+3 dB is the maximum array factor for a two element array: the max gain
over a single array element that can be realized for an array of two
identical, non-interacting radiators having uniform excitation (equal
currents).
For vertical stacking over ground, it would be unusual to achieve an array
factor of +3 dB because the ground reflections from antennas placed at two
different heights do not coincide at low angles and so the radiated fields
don't add up to give the full factor of two.
Now, the stacking gain for a pair of real antennas differs even further
from the idealized array factor because the antennas are going to interact
with each other. And that mutual coupling may result in a stacking gain of
either more or less than +3 dB depending on the details of the interaction.
Under certain simple circumstances the interaction between antennas in an
array (stack) can be constructive. This in the case for a pair of half-wave
dipoles where for separations in the vicinity of 0.7 waves the mutual
impedance is real and negative. The negative impedance lowers the radiation
resistance of the elements in the array resulting in additional gain. A
pair stacked dipoles can be described analytically with a closed-form
solution and the theoretical maximum gain for a pair of stacked dipoles in
free space is +4.9 dB over a single dipole. One can describe that net gain
as being composed of +3 dB from the array factor plus an additional +1.9 dB
from the mutual coupling.
In an array built from more "complicated" antennas, such as Yagis whose
performance as individual antennas results from the summation of fields
generated by currents flowing in multiple driven and parasitic elements,
any change to the amplitudes or phases of these currents from mutual
coupling is far more likely to result in a loss of gain than an increase.
Still, for 2 or 3 element Yagis, it would be unusual but not theoretically
impossible to find a situation in which the effects of mutual coupling due
to stacking result in a slight increase in gain rather than a slight decrease.
Because of mutual coupling, element lengths and spacings for Yagis used in
a stack may benefit from re-optimization for the specific stack in which
the antenna will be used. And when modelling how a single antenna in a
stack performs, e.g. when driving the top antenna only or the bottom
antenna only, it may be necessary to retain the un-excited antennas (and
their feed lines & terminations) in the model because there is mutual
coupling with the other antennas in the stack even when the other antennas
are not being directly driven.
73,
Mike K1MK
At 09:51 AM 3/22/02, Pete Smith wrote:
>Is there a theoretical reason why the gain resulting from stacking two HF
>yagis over real ground is limited to 3 dB? I have a model of two C-3Es
>that shows 3.5 dB increase over a single C-3E in the top position. I'm
>trying to figure out if this is a modeling anomaly of some sort...
>
>73, Pete N4ZR
Michael Keane, K1MK
k1mk@alum.mit.edu
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