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### Re: memristors?

Posted: Sun Feb 01, 2009 1:06 pm
From IEEE:
...memristor...provide a similar relationship between magnetic flux and charge that a resistor gives between voltage and current. In practice, that would mean it acted like a resistor whose value could vary according to the current passing through it and which would remember that value even after the current disappeared.
They totally loose me between these two sentences. The rest of the article is comprehensible though.

Even if you make the substitutions (available in the graphic) and get vdt =M*idt you still don't really know what M is. And that symbol, it looks like a heating element. I wonder if I can find the HP papers referenced. It's not time to throw out your electronics textbook yet.

vdt =M*idt (resembles ohms law)
M=(V/I)dt
M=Rdt
M= a change in resistance over time

Does that make sense to anyone? Better ways to rearrange the equasion?

Plugging back in:
vdt=(Rdt)Idt
Vdt=IRdt
or
vdt=(v/i)dt*idt

If I missed an I squared somewhere then I might get M=R*idt which resembles "acted like a resistor whose value could vary according to the current passing through it" making it

### Re: memristors?

Posted: Sun Feb 01, 2009 4:08 pm
"The new methods are much more sophisticated than my ultra primitive high school hybrid analog-digital language translator--but it worked."

Forest-were these pots known as MIMRISTORS ?

### Re: memristors?

Posted: Sun Feb 01, 2009 4:31 pm
Hi again,

There are different types of memristors apparently, and none of the dictionaries known any of them
The dont even know how to spell 'memristor' yet

Anyway, there are different types of memristors but to understand them basically all you have to do
is think of a device like a resistor whos resistance changes based (sometimes) on the history
of another parameter that is associated with the device. In other words, it would be almost
like measuring one parameter that changes naturally and using that measurement to force another
parameter to change. That's such a general statement i know, so here is a simple example of
a charge controlled memristor...

There is a little guy sitting next to a wire and he can see every electron that passes by. He has a
counter in his hand and every time an electron passes from left to right he clicks it up one notch,
and whenever an electron passes from right to left he clicks it down one notch.
The total accumulation on his counter is used to set a variable resistor like a pot. For this
particular memristor the resistance in ohms is equal to the absolute value of the count, so if he
counts up 10 the resistance becomes 10, and if he counts up another 10 that totals 20 so the resistance
is 20 ohms, then if he counts 10 backward the total is back down to 10 so the resistance
again becomes 10. If the count gets back down to zero the resistance goes back down to zero.
The only difference with a real life device like this is that at some point the device would
saturate, and also there would be some time response to consider.
The other interesting thing is that we dont have to assume a linear response. A possibility
is even a 'programmed' nonlinear response that is programmed in such a way as to fit the
application perfectly.

I made an very early type of memristor way back in the 60's when i connected too much
voltage to a relatively small value (1k) resistor. After it turned black it had no
trouble remembering that it went from a 1k resistor to a 500 megohm resistor

Here's a pic of another memristor being manufactured via serendipity again:

And as if that wasnt enough proof that they really do exist, here is a new manufacturing plant for
memristors in live action:

### Re: memristors?

Posted: Sun Feb 01, 2009 9:55 pm
MrAl, I don't know how to interpret those results.
You started off with a memristor non-volatile memory.
Volatility happened anyway.
Now it's no longer volatile anymore?

### Re: memristors?

Posted: Mon Feb 02, 2009 4:37 am
Hi Bob,

Just a little satire there

### Re: memristors?

Posted: Mon Feb 02, 2009 8:23 am
That looks more like a 1 bit ROM to me.

To be a memristor, the resistance shift must be reversible. Maybe you didn't show the part when you hook up the battery backward and the smoke gets sucked back in.

### Re: memristors?

Posted: Mon Feb 02, 2009 11:08 am
Hi again,

Hackle, he he...i didnt think of that !

It is reversible though, after the guts get blown out and the resistance goes up high
when i want it back down load again i just paint the inside with some Wire Glue

On the more serious side (wherever it is now he he), the one key thing that makes
this devices so special is that their characteristic looks predominantly resistive
*all* the time (or mostly so). It just has the ability to change that resistance based
on some other parameter and in many cases that parameters history.

