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I've read that there are four types of passive elements: resistances, capacitors, inductors and memristors.

The memristor was predicted 30 years before it was produced. But why couldn't you invent other type of passive element? Is there a proof?

The definition I'm using of passive elements is something with no gain, no control and linear.

jinawee
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    There's this spiffy graphic, which you might have seen. http://en.wikipedia.org/wiki/File:Two-terminal_non-linear_circuit_elements.svg Unfortunately I just find myself staring at it and thinking about memristors, rather than feeling like the question has been answered. – Phil Frost Jan 29 '14 at 20:52
  • @PhilFrost Clearly I'm not the only one who likes that graphic! – Stephen Collings Jan 29 '14 at 20:56
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    I think it's important to keep in mind that every wire displays resistance, capacitance and inductance. These are _ideal_ circuit elements but in real life they are _characteristics_ of pretty much every circuit element. The memristor doesn't fit that mold. You can't talk about the "memristance" of a wire. In my mind, the memristor does not belong in the same set as resistance, capacitance, and inductance. – Joe Hass Jan 29 '14 at 21:28
  • *I'm using of passive elements is something with no gain, no control and linear.* Then the memristor is not a passive element since it is non-linear (except for the trivial case where it is just a resistor). According to Wiki, for the memristor we have: \$v = M(q)i \$ where q is understood to be the time integral of \$i\$. If \$M(q)\$ is constant, \$v \propto i\$ and, thus, we have a resistor. Otherwise, \$v\$ is not a linear function of \$i\$. For example, if \$M(q) = mq\$ then \$\frac{dv}{dt} = m(i^2 + q\frac{di}{dt})\$ – Alfred Centauri Jan 30 '14 at 17:24
  • @AlfredCentauri So it contradicts this answer http://electronics.stackexchange.com/a/82801/24361 ? – jinawee Jan 30 '14 at 17:46
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    @jinawee, if a passive element must be *linear*, the memristor is not a passive element. From the Wiki article "Memristor": *In his 1971 paper, Chua extrapolated a conceptual symmetry between the nonlinear resistor (voltage vs. current), nonlinear capacitor (voltage vs. charge) and nonlinear inductor (magnetic flux linkage vs. current). He then inferred the possibility of a memristor as another fundamental nonlinear circuit element linking magnetic flux linkage and charge.* – Alfred Centauri Jan 30 '14 at 18:18
  • The graphic linked by PhilFrost always at first glance makes me thing, "so why there's no component on voltage-flux line? that would be so cool. Or charge-current line? Oh crap, that's just **time**". Sooo.. maybe we could make a component for the time? :D – quetzalcoatl Jan 27 '20 at 00:13

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There are four physical quantities of interest for electronics: voltage, flux, charge, and current. If you have four things and want to pick two, order not mattering, there are 4C2 = 6 ways to do that. Two of the physical quantities are defined in terms of the other two. (Current is change in charge over time. Voltage is change in flux over time.) That leaves four possible relationships: resistance, inductance, capacitance, and memristance. enter image description here

If you want another fundamental component, you need another physical quantity to relate to these four. And while there are many physical quantities one might measure, none seem so tightly coupled as these. I'd suppose this is because electricity and magnetism are two aspects of the same force. I'd further suppose that since electromagnetism is now understood to be part of the electroweak force, one might be able to posit some relationships between the weak nuclear interaction and our four elements of voltage, current, charge, and flux.

I haven't the first clue how this would be physically manifested, especially given the relative weakness of the weak nuclear force at anything short of intranuclear distances. Perhaps in the presence of strong magnetic or electrical fields affecting the rates of radioactive decay? Or in precipitating or preventing nuclear fusion? I'd yet further suppose (I'm on a roll) that the field strengths required would be phenomenal, which is why they're not practical for everyday engineering.

But that's a lot of supposition. I am a mere engineer, and unqualified to speculate on such things.

