DocumentCode :
3010341
Title :
A random input-driven resistor-capacitor series circuit
Author :
Patil, Nanasaheb S. ; Gawalwad, Balaji G. ; Sharma, Shambhu N.
Author_Institution :
Dept. of Electr. Eng., Nat. Inst. of Technol. Surat, Surat, India
fYear :
2011
fDate :
15-17 Dec. 2011
Firstpage :
100
Lastpage :
103
Abstract :
In this paper, we present the noise analysis of simple, but an appealing resistor-capacitor series circuit. As it has found applications in many circuits like RC filter in phase locked loop. The noise originates from the arbitrary thermal motion of carriers and the discreteness of charge. Noise signals are random and must be treated by statistical means. Even though we cannot predict the real noise waveform, we can envisage the statistics such as the mean (average) and variance. Generally, noise contributions to electrical circuits are not accounted for when using deterministic differential equations for their modeling and ignoring noise contributions lead to poor state estimation. A first-order Ordinary Differential Equation (ODE) is used for the response analysis of the circuit. As a result of these, in this paper, the deterministic model is replaced with a stochastic model by adding a noise term as a random voltage source, which drives the RC circuit. The Itô theory is applied to the noise analysis of the noisy dynamic circuit considered here. The Itô theory has found surprising applications in stochastic models arising from diverse field. Numerical simulations of the charge with and without noise, the mean and variance of the charge using MATLAB are discussed.
Keywords :
capacitors; differential equations; network analysis; numerical analysis; phase locked loops; resistors; Ito theory; MATLAB; RC circuit; RC filter; arbitrary thermal motion; circuit response analysis; deterministic differential equations; deterministic model; electrical circuits; first-order ordinary differential equation; noise analysis; numerical simulations; phase locked loop; random input-driven; random voltage source; real noise waveform; resistor-capacitor series circuit; Differential equations; Equations; Integrated circuit modeling; Mathematical model; Noise; Stochastic processes; Trajectory; Brownian motion process; Itô formula; Ordinary Differential Equation (ODE); RC electrical circuit; Stochastic Differential Equation (SDE);
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Recent Advancements in Electrical, Electronics and Control Engineering (ICONRAEeCE), 2011 International Conference on
Conference_Location :
Sivakasi
Print_ISBN :
978-1-4577-2146-5
Type :
conf
DOI :
10.1109/ICONRAEeCE.2011.6129733
Filename :
6129733
Link To Document :
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