[TowerTalk] grounding radials: solid or stranded?

[Jim Lux]

>
> By spreading the current out into many filaments, Litz wire reduces the
> losses due to skin effect compared to the SAME amount of the conductor in
> single strand. A given current filament is farther from any other
filament,
> so the magnetic coupling is less. Essentially, you're increasing the
surface
> area, so the effective conductor area is increased (for a given amount of
> copper).   This is fairly well covered in texts like Terman.


>>> ERROR in previous paragraph.. it's really not losses due to skin effect,
but a more fundamental reason (albeit, related to skin effect).  It's the
fact that parallel conductors have a mutual inductance, so a changing
current in one conductor induces a voltage in the other conductor.

Simple gedanken experiment..
Consider two wires, each carrying 1Amp (AC), separated by a very large
distance.  Each wire has a voltage along it due to the inductance (Lself
di/dt).   Now, bring the wires closer together.  The voltage (back emf)
along the wires will increase, because not only is there the self induced
voltage (Lself di/dt) but also the voltage induced by the changing field
from the other wire (Lmutual di/dt).

So, in the widely separated case, the total inductance is Lself/2 (because
you've got two inductors in parallel).  In the closer case, the inductance
is (Lself+Lmutual)/2, which is bigger.

Now, consider a solid wire, but divided into many tiny individual insulated
wires.  What's the lowest inductance configuration but where the strands are
still adjacent? It's the one where they are spread out the most (so the
mutual inductance between strands is lowest.. nothing you can do about the
self inductance of each strand).  Clumping them in a bundle is worst
(maximum density). Putting them in a tube is pretty good.  Putting them in a
flat ribbon is best.

If you can space them out even more (as by weaving some non-lossy substance
in with the bundle) will work even better.  And that's what Litz wire is.
It's a sort of half way step between a solid (densely packed) round wire and
a hollow tube or flat strip.

Skin effect is caused by a similar thing.  Consider a bundle of wires all
hooked in parallel.  Now push an AC current through the bundle. How will the
current divide among the strands in the bundle? The strands in middle see
the fields from all the strands around them, so they'll have the largest
back emf.  The strands on the outside only have fields from strands to one
side, but no field from the other side, so their back emf is less.  Hence
the current will tend to flow on the outside of the conductor (or, the
"skin").


The real question is whether this is practical or worthwhile at HF (>3 MHz)
frequencies.  It's certainly worthwhile at 60 Hz (HV transmission lines use
"bundles" rather than single strands to reduce series inductance (as well as
improve HV breakdown)).  It's also probably worthwhile at tens or hundreds
of kHz (as in switching power supplies, where they do use Litz wire in
transformers).

The other loss effects might dominate at HF frequencies where the skin depth
is so small.


>
> It's the same reason that if you take the same amount of copper and make a
> tube, instead of a solid round bar, it will have less AC resistance, and
why
> wide flat strips have less resistance and inductance.
>
> Woven braid, where all the strands are uninsulated, is an entirely
different
> story, although comparing the same number of strands in a solid bundle, vs
a
> woven layer around a dielectric core might be instructive.
>