Theoretical Analysis of Smooth Nonlinear Resistor–Capacitor Shunted Josephson Junction Circuit and Its Microcontroller-Based Digital Design with Graphic LCD

This paper reports on the theoretical analysis and microcontroller implementation of smooth nonlinear resistor–capacitor shunted Josephson junction (SNRCSJJ) circuit. The smooth nonlinear resistor is described by a cosine interference term. The stability of the equilibrium points obtained from the r...

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Bibliographic Details
Published inCircuits, systems, and signal processing Vol. 42; no. 1; pp. 47 - 62
Main Authors Ramakrishnan, Balamurali, Ngongiah, Isidore Komofor, Çiçek, Serdar, Chamgoué, André Chéagé, Kuiate, Gaetan Fautso
Format Journal Article
LanguageEnglish
Published New York Springer US 2023
Springer Nature B.V
Subjects
Alternating current
Capacitors
Chaos theory
Circuit design
Circuits
Circuits and Systems
Coherence
Design
Electrical Engineering
Electronics and Microelectronics
Engineering
Equilibrium
Hysteresis loops
Instrumentation
Josephson junctions
LCDs
Liquid crystal displays
Microcontrollers
Numerical analysis
Parameters
Resistors
Signal processing
Signal,Image and Speech Processing
Microcontroller-based design
Bistable and coexisting attractors
Chaotic and relaxation behaviors
Cosine interference term
Transcritical bifurcation
Josephson junction
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Summary:This paper reports on the theoretical analysis and microcontroller implementation of smooth nonlinear resistor–capacitor shunted Josephson junction (SNRCSJJ) circuit. The smooth nonlinear resistor is described by a cosine interference term. The stability of the equilibrium points obtained from the rate equations describing the SNRCSJJ circuit reveals the existence of saddle node and transcritical bifurcation. The hysteresis loop widths of current–voltage curves increase with the increase in the coherence parameter. Periodic behaviors, relaxation behaviors, chaotic behaviors, bistable periodic attractors, and coexisting attractors are found during the numerical analysis by varying the coherence parameter and modulation parameters of alternative current (AC). In order to use both in real engineering applications and for educational purposes, microcontroller-based digital design with graphic LCD (liquid crystal display) of the SNRCSJJ circuit is designed. The digital design results matched the simulation results.
ISSN:0278-081X
1531-5878
DOI:10.1007/s00034-022-02133-0