Design of a multiplier-less floating memtranstor emulator with applications in chaos and synaptic plasticity

Abstract A compact emulator for the recently proposed memtranstor − the mem-element that couples electric charge (q) to magnetic flux ( ψ ) via nonlinear magnetic behaviour is presented. The paper details a systematic design methodology for the emulator, provides a mathematical analysis establishing its memtranstance characteristics, and validates the design through circuit-level simulations. The emulator is realized using a voltage differencing transconductance amplifier (VDTA) followed by a voltage differencing current conveyor (VDCC). The magnetic flux which is proportional to the input voltage is produced by forcing a proportional current through a capacitor via the VDTA. This flux is then converted into charge proportional to the input current using the VDCC. Mathematical derivations are carried out to demonstrate the nonlinear q - ψ relation and thereby confirm the memtranstance behavior. The topology, implemented with three capacitors, one resistor, and a minimal set of active blocks, reproduces positive and negative pinched-hysteresis loops. A limited range of the constant term in the memtranstor expression, however, was identified, which constrains the generation of butterfly-shaped pinched hysteresis loop (PHL). To address this limitation, second emulator variant incorporating a resistive network is proposed; which affords full control over the constant term and enables systematic generation of diverse butterfly PHL shapes. The designs were validated using LTspice simulations with TSMC 0.18 μm CMOS models and subjected to Monte Carlo analysis to assess sensitivity to process and device variations. The custom layout of the proposed memtranstor emulator has also been presented in 0.18 μm CMOS technology. Practical utility is demonstrated via two applications namely a chaotic oscillator and an artificial synapse indicating suitability for neuromorphic systems. The memtranstor-based chaotic circuit is rigorously analyzed through the computation of Lyapunov exponents, bifurcation diagrams, the Kaplan–Yorke dimension, stability evaluation, and complex dynamical behavior assessment using both NIST randomness and the 0–1 tests.