Generalized Rule of Homothety of Ideal Memristors and Their Siblings

The pinched hysteresis loop area increasing with the square of the frequency of driving harmonic signal on the assumption of constant charge delivered within the half-period belongs to the less known fingerprints of ideal memristor. The paper proves that this fingerprint holds not only for the harmonic excitation: the v-i characteristic of a memristor driven by n-times accelerated and simultaneously n-times amplified signal of arbitrary waveform is a homothetic entity with respect to the original characteristic, with the homothetic center at the v-i origin and with the homothety ratio n. This rule holds for an arbitrary ideal memristor but not for an arbitrary general memristive element. Breaking this rule indicates reliably that the element analyzed is not an ideal memristor.