[Towertalk] limitations of stacking

[Michael Keane, K1MK]

Non sequiturs about short antennas, loading, Qs, and losses not
withstanding, application of that conceptual picture to the specific
problem that was presented fails to make physical sense. In this case,
an insistence that pattern variation  be the only determinant of gain
will lead one to draw erroneous conclusions.

The example presented was deliberately chosen for its pedagogical value.
It is symmetric with identical elements and identical currents applied
to those elements. The current in each of the array elements is
sinusoidally distributed, the same as for an isolated element in free
space. That sinusoidal distribution holds true even when mutual coupling
is present. 

Employing the simple mathematical artifice of switching on and off the
interaction terms in the equations by zeroing the mutual
impedance(easily done analytically, somewhat more difficult to
accomplish in a  MOM based analysis), one finds that the only physical
variable changing  between these two situations is the magnitude of the
equal currents (and voltages) flowing in the two elements for a given
applied power; with the distribution of those currents not changing
whether interactions are included or not. 

If the array elements have identical current distributions with and
without mutual coupling, the far field patterns in both cases must also
be identical. A distant observer cannot distinguish the case of higher
current flowing in two non-interacting elements because more power is
applied to the array from the case of increased current flow because the
mutual coupling between two real elements introduces a negative
resistance. 

Universally applicable this is not, but for the specific instance that
was put forward, while the power radiated per unit solid angle does
change when interactions are "turned on", that change is just a
proportional increase in all directions, independent of angle. A
decrease in radiative resistance is an appropriate way of summarizing
the physics underlying this behavior. This may be the best example of an
antenna system that clearly and unambiguously demonstrates this effect.
While almost universally true, the premise that gain is solely due to
changes in the angular dependence of the antenna pattern is not
rigorously correct and it is therefore potentially misleading. This is
one of the very few cases which is an exception to that rule. 

This example was mentioned to ighlight that an additional and atypical
physical mechanism was at work in causing the maximum gain when stacking
two dipoles (or arraying a pair of verticals) to be approximately +2 dB
greater than the stacking gain that can normally be achieved with a pair
of Yagis. With Yagis, detrimental changes to the pattern from mutual
coupling begin to accumulate rapidly at relatively wide spacings and
continue to increase at closer spacings thus setting the practical limit
on spacing of Yagis in a stack.

73,
Mike K1MK

On Mon, 25 March 2002, "Tom Rauch" wrote

> 
> > 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.
> 
> In my opinion it is both confusing and misleading to consider "gain" 
> occurring from decreased radiation resistance. Pattern is what 
> controls the directive gain. 
> 
> For a given applied power, and a given loss in the elements, power 
> gain is strictly a function of pattern shape. With an identical
pattern 
> and power loss (as heat) power gain will be identical regardless of 
> radiation resistance. 
> 
> Decreased radiation resistance for an array of elements of a given 
> size is the direct result of radiation of two antennas cancelling in 
> many directions (an increase in directivity). The "squeezing" of the 
> pattern causes the radiation resistance to decrease, because the 
> antenna is fighting itself with destructive interference between the 
> multiple sources of radiation. 
> 
> For example, a small loop antenna has much lower radiation than a 
> similar size small dipole, because radiation from every area of the 
> loop is cancelled by radiation from other sides. Because we apply 
> fixed power, this causes current to increase. The small dipole is 
> just as directive, and yet has much higher radiation resistance. 
> Because of the lower current (higher radiation resistance) the small 
> dipole is generally much more efficient than a small loop  when 
> reasonable Q loading is used.
> 73, Tom W8JI
> W8JI@contesting.com 

Michael Keane K1MK
k1mk@alum.mit.edu

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