# What is a mutator?

I'm reading this paper by Chua on the memristor. He claims that

Using a mutator, a memristor with any prescribed phi-q curve can be realized

(Here phi is the flux-linkage and q the charge.) The obvious search for mutator is less than helpful.

What is a mutator in this context?

"Mutator: The Chameleon Black Box

[... It] is possible to produce a mutation from one species [of the three basic network elements, resistors, capacitors, and inductors] into another another with the help of a two-port black box called the mutator. For example, it is possible to connect a resistor across port 2 of a mutator and produce an inductor across port 1. Conversely, if an inductor is connected across port 1 of the same mutator, a resistor is produced across port 2. For this reason, this class of mutators is called R-L mutators. The two other classes are the R-C mutators and the C-L mutators. An R-C mutator transforms a resistor into a capacitor, and vice versa. Similarly, a C-L mutator transforms a capacitor into an inductor, and vice versa."

(From Chua's book Introduction to Nonlinear Network Theory, McGraw-Hill, 1969, p.138)

Fig. 1 in the paper by Chua that you provided a link to, published in 1971, also shows what a mutator does and extends the concept to the memristor - the fourth basic circuit element: It is an active circuit that uses a known circuit element and mutates it into one that has memristive properties. (Known as of the paper's publishing date - today, HP has discovered something memristive.) This may still sound a bit confusing, so let's do a little detour.

You can use a gyrator when you need an element that behaves like an inductance, but all you have available is a capacitor. You pay for this "magic" with the cost of an active circuit (read: transistors, tubes, ...). A practical example for this may be integrated design: Transistors are almost free, and it's possible to build capacitors on silicon, but you can hardly wind inductors on a chip - except extremely tiny ones for very, very high frequencies. Also, inductors for audio filters often would have to be fairly large, both in Henries and in physical size; this is why you will find gyrators or (somewhat inaccurately named) solid state inductors1) on the internets. Using a gyrator, you can use a capacitor and transmogrify ("mutate", maybe even "gyrate"2)) some of its its properties into one of an inductor3). You could also go the other way round; wind an inductor and use a gyrator to obtain a capacitive circuit element (although this will hardly ever be a practical and cost-effective solution). A gyrator, in this example, and using the words from Chua's paper on memristors, would thus be something like a mutator between capacitors and inductors.

Anyone familiar with Calvin and Hobbes will, I am sure, appreciate this picture. It shows two gyrators in the shape of transmogrifiers; one makes an inductor behave like a capacitor, the other one makes a little 100 nF ceramic capacitor act like an inductor.

Now back to the memristor. Until recently, when an element with memristive properties was developed by Hewlett-Packard, you had not only the trouble of not being able to use memristors in certain processes (like IC design) - you had no memristors at all. Thus, the memristor shown in fig. 1a of Chua's paper was plain theory. The only way to get something memristic onto the screen of an actual curve tracer was using a known element like a (nonlinear) resistor (fig. 1b), a (nonlinear) inductor (fig. 1c) or a (nonlinear) capacitor (fig. 1d), and to put it through a circuit that would mutate its properties into those of the proposed memristor.

In Chua's paper, fig. 1 shows three types of black-box-like, two-port mutators. Fig. 2 shows a practical circuit that gives you a memristic behaviour looking into port 1 when you offer a (nonlinear) resistive element on port 2, say a resistor (linear) or a diode (nonlinear resistive). Therefore, fig. 2 would be a more detailed view into the black box of fig. 1b.

Aside from fig. 2 in Chua's paper, here are some other examples that show what practical implementations of mutators might look like:

From left to right: A 1N4148 diode (nonlinear resistive element) acts like a memristor (similar to figs. 1b or 2 in the paper), an inductor transmogrified into a memristor (Chua: Fig. 1c), and a 100 nF ceramic capacitor transmogrified into a memristor (Chua: Fig. 1d).

I have to admit that the examples in the pictures are non-perfect: They are white-box models instead of the original black-box models. Other that that, I promise that they actually do work! As a proof, screenshots taken with my Tek 575 curve tracer will follow ;-)

1) I have actually never seen a non-solid inductor. Gas? Liquid? Plasma? Only when a solid inductor blows, but that's on the odd side of reasoning. I guess calling these gyrators transistorized would be less misleading.

2) see here for a well-known, cardboard-box-like, real-world (!), non-electronic (?) transmogrifier. As the cited source says, when it comes to transmogrification, "Scientific Progress Goes 'Boink'" - use with caution!

3) See this question about energy storage in a gyrator for some hints on a gyrator's limitations.

• Cute pictures. One nitpick: it's certainly possible to make inductors on ICs, in the metal layers. Of course, the inductances achievable are relatively small and thus applicable mostly to >GHz RFICs. – mng Jul 20 '12 at 20:30
• @zebonaut - I don't know if you noticed it but you have edited this answer so many times that it has become a Community Wiki. Maybe you don't care about it, but if you don't want it you can flag it and ask a moderator to revert it. – stevenvh Jul 21 '12 at 8:52
• @stevenvh Yes, I've noticed. I actually care more about the learning process that happens during my edits or about improving the site by linking to related questions I found later than I care about the reputation score, so I don't worry too much. As I see it, CW happens as a penalty for having the question bumped to the top of the list after an edit. Bumping the question is not what I aim at. If there was a checkbox for minor edits that would prevent bumping, I would be more than happy to click it... And I kind of don't want to waste a moderator's time by asking for an undo of the CW flag. – zebonaut Jul 21 '12 at 9:04
• @zebonaut - Kortuk told me he didn't mind, it takes him just a second. I'm with Olin on this who says (paraphrasing): "you put much effort in giving a good answer and suddenly you don't own it anymore". For me it isn't about rep either. Have a nice weekend! – stevenvh Jul 21 '12 at 9:08
• @zebonaut - I noticed that you posted on meta about it, but seemed to have changed your mind, and deleted it. The "minor edit" been suggested before, and I think it will get support as a feature request. I wanted to undelete the question (it's great to have 10k+ rep :-)), but would like to have your permission first. Also, why did you delete it? – stevenvh Jul 21 '12 at 10:03

Q What is a mutator in this context?

A A mutator is a change or cause to change in form or nature : [ intrans. ]
e.g. a technology that continues to mutate at an alarming rate e.g. a program virus that mutates into other forms must be programmed to do this.

In this context, mutator is a gag word applied to HP's memory effect. In the digital world, all memory and all digital parts are actually based on analog characteristics of physics and chemistry with many types of memory and many electrical interfaces. They are inherently non-linear and inherently designed to store information digitally.

The context was given as a proposal but not accepted by accredited associations.

*Mutant components do not seem to be relevant to logical world of electronics, except in Fiction or defective parts or parasitic effects.