Topband: Modeling for the N6LF "Elevated Radials" QEX article

[Dan Maguire]

The recent "trimming elevated radials" thread prompted me to re-read the N6LF QEX two-part article "A Closer Look at Vertical Antennas With Elevated Ground Systems", available here:
http://rudys.typepad.com/files/qex-mar-apr-2012.pdf
and here:
http://rudys.typepad.com/files/qex-may-jun-2012.pdf

For those of you who have the AutoEZ program (or its predecessor, which is what N6LF used) I have created a general purpose model which may be used to duplicate many of the charts shown in the article as well as do other studies concerning elevated radials.  Almost all aspects of the model are controlled by variables.  I kept the N6LF usage for variables H, J, L, and N plus added a few others.  The complete set is:
H:  Vertical element length  (May be 0 to model radials only)
J:  Base height  (May be 0 for use with Perfect or MININEC ground)
L:  Radial lengths
N:  Number of radials  (May be set to 0, 1, 2, 4, 8, 16, or 32)
T:  Top wire A (above +X axis) length  (Set to 0 for no top wires)
U:  Top wire B (above -X axis) length  (see below)
V:  Angle of top wire(s), down from horizontal

All dimensions are in feet.  Variables T,U,V allow you to create a "T" or "Inverted L" radiator with either horizontal or sloping top wire(s).

As mentioned, one use of this model is to recreate the N6LF charts under different conditions.  For example, here is Fig 12 from Part 1 of the article.  In this case Average Gain is being used as a proxy for antenna efficiency.  The length of the radials is swept from 0.05 WL to 0.6 WL and the chart shows a large drop in Average Gain as the radial length approaches 0.45 WL, less so when more radials are used. 
http://ac6la.com/adhoc/MCVertFig12a.gif

Here's a similar chart, tailored for Top-Banders, produced by AutoEZ.
http://ac6la.com/adhoc/MCVertFig12b.gif

Another example relates to the section "An Explanation for the Dips in Ga" (Part 1 pg 40) in which N6LF discusses the large current peaks that develop on the radials as the length approaches 0.45 WL.  These large currents increase the E and H-field intensities in the ground.  He then states: "Since the power dissipation in the soil will vary with the square of the field intensity, it’s pretty clear why the efficiency takes such a large dip when the radials are too long."  This is illustrated with his Figs 24-26 (not shown here).

A alternate way of showing what is happening, not possible with a print publication, is to animate the E-field pattern as the length of the radials is increased.  Here is the case for N=4 with the radial lengths ranging from L=0.05 WL to L=0.6 WL, the same range as the previous chart.  Temporary variable "A" is being used to set the radial length in WL units which is then converted to the actual "L" in feet.  Values for both A and L may be seen to the right of the chart.  E-field was calculated at 1 foot below ground.  With most browsers, press Esc to stop the animation in order to take a closer look at any frame, press F5 to restart.
http://ac6la.com/adhoc/MCVertNF3D.gif

Another way to use this model is for comparison between alternate scenarios.  For example, W8JI suggested starting with two opposite radials trimmed to be a resonant dipole, then adding additional radials of the same length, then adding the vertical element and adjusting its length for feedpoint resonance.  Modeling this scenario at 1.85 MHz, H=0 (to start), J=10, and N=2, the AutoEZ "Resonate" button yields L=127.2 ft (0.24 WL) for "dipole resonance".  Then with N=8 the "Resonate" button yields H=132.0 ft (0.25 WL) for a feedpoint Z of 39+j0 ohms.

Although the SWR is already low, to minimize feedline loss you might put a matching network at the antenna base.  The AutoEZ "Create Impedance Matching Network" button allows you to easily add this to your model.  With a Lo-Pass L network (coil in series, capacitor in shunt), the computed values are coil=1.804 uH and cap=931 pF to get 50+j0 ohms at the antenna.  This is with real-world (lossy) components, assuming a coil Q of 200 and a capacitor Q of 1000, both at 1 MHz and adjusted as necessary for other frequencies.

Call this Scenario 1.  For Scenario 2 suppose you have room for radials that are only 100 ft long, you can only get the top of the vertical up to 80 ft, and you'll add two top wires to make a "T" for the remaining radiator length.

With N=8, H=70 (puts the top at 80 with J=10), and U set to "=T" (that is, U will change as T changes so that symmetry at the top is maintained), the "Resonate" button sets T=42.8 ft to give a feedpoint Z of 25+j0 ohms.  Then again adding a matching network, the computed values are coil=2.154 uH and cap=1684 pF to get 50+j0 ohms at the antenna.

Here's what the two antennas look like.  Remember, both were created from the same model file, the difference is just how the variables were set.
http://ac6la.com/adhoc/MCVertView.gif 

Finally, how do the two scenarios compare?  Here are the azimuth patterns at 22 deg elevation:
http://ac6la.com/adhoc/MCVertPolar.gif

It's easier to discern the small difference in gain as well as the slight asymmetry of Scenario 2 when the pattern is shown in rectangular rather than polar format:
http://ac6la.com/adhoc/MCVertRect.gif

And here's the SWR comparison with the matching network in place in both cases:
http://ac6la.com/adhoc/MCVertSWR.gif

The AutoEZ model can be downloaded (right click and select Save As) here:
http://ac6la.com/adhoc/Multi-Config_Vertical.weq

And for more information on AutoEZ see:
http://ac6la.com/autoez.html

Dan, AC6LA
http://ac6la.com/