On 2/27/19 2:29 PM, David Gilbert wrote:
If you think the wrong questions are being answered it's because those
formulas assume that you either know or want to know the amount of
inductance you need or have. There is no way any of those formulas are
going to tell you how much inductance you need to resonate any
particular antenna.
And what don't you know, or can't easily find out, about #8 gauge copper
wire from a big box store? Dimensions and resistivity are available in
hundreds of places online. It's even pretty easy to estimate the Q of
such a coil, at least closely enough for most needs. I could probably
even come up with a good estimate for the stray capacitance without much
effort.
I think it's pretty unreasonable to expect a single formula to account
for every possible real world scenario, the expectation being that you
know how to apply the right formulas for the task at hand.
Exactly..
BTW self C is well approximated by Medhurst's formula if the
length/diameter of the coil is say, 0.5 to 5
I would venture that any HF antenna has parameter uncertainties
significantly greater than the uncertainty due to accuracy of the simple
inductance and capacitance formulas.
(especially when it comes to soil properties)
Whether the resistivity of copper is taken as 1.64, 1.68, 1.73 etc
doesn't significantly (>1%) change the L or R. Pick a number and go
forward with it.
Where better models become important is when a lumped approximation
doesn't work well. A classic example is in a Tesla coil (addressed by
the Corums in their famous paper, but in my opinion incorrectly).. The
physical size of the coil is a tiny fraction of a wavelength (1-3km), so
clearly, we're not talking about "propagating waves" like you would with
a microwave system.
You can get a tesla coil working using the simple Wheeler and Medhurst
formulas, but it will be slightly out of tune. This is NOT because the
lumped approximation is wrong, but because the E field distribution
along the (usually long/thin) secondary is neither linear nor 1/4
sinusoid, so the "self capacitance" is wrong.
You can approach this problem a bunch of ways - you can build a more
sophisticated finite element model of the windings and the terminals -
that's computationally intensive.
You can try and find some other function that seems to fit the behavior
and rationalize why it works (Corum approach)
You can use piecewise model with external information: break the long
solenoid into chunks, and impose an external constraint of the E-field,
based on a priori information. As it happens, this provides the best
results in reasonable computation time. There have been a bunch of FEM
models run on a static (non oscillating) system so you can get the
E-field pretty easily. The system is "tiny fraction of wavelength" so
the RF field will follow the DC field.
Once you're there it's a matter of modeling the secondary as a chain of
little coupled LC sections, for which the math is pretty simple.
For instance, this would be a good way to model a loading coil inside a
can (like used on the 6BTV).
And this approach has also been used to model things like HV stress in
high power high frequency switching converters, where they have shield
cans around the windings on the cores.
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