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

2014
*
Modeling and Simulation in Science, Engineering and Technology
*

Methods for the

doi:10.1007/978-3-319-08437-4_2
fatcat:dlhdzf24qffh3jug2iiyfhrjfy
*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*. ...##
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Circuit Modelling by Difference Equation: Pedagogical Advantages and Perspectives

2020
*
Mathematical Modelling and Engineering Problems
*

This course covers fundamental principles

doi:10.18280/mmep.070104
fatcat:2uayokyepvgpfcwpm2gi2b7l7m
*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*...##
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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 ...##
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Nonlinear Model Order Reduction Based on Trajectory Piecewise Linear Approach: Comparing Different Linear Cores
[chapter]

2010
*
Mathematics in Industry
*

Refined

doi:10.1007/978-3-642-12294-1_69
fatcat:yyuocl73hzbbvo3swdxhdmgd2i
*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!. ...##
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Teaching circuits to new generations of engineers

2011
*
2011 IEEE International Symposium of Circuits and Systems (ISCAS)
*

Understanding

doi:10.1109/iscas.2011.5937781
dblp:conf/iscas/Trajkovic11
fatcat:es2q3ylknzehnccgjh46mwwhw4
*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**circuits*•*Analysis*,*modeling*,*and*design*of*an ...##
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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. ...##
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Analysis and Small Signal Modeling of Five-Level Series Resonant Inverter

2021
*
IEEE Access
*

Thus validates the

doi:10.1109/access.2021.3102102
fatcat:b2a2w2nw4jckrjwbf2rtpyofp4
*mathematical**analysis**and*the proposed small-signal LTI*model*. ... inverter*and**model*the*circuit*using small-signal AC*analysis*. ...##
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Characterizing Inductive and Capacitive Nonlinear RLC Circuits: A Passivity Test

2004
*
IFAC Proceedings Volumes
*

Linear

doi:10.1016/s1474-6670(17)30526-8
fatcat:n647mu537jgvhkuuek7dz3qokq
*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 ...##
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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 ...##
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A stabilization method of inhomogeneous ladder networks with nonlinear elements

2011
*
Archives of Control Sciences
*

The results

doi:10.2478/v10170-010-0046-z
fatcat:tlczkhwnaffrzmd2y75dbuivpu
*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. ...##
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4 Model order reduction in microelectronics
[chapter]

2020
*
Applications
*

This chapter deals with the application

doi:10.1515/9783110499001-004
fatcat:u7zdpajsc5bktmsq4gzanjxcce
*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*...##
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A Generalization of the Kramers-Kronig Relations for Linear Time-Varying Media
[article]

2020
*
arXiv
*
pre-print

Among others, we study the case

arXiv:2008.04304v1
fatcat:mf7ul7k6w5fxlgsdlic4q6pqgy
*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*[43] [44] [45]*and*state-space theory [46] -or the*model*reduction*of*the*time*-varying equivalents that result from linearizing*nonlinear*...##
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Generating Reduced Order Models using Subspace Iteration for Linear RLC Circuits in Nanometer Designs

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

doi:10.4108/icst.nanonet2007.2084
dblp:conf/nanonet/RavindraS07
fatcat:wlsylysz6jhwznow5p3wdpzkvm
*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*. ...##
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Jump Power Concepts and Some Theorems on Switching

2018
*
Journal of Electrical Systems
*

Power-like functions based on Tellegen's theorem are important tools in the study

doaj:d73b7381f84a44079a8fb3b0060325bd
fatcat:z6n6bpnrdfe5bkdfmlhsd7trky
*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*...##
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Buck-Boost DC-DC Converter Control by Using the Extracted Model from Signal Flow Graph Method

2015
*
International Journal of Applied Mathematics Electronics and Computers
*

In order to investigate a controller necessity for the converter

doi:10.18100/ijamec.04927
fatcat:brrokpyvs5g3vkck4lkuhzxone
*of*assumed parameters, the frequency*and**time*domain*analysis*are done*and*the open loop system characteristics are verified*and*the needed ... The simulation results are used to show the performance*of*the proposed*modeling**and*regulation method. ... The*nonlinear**circuit**of*the converter is*modelled*as a smallsignal continuous linear*time**invariant*(LTI) system by using averaging technique. ...
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