Analog/RF Playbook Blog

Demystifying memristors with design basics, key properties

Memristors are a type of physical element—like capacitors, inductors, and resistors—with history-dependent dynamic behavior. This behavior can be characterized by hysteresis loops in a memristor’s input-output relations. Memristor is a portmanteau of “memory” and “resistor”, a name coined by its conceptual discoverer L. Chau in the early 1970s.

With memristors, the current resistance of the device depends on the history of its input, which enables a memristor to retain memory of its past state. Later discoveries have uncovered that memristors aren’t the only memory element, and there are also memcapacitors and meminductors, whose behavior can be derived from Kubo’s response theory. These later discoveries and interest in memristors had largely faded until 2008 when Struckov et al reported having found the “missing memristor”.

During the early flurry of reinterest in memristors, it was theorized that such devices could potentially be used to store information without a power source (non-volatile storage), and could also potentially enable logic operations. Further investigations also uncovered the potential to use memristors to imitate the behavior of neural synapses.

This outlook on memristor technology led to other theorized use cases in non-traditional computing using neural networks and neuromorphic architectures. As it turns out, memristive dynamics are common in the latest nanoscale devices, and as devices continue to shrink, memristive technology becomes increasingly viable and also necessary in active device development.

Source: National Institute of Standards and Technology

Memristor basics

A memristor is a charge-controlled or flux-controlled device and is a single-valued function of charge (q) or flux (φ).

f(φ,q) = 0

The voltage to charge/flux relationship for a memristor is:

v(t) = M(q(t))*i(t)

Where, v is voltage, t is time, and M is the incremental memristive value. The current (i) through a memristor is:

i(t) = W(φ(t))*v(t)

Where W is the conductance of the memristor, which depends on the time integral of the memristor current or voltage. Hence, a memristor behaves as a resistor at any given point of time, and the resistance/conductance of the memristor depends on the entire previous history of the memristor’s current/voltage.

The result of this behavior is a current/voltage characteristic curve similar to a Lissajous pattern; hence, it’s non-linear. With a specified current or voltage, a memristor behaves as a linear time-varying resistor. If the q-φ characteristic is kept as a straight line, it can be observed that the memristor response is purely linear time-invariant resistor.

If the incremental memristor is nonnegative, then the memristor can be characterized by a differentiable charge-controlled q-φ characteristic curve that is passive. This means that the memristor in this case doesn’t require power to function. It’s a key aspect in the use of memristors as information storage.

Key memristor properties

  • Non-linear current and voltage relationship
  • Can be reduced to a single memristor element similar to a classic circuit element description
  • At high frequencies, it reduces to a single resistor element as evident by the I-V curve
  • Incapable of storing energy, unlike a capacitor or inductor, but similar to a resistor
  • Resistance ranges influence memory capacities
  • If magnetic flux and charge through the memristor have a positive relationship, non-volatile memory is viable

Future memristor applications

The main potential applications for memristors revolve around information storage of varying types or as logic elements. One large potential future application is the creation of quantum memristive devices, or quantum memristors. The idea is that a quantum memristor would be able to exhibit behavior similar to a classical memristor and also allow for quantum coherent processing, or the ability to coherently map a quantum input state to a quantum output state.

Another key aspect of memristors as memory elements is that unlike typical digital information storage devices, memristive elements can store information continuously and not just in binary states. This is where memristors could exceed digital storage technologies in use as neuromorphic storage elements, which more accurately resemble analog storage capabilities.

JJ DeLisle, an electrical engineering graduate from Rochester Institute of Technology, moved to technical editing and writing work for design publications after spending six years in the industry as an IC layout and automated test engineer. He writes about analog and RF for Planet Analog.

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1 comment on “Demystifying memristors with design basics, key properties

  1. Yuliamas
    June 30, 2022

    The knowledge about memory is very beneficial for me, I think it helps us a lot. Thanks to it, I have more time to play stumble guys

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