Noise Analysis of Electrical Circuits on Fractal Set

Last modified: November 4, 2022
Estimated reading time: 1 min
Research Article: Noise Analysis of Electrical Circuits on Fractal Set
Author: Rawid Banchuin
Email: rawid.ban@siam.edu
Department/Faculty Graduate Schools of IT, Siam University, Bangkok 10160
Published: COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Volume 41, Issue 5, pp. 1464-1490.

Citation 

Banchuin, R. (2022). Noise analysis of electrical circuits on fractal set. COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 41(5), 1464-1490. https://doi.org/10.1108/COMPEL-08-2021-0269


ABSTRACT

Purpose

The purpose of this study is to originally present noise analysis of electrical circuits defined on fractal set.

Design/methodology/approach
The fractal integrodifferential equations of resistor-inductor, resistor-capacitor, inductor-capacitor and resistor-inductor-capacitor circuits subjected to zero mean additive white Gaussian noise defined on fractal set have been formulated. The fractal time component has also been considered. The closed form expressions for crucial stochastic parameters of circuit responses have been derived from these equations. Numerical simulations of power spectral densities based on the derived autocorrelation functions have been performed. A comparison with those without fractal time component has been made.

Findings
We have found that the Hausdorff dimension of the middle b Cantor set strongly affects the power spectral densities; thus, the average powers of noise induced circuit responses and the inclusion of fractal time component causes significantly different analysis results besides the physical measurability of electrical quantities.

Originality/value
For the first time, the noise analysis of electrical circuit on fractal set has been performed. This is also the very first time that the fractal time component has been included in the fractal calculus-based circuit analysis.

Keywords: Fractal calculus, Fractal Fourier transform, Fractal Laplace transform, Fractal time component, Middle b Cantor set, Noise.


Noise Analysis of Electrical Circuits on Fractal Set

Graduate Schools, Siam University, Bangkok, Thailand

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