I know we probably wont see any of these for a long time yet but i do hope
they start making some for the general public to purchase. I guess they would
have to have a line of produces though, not just one, to fit various applications.
Should be interesting that's for sure

### Re: memristors?

Posted: Mon Feb 02, 2009 12:43 pm
From a theoretical and math POV, I still find it confusing but the physical explanation of the device was easy enough to grasp.

From IEEE
In TiO2, the dopants don't stay stationary in a high electric field; they tend to drift in the direction of the current. Such mobility is poison to a transistor, but it turns out that's exactly what makes a memristor work. Putting a bias voltage across a thin film of TiO2 semiconductor that has dopants only on one side causes them to move into the pure TiO2 on the other side and thus lowers the resistance. Running current in the other direction will then push the dopants back into place, increasing the TiO2's resistance.

I'm fond of the plumbing analogy for electronics. To wit a Memristor seems like a rusty galvanized steel pipe. When water runs one way, the rust flakes build up and impede flow. Higher pressure and flow make it worse by busting off more rust from the inside. When the water flows backward, the rust gets temporarily flushed out and impedance drops but only until the flow builds up the clog somewhere else.

Or maybe its like the alley between my house and the fence in late October. When the wind blows one way, the leaves build up on the gate impeding my egress to the front yard. Its worse if the wind is blowing hard or recently has and is calm at the time. If the wind reverses, the leaves blow all over the yard and allow easy access through the gate.

Now electron flow in a period of time (Flux) is like the wind and water. M needs to describe the mobility and concentration of the dopants that impede or enhance conduction.

This must be similar to a common metal failure mode known as electromigration where high current sweeps atom of metal away from grain boundaries eventually eroding the conductor to the point of failure (high R or open). That phenomenon is not predictably reversible and often degenerative in both directions of current flow

### Re: memristors?

Posted: Tue Feb 03, 2009 5:56 am
Hi Hackle,

Oh so you are looking into the physical reason why memristors work rather than just the electrical description?
The only reason i ask is because for many devices the device behavior can be predicted knowing the
electrical description alone, which makes life a little easier. Most of the time the devices are characterized
by their electrical description anyway even when they are rather complex (NPN transistor for example).

### Re: memristors?

Posted: Tue Feb 03, 2009 10:02 am
I was looking at both. Since the math is not well defined (not even units for M, forgeddabout worked through examples) I turned to the physical to envision applications.

The inventors invented a device which operates in a certain way. In an effort to explain its behavior with a model, they tapped the 40 year old theoretical memristor. How universal this device is WRT the theory remains to be shown.

Eventually there will have to be a clear formula which describes its operation or designers will be stuck with spice models. They obviously need some sort of math model to simulate.

Another way to look at this is to imagine a 2 terminal relay. The contacts serve as the switch and coil at the same time. Now you don't need anything to drive the coil, you just need to control the current through the switch in specific ways.

### Re: memristors?

Posted: Tue Feb 03, 2009 10:43 am
Hi again,

Hey that's an interesting idea, perhaps of the simplest flux controlled memristor of a sort.

Anyway, i am happy to see this simplicity, because i think that many people are letting their total amazement get
in the way of very simple reasoning. These devices are not that complex. For example, lets not forget that the
device major characteristic is resistance, meaning that the units of "M" would simply be "ohms". It's just that the
ohms can change based on what took place prior to the measurement of the control parameter.

I could post a circuit that could be worked through if that would be of interest.

Right after i posted this i thought of this really simple demonstration...
Take a *dc* motor with 100 ohms dc resistance, geared way down. Connect the shaft to a simple 10 ohm pot.
Now connect the positive lead of the motor to the top of the pot, also connect that to the arm of the pot.
Connect the negative lead to the bottom of the pot. Now we have a very simple and easy to understand
memristor. Notice we only have two leads also. The resistance here is whatever the pot is set to in parallel
with the motor resistance. Have the pot set midway to start with.
Now power this memristor with a dc voltage of say 5v (say the motor is a 5 or 10v motor). The shaft turns
slowly and increases the resistance of the pot a little. As we keep the same polarity voltage the pot total
resistance keeps getting a little higher, so the current through the memristor works its way up a bit.
Now we stop applying voltage. Of course we also have no current now, but then we reverse the voltage
and again apply this voltage (negative of what it was previously). Now the pot arm starts to turn in the
other direction and so the resistance starts to go down again, meaning more current starts to flow through
the memristor. Eventually we get back to mid way and the current is again what it started out to be.
If we apply more negative voltage the resistance decreases even more and more current is drawn through
the memristor.
If instead of applying the voltage directly we instead connected this memristor in series with a regular
resistor of say 10 ohms, as the voltage was applied to this voltage divider the output of the divider
would look like a curved ramp that ramped up with positive voltage and ramped down with negative
voltage or vice versa depending on the shaft rotation relative to the voltage polarity.

