Uncertain Circuit Equation

2021 ◽  
Vol 14 (03) ◽  
Author(s):  
Yang Liu
Keyword(s):  
Differential Equation ◽  
Method Of Moments ◽  
Time Domain ◽  
Electrical Circuit ◽  
Unknown Parameters ◽  
Uncertainty Distribution ◽  
Liu Process ◽  
The Time Domain ◽  
Steady State Solutions ◽  
Transient And Steady State

Differential equation is a powerful tool for investigating the transient and steady-state solutions of electrical circuit in the time domain. By considering the noise in actual circuit system, this paper first presents an uncertain circuit equation, which is a type of differential equation driven by Liu process. Then the solution of uncertain circuit equation and the inverse uncertainty distribution of solution are derived. Following that, two applications of solution are provided as well. Based on the observations, the method of moments is used to estimate the unknown parameters in uncertain circuit equation. In addition, a paradox for stochastic circuit equation is also given.

scholarly journals Modeling RL Electrical Circuit by Multifactor Uncertain Differential Equation

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2103
Author(s):  
Yang Liu ◽  
Lujun Zhou
Keyword(s):  
Differential Equation ◽  
Method Of Moments ◽  
Complex Structure ◽  
Internal Noise ◽  
External Noise ◽  
Electrical Circuit ◽  
Uncertain Differential Equation ◽  
Unknown Parameters ◽  
Uncertainty Distribution ◽  
Symmetry Principle

The symmetry principle of circuit system shows that we can equate a complex structure in the circuit network to a simple circuit. Hence, this paper only considers a simple series RL circuit and first presents an uncertain RL circuit model based on multifactor uncertain differential equation by considering the external noise and internal noise in an actual electrical circuit system. Then, the solution of uncertain RL circuit equation and the inverse uncertainty distribution of solution are derived. Some applications of solution for uncertain RL circuit equation are also investigated. Finally, the method of moments is used to estimate the unknown parameters in uncertain RL circuit equation.

Analysis on the time and frequency domain for the RC electric circuit of fractional order

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Manule Guía ◽  
Francisco Gómez ◽  
Juan Rosales
Keyword(s):  
Differential Equation ◽  
Frequency Domain ◽  
Time Domain ◽  
Cutoff Frequency ◽  
Electric Circuit ◽  
Electrical Circuit ◽  
High Frequencies ◽  
The Laplace Transform ◽  
Fractional Differential ◽  
The Time Domain

AbstractThis paper provides an analysis in the time and frequency domain of an RC electrical circuit described by a fractional differential equation of the order 0 < α≤ 1. We use the Laplace transform of the fractional derivative in the Caputo sense. In the time domain we emphasize on the delay, rise and settling times, while in the frequency domain the interest is in the cutoff frequency, the bandwidth and the asymptotes in low and high frequencies. All these quantities depend on the order of differential equation.

A Straight-Forward Method of Moments Procedure to Solve the Time Domain Integral Equation Applicable to PEC Bodies via Triangular Patch Modeling

2020 ◽  
Vol 35 (8) ◽  
pp. 843-854
Author(s):  
Sadasiva Rao
Keyword(s):  
Method Of Moments ◽  
Time Domain ◽  
Moment Matrix ◽  
Triangular Patch ◽  
Gaussian Plane ◽  
Time Marching ◽  
Time Domain Integral Equation ◽  
Time Variables ◽  
The Moment ◽  
The Time Domain

In this work, a simple and straight-forward method of moments solution (MOM) procedure is presented to obtain the induced current distribution on an arbitrarily-shaped conducting body illuminated by a Gaussian plane wave directly in the time domain using a patch modeling approach. The method presented in this work, besides being stable, is also capable of handling multiple excitation pulses of varying frequency content incident from different directions in a trivial manner. The method utilizes standard Rao-Wilton-Glisson (RWG) functions and simple triangular functions for the space and time variables, respectively, for both expansion and testing. The method adopts conventional MOM and requires no further manipulation invariably needed in standard time-marching methods. The moment matrix generated via this scheme is a block-wise Toeplitz matrix and, hence, the solution is extremely efficient. The method is validated by comparing the results with the data obtained from the frequency domain solution. Several simple and complex numerical results are presented to validate the procedure.

