Circuit Theorems Research Articles

Extended and Generic Higher-Order Elements for MEMS Modeling

State-dependent resistors, capacitors, and inductors are a common part of many smart engineering solutions, e.g., in MEMS (Micro-Electro-Mechanical Systems) sensors and actuators, Micro/NanoMachines, or biomimetic systems. These memory elements are today modeled as generic and extended memristors (MR), memcapacitors (MC), and meminductors (ML), which are more general versions of classical MR, MC, and ML from the infinite set of the fundamental elements of electrical engineering, known as Higher-Order Elements (HOEs). It turns out that models of many complex phenomena in MEMS cannot be constructed only from classical and state-dependent elements such as R, L, and C, but that other HOEs with generalized behavior should also be used. Thus, in this paper, generic and extended versions of HOEs are introduced, overcoming the existing limitation to MR, MC, and ML elements. The relevant circuit theorems are formulated, which generalize the well-known theorems of classical memory elements, and their application to model complex processes of various physical natures in MEMS is shown.

Analytical expression for estimation of the fault location in cable line

A new method for the fault location in a short cable line is proposed in this study. Based on the transmission line theory and circuit theorems, an analytical expression for estimating the fault location in the cable line is derived. According to the problem of incorrect estimation in the high-frequency band, the corresponding essential reason is comprehensively explained. By solving this problem, the fault location can be obtained accurately by the proposed method. To validate the proposed method, some experiments with a 50 Ω coaxial cable are implemented and the accuracy of the proposed method is tested. Meanwhile, it has been validated in these experiments that the proposed method is independent of the fault impedance and terminal impedances.

Models for Implementation of Linear, Non-linear, and Parametrical Circuits in Traffic Safety Control Devices

The range of new approaches based on interconnected circuit theorems was considered to implementation, synthesis, and diagnostics of devices providing the traffic safety. The methodology for new devices implementation is based on the mathematical tools: theory of operators, Laplace transformation, modern methods for synthesis of the named classes of circuits and systems, possibility of excluding inductive elements use. It allows applying micro-electronic devices and hybrid systems together with computing machinery which makes it possible to decrease volume and weight, improve structures functionality and optimize the quantity of input elements as well as sensitivity functions which can be received with an accelerated method. An example of circuits’ implementation without inductive elements is provided.

An optimal linear system approximation of nonlinear fractional-order memristor–capacitor charging circuit

The analysis of nonlinear fractional-order circuits is a challenging problem. This is due to the lack of nonlinear circuit theorems and designs particularly in the presence of memristive elements. The response of a series connection of a simple resistor with fractional order capacitor and its analytical formulation in both charging and discharging phases is considered. The numerical simulation of fractional order HP memristor in series with a fractional order capacitor is also discussed. It is a demonstration of a simple nonlinear fractional-order memristive circuit in both charging and discharging cases. Furthermore, this paper introduces an approach to approximate nonlinear fractional-order memrisitve circuits by linear circuits using a minimax optimization technique. Hence, the new circuit can be analyzed using the conventional linear circuit theorems. The charging and discharging of a series fractional-order memristor with a fractional-order capacitor are discussed numerically. The effect of fractional-order parameters and memristor polarity are also investigated. Using a suitable optimization technique, an accurate approximation by a circuit that include a resistor and a fractional-capacitor is obtained for both charging and discharging cases. A great matching was observed between the frequency responses of the fractional-order nonlinear low pass filter based on fractional-order memristor and fractional-order capacitor and that of the optimized linear fractional order case. Similar matching is observed for the nonlinear and optimized cases when a periodic triangular waveform is applied using Fourier series expansion.

