[TowerTalk] W0IYH Feed line Choke Performance

[Chuck Counselman]

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