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Analytical determination of harmonic components of current in electric circuits containing semiconductor converters with the use of a small parameter method (SPM) in frequency domain. The paper aims to discuss these issues.

A SPM realized in frequency domain was used in the analytical analysis of electric circuits with semiconductor converters. An automated method of formation of orthogonal harmonic components of electrical values on the basis of discrete convolution algorithm was used to provide the possibility of realization of calculation in frequency domain. A nonlinear characteristic of a semiconductor converter was presented by the method of numerical approximation. A numerical structured simulation method was applied to determination of the reference values of current in the analyzed circuit. Laws of theoretical electrical engineering were used for formation of the equations of voltage balance in the circuit with a nonlinear element.

It is shown that application of a SPM with its realization in frequency domain enables significant simplification of the process of the analysis of electric circuits with semiconductor converters in an analytical form and facilitation of calculation automation. Analytical and numerical calculation of a circuit with a diode under active-inductive load demonstrated efficiency and sufficient accuracy of the proposed method. It is shown that increase of the order of approximating polynomial and of the number of the analyzed harmonics provides the improvement of the accuracy of numerical calculations.

The results of the work can be used in calculation of electrotechnical devices containing semiconductor appliances and electric devices with nonlinear characteristics. Moreover, the obtained results enable studying the processes of compensation of current higher harmonics in electric networks with a nonlinear load containing semiconductor converters.

For the first time it was proposed to apply a SPM with its realization in frequency domain to the analysis of nonlinear electric circuits. The significance of the paper consists in the fact that the offered method makes it possible to carry out both circuit analytical and numerical analysis with the possibility of its automation.

The purpose of this study is to identify a novel methodology for direct calculation of steady-state periodic solutions for electrical circuits described by nonlinear differential equations, in the time domain.

An iterative algorithm was created to determine periodic steady-state solutions for circuits with nonlinear elements in a chosen set of time instants.

This study found a novel differential operator for periodic functions and its application in the steady-state analysis.

This approach can be extended to the determination of two- or multi-periodic solutions of nonlinear dynamic systems.

The complexity of the steady-state analysis can be reduced in comparison with the frequency-domain approach.

This study identified novel difference equations for direct steady-state analysis of nonlinear electrical circuits.

This paper seeks to give an outline about the geometric concept of electronic circuits, where the jump behavior of nonlinear circuits is emphasized.

A sketch of circuit theory in a differential geometric setting is given.

It is shown that the structure of circuit theory can be given in a much better way than by means of a description of circuits using concrete coordinates. Furthermore, the formulation of a concrete jump condition is given.

In this paper, an outline is given about the state of the art of nonlinear circuits from a differential geometric point of view. Moreover, differential geometric methods were applied to two example circuits (flip flop and multivibrator) and numerical results were achieved.

This paper deals with the two‐dimensional finite element analysis in the frequency domain of saturated electromagnetic devices coupled to electrical circuits comprising nonlinear resistive and inductive components. The resulting system of nonlinear algebraic equations is solved straightforwardly by means of the Newton‐Raphson method. As an application example we consider a three‐phase transformer feeding a nonlinear RL load through a six‐pulse diode rectifier. The harmonic balance results are compared to those obtained with time‐stepping and the computational cost is briefly discussed.

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 a SPICE model to represent antennas in receiving mode. The model can be used to evaluate the performance of the antenna when it is coupled to several different nonlinear electric circuits. The proposed methodology is particularly suitable for rectenna applications, as it allows the analysis of different configurations for a rectenna more efficiently than using full-wave analysis simulators coupled directly to each rectifier circuit.

The model presented uses reciprocity theory to calculate the ideal voltage source of the Thevenin-equivalent circuit for an antenna. Vector fitting is then used to approximate the model to rational functions that can be converted to Resistor, Inductor and Capacitor circuits. Additional components are added to the circuit to prevent numerical instability.

Two rectennas are used to illustrate the performance of the proposed model, one based on a 2.45-GHz rectangular patch antenna and another based on a planar spiral antenna. The second antenna has impedance with positive and negative real parts along the frequency range, which could lead to numerical instabilities. The proposed method is shown to be stable while working with these negative resistance values, which may appear during circuit parameterization.

The equivalent SPICE circuit model for the antenna makes it easy to simulate nonlinear circuits connected to the antenna and perform transient analyses. The computational cost of antenna analysis is reduced, being more computationally efficient than methods that involve full-wave simulation. This characteristic makes it an interesting approach for working with rectennas, or any application where the time constant of the circuit is much longer than the period of the incident wave.

For most antenna applications, the numerical stability of the circuit can be achieved using passive enforcement. However, depending on the phase response of the antenna, the impedance that represents its far-field characteristic may present a negative real part, in which case, passive enforcement will fail. In this paper, the problem of numerical instability is solved by introducing an offset resistance and a current-controlled voltage source to the model.

The purpose of this paper is to aim to an application of element of the theory of differential geometry for building the state space transformation, linearizing nonlinear dynamic system into a linear form.

It is assumed that the description of nonlinear electric circuits with concentrated parameters or electromechanical systems is given by nonlinear system of differential equations of first order (state equations). The goal is to find transformation which leads nonlinear state equation (written in one coordinate system) to the linear in the other – sought coordinate system.

The necessary conditions fulfilled by nonlinear system undergoing linearization process are presented. Numerical solutions of the nonlinear equations of state together with linearized system obtained from direct transformation of the state space are included (transformation input – the state of the nonlinear system).

Application of first order exact differential forms for determining the transformation linearizing the nonlinear state equation. Simple linear models obtained with the use of the linearizing transformation are very useful (mainly because of the known and well-mastered theory of linear systems) in solving of various practical technical problems.