Bob said:
OK -- I dug up the Amidon application notes. The reasoning that I used to
justify a large bundle is as follows:
Loop induced voltage = 2*Pi*N*A*Mu_sub_epsilon*F / Lambda
where :
Mu_sub_epsilon = effective permeability of the rod
F = Field strength in microvolts per meter
N = number of turns
A = cross sectional area of loop in square meters
Lambda = wavelength in meters
The idea is to maximize A. The usual assumption is that the dominant noise
is the noise in the receiver bandwidth and not atmospheric noise.
When atmospheric noise dominates, the strategy fails as someone has pointed
out.
I have no argument with any of that.
The rod is intercepting the energy in a volume by steering the flux
passing through some cross sectional area larger than the area of the
ends of the rod, through the length of the rod, and thus, through the
coil. I say an area larger than the area of the ends of the rod,
because the high permeability of the rods gathers flux that would have
gone past the rod if it has been air. Larger end areas allow flux
that is further from the rod's center line to detour through the rod
without having to crowd in near the more central flux as much. So
larger ends gather more flux. A simple rod may be easy to
manufacture, but it is not the optimum shape to gather flux from space
and transfer energy into a coil.
My point is that the *effective* area of flux intercepted by the rod
is related to the areas of its ends, not to the cross sectional area
of its middle, as long as the permeability of the middle is high
enough that the flux isn't held back by too small a center area.
This is from the "Rod Permeability vs. Rod Length divided by Rod
Diameter" graph on:
http://www.amidoncorp.com/aai_ferriterods.htm
Note that for a permeability 10 rod, it poops out when the length
reaches 10 times the diameter. At that length, flux near the rod has
little incentive to dip towards the ends and crowd in along with other
flux to go through the rod, and will just as well run along side the
rod. I have added a factor of center area to end area to this graph
which has assumed this factor is always 1.
So, for 33 material, with a permeability at least 800, as long as the
overall length is much shorter than 800 times the end diameter times
the middle area divided by the end area, most of the available nearby
flux that would have passed through a constant diameter rod will take
the short cut through the rod (and through your coil), even though it
is necked down in the middle.
For example, if you used 1.5 inch beads with half inch holes on each
end of a half inch rod, the combination would gather as much flux as a
1.5 inch diameter solid rod as long as the overall length was much
less than:
800*1.5*(pi*0.25^2)/(pi*0.75^2)=133 inches, so your 7.5 inch rod
extended by, perhaps a couple inches, by the beads, is well within
"much shorter than". Gluing two rods end to end would more than
double the output because the volume of space that flux is gathered
from would more than double. This is because the effective area of
flux gathering is bigger than the end areas, and how much bigger
depends on the rod length, which is not included in the formula. The
formula looks pretty suspect to me (like it is for an air core coil)
because there is no reference to rod length. It gives the same result
for a zero length rod, unless "effective permeability" does not mean
rod permeability, but some combination of rod permeability and length.
Doing it my way should cut your winding resistance and capacitance
down by a factor of about 4 (with the thin form) while keeping the
intercepted energy a little higher (assuming the beads have an outside
diameter 3 times the rod's diameter and extend its length to something
like 9.5 inches). To me, that equates to higher Q and higher energy
output.
