A Nonlinear Circuit Analysis Technique for Time-Variant Inductor Systems

Abstract

Time-variant inductors exist in many industrial applications, including sensors and actuators. In some applications, this characteristic can be deleterious, for example, resulting in inductive loss through eddy currents in motors designed for high efficiency operation. Therefore, it is important to investigate the electrical dynamics of systems with time-variant inductors. However, circuit analysis with time-variant inductors is nonlinear, resulting in difficulties in obtaining a closed form solution. Typical numerical algorithms used to solve the nonlinear differential equations are time consuming and require powerful processors. This investigation proposes a nonlinear method to analyze a system model consisting of the time-variant inductor with a constraint that the circuit is powered by DC sources and the derivative of the inductor is known. In this method, the Norton equivalent circuit with the time-variant inductor is realized first. Then, an iterative solution using a small signal theorem is employed to obtain an approximate closed form solution. As a case study, a variable inductor, with a time-variant part stimulated by a sinusoidal mechanical excitation, is analyzed using this approach. Compared to conventional nonlinear differential equation solvers, this proposed solution shows both improved computation efficiency and numerical robustness. The results demonstrate that the proposed analysis method can achieve high accuracy.

Floquet topological photonic crystals with temporally modulated media

“…In this section, the possible experimental realization is discussed. To implement the proposed temporal dielectrics, a metamaterial scheme in microwave region may be employed as this frequency range suits the use active electrical elements such as time-variant inductors [27]. Consider a ring of conducting thin wires circulating around a PEC cylinder, as shown in Fig.…”

“…Each wire, whose radius equals 0.015a, is connected with a time-variant inductor to introduce temporal modulation. With TE polarization, the current density J z in a lossless wire can be expressed as [27][28] d…”

Contribution to Speeding-Up the Solving of Nonlinear Ordinary Differential Equations on Parallel/Multi-Core Platforms for Sensing Systems

“…The starting vector for this algorithm is calculated by a suitable scheme like the DOPRI5 method [41], and each value of F is approximated by using the previous steps of the solution vectors by using the Equation (7). For each calculation stage, we have a (h × g ) step size advantage w.r.t.…”

“…Sensors 2020, 20, 6130 2 of 17 Specifically in sensors, ODEs are involved in various processing endeavors such as to detect anomalies in machines related sensor data [6], or to model nonlinear sensors like time-variant inductors [7] or piezoelectrically actuated microcantilever sensors [8], and/or to study sensors' behavior or to optimize sensors' performance. ODEs also used to find sensor's optimal location [9].…”

Singular Perturbation-based Reinforcement Learning of Two-Point Boundary Optimal Control Systems

“…Control and analysis of time varying (dynamic) systems has been extensively investigated over the last decade. Applications such as rocket landing [1], [2], energy conservation in electronic circuits [3], [4] can be categorized as finite-horizon time-varying systems. Solving this category of problems requires solving the time varying Riccati equation for linear time-variant systems or time-varying Hamiltonaian Jacobi equation for nonlinear systems.…”