[Ktechlab-devel] Memristors are a headache.

[Alan Grimes]

I spent my afternoon trying to understand the memristor.

My first learning is that I'm going to have to double my understanding
of electronics to even make sense of it. =P


Everybody should know ampres and voltage.

To even begin to understand memristors, it looks like we need two new
units, Webers and Coulombs.

Coulombs(C) (Unfortunately it seems they decided to confuse us by using
the same abbreviation as capacitance, which is related but not the
same...) are probably easier to understand than the name is to spell, if
only slightly. In this universe, charge is carried by particles such as
electrons and protons. Therefore you have some integer number of charged
particles you're dealing with. Therefore the Coulomb is quantum in
nature, and could be expressed perfectly with an extremely large
integer. =P My big old book that I paid way too much for many many years
ago defines it as Ampres times Seconds. So if you measure a current of 2
ampres for two seconds then you have four coulombs worth of electrons.

Capacitance is therefore defined as a ratio between coulombs and volts.
If you have 1C/1V then you have 1F. =P If that ratio is much smaller,
say 1e-6 C /V then you have a microfarad and obviously you will not have
to move nearly as many electrons (counted in coulombs) to change the
voltage.

After staring at the code for capacitance that I've gone over several
times during cleanup, I think I can almost see what's going on.

The body of the matrix is set to basically a resistance matrix based on
the reactance of the capacitor over the time period of the simulation
step. A current is then injected into the circuit through the cnodes to
create the static voltage. If everything is in balance, then there will
be a phantom current through the capacitor that is not seen in the UI.
However, if there is an imbalance, then the capacitor will appear to be
either charging or draining.

The Weber(Wb) is the unit of magnetic flux. I can't say I even begin to
understand it right now. It is measured in volts * seconds. It gives us
"Voltseconds law" because you can think of charging up an inductor with
flux and then draining it out just as you can a capacitor. An inductance
(in Heneries) is defined as Wb/I, and basically works like a capacitor.

Memristance(M), is defined as Wb/Coulombs. Instant by instant, it IS a
resistor. I'm still having a gawdawful headache trying to connect it
back to a circuit of volts and ohms, or even really understanding what
it means. =\

I think the next step is to experimentally create new node types (see
Element.h) for Webers and Coulombs, and then see what we can do with
those. Unfortunately, this will require a significant rework of
ElementSet. =(

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