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Practical approach to programmable analog circuits with memristors
Yuriy V. Pershin, Massimiliano Di Ventra
TL;DR
The paper addresses the apparent difficulty of using memristors as stable analog elements. It proposes low-voltage analog operation with high-voltage state-programming pulses, and demonstrates programmable threshold, gain, and frequency using memristor-based circuits and an emulator. The authors conclude that controlled memristors can provide a simple digital-potentiometer realization for programmable analog circuits.
Problem
Ideal-memristor behavior suggests that dc components during analog operation would significantly change the programmed state, limiting analog use.
Method
The approach uses low voltages during analog operation and high-voltage pulses to program memristor states, demonstrated with a memristor emulator and analog circuits.
Results
The built circuits demonstrate memristor-based programming of threshold, gain, switching thresholds, and frequency.
Takeaways & Limitations
A memristor with a control scheme provides a simple realization of digital potentiometers for programmable analog circuits.
Abstract
from arXiv · showhide
We suggest an approach to use memristors (resistors with memory) in programmable analog circuits. Our idea consists in a circuit design in which low voltages are applied to memristors during their operation as analog circuit elements and high voltages are used to program the memristor's states. This way, as it was demonstrated in recent experiments, the state of memristors does not essentially change during analog mode operation. As an example of our approach, we have built several programmable analog circuits demonstrating memristor-based programming of threshold, gain and frequency.
I. INTRODUCTION
The paper addresses why analog memristor applications appear limited under ideal-memristor assumptions and proposes using experimentally observed threshold behavior for programmable analog circuits.
- Motivation: Ideal memristors would change state significantly under dc components, making their use as analog elements appear limited.Only perfect ac signals would avoid significant state change under that assumption.
- Terminology: Experimentally realizable memristors are non-ideal memristive systems with more complex behavior than ideal memristors.The paper uses “memristor” for both experimentally realized memristive systems and ideal devices, reserving “ideal memristor” for Chua’s definition.
- Contribution: The proposed approach uses low voltages during analog operation and high-voltage pulses to program the memristor state.This produces a circuit element operating similarly to a digital potentiometer with a simpler realization.
- Scope: The paper demonstrates programmable threshold, gain, switching thresholds, and frequency using memristor-based analog circuits.The demonstrations use a memristor emulator before discussing applications in analog circuits.
A. Circuit elements with memory
The paper formalizes circuit elements with memory and specializes the framework to voltage-controlled and current-controlled memristive systems, whose state and resistance evolve with electrical inputs.
- General memory devices: An nth-order memory device is described using internal state variables x, input u(t), output y(t), and generalized response function g.The input and output may be current, charge, voltage, or flux.
- State dynamics: The internal state evolves according to a continuous vector function f, under an assumption of a unique solution from an initial state.This is stated as a physical assumption for the state dynamics.
- Memristive systems: Memristive systems are defined as a class of memory devices, distinct from memcapacitive and meminductive systems by their constitutive variables.The paper focuses on memristive systems rather than the other two classes.
- Voltage control: For voltage-controlled systems, memristance relates voltage and current while the internal state depends on voltage; memductance is its inverse.RM denotes the scalar memristance, and VM(t) and I(t) are the device voltage and current.
- Current control: Current-controlled systems instead describe voltage as memristance times current, with state dynamics depending on current.A charge-controlled memristor is a special case in which resistance depends only on charge, with I = dq/dt.
- Properties: Memristors exhibit pinched hysteresis, behave as linear resistors at infinite frequency, and become nonlinear resistors at zero frequency when a steady state exists.Their ability to adjust to slow bias changes but not extremely high-frequency oscillations explains this frequency-dependent behavior.
- Circuit element: The digital potentiometer uses control signals Vpp and Vpn to program RM between limiting resistance values R1 and R2.Programming voltage Vpr must exceed the memristor threshold voltage.
B. Memristors in programmable analog circuits
The proposed circuit strategy exploits voltage-dependent memristance rates: low-voltage analog operation preserves the programmed state, while higher-voltage pulses change resistance for tuning.
- Operating principle: Below a threshold, memristance changes extremely slowly; above threshold VT, it changes rapidly.The rate of memristance change depends essentially on the magnitude of applied voltage.
- Operating principle: The circuit uses low voltages during analog operation and threshold-exceeding pulses to program the memristor state.This makes programmable memristors operate basically as digital potentiometers.
- Potential advantages: Memristor-based digital potentiometers can be much smaller, with reported memristor dimensions down to 30×30nm2.The paper also identifies reduced transistor requirements because resistance information is written directly into the memristor.
- Implementation: A pair of FETs applies ±Vpr above the memristor threshold to change resistance in a direction determined by voltage polarity.The analog circuitry is connected to one terminal, while the other terminal is grounded in the simplified implementation.
- Programming protocol: Positive voltage can increase RM and negative voltage decrease it, enabling programming toward maximum or minimum resistance states.Starting from an unknown resistance, sufficiently long positive programming can drive the device toward Rmax.
- Device modeling: The paper reports that the original charge-based TiO2 model fails to describe later experimental results.Subsequent work showed that experimentally observed behavior requires a model beyond simple proportionality between resistance and charge.
