The elusive memristor: properties of basic electrical circuits

Abstract

We present a tutorial on the properties of the new ideal circuit element, a memristor. By definition, a memristor M relates the charge q and the magnetic flux $\varphi$ in a circuit, and complements a resistor R, a capacitor C, and an inductor L as an ingredient of ideal electrical circuits. The properties of these three elements and their circuits are a part of the standard curricula. The existence of the memristor as the fourth ideal circuit element was predicted in 1971 based on symmetry arguments, but was clearly experimentally demonstrated just this year. We present the properties of a single memristor, memristors in series and parallel, as well as ideal memristor-capacitor (MC), memristor-inductor (ML), and memristor-capacitor-inductor (MCL) circuits. We find that the memristor has hysteretic current-voltage characteristics. We show that the ideal MC (ML) circuit undergoes non-exponential charge (current) decay with two time-scales, and that by switching the polarity of the capacitor, an ideal MCL circuit can be tuned from overdamped to underdamped. We present simple models which show that these unusual properties are closely related to the memristor's internal dynamics. This tutorial complements the pedagogy of ideal circuit elements (R,C, and L) and the properties of their circuits.

22 pages, 12 figures, substantial text revision

References in corpus (1)

• Spin memristive systems

Cited by in corpus (26)

• Non-Hermitian Physics
• Memory effects in complex materials and nanoscale systems
• Practical approach to programmable analog circuits with memristors
• Neuro-memristive Circuits for Edge Computing: A review
• The Fourth Element: Characteristics, Modelling, and Electromagnetic Theory of the Memristor
• Variability in Resistive Memories
• A Survey of Memristive Threshold Logic Circuits
• Applicability of Well-Established Memristive Models for Simulations of Resistive Switching Devices
• Quantum Memristors with Superconducting Circuits
• Stochastic memory: memory enhancement due to noise
• MemTorch: An Open-source Simulation Framework for Memristive Deep Learning Systems
• Quantum Memristors in Quantum Photonics
• Analysis of Dynamic Linear and Non-linear Memristor Device Models for Emerging Neuromorphic Computing Hardware Design
• Simulation platform for pattern recognition based on reservoir computing with memristor networks
• $\mathcal{P}\mathcal{T}$ phase transition in open quantum systems with Lindblad dynamics
• Resistive Threshold Logic
• Experimental evidence of chaos from memristors
• Memristor model based on fuzzy window function
• Ergodicity, lack thereof, and the performance of reservoir computing with memristive networks
• Fourier Response of a Memristor: Generation of High Harmonics with Increasing Weights
• Parity-time symmetric systems with memory
• A superstatistics approach to the modelling of memristor current-voltage responses
• Resistive Switching Assisted by Noise
• Accuracy Enhancement of Pickett Tunnelling Barrier Memristor Model
• Recent advances on information transmission and storage assisted by noise
• Learning Dynamics in Memristor-Based Equilibrium Propagation