Pretty simple right?

### Re: memristors?

Posted: Tue Feb 03, 2009 12:06 pm
Here are a few waveforms of said system of motor and pot with a few different values.

Little note: If M is a function of charge for example, then M(q) is in units of ohms.

### Re: memristors?

Posted: Wed Feb 04, 2009 3:28 am
Hackle & MrAl,
Excellent discussion. I think I finally understand.
Hackle, you made the math simple & to the point. MrAl, your motor & pot analogy seems dead on.
There, that wasn't so hard now, was it?
Seriously, thanks guys. I'm awed by the knowledge available here.

### Re: memristors?

Posted: Wed Feb 04, 2009 7:48 am
Jim Barrett wrote:Hackle & MrAl,
Excellent discussion. I think I finally understand.
Hackle, you made the math simple & to the point. MrAl, your motor & pot analogy seems dead on.
There, that wasn't so hard now, was it?
Seriously, thanks guys. I'm awed by the knowledge available here.
Hi Jim,

I am too! I often get good ideas from just reading the posts here.

I also wanted to make one slight correction to the waveforms i posted. The blue wave that is
labeled "scaled charge" should actually read "scaled angular shaft position" or even
"scaled pot position". I used charge to simulate the pot position and forgot to write in
what it actually meant to the motor/pot system rather than 'charge'.

I also realized that a thermistor is a sort of thermally controlled memristor, if used
accordingly. If you apply a high enough voltage to the thermistor it will heat up
(not enough to blow it out of course) and thus its resistance will go down (negative
temp co of course). As the voltage is reduced it will cool off and the resistance
will go back up again.
It shouldnt take much to get this to happen either, and manufacturers usually provide
a maximum power dissipation to prevent self heating to keep 'accuracy' within
reason too. Of course when they say 'accuracy' they mean to use it as a temperature
measuring device not a memristor

Also, i think someone mentioned DSP? Did anyone mention MSP yet (Memristor Signal Processing)?
If they can be designed to be fast enough they can do what some DSP devices do today.

### Re: memristors?

Posted: Wed Feb 04, 2009 8:04 am
Bob Scott wrote:
MrAl wrote:Yes, i envision a matrix similar to the old magnetic core memories only on a die.
MrAl wrote:For just one out of a billion or more incredible examples, here is one possible memristor in action...
At the moment i dont think i can even grasp how this could change things...
That's my problem too: envisioning what the heck a "4th quadrant" device actually does. IEEE has made a big assumption here. I think maybe the article in the May issue may have just missed its intended April 1st issue publication date.

In this diagram, the magical memresistor has the capability of passing a fundamental sine wave frequency but it completely blocks the odd harmonics. How does it discriminate between a fundamental sine wave at any frequency and the odd hamonic sine waves? What does it do with a rectangle wave containing even harmonics? (including the DC offset)

Or are you just pulling our collective legs?
Sorry Bob, i must have missed this post previously, maybe because of the spam attack.
Anyway, the view here is not from the standpoint of the frequency domain as much as from
the time domain. The instantaneous voltage or current history causes a change in the memristor
and that changes its resistance characteristic. Just how this relationship plays out depends on
how the memristor is designed internally (based on charge, heat, flux, chemical, etc.).
I simply envisioned one that was designed for the sole purpose of converting a square
wave (perhaps at a given frequency) into a sine wave.
Another type would convert a triangle wave into a sine wave, and we see this in action
already in such devices as the Exar XR2240 function generator chip, where it uses a few very
nonlinear (but certainly predictable) circuits to convert triangle of any frequency to
a sine of that same frequency. These nonlinear circuits may be called a memristor
of some type perhaps, although that might be stretching the definition a bit.