### Part 3: Answers, Horizontal polarization

In the part of the exercise we will use the model to look at how the antenna performs when horizontal and at various heights above a ground plane.
• What is the bandwidth of the antenna?
• What is the resonate frequency of the antenna?
• What is the radiation pattern?
• How high should the antenna be mounted?
The approach I am going to take in answering these questions is to use the model developed in the previous parts and run the analysis at various elevations. First the resonate frequency in free space will be determined, then a ground plane will be added and the elevation set to 1/2 wave length at the resonate frequency. That is really too low for a 2m antenna, but you have to start somewhere. The analysis will be repeated every 1/2 wave length up to 16.

#### Resonate Frequency and Bandwidth

For this analysis we'll start with the V2 model and change the frequency card to do the calculations at 500KHz intervals:
`FR  0   18    0    0  1.420E+02 0.500E+00`

Run the analysis. While you could look through the output files for the sections that look like this,
`                      ----- ANTENNA INPUT PARAMETERS -----`
`  TAG   SEG       VOLTAGE (VOLTS)         CURRENT (AMPS)         IMPEDANCE (OHMS)        ADMITTANCE (MHOS)     POWER`
`  NO.   NO.     REAL      IMAGINARY     REAL      IMAGINARY     REAL      IMAGINARY    REAL       IMAGINARY   (WATTS)`
`   2    35  1.0000E+00  0.0000E+00  2.5208E-02  1.6486E-02  2.7786E+01 -1.8172E+01  2.5208E-02  1.6486E-02  1.2604E-02`

the xnecview output reformats the information onto a single line per frequency:
`#  freq.       Zr       Zi      SWR     gain      f/b      phi    theta`
`     142   27.786  -18.172  2.12152     9.02    10.99       89       90`
`   142.5   29.218  -13.825  1.90021     9.11    11.42       89       90`
`     143   30.839  -9.4171  1.71125     9.19    11.72       89       90`
`   143.5   32.692  -4.9434  1.55522     9.26     11.9       89       90`
`     144   34.833 -0.40102   1.4356     9.32    11.95       90       90`
`   144.5   37.337    4.205  1.36016     9.36    11.89       89       90`
`     145     40.3   8.8567  1.33854      9.4    11.73       89       90`
`   145.5    43.85   13.514  1.37133     9.42    11.49       89       90`
`     146   48.152   18.097  1.44578     9.44    11.21       89       90`
`   146.5   53.417   22.462  1.54677     9.45    10.88       90       90`
`     147   59.907   26.346  1.66327     9.44    10.54       89       90`
`   147.5   67.916   29.286  1.78772     9.43     10.2       89       90`
`     148   77.688   30.491  1.91432     9.41     9.85       90       90`
`   148.5   89.184   28.672    2.038     9.38     9.51       90       90`
`     149   101.53   21.993  2.15412     9.34     9.19       90       90`
`   149.5   112.13   8.6277  2.25914     9.29     8.89       89       90`
`     150   116.18  -11.304  2.35053     9.24     8.61       90       90`
`   150.5   109.03  -33.166  2.42933     9.18     8.37       89       90`

Resonance is defined as the point where Zi = 0 and that occurs between 144MHz and 144.5MHz.

We can also see that the bandwidth (SWR < 2) is about 6MHz (148.5MHz - 142.5MHz = 6MHz).

If you want to know either value more precisely you can change the FR card and re-run the analysis. However these numbers are really good enough.

#### Max Gain

The output from xnecview includes three more columns that will be important to the rest of our analysis: `gain`, `phi`, and `theta`. These three numbers represent the magnitude and direction of the maximum gain of the antenna. The gain is in db and the angles are in degrees. Phi is an angle in the horizontal plane. The angle is measured counter-clockwise (when viewed from above) from the  the x-axis. Theta is an angle  in the vertical plane measured from the z-axis, 0 degrees is straight up and 90 degrees is horizontal.

#### Ground plane

One of the strengths of NEC2 is that it can model non-ideal grounds. To use the non-ideal ground we need the dielectric constant and conductivity for the local ground. I don't know how to measure those, but 5B4AZ (Neoklis Kyriazis ("Nick")) has provided a table of typical values that we can use. For the area where this antenna will be used I think the soil is dry, flat, coastal which would be represented by a GN card that looks like this:

`GN  2  0  0  0  1.0000E+01  2.000E-03`

A ground plane has a striking effect on the radiation pattern as shown by these two graphs. The important feature here is that the radiation pattern now has multiple lobes that are not horizontal. So the maximum gain is no longer in the horizontal plane.

#### Setting the Antenna Height

Back in the first part of the exercise I highlighted the use of a GM card to set the antenna height. Now is when that pays off. By simply changing one number we can easily change the antenna height.

Using 144MHz as the resonance frequency gives us a wave length of 300/144 = 2.08 meters.

Before running any of the analysis, change the 1001 value on the RP card to 1000 to disable the average gain calculation. The average gain calculation is not relevant when the antenna is modeled over a ground plane.

Also change the FR card to run the analysis at a single frequency, 144MHz.

I used the attached python script, deltaElev.py, to generate a number of data files. Then a few shell commands and I had a CSV file ready for analysis.

`\$ python ./deltaElev.py `
`\$ for f in *.nec; do ../nec_run.sh -n \$f; done | tee results.txt`
`\$ grep 144 results.txt | tr -s " " "," | nl > results.csv`

I loaded results.csv into OpenOffice and generated these theta vs antenna height plots. Theta vs Height in Wave-lengths(click image to enlarge) Theta vs Height in Meters(click image to enlarge)

Keep in mind that theta is measured from vertical, so 90 degrees is horizontal. A yagi antenna over a ground provides maximum gain at upward sloping angle. That angle change with the height of the antenna above ground.

ċ
JERRY DUNMIRE,
Apr 20, 2012, 8:08 PM