Symmetric Arc Solutions of ζ¨ = ζn

1968 ◽  
Vol 35 (3) ◽  
pp. 565-570
Author(s):  
C. P. Atkinson ◽  
B. L. Dhoopar
Keyword(s):  
Differential Equation ◽  
Time Domain ◽  
Complex Variable ◽  
Digital Computer ◽  
Nonlinear Differential Equations ◽  
Time Derivative ◽  
Approximate Solutions ◽  
Complex Variables ◽  
Complex Modes ◽  
The Time Domain

This paper, “Symmetric Arc Solutions of ζ¨ = ζn,” presents periodic solutions of this differential equation relating the complex variable ζ(t) = u(t) + iv(t) and its second time derivative ζ¨ The solutions are called symmetric arc solutions since they form such arcs on the ζ = u + iv-plane. The solutions, ζ(t), are “complex modes” of coupled nonlinear differential equations in the complex variables z1 and z2. Symmetric arc solutions are presented for a range of n from n = 3 to n = 101. Approximate solutions are presented and compared with solutions generated by digital computer. Solutions are presented on the ζ-plane and in the time domain as u(t) and v(t).

scholarly journals Structural System Identification in the Time Domain using Evolutionary and Behaviorally Inspired Algorithms and their Hybrids

2009 ◽  
Vol 6 (2) ◽  
pp. 64
Author(s):  
S. Sandesh ◽  
Abhishek Kumar Sahu ◽  
K. Shankar
Keyword(s):  
System Identification ◽  
Time Domain ◽  
Numerical Models ◽  
Parametric Identification ◽  
Lumped Mass ◽  
Unknown Parameters ◽  
Mass System ◽  
The Time Domain ◽  
Structural System Identification ◽  
Speed And Accuracy

 In this study, parametric identification of structural properties such as stiffness and damping is carried out using acceleration responses in the time domain. The process consists of minimizing the difference between the experimentally measured and theoretically predicted acceleration responses. The unknown parameters of certain numerical models, viz., a ten degree of freedom lumped mass system, a nine member truss and a non-uniform simply supported beam are thus identified. Evolutionary and behaviorally inspired optimization algorithms are used for minimization operations. The performance of their hybrid combinations is also investigated. Genetic Algorithm (GA) is a well known evolutionary algorithm used in system identification. Recently Particle Swarm Optimization (PSO), a behaviorally inspired algorithm, has emerged as a strong contender to GA in speed and accuracy. The discrete Ant Colony Optimization (ACO) method is yet another behaviorally inspired method studied here. The performance (speed and accuracy) of each algorithm alone and in their hybrid combinations such as GA with PSO, ACO with PSO and ACO with GA are extensively investigated using the numerical examples with effects of noise added for realism. The GA+PSO hybrid algorithm was found to give the best performance in speed and accuracy compared to all others. The next best in performance was pure PSO followed by pure GA. ACO performed poorly in all the cases. 

scholarly journals Modeling And Characterization of Carrier Mobility For Truncated Conical Quantum Dot Infrared Photodetectors

2021 ◽  
Author(s):  
Yasser M. El-Batawy ◽  
Marwa Feraig
Keyword(s):  
Differential Equation ◽  
Quantum Dot ◽  
Time Domain ◽  
Carrier Mobility ◽  
Carrier Transport ◽  
Infrared Photodetectors ◽  
Generic Model ◽  
Quantum Dot Infrared Photodetectors ◽  
The Time Domain

Abstract In the present paper, a full theoretical model for calculating the carrier mobility coming as a result of the existence of a truncated conical quantum dots of n-type quantum dot infrared photodetectors (QDIPs) is developed. This model is built on solving Boltzmann’s transport equation that is a complex integro-differential equation describing the carrier transport. The time-domain finite-difference method is used in this numerical solution. The influences of dimensions and density of the QDs for this structure on the carrier mobility are studied. Eventually, the calculated mobility for truncated conical InAs/GaAs QDIP is contrasted to other conical, spherical, and hemispherical QD structures. The model put forward is a generic model that is applicable to various structures of truncated conical QDs devices.

scholarly journals Time domain solution of electromagnetic radiation model of the grounding system excited by pulse current

2020 ◽  
Vol 35 (1) ◽  
pp. 74-81
Author(s):  
Nedis Dautbasic ◽  
Adnan Mujezinovic
Keyword(s):  
Differential Equation ◽  
Electromagnetic Radiation ◽  
Time Domain ◽  
Gauge Condition ◽  
Pulse Excitation ◽  
Solution Technique ◽  
Grounding System ◽  
Integro Differential Equation ◽  
Transient Voltage ◽  
The Time Domain

This paper deals with an advanced electromagnetic radiation approach for analyzing the time-domain performance of grounding systems under pulse excitation currents. The model of the grounding systems presented within this paper is based on the homogeneous Pocklington integro-differential equation for the calculation of the current distribution on the grounding system and Lorentz gauge condition which is used for the grounding system transient voltage calculation. For the solution of the Pocklington integro-differential equation, the indirect boundary element method and marching on-in time method are used. Fur- thermore, the solution technique for the calculation of the grounding system transient voltage is presented. The numerical model for the calculation of the grounding system transients was verified by comparing it with onsite measurement results.

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