A Scheme for Analysis and Design of Analogue Circuits

Network theorems or circuit theorems are special aids, which can reduce the amount of effort involved in circuit analysis to a considerable degree. For linear networks, there exists interdependence between various network theorems. Thus, by careful analysis, one theorem can verify in terms of another theorem and it is advantageous for pedagogical reasons. A scheme for analogue circuit analysis is presented in this paper. Here piece-by-piece or part-by-part analyzing strategy is employed which can reduce the complexity associated with analyzing or biasing design of large analogue circuits. Fixatornorator pair plays the key role in this methodology. Hybrid equivalent circuit, an alternative for Thevenin’s or Norton’s equivalent model is realized with fixator-norator pair, and is seen to be more dynamic and flexible since it contains both voltage source and current source. Thevenin’s theorem, compensation theorem and maximum power transfer theorem are analyzed in terms of fixator norator pairs, and the study indicates the importance and capabilities of fixator-norator pair and hence hybrid equivalent circuit in analogue circuit design and analysis. Keywords: Compensation Theorem, Fixator-norator Pair, Hybrid Equivalent Circuit, Maximum Power Transfer Theorem, Thevenin’s Theorem

PSpice for Circuit Theory and Electronic Devices

PSpice for Circuit Theory and Electronic Devices is one of a series of five PSpice books and introduces the latest Cadence Orcad PSpice version 10.5 by simulating a range of DC and AC exercises. It is aimed primarily at those wishing to get up to speed with this version but will be of use to high school students, undergraduate students, and of course, lecturers. Circuit theorems are applied to a range of circuits and the calculations by hand after analysis are then compared to the simulated results. The Laplace transform and the s-plane are used to analyze CR and LR circuits where transient signals are involved. Here, the Probe output graphs demonstrate what a great learning tool PSpice is by providing the reader with a visual verification of any theoretical calculations. Series and parallel-tuned resonant circuits are investigated where the difficult concepts of dynamic impedance and selectivity are best understood by sweeping different circuit parameters through a range of values. Obtaining semiconductor device characteristics as a laboratory exercise has fallen out of favour of late, but nevertheless, is still a useful exercise for understanding or modelling semiconductor devices. Inverting and non-inverting operational amplifiers characteristics such as gain-bandwidth are investigated and we will see the dependency of bandwidth on the gain using the performance analysis facility. Power amplifiers are examined where PSpice/Probe demonstrates very nicely the problems of cross-over distortion and other problems associated with power transistors. We examine power supplies and the problems of regulation, ground bounce, and power factor correction. Lastly, we look at MOSFET device characteristics and show how these devices are used to form basic CMOS logic gates such as NAND and NOR gates.

Variational solution of lumped element and distributed electrical circuits

Electrical circuits exhibit a stationary power property and are solvable via variational methods. An analytic technique based on this property is enunciated and the relation to classic circuit theorems is discussed. Linear and nonlinear circuit problems are presented as examples with graphically, illustrated solutions provided where appropriate. A method of determining the harmonic content of signals in nonlinear circuits is described and the unified solution of a combined distributed field problem with lumped element components is also presented.

Bijective proofs of two broken circuit theorems

AbstractWe prove, by means of explicit bijections, theorems of Whitney and Stanley that express the coefficients of the chromatic polynomial of a graph G and the number of acyclic orientations of G in terms of numbers of sets of edges that contain no broken circuits of G.

An Approach to the Teaching of Difference Amplifiers

The bisection theorem is normally used in the analysis of difference stages. An approach utilising only the basic circuit theorems, is presented. Generalisation is demonstrated for arbitrary input, output and stage configuration using the Z-matrix of linear, two-port network theory.

Exact circuit analysis of spherical waves

A circuit representation for the impedance of spherical waves radiating from a spherical boundary was derived using a partial fraction expansion by Chu in order to establish gain bandwidth limitations for antennas. These circuits are derived directly from the recurrence relations for spherical Bessel functions. They provide an exact analog of the field solution both inside and outside of a spherical surface for any values of permittivity ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\epsilon</tex> ) and permeability ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\mu</tex> ). Since the circuits have the form of high-pass filters, they provide significant physical insight into scattering and radiation problems, suggest suitable asymptotic or approximate forms and allow circuit concepts and theorems to be brought to bear in order to solve specific configurations or to set general performance bounds. As an example of their application, compact computer programs for the radar cross section of conducting and dielectric spheres, the minimum <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> 's for antennas, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> 's and resonant frequencies of dielectric spheres and the induced current at the specular and shadow points of a conducting sphere are given. Other illustrative results are the short pulse responses of a solid dielectric and a dielectric-coated sphere computed using the circuit surge impedance and multiple reflection terms; and the response of a hypothetical scatterer in which the TE and TM modes are coupled.