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An introduction to the memristor – a valuable circuit element in bioelectricity and bioimpedance


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Fig. 1

The first realized memristor, produced in the HP lab. Seventeen nano-memristors are shown in parallel. (This image was produced by R. Stanley Williams of the HP lab and it is reproduced with permission from R. Stanley Williams.)
The first realized memristor, produced in the HP lab. Seventeen nano-memristors are shown in parallel. (This image was produced by R. Stanley Williams of the HP lab and it is reproduced with permission from R. Stanley Williams.)

Fig. 2

Symmetry diagram showing the 6 distinct possible realizations based on the four circuit variables. Courtesy of C. Lütken [4].
Symmetry diagram showing the 6 distinct possible realizations based on the four circuit variables. Courtesy of C. Lütken [4].

Fig. 3

Symbol representing a memristor in an electric circuit.
Symbol representing a memristor in an electric circuit.

Fig. 4

Cross-section of the first HP TiO2-memristor consisting of a high conductive (doped) and a low conductive (undoped) part placed in between two platinum electrodes. The boundary between the two parts is dynamic and is moved back and forth by the passing charge carriers. The parameter w(t) is a mathematic variable that describes the position of this boundary [4]. Courtesy of C. Lütken.
Cross-section of the first HP TiO2-memristor consisting of a high conductive (doped) and a low conductive (undoped) part placed in between two platinum electrodes. The boundary between the two parts is dynamic and is moved back and forth by the passing charge carriers. The parameter w(t) is a mathematic variable that describes the position of this boundary [4]. Courtesy of C. Lütken.

Fig. 5

Pipe model of a memristor. Here, the thick tube, A represents the high conductive part of the memristor, whereas the thin tube, a represents the high resistive part. Depending on the direction of the water flow, the piston is pushed either to the left or to the right. Hence, the net resistance of the memristor is altered when water is flowing through it. This model has also earlier been presented in [4]. Courtesy of C. Lütken.
Pipe model of a memristor. Here, the thick tube, A represents the high conductive part of the memristor, whereas the thin tube, a represents the high resistive part. Depending on the direction of the water flow, the piston is pushed either to the left or to the right. Hence, the net resistance of the memristor is altered when water is flowing through it. This model has also earlier been presented in [4]. Courtesy of C. Lütken.

Fig. 6

Typical behavior of memristors. The memristance of the memristor depends on the amount of electric charge that has passed through the device. Consequently, the current is nonlinear with the applied voltage, resulting in hysteresis loops rather than straight lines. If the signal frequency, ω, is sufficiently high, the memristance of the memristor has too little time to respond to the passing charge, resulting in the collapse of the hysteresis loops to straight lines. The inset figure shows that memristors require nonlinear q-φ-plots. Reprinted from Nature with permission [2].
Typical behavior of memristors. The memristance of the memristor depends on the amount of electric charge that has passed through the device. Consequently, the current is nonlinear with the applied voltage, resulting in hysteresis loops rather than straight lines. If the signal frequency, ω, is sufficiently high, the memristance of the memristor has too little time to respond to the passing charge, resulting in the collapse of the hysteresis loops to straight lines. The inset figure shows that memristors require nonlinear q-φ-plots. Reprinted from Nature with permission [2].

Fig. 7

Cross-sectional view of a sweat pore in the skin. From New Scientist with permission [16], (© 2011 Reed Business Information Ltd, England. All rights reserved. Distributed by Tribune Media Services).
Cross-sectional view of a sweat pore in the skin. From New Scientist with permission [16], (© 2011 Reed Business Information Ltd, England. All rights reserved. Distributed by Tribune Media Services).

Fig. 8

Equivalent electrical circuit model of the skin, now also with the memristor to capture the sweat duct properties.
Equivalent electrical circuit model of the skin, now also with the memristor to capture the sweat duct properties.

Fig. 9

Equivalent electrical circuit of the Hodgkin-Huxley nerve membrane model in its original form. Here, “inside” and “outside” denote the interior and exterior of the cell with the membrane separating these two parts. Furthermore, C is the membrane capacitance, RNa and RK describe the sodium and potassium time-varying conductivities, respectively, Rl describes the leakage resistance, ENa, EK, and El are the reverse ion channel potentials.
Equivalent electrical circuit of the Hodgkin-Huxley nerve membrane model in its original form. Here, “inside” and “outside” denote the interior and exterior of the cell with the membrane separating these two parts. Furthermore, C is the membrane capacitance, RNa and RK describe the sodium and potassium time-varying conductivities, respectively, Rl describes the leakage resistance, ENa, EK, and El are the reverse ion channel potentials.

Fig. 10

Memristive Hodgkin-Huxley model. Note that the time-varying resistances in figure 9 are replaced by memristors.
Memristive Hodgkin-Huxley model. Note that the time-varying resistances in figure 9 are replaced by memristors.