At 9:55 PM -0700 8/19/03, Jim Smith wrote:
>...if 500 ohms really is enough impedance to reduce the common mode
>current to a negligible amount then none of this matters....
It depends on the "impedance" (i.e., the ratio of the voltage to the
current) of the common-mode wave at the point on the common-mode
transmission line where you insert the choke. (I put "impedance" in
quotes 'cuz I'm glossing over the important facts that common-mode
waves travel both ways on the line; the complex amplitude of the
voltage at a point is the sum of the complex amplitudes of the
voltages of the two waves; and the complex amplitude of the current
at a point is the difference of the complex amplitudes of the
currents of the two waves.)
Typically the standing-wave ratio (SWR) of the common mode is high;
in other words, there are significant maxima (peaks) and minima
(nodes) of common-mode current and voltage along the line. One
reason for the typically high SWR is that the characteristic
impedance Zo of the common-mode transmission line is far from
uniform. Consider, for example, the common-mode transmission line
formed by the outer surface of the shield/braid of a coaxial cable,
and "ground." The diameter of the shield/braid may be uniform from
one end of the cable to the other, but the distance between this
conductor and the effective "ground" or return conductor may vary
radically. E.g., the cable may be be taped to one leg of a tower
from the top of the tower to the bottom; then the cable may run
through a 6-inch conduit from the bottom of the tower to the house;
then the cable may have a lot of open space surrounding it on its way
through the house to the shack; in the shack, the shield/braid
connects to the rig, and the effective "diameter" of this conductor
balloons by orders of magnitude; then the conductor becomes the AC
power distribution network within the house; and so on. Perhaps even
more important are the common-mode wave reflections occurring where
the coaxial cable shield/braid is connected to lightning "grounds."
If you inserted a common-mode choke at a voltage node where the
"impedance" of the wave was, say, 25 ohms, then a 500-ohm choke could
be effective; but you inserted a common-mode choke at a current node
where the "impedance" of the wave was, say, 2500 ohms, then a 500-ohm
choke would be utterly ineffective.
If the SWR of the common mode were near unity, then the effectiveness
of a choke would depend on the ratio of its impedance to the
characteristic impedance Zo of the common-mode transmission line. A
rough order-of-magnitude estimate Zo can be obtained from the
well-known formula for Zo of a coaxial transmission line,
Zo = [(138 ohms)/sqrt(eps/eps0)] log (b/a),
using eps/eps0 = 1 for air, a = 0.005 m for the braid of RG-8-size
cable, and b = 1 m for coax running through a house: Zo equals about
300 ohms. A 500-ohm choke would not be effective here.
Bottom lines:
1. I wouldn't waste my time or money with a choke whose impedance was
less than 3000 ohms.
2. If 3000-ohm chokes were available, I would use more than one of
them, separated by a quarter-wavelength along the line.
3. In general, the best places to insert chokes are where you know
the common-mode current is near-maximum: wherever the transmission
line connects to a much fatter conductor, such as your lightning
"ground" or your rig.
73 -Chuck, W1HIS
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