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Antenna Modelling… A Learning Experience

One of our Tech Topics 

My OCF dipole came down in the wind over a year ago, so I decided it was time to replace it with something else, at least for 80m.  I have lots of trees in the yard, but the high ones really don’t lend themselves to a horizontal wire because they are all clustered together.  I researched other options and decided I could probably make an 80 m inverted L work.   Since my trees are all over 30 m high with the lower branches stripped off, I figured they should accommodate 20 m or more wire in the air, especially since only part of the antenna is vertical.   The relative proportion between vertical and horizontal legs is apparently not too critical to its performance.  This antenna is actually a quarter-wavelength vertical therefore it requires counterpoise, or ground radials. 

While the weather was good over the summer I began the project by installing a 1½ ” ABS conduit below ground from the house to the location of the antenna feed point, so that the coax would not have to run over the surface of the ground.  Next challenge was to get attachment points up in the trees, a job which requires a tree climber – a big challenge as tree climbers are very casual about returning calls and showing up for the job.  Finally it all came together just as the weather started to turn cold in October.  I had him tie a pulley and rope as high as possible on two trees which are about 10 m apart.  In order that there be no obstruction to the future wire, he had to remove a few limbs but, what the heck, most of them were dead anyway.  The ropes and pulleys went up at about the 20 m level on both trees without a problem.  

I have always wanted to learn about antenna modeling and saw this as an opportunity to get my feet wet.  Several different modeling software packages are available, either free or at low cost, but I elected to use EZNEC demo v 6.0, as it is supposed to do almost everything that the more sophisticated products will do, it has good documentation and is free.  After reviewing the instructions provided with the package, I had no trouble working through the examples to get familiar with its features.  There are also several good tutorials available on You-Tube.   EZNEC does assume that you have a basic understanding of impedance, resistance and reactance which are expressed in the form of complex numbers (Z=R ±jX) as well as familiarity with x-y-z rectangular coordinate systems, but that’s about as complicated as it gets.   I was pleasantly surprised to find out how intuitive the software is to use. 

Taking my guidance from the ARRL Antenna Book, here is the basic configuration that I planned to model: the top portion of the antenna above ground is around ¼ λ long and the other ¼ λ is in the ground in the form of radials or counterpoise.  The bend to make the above-ground wire into an L can be done at any convenient place, but I intended to make most of the antenna vertical. This configuration under normal circumstances will provide a usable swr over most of the 80 m band, with the help of a tuner.  

However, due to the proximity of the wire to ground, its radiation resistance (R) is said to be lower than 50 Ω.  I wanted to aim for 50 Ω at resonance to match the feedline impedance.  If the antenna were to be made somewhat longer than ¼ λ, the R value can be increased to 50 Ω.  However, with the antenna now longer than ¼ λ it becomes inductively reactive.  So I would cancel out the inductive reactance by introducing an equivalent (of opposite sign) series capacitive reactance at the feedpoint – or, as expressed in mathematical form, the impedance would be Z = 50 ±j0 at  resonance.

My objective was to locate the minimum swr at 3.75 MHz, the centre of the 80 m band.  A critical parameter is ground loss but the demo version of EZNEC does not allow modeling of the counterpoise system.  Instead, the ground loss was estimated based on advice in one of the tutorials.  I chose a series load loss of 10 Ω to represent an acceptable but less-than-perfect ground radial system, since I hoped to get by with only 5 radials.  I was soon to find out that 5 isn’t a sufficient number.

After much EZNEC trial-and-error, here is the final antenna configuration:

The Far Field elevation and azimuth plots with the maximum gain 25 deg above the horizon, and the antenna is nearly omni-directional, not unexpected for an antenna which is basically a dipole turned on its side.   This antenna will not likely be effective at short range as there is little vertical component to the elevation pattern.

Wire #1 represents a 6’ length of copper pipe to which the counterpoise wires are attached at the bottom; wire #2 is a short horizontal connection from the top of the pipe to the bottom of the vertical wire with the “feedline box” located approximately midway between the two; wire # 3 is the main vertical radiator, and Wire #4 is the short horizontal leg.  The small rectangle shows the location of the coax feed point, and the small circle is ground. 

The total length of the above-ground portion (wires 1-4) is 22.3 m, which is longer than ¼ λ, as intended.  After compensating for the inductive reactance by insertion of a series XC  of -89 Ω in the model, the predicted SWR graph came out as shown below.  At the target frequency of 3750, R was 48 Ω and the reactance virtually zero.

I was also interested in the conditions at the feed point and capacitor.  Since I may want to run at full power, I specified the power as 1500 watts in the EZNEC Options menu.  The result shows that the series reactance-compensating capacitor should have a spacing on the plates that will withstand at least 540 v without arcing when operating within the band. To provide -89 Ω of XC, the capacitance would be about 480 pF based on the formula XC = 1/2πfC.

And now for the construction

Three items were included in the feedline junction box: 
  • a common mode choke, 
  • a 30-1000 pF variable capacitor to introduce series capacitive reactance as described above, and 
  • a surge arrestor, all as shown in the photo.   

Five counterpoise wires, each 22.3 m long and buried 10 cm below the surface of the ground, were soldered to a 6 ft. ½ inch copper pipe driven into the ground and connected at the top to one side of the choke.   The ground wires ran from the base of the copper pipe all around the yard wherever I could fit them in, in all cases with bends to accommodate obstructions and the constraints of the property boundary. Instead of the store-bought choke I could have used a coax coil looped through ferrite toroids, which would have done the same thing.  I put insulation around the ground rod to protect children and animals from RF.

Since the feed point for this antenna is at ground level, it made it possible to conduct measurements right at the antenna without the presence of a feedline.  

Above, the scans  of SWR, R and X were made with the club’s RigExpert AA-600 analyzer. 

You will note that the minimum SWR is about 1.5 and it is also shifted slightly from 3750 kHz.  The higher SWR than predicted is because the impedance is not 50 Ω but 79 Ω – comprised almost entirely of R since the reactance was tuned out (observe the green reactance line crosses the 0 Ω axis at 3750 kHz).

Now this would actually be a very acceptable match across the entire band, but it does indicate that more counterpoise wires would be beneficial in order to match the model.  If we return to the model and simulate a poor ground by increasing the load R from 10 Ω to 30 Ω, the model confirms that the minimum SWR does in fact rise to 1.5.   So I plan to add more ground wires while I monitor the SWR and  impedance (both of which should come down) as the work progresses.  

I was gratified to find that changes made to the physical configuration were consistent with the model’s predictions.  This exercise has given me confidence in the modeling software and a better understanding of how the components of impedance inter-relate with the physical characteristics of the antenna. 

In the next installment I intend to outline a few things that did not make sense, and ask for advice in their interpretation, e.g. 
1) how 3 different analyzers gave me 3 distinctly different results and 
2) how introduction of the feedline also affected the results.

~ John VA7XB

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