# Inventor flames *Reg*, HP in memristor brouhaha

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### Not so says HP, not so at all

Williams agrees Chua broadened his definition but this had nothing to do with saving HP's face, nothing at all.

This issue was made much clearer in a second paper^{8}published with his then student Sung Mo Kang ... a critical generalization of the simple memristor concept of the first paper.Chua and Kang introduced the fact that a 'memristive device' has a state variable (or variables), indicated by w, that describes the physical properties of the device at any time. A memristive system is characterized by two equations, the 'quasi-static' conduction equation that relates the voltage across the device to the current through it at any particular time, v = R(w,i) i, and the dynamical equation, which explicitly asserts that the state variable w is a time varying function f of itself and possibly the current through the device, dw/dt = f(w,i).

Neither the flux φ nor the charge q appears in either of these two equations, but it is relatively 'easy to show' that if both R and f are independent of the current i, the two equations reduce to the original definition of a memristor.

Williams then notes that Chua and Kang introduce a key new idea:

Furthermore, the quasi-static conduction equation places a requirement on the current-voltage characteristic of the device – if a memristive system is driven with some type of cyclic excitation, such as a sinusoidal current, the plot of the voltage vs. the current will be a Lissajous curve for which the voltage is always equal to zero when the current is zero, and vice versa.Chua called this curve a 'pinched hysteresis loop', and it has an important physical interpretation – neither a memristor nor a memristive system stores either charge or energy (like a capacitor, for example), but they do 'remember' their history because of their changing resistance.

This generalised memristor idea was independent of any physical mechanism at the time. In Williams' view: "The key result was that any electronic circuit element that displayed a pinched hysteresis loop in its current-voltage characteristic could be described mathematically by the two memristive system equations."

This led on the generalised memristor idea:

As more researchers began to cite the original works, it became clear to most that the distinctions between 'memristors' and 'memristive systems' were unimportant, so Chua has recommended that the nomenclature be simplified by referring to both as memristors.

### What is a memristor?

William's document provides a memristor definition:

According to the general mathematical model, a memristor is any passive electronic circuit element that displays a pinched hysteresis loop in its i-v characteristic, independent of what the physical mechanism is that causes the hysteresis.

The 2-terminal passive electronic circuit restriction has gone away.

Williams says: "Examples of memristors include bipolar and unipolar resistive switches, often called RRAM or ReRAM; 'atomic switches'; spin-torque transfer RAM devices, phase-change memory devices, and several other systems based on a wide variety of materials and mechanisms^{9}."

Mouttet is quite wrong. There is no HP propaganda campaign to take credit for the memristor. HP Is not trying to impose an HP brand on the memristor idea: "We have chosen to use the term memristor to describe the devices in our papers, not because we are trying to impose an 'HP brand' (especially since the term was invented by Leon Chua), but because we feel the general term connotes a broader range of applications."

Also the memristor was a distinct discovery:

It is a rigorous mathematical model that can be used to predict the behavior of a wide variety of physical devices. There have been many developments of different types of memristors, now called by many different names, based on different materials and physical mechanisms, but they are all described by the same general mathematical formalism developed by Chua.

To get deeper into these matters read Williams' short history of memristor development, and make your own mind up whether HP has discovered the Fourth Element or not.

Compliments of the season to you all. ®

**Notes** 1. Blaise Mouttet assisted in the formation of the patent class for nanotechnology used by the US Patent and Trademark Office. He maintains a blog devoted to reviewing newly issued U.S. patents in nanotechnology and is an inventor in 11 US patents related to memristive electronics applied to signal processing and adaptive control. He has given presentations related to memristive devices at the 1st Memristor and Memristive Systems Symposium held at UC Berkeley in 2008 and at the IEEE International Symposium on Circuits and Systems (ISCAS) held in Paris, France in 2010.

2. Strukov et al., *The missing memristor found*, Nature 453, 80-83 (2008)

3. S Thakoor *et al*, *Solid-state thin-film memsistor for electronic neural networks*, *Journal of Applied Physics*, v67, n.6, 1990.

4. L. O. Chua, Memristor – the missing circuit element, IEEE Trans. Circuit Theory 18, 507-519 (1971)

5. Read Mouttet's *Memsistors, Memristors, and Memresistors* paper to get into the detail here.

6. L. Chua, *Resistance switching memories are memristors*, Appl. Phys. A 102, 765-783 (2011)]

7. *Memristive Systems and Devices*, published in the *Proceedings of the IEEE*, vol 64, No 2, 1976.

8. L. O. Chua & S. M. Kang, *Memristive devices and systems*, Proc. IEEE 64, 209-223 (1976).

9. L. Chua, *Resistance switching memories are memristors*, Appl. Phys. A 102, 765-783 (2011)