Steve Nosko wrote:
Roy,
I'd appreciate your further comment on this. I 'know', from history,
that the spacing of two collinear half waves in phase affects the gain and
that there is an optimum spacing for gain that places the two collinear
elements apart (not close enough for a 1/4 wave shorted stub to be used for
a common feed). I had theorized that this "optimum" spacing results in the
most compressed lobe (without excessive secondary lobe formation) which is
simply due to the far-field phase summation of the two elements radiation.
Is this different than the mutual coupling to which you refer, or is this
another effect?

73, Steve, K;9.D,C'I

It's actually the same effect.

If we assume no loss (a reasonable assumption for this kind of antenna),
all the power applied to the antenna is radiated. So any change in gain
is accompanied by a change in pattern -- if there's a single major lobe,
the more gain you have the narrower the lobe is. But if the element
currents are in phase, there will always be a maximum broadside to the
array regardless of the spacing, because the fields from the elements
will always add in phase in that direction.

But why is the gain different for different element spacings? You get
different gains for different spacings, which means that the sum of the
fields changes as you change spacing -- and this means that the field
from each element changes as you change the spacing. If you put 100
watts into the array, each element will radiate 50 watts, again
regardless of the spacing. So why does the 50 watts produce a larger or
smaller field broadside to the array as you change the spacing? What's
happening?

As the spacing changes, the mutual coupling between elements changes.
This alters the feedpoint resistances (and reactances, which aren't
important to this discussion) of the elements. And this in turn modifies
the amount of current flowing on each element for that 50 watts of
applied power. (It can be more reasonably argued that the mutual
coupling changes the current, and that changes the resistance. Or that
the mutual coupling produces a feedpoint voltage which alters the
current and resistance. But you reach the same conclusion via any of
those paths.) The essential fact is that the field gets stronger or
weaker as the element current increases or decreases as a result of
mutual coupling. The combination of the changed pattern shape due to
spacing and the changed maximum pattern size due to mutual coupling
always result in all 100 watts being radiated.

Chapter 8 of the ARRL Antenna Book has a graph of gain vs spacing for
two half wave elements placed end-to-end, compared to a single half wave
element. The gain peaks at about 3.2 dB at a spacing of about a half
wavelength. When the elements are very close, as they are in the super
J-pole, the gain is only about 1.6 dB greater than a dipole. That's why
I felt the J-pole gain wouldn't be as high as claimed.

Note: The current distribution on the elements also changes as a result
of mutual coupling -- see
http://eznec.com/Amateur/Articles/Current_Dist.pdf. But I don't believe
the effect is very significant on a collinear array with thin elements.
Anyone wanting to find out for sure, though, can do so with EZNEC or a
similar program.

Roy Lewallen, W7EL