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### Mathematical Modeling and Analysis of Nonlinear Time-Invariant RLC Circuits [chapter]

Timo Reis
2014 Modeling and Simulation in Science, Engineering and Technology
Methods for the modeling of circuits by differentialalgebraic equations are presented. The second part of this paper is devoted to an analysis of these equations.  ...  We give a basic and self-contained introduction to the mathematical description of electrical circuits which contain resistances, capacitances, inductances, voltage and current sources.  ...  The purpose of this article is a detailed and self-contained introduction to mathematical modeling of the rather simple but nevertheless important class of time-invariant nonlinear RLC circuits.  ...

### Circuit Modelling by Difference Equation: Pedagogical Advantages and Perspectives

2020 Mathematical Modelling and Engineering Problems
This course covers fundamental principles and analysis methods of basic circuits commonly employed in the forthcoming courses.  ...  The novelty of the proposed approach not only lies in its intuitive simplicity but also in its contribution to the understanding and visualization of students in the real-time response of linear and non-linear  ...  Non-linear-time invariant circuit To show the effectiveness of the proposed methodology for instruction of non-linear circuits, assume that the inductance of the circuits shown in Figure 1 is now nonlinear  ...

### Page 4786 of Mathematical Reviews Vol. , Issue 83k [page]

1983 Mathematical Reviews
A. 83k:94038 Les F.E.M. limite pour le circuit RLC. (English and Portuguese summaries) [Limit electromotive forces for an RLC circuit] Mat. Apl. Comput. 1 (1982), no. 1, 39-52 (loose errata).  ...  Authors’ summary: “Using a formalism analogous to that of limit analysis in mechanics, we define two methods for the calculation of the convex set of the electromotive forces that an RLC circuit can support  ...

### Nonlinear Model Order Reduction Based on Trajectory Piecewise Linear Approach: Comparing Different Linear Cores [chapter]

Kasra Mohaghegh, Michael Striebel, E. Jan W. ter Maten, Roland Pulch
2010 Mathematics in Industry
Refined models for MOS-devices and increasing complexity of circuit designs cause the need for Model Order Reduction (MOR) techniques that are capable of treating nonlinear problems.  ...  In time-domain simulation the Trajectory PieceWise Linear (TPWL) approach is promising as it is designed to use MOR methodologies for linear problems as the core of the reduction process.  ...  Acknowledgements The work presented is supported by the Marie Curie RTN COMSON and ToK project O-MOORE-NICE!.  ...

### Teaching circuits to new generations of engineers

Ljiljana Trajkovic
2011 2011 IEEE International Symposium of Circuits and Systems (ISCAS)
Understanding circuits is fundamental to electrical engineering and continuing to offer courses in theory and applications of electric circuits to new generations of engineering students remains an important  ...  Attracting new generations of students to circuits is a challenging task that calls for new approaches, methodologies, and projects that will appeal to current generations of both educators and students  ...  Sample projects: • Stimulations of negative resistance circuits • Analyzing stability of nonlinear circuits • Computing dc operating points of nonlinear circuitsAnalysis, modeling, and design of an  ...

### Page 919 of Mathematical Reviews Vol. , Issue 82b [page]

1982 Mathematical Reviews
Marotto’s theorem (Japanese) (pp. 154-164); Norio Akamatsu, An accurate model of bipolar transistors for computer-aided circuit analysis (pp. 165-173); Akira Koriyama and Hiroshi Matsuoka, On dynamical  ...  of transfer functions of passive RLC networks.  ...

### Analysis and Small Signal Modeling of Five-Level Series Resonant Inverter

2021 IEEE Access
Thus validates the mathematical analysis and the proposed small-signal LTI model.  ...  inverter and model the circuit using small-signal AC analysis.  ...

### Characterizing Inductive and Capacitive Nonlinear RLC Circuits: A Passivity Test

Eloisa Garcia Canseco, Dimitri Jeltsema, Romeo Ortega, Jacquelien M.A. Scherpen
2004 IFAC Proceedings Volumes
Linear time invariant RLC circuits are said to be inductive ( capacitive ) if the current waveform in sinusoidal steady state has a negative (resp., positive) phase shift with respect to the voltage.  ...  In this paper we propose a framework, based on passivity theory, that allows to extend these intuitive notions to nonlinear RLC circuits.  ...  Two multiport systems associated to the RLC network of Fig. 1 . + i vs d dt + - v is d dt - I C a) b) LINEAR TIME INVARIANT CIRCUITS In this section we study the LTI case. 5 We give the characterization  ...

### Page 882 of Mathematical Reviews Vol. , Issue 83b [page]

1983 Mathematical Reviews
The established block canonical forms in the time domain, and developed algebraic theorics, provide additional mathematical tools for the analysis and synthesis of a class of MIMO control systems and matrix  ...  The applications of block modal matrices to block partial fraction expansions, analytical time-response solutions, and model reductions of high-degree matrix fraction descriptions and high-order state  ...

### A stabilization method of inhomogeneous ladder networks with nonlinear elements

Pawel Skruch
2011 Archives of Control Sciences
The results of computer simulations are included to verify theoretical analysis and mathematical formulation.  ...  A stabilization method of inhomogeneous ladder networks with nonlinear elements PAWEL SKRUCH In the paper, different structures of electric ladder networks are considered: RC, RL, and RLC.  ...  In Section 2, nonlinear circuit elements are mathematically characterized. Mathematical models of selected electrical ladder networks are described in Section 3.  ...

### 4 Model order reduction in microelectronics [chapter]

2020 Applications
This chapter deals with the application of model order reduction (MOR) in the area of microelectronics.  ...  Several application examples are presented to highlight the performance and computational advantages attained by using MOR techniques within the circuit simulation environments.  ...  Formulation of circuits with lumped elements The presence of nonlinear elements in virtually all circuit designs mandates that the natural domain for mathematically describing general circuits is the time  ...

### A Generalization of the Kramers-Kronig Relations for Linear Time-Varying Media [article]

2020 arXiv   pre-print
Among others, we study the case of a Lorentzian dielectric response with time-varying volumetric density of polarizable atoms and present the varying circuital equivalents of the governing differential  ...  equation, which in turn allow us to use the notion of generalized time-varying impedances/admittances of a time-dependent resistor, inductor and capacitor.  ...  engineering-both from the perspective of functional analysis    and state-space theory  -or the model reduction of the time-varying equivalents that result from linearizing nonlinear  ...

### Generating Reduced Order Models using Subspace Iteration for Linear RLC Circuits in Nanometer Designs

J.V.R. Ravindra, M.B. Srinivas
2007 Proceedings of the Second International Conference on Nano-Networks
This paper shows that the subspace iterative scheme produces reduced systems that accurately follow the time-and frequency-domain responses of the original system.  ...  This paper presents a model order reduction technique using subspace iterative scheme for high speed coupled integrated circuit interconnects in nanometer designs.  ...  This paper is organized as follows: Section 2 gives an overview of the model order reduction. Section 3 provides a mathematical framework of dynamic RLC circuits.  ...

### Jump Power Concepts and Some Theorems on Switching

Simone Barcellona, Gabrio SupertiFurga
2018 Journal of Electrical Systems
Power-like functions based on Tellegen's theorem are important tools in the study of electrical networks. Networks containing power converters are nonlinear and/or time-variant.  ...  The topologies of existing converters are multiform and there is not one single general approach to them.In terms of circuit theory, a number of theorems regarding ideal switching can be derived.  ...  Some Theorems based on Jump Power Let us define the RLCS network as an electrical network composed of passive timeinvariant resistors, strictly passive time-invariant inductors, strictly passive time-invariant  ...