On the pinched hysteresis behavior in a state-controlled resistor

We show that the pinched hysteresis behavior observed in a voltage-controlled resistor with state-feedback self-control can be attributed to the current flowing in the parasitic capacitance holding the voltage across this resistor. A mathematical model describing this circuit structure is derived and validated numerically. To provide experimental evidence of this proposal, a circuit representing a voltage-controlled resistor is placed in parallel with a capacitor and then the current in this capacitor, which is proportional to the derivative of the applied voltage, is sensed, converted into a voltage and used to control the resistance value. This leads to the appearance of a pinched hysteresis loop as theoretically predicted. This work provides further insight into the origin of this behavior in fabricated solid-state devices that can be shown to follow the proposed circuit structure.