III. MEMRISTOR EMULATOR
The paper builds a programmable memristor emulator around a digitally controlled potentiometer whose resistance follows programmed memristive-system equations. Experiments reproduce memristive I–V behavior, while emulator limits depend on the chosen electronic components and model.
- Emulator architecture: The emulator uses a digital potentiometer, ADC, and microcontroller to update resistance according to programmed voltage- or current-controlled memristive-system equations.The ADC measures the applied voltage, and the microcontroller calculates the potentiometer code.
- Emulator model: The activation-type model sets memristance equal to x and limits resistance between Rmin and Rmax.The model distinguishes memristance rates below and above the threshold voltage VT.
- Experimental validation: The emulator produces pinched hysteresis loops and frequency-dependent hysteresis in measured current–voltage curves.These are reported as typical features of memristive systems.
- Hardware characteristics: 50Ω to 10kΩ resistance is available in 256 steps, while 1kHz ADC sampling limits applied-signal operation to approximately 50Hz.These characteristics are specific to the present emulator implementation.
- Model dependence: The emulator’s behavior follows the pre-programmed model within the component limits, making model selection important for correspondence with real memristors.The employed model is simple but is described as containing important physics of activation-type solid-state memristive devices.
IV. APPLICATIONS
The paper identifies programmable analog circuits as applications in which memristors can operate under low-voltage analog conditions while retaining programmable behavior.
- Applications: The paper presents programmable analog circuits as examples of applications where memristors can operate under the conditions described in Section II.The section introduces these as a selection of application examples rather than an exhaustive set.
- Applications: The applications are framed around using memristors as analog circuit elements under constrained operating voltages.
- Applications: The section reports several examples without specifying that the examples cover all suitable memristor-based analog circuits.
A. Programmable threshold comparator
The programmable threshold comparator uses a memristor-based resistance divider to set its switching threshold. Low-voltage analog operation is separated from higher-voltage programming pulses that change the stored resistance.
- Circuit principle: During analog operation, both programming FETs are off and the maximum memristor voltage remains below the selected 1.75V threshold.The design aims to keep analog-mode voltage drops below the memristor switching threshold.
- Experimental response: Starting from RM = 10kΩ, a 1.3V sinusoidal input produces narrow positive output pulses because Vin exceeds the initial 1.25V comparator threshold only briefly.
B. Programmable gain amplifier
The programmable gain amplifier replaces a feedback resistor with a memristor whose resistance is selected by programming pulses. With constant input, resistance changes produce discrete gain steps, while longer pulses enable coarser control.
- A memristor replaces one resistor in a standard non-inverting amplifier, with two FETs programming its resistance and selecting the gain.The capacitor C1 = 0.1µF suppresses noise.
- The amplifier’s gain is controlled using constant-width pulses of either 10ms or 20ms.The input signal remains continuously applied during the measurements.
- With RM = Rmax = 10kΩ at t = 0, the circuit gain is about 2 and Vin = 0.2V produces Vout = 0.4V.
- Negative pulses decrease RM, positive pulses increase RM, and the resulting resistance changes appear as steps in Vout.The input voltage Vin is kept constant during the experiment.
- The circuit gain changes approximately from 2 to 11, while longer pulses produce larger resistance changes and coarser gain control.
C. Programmable switching thresholds Schmitt trigger
The memristor programs the switching thresholds of an inverted Schmitt trigger by changing its resistance. Positive pulses raise the resistance and shift switching to different input-voltage values.
- Initially, the memristor’s low resistance produces low switching thresholds, so output transitions occur when Vin is near zero.
- A train of positive 10ms pulses applied between 2 and 4 seconds increases RM and consequently increases the Schmitt trigger’s switching threshold.
- After 4 seconds, the output switches at different values of Vin than it did initially.
D. Programmable frequency relaxation oscillator
The programmable relaxation oscillator uses a memristor-based digital potentiometer to vary Schmitt-trigger thresholds and thereby control oscillation frequency. Lower memristor resistance produces faster oscillations.
- The oscillator’s period depends on both its RC components and the Schmitt trigger’s switching thresholds.
- A memristor-based digital potentiometer varies the Schmitt-trigger thresholds to control the relaxation oscillator frequency.
- Decreasing RM increases the relaxation oscillator frequency.The decrease in switching threshold shortens capacitor charging time because the capacitor charges to a smaller voltage.
V. DISCUSSION AND CONCLUSION
The approach is demonstrated with emulator-based programmable analog circuits, while practical solid-state implementations face drift and programming-precision challenges. Low-voltage operation can reduce drift, with periodic resetting or calibration offering possible corrections.
- Discussion: Low-voltage operation reduces the importance of long-term memristance drift, but the drift rate is difficult to estimate because experimental data are limited.Drift may become important only after several months or years of operation.
- Discussion: Periodic resetting or circuit calibration can correct parasitic memristance drift during practical operation.The direction of drift depends on the particular application scheme.
- Discussion: Precise state programming requires an operation model with reproducible devices, precise pulses, or an electronic calibration procedure.Experiments with TiO2 thin films show significant noise in hysteresis curves, while colossal magnetoresistive thin films may be more suitable for analog applications.
- Conclusion: The demonstrated circuits program threshold, gain, and frequency using trains of pulses, showing a memristor control scheme can realize digital potentiometers.The demonstrations used a memristor emulator built from inexpensive off-the-shelf components.