NDLI: Perturbation-Based Stochastic Modeling of Nonlinear Circuits

Content Provider	Springer Nature Link
Author	Rathee, Akash Parthasarathy, Harish
Copyright Year	2012
Abstract	This paper presents a general model for a nonlinear circuit, in which, the circuit parameters (e.g. resistance and capacitance) are subject to random fluctuations due to noise, which vary with time. The fluctuating amplitudes of these parameters are assumed to be Ornstein–Uhlenbeck (O.U.) processes and not the white noise owing to temporal correlations. The nonlinear circuit is represented by a system of nonlinear differential equations depending upon a set of parameters that fluctuate slowly with time. To model these fluctuations, we use the theory of Ito’s stochastic differential equations (SDEs). Then the driving force of the circuit dynamics is in accordance with the general perturbation theory decomposed into the sum of a strong linear component and a weak nonlinear component by the introduction of a small perturbation parameter. The circuit states are expanded in the powers of this small perturbation parameter and recursive solutions to the various approximates obtained. Finally, the approximate expressions for the output states are obtained as stochastic integrals with respect to Brownian motion processes. The proposed method is applied to a half-wave rectifier circuit which is built out of a diode, a resistor and a capacitor. The diode is represented by nonlinear voltage–current equation, and resistance and capacitance are subject to random fluctuations due to noise, which vary slowly with time. The results, obtained using the proposed method, are compared with those obtained via the conventional perturbation-based deterministic differential equations model for a nonlinear circuit. Hence, the noise process component, present at the output, is obtained.
Starting Page	123
Ending Page	141
Page Count	19
File Format	PDF
ISSN	0278081X
Journal	Circuits, Systems, and Signal Processing
Volume Number	32
Issue Number	1
e-ISSN	15315878
Language	English
Publisher	SP Birkhäuser Verlag Boston
Publisher Date	2012-07-18
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Perturbation technique Nonlinear circuit Stochastic differential equation Ornstein–Uhlenbeck process Electrical noise Circuits and Systems Electrical Engineering Signal, Image and Speech Processing Electronics and Microelectronics, Instrumentation
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Signal Processing

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