[TowerTalk] OT: Inductor Calculator

[jimlux]

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.