On 9/3/2013 1:54 PM, Jim Brown wrote:
Now, getting to the original question -- how to calculate the needed
length of delay lines for stacked antennas when those antennas are
different from each other. If I were faced with this problem, I
would build an NEC model of both antennas, with the geometric
relationship between them as close as I could get to how I could
mount them, add the feedlines to the model, and tweak the line
lengths until I got the far field patterns I wanted. Why? Two very
important reasons. First, the amplitude and phase of the field from
the two antennas will be different at every vertical and horizontal
angle, and the far field pattern will be the result of the complex
addition (magnitude and phase) at every angle. Second, the phase
shift in the delay lines will be dependent upon the complex impedance
at the feedpoint of the antenna. There's a discussion of this second
effect in the ON4UN book -- look for Christman feed in the index.
It's in the chapter on phased vertical antennas.
Before doing that do a simple model of two identical yagis *over ground*
with fixed phase differences of 0, 10, 20, 30, 45 and 90 degrees. Try
antennas at 1 and 2 wavelengths above ground (70/140' on 20, 35/70' on
10) as well as 3/4 and 1 1/2 wavelength (50/100' on 20 or 25/50' on 10).
One will find the take off angles, gain and nulls are only slightly
impacted by 30 degrees or more of phase difference. *Image* (ground
reflection) and terrain tend to dominate the performance at low heights
(<10 wavelength or so) much more so than the actual phase differences.
"Beam tilt" or beam steering only starts to become practical when the
ground reflection component drops away and the direct wave becomes
dominant. Until that time, any change one makes in the direct wave is
to a large extent *cancelled* by the *opposite* effect that occurs in
the *reflected* (image) wave and it is only the gross differences -
e.g. in phase or out of phase - that truly effect the vertical
pattern (much like moving a single antenna from an odd multiple of
1/4 wave above ground to a multiple of 1/2 wave above ground.
This obsession over a foot or two of feedline or driven element
offset (1% or 3 degrees at 20 meters) is completely misplaced for
HF antennas and even six meter antennas for "sky wave" propagation.
73,
... Joe, W4TV
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