I've never been convinced that the memristor is worthwhile to consider as a "fundamental passive device" as everyone seems to want to claim. There are a few reasons for this:
(1) It's underspecified compared to the fundamental passive circuit elements. For linear R, L, and C, each has one parameter, its value. Ignoring trivial cases (viz., resistors), a memristor has as its memristance an arbitrary function of V and I. As a result, any interesting memristor is automatically not LTI.
(2) It's not particularly special. Why don't we also define a memcaptor, whose capacitance is a function of its current history? I could easily do this, for example, by making a capacitor where one plate is attached by a spring to a fixed support; then, by adding charge, I move the plate and increase the capacitance (or, by removing, I decrease it). Oh wait, that's just a nonlinear capacitor. In the same way, the memristor is just a funny name for a particular kind of nonlinear resistor.
(3) It's not particularly practical (for the moment). It can't be made in anything but a very specialized, presumably extremely expensive process. I hope this changes---I'm sure it'll encourage someone to use them!---but at the moment this really limits my excitement.
(4) There's nothing I can build with a memristor that I couldn't build already. This isn't like the invention of the vacuum tube: you give me a memristance function, and I can build you a pseudo-memristor out of transistors, Rs, Ls, and Cs. Yes, it could be less {space,power,?} efficient, but this is not a quantum leap in technology the way the vacuum tube was (one could not, with 1890s technology, reasonably build something that emulates a vacuum tube).
I'll admit that strictly interpreting my last argument, the vacuum tube could be made to emulate a transistor and thus the transistor wouldn't count as a quantum leap---clearly ridiculous. However, I'd contend that the real value of the transistor was only evident once it was sufficiently miniaturized and its production was sufficiently cheap. You show me memristors that are six orders of magnitude cheaper than transistors and by golly I'll be a convert. Even then, it'll just be yet another nonlinear device with which we can do interesting things---and just like the transistor, the memristor will simply never be as fundamental as R, L, or C.
Regarding your (1), I'm not sure I follow, isn't the fundamental unit of resistance, ohms, just a function of V and I? Namely V/A. Likewise for capacitance, the Farad is simply (A/V)s. Basically, your argument feels like it is begging the question -- we gave those functions of V and I names, so now they are fundamental units but not the memristor one... because it doesn't have a name?
memcapacitor and meminductors have been proposed in 2009.
You can build the memresistors out of combinations of components but it doesn't allow for miniaturization and low power usage. I.e. the application in RAM is going to be huge!
It'll be huge assuming that they're reliable, can be manufactured cheaply, and perform well. DRAM is a very advanced technology. It'll be a while before memristor-based RAMs enjoy the benefits of that kind of background.
In the end, like I said above, you show me memristors that blow transistors out of the water and I'll start designing with them tomorrow.
(Of course, I have my reservations that they'll be much help for analog circuit design: with regard to CMOS, the last few generations have been friendly to digital designers but decidedly unfriendly for analog design. (Give me 0.18u or 0.13u CMOS any day.)
Really, almost all analog CMOS chips, even at advanced nodes, still have older, bigger devices integrated as well. Even at 65nm, good old 0.35u or 0.25u devices are used for i/o and a large amount of analog design because the advantage of using smaller devices is between somewhere between negligible and negative for a lot of designs.)
I question whether the article is correct about the "J-Damper" being a meaningless code-name. In circuit theory, a capacitor can be thought of as a resistor with purely complex (and frequency varying) impedance. Since "J" is the standard symbol for the square root of -1, and given the fact that this device had never been used before, "Imaginary Damper" seems entirely appropriate.
Charge being equivalent to position doesn't make much sense to me.
When I learned systems modelling, we studied spring-mass-damper systems right next to electrical circuits and I have ever since thought of a capacitor as equivalent to potential energy, an inductor as equivalent to inertia and a resistor as equivalent to friction.
That's a common view, since force ~ voltage, current ~ velocity (i.e. charge ~ position) seems "intuitively" correct, but it breaks down when you look at what would be the equivalents of KVL and KCL. KCL states that currents sum to zero at a node in the absence of capacitance: this is similarly true of forces (capacitance in this case representing the ability of the node to change position/"charge").
KVL states that voltage differences sum to zero around a loop: this is similarly true of velocity differences. This can be difficult to visualize, but imagine a loop of N springs. Assume the loop can have no net translational motion (as above, this means it is not capacitive). Now imagine the different ways each spring can move individually. The loop could rotate as a whole, meaning half the springs have are moving "up" (i.e. have a positive voltage across them) and the other half "down" (i.e. have a negative voltage across them). The loop could be still, but for one element compressing and its neighbor expanding (i.e. all zero voltages with one positive and one negative).