Stephen Collings
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    I think it's more like "someone decided there are four physical quantities of interest for electronics". And really maybe there are only two, since charge is the integral of current, and flux the integral of voltage. Temperature is pretty important. So is power, or its derivative, energy. Or maybe I want to integrate flux to get a new thing, and define a component about that. – Phil Frost Jan 29 '14 at 21:24
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    I think maybe the proof lies in the requirement (set in the question) that these passive components are *linear*, and that means that they have some linear relationship between current and voltage, thus there can't be other physical quantities of interest, by definition. But I'm just guessing. – Phil Frost Jan 29 '14 at 21:26
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    Resistance is *not* defined as \$R = \frac{dv}{di}\$ but, rather, as the *constant of proportionality* of voltage and current, \$R = \dfrac{v}{i}\$ so, *at best*, this graphic is misleading. For example, an ideal voltage source in series with an ideal resistance \$R\$ satisfies \$R = \frac{dv}{di}\$ *but such a combination is not a fundamental passive circuit element*. – Alfred Centauri Jan 30 '14 at 04:05
  • @AlfredCentauri There's a bit of explanation in the Wikipedia article for memristor that explains [why everything was written as differential equations](http://en.wikipedia.org/wiki/Memristor#Theory). I can't say I follow it (I don't speak math very well), but I understood it as "because it makes it easier to argue for memristors." – Phil Frost Jan 30 '14 at 12:51
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    Personally I would have chosen to define M the other way round, so dq=MdΦ, then you could compare with dq=Cdv and justifiably call them flux-capacitors – Pete Kirkham Jan 30 '14 at 13:49
  • @PhilFrost: In what way is relating the four quantities as shown more "correct" than saying that capacitors, resistors, and inductors establish a ratio between current and either dV/dt, V, or integral(Vdt), or between voltage and integral(Idt), I, or dI/dt? – supercat Jan 30 '14 at 16:49
  • @supercat sorry, I have no clue. When I see math for something about which I don't already have an intuitive explanation, my head melts. I just wanted to provide the link for reference. – Phil Frost Jan 30 '14 at 19:49
  • Really the only reason flux is in this diagram is so they could put two derivatives in all of the equations - from a circuit theory point of view flux and charge aren't really involved at all. What's wrong with V=RI, V=LI', and V'=(1/C)I ? (where ' denotes derivative with respect to time) – user253751 Apr 10 '17 at 04:20
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But why couldn't you invent other type of passive element? Is there a proof?

Well, there is a proof, but it's circular. If you take "the four fundamental electronic variables", there are only six ways to combine them linearly. Four of the ways are components, and the other two are definitions. Stephen's answer explains this well. There are only four passive components because whoever made that claim only allowed four variables.

I can "invent" more "missing components" by introducing more variables. Current is the derivative of charge with respect to time:

$$ i = \frac{\mathrm dq}{\mathrm dt} $$

I'm going to define a new term: surgingness. It's the derivative of current with respect to time:

$$ s = \frac{\mathrm di}{\mathrm dt} $$

Mind blown? Put it back together. We do this all the time in physics. These sequences are analogous:

  • position, velocity, acceleration
  • charge, current, surgingness

We can differentiate variables as many times as we want and give the results names, if we want. Physics even has a name for the derivative of acceleration: jerk.

Now we can stick surgingness in that graphic from Stephen's answer. It goes below and to the left of current.

Now we can ask, what's the component that connects surgingness with voltage? It would be a component that obeys:

$$ \mathrm dv = P \mathrm ds $$

I'm going to call \$P\$ Philistance. The component is called a Philator.

What's the utility of this component? I haven't a clue, but I predict it exists. In a few decades, when it's invented, I'll say "I told you so" and be famous.

