with the Monte-Carlo SPICE simulation and with orders of magnitude improvement in runtime.

The proposed framework is the scheme giving the low estimation time with plausible accuracy compared to other schemes. The comparison exhibits that the designer can save its estimation time in terms of performance and complexity. The deterministic-based methods also are able to evaluate the SER of combinational circuit, yet in an unacceptable time.

The purpose of this paper is to show that the computation of time-periodic signals for coupled antenna-circuit problems can be substantially accelerated by means of the single shooting method. This allows an efficient analysis of nonlinearly loaded coupled loop antennas for near field communication (NFC) applications.

For the modelling of electrically small coupled field-circuit problems, the partial element equivalent circuit (PEEC) method shows to be very efficient. For analysing the circuit-like description of the coupled problem, this paper developed a generalised modified nodal analysis (MNA) and applied it to specific NFC problems.

It is shown that the periodic steady state (PSS) solution of the resulting differential-algebraic system can be computed very time efficiently by the single shooting method. A speedup of roughly 114 to conventional transient approaches can be achieved.

The proposed approach appears to be an efficient alternative for the computation of time PSS solutions for nonlinear circuit problems coupled with discretised conductive structures, where the homogeneous solution is not of interest.

The present paper explores the implementation and application of the shooting method for nonlinearly loaded coupled antenna-circuit problems based on the PEEC method and shows the efficiency of this approach.

This paper aims to present an accurate magnetic equivalent circuit for modeling the cylindrical electromagnet so that by analyzing it, the magnetic flux density in different parts of the electromagnet, as well as its lifting force, can be calculated.

The structure of the electromagnet is divided into parts that can be modeled by lumped element parameters. Mathematical equations for calculating these elements are presented and proved. The axial symmetry of the cylindrical electromagnet made it possible to use planar circuits for its modeling. To increase the accuracy of the proposed equivalent circuit, attention has been paid to the leakage flux as well as the nonlinear behavior of the ferromagnetic core. Also, the curvature of the magnetic flux path is considered in the calculation of the corner permeances of the core.

The magnetic flux density in different parts of the electromagnet was calculated using nodal analysis of the circuit and compared to the results of the finite element method. Also, a test bed was established to measure the lifting force of the electromagnet. Comparing the results shows a difference of less than 3% which indicate the good accuracy of the proposed circuit. In addition, due to the curvature of the flux path, there is a no-flux region in the center of the disk, the extent of which depends on the thickness of the disk and the diameter of the middle leg.

Magnetic equivalent circuit is a new contribution to analyze the cylindrical electromagnet and calculate its lifting force with good accuracy. The circuit lumped elements can be quickly calculated using mathematical equations and software such as MATLAB according to the actual path of the magnetic flux. Compared to other methods, the proposed circuit analyzes the electromagnet in a shorter period of time. This is the most important advantage of the proposed circuit model.

This paper aims to propose a new approach on the problem of circuit optimisation by using the generalised optimisation methodology presented earlier. This approach is focused on the application of the maximum principle of Pontryagin for searching the best structure of a control vector providing the minimum central processing unit (CPU) time.

The process of circuit optimisation is defined mathematically as a controllable dynamical system with a control vector that changes the internal structure of the equations of the optimisation procedure. In this case, a well-known maximum principle of Pontryagin is the best theoretical approach for finding of the optimum structure of control vector. A practical approach for the realisation of the maximum principle is based on the analysis of the behaviour of a Hamiltonian for various strategies of optimisation and provides the possibility to find the optimum points of switching for the control vector.

It is shown that in spite of the fact that the maximum principle is not a sufficient condition for obtaining the global minimum for the non-linear problem, the decision can be obtained in the form of local minima. These local minima provide rather a low value of the CPU time. Numerical results were obtained for both a two-dimensional case and an N-dimensional case.

The possibility of the use of the maximum principle of Pontryagin to a problem of circuit optimisation is analysed systematically for the first time. The important result is the theoretical justification of formerly discovered effect of acceleration of the process of circuit optimisation.

One of the main issues which microelectronics industry encounter is reliability as feature sizes scale down to nano-design level. The purpose of this paper is to provide a probabilistic transfer matrix based to find the accurate and efficient method of finding circuit’s reliability.

The proposed method provides a probabilistic description of faulty behavior and is well-suited to reliability and error susceptibility calculations. The proposed method offers accurate circuit reliability calculations in the presence of reconvergent fanout. Furthermore, a binary probability matrix is used to not only resolve signals correlation problem but also improve the accuracy of the obtained reliability in the presence of reconverging signals.

The results provide the accuracy and computation time of reliability evaluation for ISCAS85 benchmark schemes. Also, simulations have been conducted on some digital circuits involving LGSynth’91 circuits. Simulation results show that proposed solution is a fast method with less complexity and gives an accurate reliability value in comparison with other methods.

The proposed method is the only scheme giving the low calculation time with high accuracy compared to other schemes. The library-based method also is able to evaluate the reliability of every scheme independent from its circuit topology. The comparison exhibits that a designer can save its evaluation time in terms of performance and complexity.