The Realization and Working Conditions of Memristor Based on Multisim

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Figure 6. The u-t relation for different km.

approaches to a straight line and closes to i axis when km

increasing, while the shape of the u-t curve does not

change but the voltage peak decreasing. Assigning km =

5000, hm = 0.4, and the VCR of the equivalent circuit is

shown in Figure 7, in which both the horizontal axis

scale and the longitudinal axis scale are 500 mV/Div.

Increasing km until the oscilloscope can not display, how-

ever the shape of VCR still remains the same. Decreasing

km, the VCR of the equivalent circuit gradually ap-

proaches to a straight line and closes to u axis. When km

changes very little, the shape of u-t curve does not

change but the voltage peak increasing. When km is

smaller than 10-7, the u-t curve of the equivalent circuit

approaches to the sinusoid and shows the properties of

linear resistor rather than memristor with changing me-

mrisistance. Assigning km = 10−7，hm = 0.4, and the u-t

relation of the equivalent circuit is shown in Figure 8,

and in which the horizontal axis scale is 500 us/Div and

the longitudinal axis scale is 500 MV/D iv. It can be seen

that the curve is very close to sinusoid. Because some

elements of the equivalent circuit are active elements, the

circuit takes some time to get stable, the stability of the

circuit will not be changed when changing km, that is the

VCR curves will never overlap. In a word, when hm = 0.4,

the error of the circuit is small if km is between 10 and

104.

The impact of hm on the equivalent circuit is different

from that of km. For the same current source, the time the

voltage in the u-t curve reaching zero is the same for dif-

ferent hm, and that is right for the voltage reaching the

peak. hm has no impact on the time the voltage reaching

the peak. The simulation waveform in Multisim is dif-

ferent from that of the theoretic analysis. For the same

current source, the bigger hm, the bigger the voltage peak

will be. That is mainly because the VCR of the diode is

only approximately exponential. Assuming

(8)

Put Equation (2) into Equation (8), do differential both

sides of Equation (8) and simplify it.

(9)

Figure 7. The VCR when km = 5000.

Figure 8. The u-t relation when km = 10−7.

It can be seen that if VCR is not standard exponential

relationship, the equivalent circuit will be affected by hm.

Assigning L = 1 mH, C = 1 mF, i = sin(2πƒt)A and ƒ =

1 kHz. When hm is not largely changed, only the voltage

peak in the u-t curve increasing, while the shape of the

curve does not changing. When hm is bigger than 104, the

shape of the u-t curve will obviously change, the voltage

peak is not being constant, the voltage near the peak va-

ries very quickly and the maximum positive value and

the maximum negative value is not equal. Assigning km =

1000, hm = 104, the u-t curve of the equivalent circuit is

shown in Figure 9. The scales of the horizontal axis and

the longitudinal axis are 500 us/Div and 5 V/Div respec-

tively. It can be seen that the u-t relation is no longer

periodic.

In the same way, increasing hm, the u-i curve of the

equivalent circuit changes a lot, from a convex and obli-

que “8” changes to a concave and oblique “8”, which is

quite different from the u-i curve in literature [1]. Figure

10 is the u-i curve when km = 1000, hm = 104. Both the

scales of the horizontal axis and the longitudinal axis are

1 V/Div. It can be seen that the curve obviously twists

and different from the curve in Figure 4. Figure 11 is

the amplified curve partially by changing the scale of the

horizontal axis to 10 V/Div and the longitudinal axis to

50 mV/Div. It can b e seen that the u-i curve is composed

of many intersected curves. So when hm = 104, the equiv-

alent circuit is no longer stable and changes in every pe-

riod of the current source, which is also why the voltage

peak in Figure 10 is a fixed value.

Not only the voltage peak and the u-t relation, but also

the stability of circuit will be affected by increasing hm.

The bigger hm, the less stable the circuit. The u-i curve of

the equivalent circuit gets flatter, approaches a straight

line and closer to the horizontal axis when decreasing hm.

Assigning km = 1000, hm = 0.1, the simulated VCR is