# Why is flux-linkage a fundamental circuit variable?

In his paper Memristor - The Missing Circuit Element, Chua theoritizes the memristor based on observations relating to what he calls

the four fundamental circuit variables, namely, the current i, the voltage v, the charge q, and the flux-linkage phi.

Why is the flux-linkage one of the few "fundamental" circuit variables?

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There were historically 5 fundamental circuit elements: resistor, capacitor, inductor, and current and voltage sources. They could be described by very simple equations:

Voltage source: V = constant with respect to I

Current source: I = constant with respect to V

Resistor: $V = I R$

Capacitor: $Q = V C$

Inductor: $\Phi = I L$

with $Q = \int{I dt}$ and $\Phi = \int{V dt}$.

If we extend the concepts of these fundamental circuit elements to include nonlinear behavior, and multiport behavior (controlled sources, 2-port networks), we can model all other circuit elements we use. For example, a diode is a nonlinear resistor, and a transistor can be described by a nonlinear 2-port impedance matrix.

$\Phi$ is considered a fundamental circuit variable because it is the variable that describes the state of an inductor, just as stored charge defines the state of a capacitor.

The memristor, of course, is the missing "fundamental circuit element" that connects charge and flux linkage together without reference to voltage or current: $\Phi = M Q$ (someone correct me if I've inverted this one).

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So I guess the question boils down to why the resistor, capacitor and inductor are the 3 "fundamental" circuit elements. – Randomblue Jul 18 '12 at 22:17
They aren't. For example, there's voltage and current sources, both independent and dependent. – Alfred Centauri Jul 19 '12 at 0:33
@AlfredCentauri, OK, I'll grant you voltage and current sources as 2 more fundamental elements. But given resistors, capacitors, inductors, and sources, and extending those concepts to include nonlinear and multiple-port behavior, we can model every other device or element we know. – The Photon Jul 19 '12 at 2:19
Also, edited to reflect your comment... – The Photon Jul 19 '12 at 2:25
OK, I can't resist the urge to namedrop...I actually learned this material in my first upper division EE class, around 1991-92, taught by ... L. O. Chua. – The Photon Jul 19 '12 at 3:15
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It is not a standard part of the IEC, IPC , IEEE or any international standards committee. It was a hyped name from HP to gain advantage on patents. They use symbols for analog non-linear parts such as; diodes, Schottky diodes, Diacs, SCR's and Triacs.

Although not being on these committees, I can not confirm but I suspect the reason was not to open a pandora's box for new schematic logic symbols for memory technology when this level of complexity added to schematics offers no readability enhancement to a block with signal names and Reference Designator U1, U2 for memory array chips.

All complex VLSI chips are designed with detailed schematics inside the chip as are memory cards and chips, but for users at the integration level, digital logic at high complexity is simplified to rectangles with P/N's pin #'s & signal names.

If HP did that, anyone could claim they have a new part.. Take my invention of the ANALOGIC capture array which is both analog and digital. It captures a finger print in 3D and converts it a 2D unique digital signature and used globally around the world. I may be able to get patent rights for the this new A-L symbolic part name and in 3 color senses I will call it the tridactor image memory cell or AnalLogic A-L for short;) .

All jokes aside, if we had a different logic symbol for every memory or imaging technology invented in the last 5 years and the next 5 years, they would outnumber all the rest of the analog symbols in use and offer no improvement in logic for reading schematics or ordering parts.

next...

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I don't see any relationship between this answer and what was asked. Flux-linkage was a fundamental circuit variable long before HP created a physical memristor, and the use of the 'phi' symbol to denote flux-linkage in equations has nothing to do with the symbols used for parts on schematics. – The Photon Jul 18 '12 at 22:12