I'm trying to get an intuitive understanding of high frequency and its effect on inductance and capacitance. Envision a coax made of solid copper inner and solid copper outer and air as the dielectric.
It is possible to calculate the inductance per unit length using femm
4.2 as a function of frequency, and also obtain the skin effect increase in resistance per unit length for each of the inner and the outer conductors. Final results are a table of inductance/len and resistance/len vs frequency.The results show that as skin effect starts taking over and the electrons bunch to the surface, the inductance drops.
Embarrassing, but have to ask...
Isn't this drop in inductance caused by the fact that the electrons are traveling in a 'different' position than they were at lower frequencies? The carriers have moved from some distance apart - with a relatively higher value of inductance, to very close together since they're almost completely on the surface and not 'buried' inside each conductor - thus the inductance drops as the carriers' paths are closer.
If yes, than shouldn't this also affect capacitance? Usually capacitance is simply dielectric times area over gap and you use the distance between the surfaces of the metal to define the gap.
It would seem that capacitance can be calculated from metal to metal, but wait, the inductance changed as a function of frequency, wasn't that due to the change in the 'location' of the electrons traveling? If so, that implies the capacitance should also shift as a function of frequency as the 'cloud' of carriers moves closer to each other, traveling along the surface only. [my description is kind of bouncing back and forth between parallel plate capacitor and the coax capaictor. But I mentioned the coax so no one would get hung up on 'edge effects'] Here, implying that the capacitance per length should increase as a function of frequency, since the carriers are now 'tightly' bundled on each surface, as close as possible to each other. As a correlary that's like comparing two capacitors made with the same gap, but one is made of 100 mil thick conductors and the other is made of 1 mil thick conductors and expecting the two caps to have different values. Then my mind goes back to the thought of a cloud of electrons in the conductors and we're simply integrating their uniform distribution in the conductor over the gap.
!! Possibly, it all works out *if* the capacitance is thought of as electron distance through metal with dielectric extremely high, air gap between metal, and then distance through high dielectric metal to another electron buried inside the other plate. THAT would yield a fixed capacitor value as a function of frequency, by simply assuming the dielectric constant of metal is close to infinity [a dead short] and there can be little to NO effect from increasing frequency.
As I said, really embarrassing lack of understanding on my part, but is the explanation simply that the metal ALWAYS provides a dead short to its surface, and thus, capacitance does NOT change versus frequency? Then again, what *if* the conductor does NOT act like a dead short to the surface as frequency increases?
The overall effect caused by the inductance change will be a lower Zo as frequency increases, but if the capacitance also changes, then Zo will drop by more than one would calculate using the above inductance table and a fixed value for C. May be as L is decreasing. C is increasing.
I'm looking for a 'thought' argument here, a URL describing in better terms what's going on. As a last resort, I'll take the math form and try to sort it out.
I assume Maxwell's equations describe this perfectly. Anybody out there who can translate Maxwell Eqns to English?