The reason the examples in your systems class worked was likely because the circuits were simple enough that their duals shared the same, or similar, network structure. You can see this with a purely electrical circuit -- analyze a simple LCR loop, and then swap the L & C equations and you should get the same result. This breaks down for larger circuits, where you must find the dual network in addition to swapping Ls and Cs.
The invetor's slides say that the only time the analogy breaks down is with ungrounded capacitors, though its unclear to me what exactly that means (I don't really feel like thinking too hard about it). See slide 17
http://www-control.eng.cam.ac.uk/~mcs/lecture_j.pdf
There are actually a few different analogies you can make between electrical/mechanical devices. See the top table "Key Concept: Analogous Quantities". This is part of the reason why I don't feel like thinking too hard about what the inventor means when he says the analogy "breaks down" with ungrounded capacitors.
http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Analogs/E...
The inventor has created a "new analogy" where the inerter is a capacitor. I read your post as saying the old analogies don't work. Is that correct?
The point you're making is orthogonal to the one I was making: the force ~ voltage analogy breaks down at KCL/KVL (as well as ungrounded inductors), while the force ~ current analogy breaks down only for ungrounded capacitors.
"Ungrounded capacitors" refers to capacitors which do not have at least one terminal connected to the reference voltage (ground). These break the force ~ current analogy because with that analogy, capacitors, which are two-terminal devices, are analogous to flywheels, which are one-terminal devices. The velocity (voltage) of the second terminal is effectively zero.
Your reading of my post is close to correct. The force ~ voltage analogy is incorrect however you look at it because KCL and KVL don't hold. The "old" force ~ current analogy does hold except for the case of ungrounded capacitors, which the replacement of flywheels with inerters remedies.
No, charge would be equivalent to potential energy, resistance would be equivalent to friction, etc. You're confusing a property and objects that effect that property.
Another interesting question. Given we can move between mechanical and electrical systems with circuit theory. Are their other systems that we could apply circuit theory to (i.e. non electrical and non mechanical systems). Light and space circuits for example?
Audio Systems consist of electrical circuits (amplifier, player), mechanical circuits (loudspeaker-membrane) and acoustical circuits (air, room acoustics). All these parts can be modeled as circuits that directly interact with each other.
You can actually calculate the electrical properties of the mechano-acoustical loudspeaker+room or the acoustical properties of the electro-mechanical loudspeaker+amp. This is extremely helpful when designing loudspeakers since you can see the electrical, mechanical and acoustical properties all in one notation.
You can also model some hydraulic systems using components analogous to electronics (flow=current, pressure=voltage, pipes=resistance). For example a certain pressure applied to a pipe of given size (cross-section + length) and material will result in a predictable rate of flow.
Basically any LTI differential equation can be modeled as a network of Rs, Ls, and Cs. You can get fancier if you want by adding nonlinear elements.
In other words, anything you can describe as a differential equation has an analogous circuit. In fact, I've read the claim (though I cannot, for the moment, find the reference) that the term analog was first applied to circuits which were being built to solve LTI differential equations: the circuit was the analogue of the equation, thus it was an analogue (eventually, just analog) circuit.
"I have always thought that the memristor is rather a weak concept. It is defined as a device with a nonlinear relationship between flux and charge. A linear memristor is the same as a resistor, so in linear circuits the element is not meaningful. The definition does not pin down the type of nonlinearity. So the difference between a variable resistor and a memristor is not sharply defined. The mechanical equivalent of a variable resistor is of course a variable damper. Variable dampers and semi-active dampers are of course used a lot in suspension systems"
From a friend: "The quantum mechanics stuff sounds very unlikely. Although if you wanted to try and go in that direction you would have to figure out whether circuits have a strong analogy to the Hamiltonian formulation of quantum mechanics (i.e. no discussion of forces!) - then you would be in business. You could then probably formulate a "quantum circuit" in which measurements of voltage and current obey an uncertainty principle"
My own experience... I know why this concept sounds so familiar to me. I had one when I was little.
There are many childrens toys with a flywheel and a ripcord. That system is an "Inerter"... If the ripcord is a rigid toothed rack and pinion setup then it can act as an "Inerter" in compression as well as tension.
Because flywheels have only one usable node; the other is effectively "grounded". They're also rotational; if you're working with translational systems (e.g. suspensions), you need something else.
An inerter, being basically a flywheel connected to a rack gear, meets both these requirements. You have two nodes (the flywheel's axis, and the rack gear) and the motion is translational.
Additionally: a rotational inerter can be made by connecting the ring gear of a differential to a flywheel. The two nodes are then the two side gears of the differential.
http://www.quora.com/What-is-the-mechanical-element-equivale...