Abstract
Efficient simulation of probabilistic memristors and their networks requires novel modeling approaches. One major departure from the conventional memristor modeling is based on a master equation for the occupation probabilities of network states [arXiv:2003.11011 (2020)]. In the present article, we show how to implement such master equations in SPICE - a general-purpose circuit simulation program. In the case studies, we simulate the dynamics of ac-driven probabilistic binary and multi-state memristors, and dc-driven networks of probabilistic binary and multi-state memristors. Our SPICE results are in perfect agreement with known analytical solutions. Examples of LTspice codes are included.
Highlights
SPICE simulation [1,2] is a powerful tool in the hands of an electrical engineer
In this article, we introduce a methodology to simulate the probabilistic memristive networks in SPICE
The application of the master equation to probabilistic memristor networks is a paradigm change in the probabilistic memristor modeling, and its SPICE implementation makes it affordable to students and researchers working in the field
Summary
SPICE simulation [1,2] is a powerful tool in the hands of an electrical engineer. In the last decade significant progress has been made in developing SPICE models of memristive devices [3,4,5,6,7,8,9,10,11,12,13,14], as well as memcapacitive and meminductive elements [9, 15]. We have introduced a master equation approach for the occupation probabilities of the network states [24] that can be used to describe circuits that include binary and multi-state memristors, resistors, voltage and current sources, and possibly some other components. The master equation was solved analytically for networks containing binary memrstors connected inseries or in-parallel driven by a constant voltage source [24]. We start with an overview of the master equation in relation to binary and multi-state probabilistic memristor networks This is followed by a description of the SPICE implementation scheme supplemented by several examples. The approach presented in this work is relatively general and can be used to model networks combining resistors, probabilistic memristors, constant and time-dependent voltage and current sources.
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