When placing a stack control box at the base of a tower, one should
consider using equal length coax to feed all the antennas in the stack
-- not just a convenient even (or odd) multiple of a half-wavelength.
If the coax lines are unequal, the phasing will get skewed as one moves
across the band.
Example: 3 Yagi stack on 20m, designed for 14.150 MHz. Wavelength
21.19m. Antennas mounted at 3/4 wave intervals; e.g., 15.9m, 31.8m and
47.7m.
Assume the coax has a velocity factor of 0.67, and the driven element
requires 3m of cable to get from the tower to the matching network
connector.
If one cuts cable to the nearest multiples of 1/2 wavelength (7.10m of
cable), then one might be tempted to economize on the cable by running:
21.3m of cable to the bottom Yagi (3 half-waves at 14.1 MHz).
35.5m of cable to the middle Yagi (5 half-waves at 14.1 MHz).
56.8m of cable to the top Yagi. (8 half-waves at 14.1 MHz).
The above assume the switch box is located very close to the earth.
This arrangement requires a slight trick because the top antenna's
driven element feed attachment must be inverted (left to right) to keep
this Yagi in phase with the rest.
But look at the cable lengths at 14.0 MHz (21.41m wavelength). Here a
half-wave of cable is 7.17m. These three cables are 2.97, 4.95, and
7.92 half-waves at 14.0 MHz. The drive point impedance transformations
(of a complex impedance for an off-resonant Yagi) will be unequal for
the three lines and the three antennas will be less in phase and with a
less-equal power division. The actual change depends on the
implementation of the power-splitting arrangement and the specific
off-resonant driving impedances.
Even if the drive point impedance was still perfectly matched to the
coax at 14.0 MHz, the top antenna would lag the bottom. The cable
lengths in degrees are 535, 891, and 1426... or a net length relative to
the bottom Yagi of -4 degrees and -9 degrees for the top Yagi (after
reversing the feedpoint attachment). The relative phase difference will
be different for mis-matched lines.
Nine degrees may not be a significant degradation, but it is one more
source of error in the system. You have to decide if the errors are
important to you when you balance, cost, performance, and ease of
maintenance.
The shift can be much larger on 10m because the band is larger (28.0 MHz
is proportionately a further off resonance from, say, a 28.4 MHz design
frequency) and the cables are longer (in terms of wavelength) if the 10m
stack runs all the way up to 48m or so on the tower.
This source of error can be eliminated if all the cables are the same
length; e.g., 56.8m in this 20m example. Making all cables the same
length raises the costs, but you might be willing to pay that to avoid a
winter tower climbing trip to make a repair in the middle of a contest.
-- Eric K3NA
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