Features of simulation of periodic steady-state in nonlinear networks with memristor devices

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Abstract

The numerical properties of applying the method to compute the periodic solutions in the analysis of circuits with memristor devices are considered. The modification of the iterative procedure is proposed, which makes it possible to improve numerical properties in simulation of periodic modes by taking into account the characteristics of memristors. Examples of simulation confirming the operability of the developed computational procedure are given.

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About the authors

S. G. Rusakov

Institute for Design Problems in Microelectronics of RAS

Author for correspondence.
Email: rusakov@ippm.ru
Russian Federation, Zelenograd, Moscow

S. L. Ulyanov

Institute for Design Problems in Microelectronics of RAS

Email: rusakov@ippm.ru
Russian Federation, Zelenograd, Moscow

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Supplementary files

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2. Fig. 1. Schematic diagram of a frequency modulation demodulator based on the average level shift of the memristor resistance [25].

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3. Fig. 2. An example of modeling a demodulator circuit: time diagrams of changes in the memristor state variable and output voltage in the integration interval variants of 60 periods (a), 600 periods (b), 6,000 periods (c). In variant (c), a steady-state solution independent of the initial conditions is obtained. The initial resistance of the memristor: 8 (curves 1), 11 (curves 2), and 15 kOhm (curves 3).

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4. Fig. 3. Low-pass filter based on MC circuit [21, 22].

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5. Fig. 4. Different periodic solutions obtained in modeling the MC circuit (Fig. 3) for different initial values ​​of the memristor resistance: for a large value of R(0) (curves 1), for a small value of R(0) (curves 2). Here V(1)–V(2) is the voltage on the memristor (a), z is the state variable (b).

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6. Fig. 5. Controlled active filter with a memristor device [19]; ​​OP – operational amplifier.

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7. Fig. 6. Output signal diagram for z0 = 0.2 (curve 1) and z0 = 0.9 (curve 2).

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8. Fig. 7. Periodic solutions obtained by simulating the demodulator circuit (Fig. 1) for the initial values ​​of the memristor state variable z0 0.1 (curve 1) and 0.9 (curve 2).

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9. Fig. 8. Schematic diagram of a bridge rectifier [49].

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10. Fig. 9. Timing diagrams for the input sinusoidal signal Vin (curves 1), output voltage Vout = V(1) – V(2) across the resistance R1 (curves 2), changes in the states of the memristors z1, z2 (curves 3, 4), obtained during the simulation of the bridge rectifier (Fig. 8) for the initial values ​​of the memristor resistances of the devices: (a) — R1(0) = R4(0) = 2 kOhm, R2(0) = R3(0) = 8 kOhm, (b) — R1 (0) = R4 (0) = 8 kOhm, R2(0) = R3(0) = 2 kOhm.

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11. Fig. 10. The correct periodic solution obtained by using a two-level iterative procedure for modeling the controlled active filter circuit (Fig. 5). Vout is the output signal of the circuit, z is the state variable of the memristor model.

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12. Fig. 11. Timing diagrams for: output voltage Vout = V(1)–V(2) on resistance R1 (curve 1) and changes in the states of memristors z1, z2 (curves 2, 3), obtained during modeling of a bridge rectifier (Fig. 8) for initial values ​​of memristor resistances R(0) = 2 kOhm and state variable z0 = 0.88 of devices M1 and M4.

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13. Fig. 12. Results of calculating the steady-state periodic mode when simulating a low-pass MC filter: time diagrams of the state variable (a) and the voltage on the memristor VM = V(1)–V(2) (b) for the initial value of the state variable z0: 0.11 (curves 1) and 0.92 (curves 2).

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14. Fig. 13. Timing diagrams for modeling the steady-state periodic operating mode of the demodulator (Fig. 1): (a) — output signal; (b) — memristor state variable for the initial values ​​of the memristor state variable z0: 0.14 (curves 1) and 0.86 (curves 2).

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