Analytical Solution of the Current-Voltage Characteristics of Circuits With Power-Law Dependence of the Current on the Applied Voltage Using the Lambert-Tsallis Wq Function

The circuit formed by a diode with series resistance is a basic electronic circuit whose analytical solution of the electrical current requires the usage of the Lambert {W} function. However, in circuits where the current-voltage relation follows a power-law, like in an RCD (resistor-capacitor-dio...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. II, Express briefs Express briefs, 2022-03, Vol.69 (3), p.769-773
Main Authors: de Andrade, Joacir Soares, Nobrega, Kleber Zuza, Ramos, Rubens Viana
Format: Article
Language:English
Subjects:
Circuits and systems
Diode
Lambert-Tsallis function
Mathematical model
Nanowires
Power supplies
Resistors
Semiconductor diodes
Space charge
space charge limited current
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Summary:The circuit formed by a diode with series resistance is a basic electronic circuit whose analytical solution of the electrical current requires the usage of the Lambert {W} function. However, in circuits where the current-voltage relation follows a power-law, like in an RCD (resistor-capacitor-diode) circuit in the continuous-time domain, the Lambert function is not useful. The power-law behavior also appears in some nanostructures like in the Mark-Helfrich equation for the space charge limited current in nanowires. In this work, we provide analytical solutions for both cases using the recently proposed Lambert-Tsallis {W} _{q} function, showing that the {W} _{q} function is a useful mathematical tool for finding analytical solutions of electronic circuit equations where the current-voltage characteristics follows a power-law.
ISSN:1549-7747
DOI:10.1109/TCSII.2021.3110407