[TowerTalk] Funniest thing I've seen in weeks

[Jim Lux]

At 05:08 PM 6/30/2004 -0500, you wrote:
>The parasitic element that reflects back toward the driven element is called
>the reflector.  I think the name origin is obvious.  If it were shorter than
>the driven element it would not exhibit this characteristic.  It is usually
>placed 1/4 wavelength from the driven element so that the magnetic field set
>up in the parasitic element is 180 degrees out of phase.  This induces a
>voltage in the driven element that is in phase with and increases the
>forward radiation.


Not exactly...

The far field created by the antenna (any antenna) is the sum of the 
contributions from the current flowing in each of the elements (or, for 
that matter, from each little section of each element).  If you put two 
wires parallel to each other, spaced by some distance, the magnetic field 
from the AC current in one wire will induce an AC current in the other 
wire.  Now, you've got two wires, each with its own magnetic field.  Every 
cycle, some of the energy in those magnetic fields radiates away and some 
just stays in the element as charge (or couples to other elements).  The 
superposition of all those radiated fields is the field produced by the 
whole antenna.

If you arrange so that the phase of the currents is such that there is a 
nice progression of phases as you move along the antenna, it will form a 
beam, or have some amount of directivity.  The classic two monopoles, 1/4 
wave apart, driven 90 degrees out of phase exhibits this nice directivity 
with a cardioid pattern, with a null in one direction.  heading in one 
direction, the phase of the field radiated from one element exactly lines 
up with the phase of the field radiated from the other element, creating a 
lobe.  In the other direction, the phase of the field from one element is 
exactly out of phase with the field from the other element, making a 
null.  Anywhere in between, you get some combination so you get the 
1+cos(theta) kind of pattern.

You can drive the elements with currents explicitly, or you can carefully 
choose element lengths and spacings so that the mutual coupling causes the 
right currents to flow.  To a first order, if you had identical elements, 
the phase of the current in the "coupled to" element will be delayed by the 
distance between the elements (i.e. put the element 1/4 wavelength away, 
and the current will be 90 degrees behind that in the driven element. The 
current in the undriven element will be slightly less than the current in 
the driven element (because some of the driven elements energy is radiating 
away (and not available for coupling), and because the energy spreads (so 
the undriven element "intercepts" less of it), so you won't get such a nice 
sharp null as you do with the classic 1/4 wave, 90 phased.

It turns out that you can get more gain than you'd get with a simple phase 
progressing in proportion to the distance traveled by advancing the phase a 
bit more. Say you had a row of 4 elements 1/4 wave apart. Say you feed them 
0,-90,-180,-270... As the wave from the first element gets to the second 
element (90 degrees away), it will be exactly in phase with the signal 
being radiated from that element (which was delayed 90 degrees 
electrically), and so forth, so you form a directive beam.   Now, say you 
fed them 0, -120, -240, -360.  You'd find that the beam is narrower and the 
directivity higher.  This is called the superdirective condition (The 
actual phase advance is a bit different, but that's the idea, and it's 
close) The W8JK flattop with two elements driven out of phase, and much 
closer than 1/2 lambda is an example, also.

But, if you just relied on mutual coupling, it's hard to get that extra 
phase shift.  The elements are only 90 degrees apart, and you need 120 
degrees of phase shift.  Well, here's where the reactive properties of the 
elements come in.  If you add some capacitance or inductance to the 
element, you can change the phase of the current, just as changing the L 
and C in any resonant circuit changes the phases of the currents.  In an 
antenna, you could either put a lumped component in, or, you could just 
make the element a bit longer (inductive) or shorter (capacitive).

Voila... you can now make a superdirective array with only passive 
coupling.  You fiddle with the lengths and spacings to make the currents 
come out right.  Moving the element closer increases the current, but 
results in less phase shift. So, you add L or C as appropriate, which adds 
phase shift, and now, you're all set.


However, an interesting thing occurs... you're now storing more energy in 
the element and it's related components than you were before.  That stored 
energy is in the form of reactive power, which is subject to resistive 
losses, and, the reactive power isn't radiating.  So there's the practical 
limit on superdirective antennas.  You have to use real materials with 
loss, and at some point, the losses overcome the increase in directivity, 
so the forward gain (which is the directivity less the loss) maxes out.

Very long boom Yagis with lots of elements tend not to be superdirective 
for this reason.  Their gain linearly follows the length.

There's actually a picture of this whole stored energy thing on the cover 
of one of the Antenna Compendia.

In any case, there's no "reflecting" going on.




>I witnessed a demonstration of antenna radiation patterns using a
>transmitter/receiver in the 3-4GHz range.  The antenna samples were made
>with 22 gauge copper wire and were quite small.  All of the 10 samples
>together could be held in one hand.  A simple Yagi with one reflector had
>about 85 percent of the gain of another with one reflector and 4 directors.
>There was also another sample that used two reflectors, and it did not show
>a noticeable gain over the single.  I think this is because there is little
>RF to work with behind the first reflector.

Or, because the design wasn't optimized.  It's fairly straightforward to 
create a design with a driven element in the front and two undriven 
elements in the back that has almost as much gain as one that has the 
driven element in the middle.  Any of the Yagi Optimizer programs should be 
able to do it (certainly, a generic optimizer like that in 4nec2 can do 
it).  Just take a standard 3 element design, and move the feedpoint to the 
front element.  Even with no changes in the element lengths, it will 
probably have gain within a couple dB of the original antenna.



Jim, W6RMK