A memristor is an electrical element, which has been conjectured in 1971 to complete the lumped circuit theory. Currently, researchers use memristor emulators through diodes, inductors, and other passive (or active) elements to study circuits with possible attractors, chaos, and ways of implementing nonlinear transformations for low-voltage novel computing paradigms. However, to date, such passive memristor emulators have been voltage-controlled. In this study, a novel circuit realization of a passive current-controlled passive inductorless emulator is established. It overcomes the lack of passive current-controlled memristor commercial devices, and it can be used as part of more sophisticated circuits. Moreover, it covers a gap in the state of the art because, currently, only passive circuit voltage-controlled memristor emulators and active current-controlled emulators have been developed and used. The emulator only uses two diodes, two resistors, and one capacitance and is passive. The formal theory and simulations validate the proposed circuit, and experimental measurements were performed. The parameter conditions of numerical simulations and experiments are consistent. Simulations were performed with an input current amplitude of

A memristor is an electrical two-terminal passive nonlinear resistance element that exhibits a well-known pinched hysteresis loop at the origin of the voltage-current plane when any bipolar periodic zero-mean excitatory voltage or current of any value is applied across it. However, there are disagreements regarding whether a memristor can be considered a fundamental element and whether its dynamic is purely electromagnetic, as originally conjectured, or if there are other mechanisms involved such as ionic transport. Despite the controversy surrounding the technological realization, the amount of research into the properties of the pinched hysteresis loop continues to increase. Irrespective of whether the memristor is implemented by emulating its behavior through circuitry composed of other active or passive components, new studies continue to generate and sustain optimistic expectations in the scientific community about the use and advantages of the memristor. The research interest in the memristor is motivated by its promising potential for building novel integrated circuits and computing systems, as has been proposed in [

There is neither implementation nor a proof-of-concept for a passive current-controlled memristor system-on-chip but yes for an active current-controlled memristor [

To summarize, (a) background: to the best of our knowledge and after searching in database providers, we have concluded that a passive and current-controlled memristor emulator has not been published previously (only active current-controlled memristor [

Memristors exhibit three characteristics for any bipolar periodic signal excitation: (i) there is a pinched hysteresis loop in the voltage-current plane, (ii) the area of the hysteresis loop decreases and shrinks to a single-valued

Novel current-controlled memristor emulators have been introduced recently in [

(a) Proposed current-controlled memristor circuit emulator and (b) generalized symbol of the memristor device.

We construct the equations by beginning with the Shockley diode equation (both diodes are equal and without considering high-frequency effects that produce unwanted dynamic effects):

Therefore,

According to the voltage drop,

The current

Using equation (

However, from equation (

Then, the

Because

Next, we focus on the

Because

Finally, equation (

Next, we focus on the state equation:

Now, to complete the state equation, we have to calculate

Therefore, from equation (

By introducing equation (

Because

Finally, this circuit dynamic can be written as follows (where

From equation (

According to equation (

Note that

Current-voltage characteristics obtained through the LTspice simulations of the memristor emulator driven by a current source

The following parameters were used to simulate the memristor circuit emulator proposed in Figure

Simulated pinched hysteresis loop of the memristor emulator driven by a current source

The following observations can be made from the simulation results. The loci in the

The experimental setup is shown in Figure

(a)

We can see the emulator under test and also the oscilloscope-waveform generator Analog Discovery 2 [

For completeness and comparison, the

The excitatory signal is a sinusoidal waveform of frequency

We conclude that the experimental measurement shows the same waveform pattern and the performance predicted by theory (Figure

For completeness and comparison, the

The emulator should not retain its value when no input signal is applied. The volatile memristor that features decay of device memory has high similarity to the biological synapses of neurons, and since neuromorphic computing is becoming more important, the decay is a desired feature.

At this point, it is important to underline that this kind of memristor emulator is not suitable for the logic-in-memory (LiM) paradigm, nor high-frequency applications; instead, our proposed circuit can be used practically for neuromorphic computing and as a candidate for mimicking biological synaptic functions. It is enough to show as example Figure

Variation of

This work shows a passive circuit current-controlled memristor emulator. It overcomes the lack of current-controlled memristor commercial devices. Moreover, it covers a gap in the state of the art because, currently, only passive circuit voltage-controlled memristor emulators have been developed and used. The mathematical model of the proposed memristor emulator was derived and verified by simulations (the mathematical treatment was simplified and the diode parasitic capacitance was not taken into account because in that case the device dynamics should be studied with intensive numerical simulations (using for instance MATLAB) because the system is strongly nonlinear. Nevertheless, the SPICE simulator has the complete diode model with junction capacitance included; then, numerical circuital simulations are accurate). The circuit can be improved to be less symmetric in order to have a different clockwise and anticlockwise slope.

Simulation files link can be found at

Part of this manuscript was submitted as a preprint in the link “

The authors declare that they have no conflicts of interest.