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RE: [TowerTalk] Funniest thing I've seen in weeks

Subject: RE: [TowerTalk] Funniest thing I've seen in weeks
From: Jim Lux <>
Date: Wed, 30 Jun 2004 16:21:28 -0700
List-post: <>
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


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