Memristor Response to Square Wave

A constant programming voltage causes current to change as the memristor resistance evolves.

Circuit operation

V1 alternates between −3 V and +3 V every 5 ms. RS limits current slightly. During each constant-voltage interval, the resistance continues to change, so current is not a square wave.

Expected behavior

$$\frac{dR}{dt}\approx\pm\beta(|v|-V_t)$$ $$|i|=|v|/R$$

Positive programming voltage increases resistance and reduces current magnitude. Negative programming voltage decreases resistance and raises current magnitude. Once a resistance limit is reached, the corresponding current interval becomes almost flat. This is a bounded state model, not a capacitor charging law.

Reading the results

The first voltage probe is green; the second, when present, is red. The first current probe is blue. The schematic opens fitted to its extents. The saved transient spans 30 ms with a maximum step of 2 µs. The chart uses separate voltage and current lanes, and the table retains the same probe order.

Try a change

Double the input frequency. Less state change occurs during each half-cycle, so the current response approaches that of a fixed resistor. Restore the saved values after comparison.

Model limits

MR1 uses the ngspice voltage-threshold memristor model. Alpha is zero, so subthreshold reads preserve state. Rmin, Rmax, Rinit, Vt, and Beta are illustrative values. This is a memristive-system model, not a material-specific or thermal model.

Reference: ngspice memristor model and threshold-model paper.