Posted 28th October 2017 by WVØH Myron

Vertical Antenna Considerations

Introduction

Vertical antennas come in all shapes, sizes, lengths, and whether or not ground radials are used. My success with using EZNEC to accurately tell what the gain will be has always eluded me. Until now.

EZNEC
The use of W7EL's EZNEC comes with two calculating engines, NEC2 and NEC2D. I have always used the NEC-2D engine. Apparently there is a way to incorporate use of the NEC-4 engine but only after you have acquired it and I haven't acquired it. The NEC-4 engine is better suited for modeling verticals that have ground radials over or in earth ground whereas the NEC-2D engine is less capable in this regard. But there is a way to work with this limitation by using measured data from an antenna analyzer to back into a solution that is close enough.

Step 1: Obtain an Impedance Measurement of 2 Wires on Ground

This was my missing link that came about by playing with a ground plane vertical last weekend. It got me thinking of actually measuring the 2 ground radials alone (a dipole, in essence) laying on the grass with an antenna analyzer. To my surprise I was actually able to get a reading that had a "shape" to the SWR response. Each radial was just over 14 feet long. I use one radial for my MFJ-1820 whip deployment. That's got to be lossy.

I used that radial and put out another radial for my experimentation. These two radials were just laying there when I had the idea to measure them like a dipole laying on the ground. The earth had to have some affect on the electrical length. The wires laid on the ground were approximately 14 feet long each. The lengths aren't critical because when we hook up the analyzer, all we are after is the value of R when X is = 0 and the frequency of that crossing.  

Okay, so I deviated away from that #24 wire and used #16 enameled copper wire (not my portable rig's radials) and the Z turned out to be 130-j12 Ω and 12 MHz, the close enough resonant frequency of these 2 ground radial wires.

I used to plastic clamps and a screwdriver to hold the ends from coiling up and moving around.

Step 2: Build a Vertical Radiator for the Resonant Frequency

We want to build a vertical for 12 MHz because it is the frequency at which the reactance of the two ground radials is zero, resonant. This is easy; use the quaterwave formula (234/12) which results in 19.5 feet. I suspend it from a fiberglass pole because we don't want any effects from carbon fiber at this point.

Step 3: Measure the Antenna (and Counterpoise) with Antenna Analyzer

Attach a Binding Post adapter to your analyzer and hook the vertical wire to the center or red post and attach both ground radials to the black post. No need for a balun. I used my AA-600 and it native calibration is fine for HF use.

This is the response at 12MHz but shifted a bit. Readjust for resonance to avoid any mismatch loss.

Here is the frequency where the reactance is the smallest, 12.225MHz at least in the 25kHz steps that I had the analyzer set. (It's a function of 80 data points over a selected frequency span in the analyzer). Note the resonant frequency and it's resistance at this point. In my case, it was 67Ω.

Step 4: Get Out the Books and Calculator

A quarterwave vertical over an infinitely conducting ground plane's input impedance is 36.5+j21.25 Ω. Since this is a perfect quarterwave we have to compare our results to the theoretical maximum efficiency. Since we can keep everything resonant there's no need for complex math. Simply ratio the two Resistances to obtain an overall efficiency which is (37/67) = 0.55 or 55% efficient or (10*log(0.55)) = -2.6 dBi. Hmm, let's confirm this in EZNEC.

Step 5: Set Up a Model in EZNEC That Represents the 2 Wire Ground Plane

In EZNEC, there are a myriad of knobs to tweak to produce readings that can get close to our ground radial impedance we obtained in Step 1, |Z| ~ 130 Ω.

With the source placed at 50% from end 1, the #16 copper wire is 0.5 inches above high accuracy ground, and is 345 inches long (±172.5 inches from the center). I swept the SWR (set to Smith chart) from 11-14MHz at 0.1MHz steps.

I found it easier to start with an "Average" ground and a Z-distance of the wires at 2 inches up. I had to tweak the Z height, ground conductivity, and dielectric constant in order to dial-in a result that was close to 130 Ω at 12MHz. I ended up with a ground media of: 0.008S/m and a dielectric constant of 7 at the 0.5 inch height. That height was probably closer to my measurement because my grass in the back yard is pretty thin.

Getting a feel for what adjusted what in EZNEC was a trick but in the end I ended up with 0.008 S/m and 7 dk at a Z height of 0.5 inches.

Step 6: Add the Vertical to EZNEC and Push the Button

Adding a proper length vertical wire turns out to be trickier than anticipated. End effects and wire thickness all play a role in shifting the response around a bit. But in the end "close" is good enough. I used a 234 inch length vertical (19.5 feet) with #16 Cu and 234 segments.

The response is shifted a bit. But what matters is the gain at 12 MHz, minimizing the mismatch loss.

Here we see the gain to be -2.6 dBi, compared which is in good agreement with the -2.6 dBi we obtained in Step 4.

Final Thoughts

In order to obtain a perspective of how much gain we can expect from a vertical, I modeled a perfect vertical in EZNEC, no losses in any component or ground. It's gain is 5.1 dBi.

With this reference in mind you can gain an appreciation for the differences between what you have and what is theoretically possible. The one big difference between obtaining what is possible between verticals and dipoles is that one is achievable anywhere, the other is only achievable if you live near sea water in every direction.

20m inverted Vee up 39 feet with high accuracy, average ground model.

Further Steps

Once you have these ground properties for a set of radials you can change the length of the vertical radiator and see what gain you have on other bands or run this 19.5 foot wire out portable and enjoy some ops.

73
Myron WVØH
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