Community
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Phil Frost
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    I think you're just a Philistine. – hobbs Jan 30 '14 at 01:55
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    If \$s = \frac{di}{dt}\$ and \$dv = P ds\$ then \$v = P\frac{di}{dt} + V\$, i.e., the *Philator* is just an inductor in series with a constant voltage source. – Alfred Centauri Jan 30 '14 at 04:53
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    @AlfredCentauri Which means that if you make a _passive_ Philator, you will indeed be very famous. – Buhb Jan 30 '14 at 06:51
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    @Buhb, a *passive* Philator would be like a *married* bachelor. – Alfred Centauri Jan 30 '14 at 12:41
  • @AlfredCentauri If you say so. I never was very good at math :) I was wondering, what if I integrate charge and integrate flux, then imagine there is some passive component there. Perhaps a "Forgistor"? Or is that also some combination of things we already have? – Phil Frost Jan 30 '14 at 12:45
  • Extending the physics analogy, the full list up to the seventh derivative is "position, velocity, acceleration, jerk, snap, crackle, pop" – AJMansfield Jan 30 '14 at 23:20
  • @Buhb `if you make a passive Philator, you will indeed be very famous` made my day much better, thank you! It's been a long time I laughed this hard – quetzalcoatl Jan 27 '20 at 00:18
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jinawee,

I think there are a large number of "passive" components yet to be both discovered and invented. "Passive" is a somewhat deceptive and ambiguous term we use in electronics. In electronics we have a lot of loose terminology that throws beginners a curve ball. You would think that for an exact science we would use more exact language. Not so.

As other posters have indicated the big three passives are resistors, capacitors and inductors. I don't know about this memristor gizmo. In my 50+ years of electronics experience I never held one in my hand or had one come up in a circuit design I've worked on.

Nevertheless, I think if you could come up with a device which could convert frequency to a proportional DC voltage, like a thermocouple converts temperature to voltage, you might join the likes of Michael Faraday in EE Heaven.

Likewise, if you could invent a device which converts electron flow directly to sound without the use of a magnet and coil, you might be onto something big as well.

Or for that matter an elastic material that directly converts current to motive force - the elusive artificial muscle tissue. That would forever change the world of pornography as much as Michael Faraday's vibrating coil did.

It's been quite a while since the EE world has enjoyed a new passive component. Keep us posted on your progress.

FiddyOhm
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    `convert frequency to a proportional DC voltage` - you mean like a low pass filter commonly used to convert a PWN output to a voltage for a cheap,DAC? – Michael Jan 30 '14 at 04:53
  • `a device which converts electron flow directly to sound without the use of a magnet and coil` - or what about a device that bends light without the use of a material lens? – Michael Jan 30 '14 at 04:56
  • `an elastic material that directly converts current to motive force` - or a holo-diode? – Michael Jan 30 '14 at 04:57
  • Michael, are you sure your last name is NOT Faraday? Your ideas may sound crazy, but so did the idea of recording a voice on a piece of tinfoil 130 years ago, or sending a message thru a piece of fence wire 20 miles long 200 years ago. – FiddyOhm Jan 30 '14 at 12:00
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    @Michael "what about a device that bends light without the use of a material lens?" Look up in the sky on a clear day and you'll see one shining bright. – JAB Jan 30 '14 at 13:45
  • @JAB exactly, gravity seems to be required. but creating enough gravity to bend light and fitting it into something that fits in the lab, or even on one's face, now that is a challenge. – Michael Jan 30 '14 at 16:33
  • @Michael I'd be wary about putting something with enough gravitational force to bend light that's also small enough to fit on someone's face on someone's face. Seems kind of dangerous given the amount of mass required; what happens if it falls on the person's foot? – JAB Jan 30 '14 at 16:47
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    @JAB I'd be more worried about what would happen if the planet fell on the device. – AJMansfield Jan 30 '14 at 23:22
  • `In my 50+ years of electronics experience` with all possible respect, please note that first actual memristors were constructed only recently, so no wonder you did not.. this doesn't mean much. I never held a gas-laser, and I've seen quite a large number of other light-emitting devices.. Not helding / seeing-live one of them does not mean these devices don't (or can't) exist or be useful. – quetzalcoatl Jan 27 '20 at 00:23