R X (t) is the memristance that changes with respect to time. R SET and R STI571 order RESET are SET and RESET resistance, respectively. w(t) is the effective width of the memristor. D is the total drift length

of w(t). q(t) is an accumulated charge flow through the memristor. Q CRIT means an amount of critical charge to RESET-to-SET transition. When q(t) becomes equal to QCRIT, R X (t) is changed to R SET from R RESET. Here μ v is the mobility of dopant in Equation 1 [1, 2]. To describe the memristive behavior that follows the relationship of current and voltage in Equation 1, a few emulator circuits have already been proposed [3–5]. Pershin and Ventra proposed an emulator circuit that is GSI-IX nmr composed of an analog-to-digital converter and micro-controller that are implemented by discrete off-chip devices. Thus, they can be considered too much complicated and too large to be integrated in a single chip [3]. Jung et al. proposed an emulator circuit that is based on CMOS technology [4], where a memristor that should change its resistance in response to the applied current and voltage is implemented by an array of resistors. In the emulator circuit with resistor array, the analog-to-digital converter and the decoder circuit select a proper resistor among many resistors that are placed in the resistor array according to the applied voltage or current [4].

One problem in the emulator circuit [4] is that the voltage-current relationship seems sawtooth. This is because the resolution of memristance change is decided by the resolution of the analog-to-digital converter, as you see in [4]. If we have 4-bit analog-to-digital converter BKM120 in the emulator circuit, it means that cAMP only 16 values of memristance are available. As a result, when we apply a voltage that is a sinusoidal function to the memristor, we can know that its current is increased or decreased like

sawtooth. To improve the resolution of memristance change, the resolution of the analog-to-digital converter should be increased too. If the resolution of the analog-to-digital converter is improved from 4 to 5 bit, the voltage-current relationship of the emulator circuit with 5 bit seems to be much finer than the emulator circuit with a 4-bit analog-to-digital converter, as shown in [4]. To improve the resolution twice, however, the number of resistors in the resistor array should be double too. It can cause a large area overhead in realizing this emulator circuit in a single chip. Especially, in implementing memristor array with this emulator circuit, this large area overhead of each memristor emulator cell can be a serious problem because each cell in the memristor array should be realized by this large-area single memristor emulator. To mitigate the large area overhead of the previous emulator circuit, we propose a new emulator circuit of memristors that is more compact and simpler than the previous emulator circuits [6].