"Net Gain" Frequency Sweep Procedure
Hi Folks,
In
http://www.digitalhome.ca/forum/showthread.php?t=83772&page=4 Post 47, I found Autofils' method for calculating the Net Gain. I don't have to understand where the formulas came from, but I would like to be able to pull the right data out of the 4NEC2 frequency sweep plots and to execute the calculations properly. So, I have worked up a little example. I would appreciate it if y'all would walk through this example to verify whether I got it right or not.
In
http://www.digitalhome.ca/forum/showthread.php?t=81982&page=19, Post 284, I found a drawing by Elvis Gump of the First Generation Gray Hoverman Antenna developed by Autofils and others. I entered the measurements in inches from this drawing into 4NEC2's geometric editor and save the file as GH12.NEC. The content of this file follows:
CM Active Driver Assemblies for a Gray Hoverman Antenna (6 Gage Wire)
CM Measurements Taken from a Drawing by Elvis Gump
CM Including 12 Element Co-Linear Reflector
CE
GW 1 13 0 5.885 15 0 11.475 15 0.08101138
GW 2 15 0 5.885 15 0 0.885 10 0.08101138
GW 3 15 0 0.885 10 0 5.885 5 0.08101138
GW 4 15 0 5.885 5 0 0.885 0 0.08101138
GW 5 15 0 0.885 0 0 5.885 -5 0.08101138
GW 6 15 0 5.885 -5 0 0.885 -10 0.08101138
GW 7 15 0 0.885 -10 0 5.885 -15 0.08101138
GW 8 13 0 5.885 -15 0 11.475 -15 0.08101138
GW 9 13 0 -5.885 15 0 -11.48 15 0.08101138
GW 10 15 0 -5.885 15 0 -0.885 10 0.08101138
GW 11 15 0 -0.885 10 0 -5.885 5 0.08101138
GW 12 15 0 -5.885 5 0 -0.885 0 0.08101138
GW 13 15 0 -0.885 0 0 -5.885 -5 0.08101138
GW 14 15 0 -5.885 -5 0 -0.885 -10 0.08101138
GW 15 15 0 -0.885 -10 0 -5.885 -15 0.08101138
GW 16 13 0 -5.885 -15 0 -11.48 -15 0.08101138
GW 17 5 0 -0.885 0 0 0.885 0 0.08101138
GW 18 25 -3.94 -12.5 15 -3.94 -0.3935 15 0.08101138
GW 19 25 -3.94 0.3935 15 -3.94 12.5 15 0.08101138
GW 20 25 -3.94 -12.5 7.5 -3.94 -0.3935 7.5 0.08101138
GW 21 25 -3.94 0.3935 7.5 -3.94 12.5 7.5 0.08101138
GW 22 25 -3.94 -12 2.5 -3.94 -0.3935 2.5 0.08101138
GW 23 25 -3.94 0.3935 2.5 -3.94 12 2.5 0.08101138
GW 24 25 -3.94 -12 -2.5 -3.94 -0.3935 -2.5 0.08101138
GW 25 25 -3.94 0.3935 -2.5 -3.94 12 -2.5 0.08101138
GW 26 25 -3.94 -12.5 -7.5 -3.94 -0.3935 -7.5 0.08101138
GW 27 25 -3.94 0.3935 -7.5 -3.94 12.5 -7.5 0.08101138
GW 28 25 -3.94 -12.5 -15 -3.94 -0.3935 -15 0.08101138
GW 29 25 -3.94 0.3935 -15 -3.94 12.5 -15 0.08101138
GS 0 0 0.0254 ' All in in.
GE 0
EK
EX 0 17 3 0 1 0
GN -1
FR 0 1 0 0 585 0
Then, I brought up 4NEC2's Generate (F7) screen. I set the first group of radio buttons to "Far Field pattern". The Frequency was set to 585 MHz. The third group of radio buttons was set to "Full". The resolution was set to 5 degrees. I checked the "Run Average Gain Test" and clicked the "Generate" button. After a short time, the "AGT results" were displayed on the Main (F2) screen as "1.02 (0.08 dB)". I think this is trying to tell me that the "Raw Gain" estimated at 585 MHz might be in error by as much a 0.08 dB. In my book that is very small error. If the error had been a lot larger, I would have increased the number of segments in each wire and tried again. I remember reading something about the "Convergence Test" but I have not tried it yet. Anyhow... the "Average Gain Test" looks pretty good. So, I take it that the output data can be trusted.
Next, I brought up the 4NEC2's Generate (F7) screen again. I set the first group of radio buttons to "Frequency sweep". The third group of radio buttons was set to "Hor.". The resolution was set to 5 degrees. The Starting Frequency was set to 473 MHz, the Stop Frequency was set to 695 MHz and the Step size was set to 6 MHz. The Forward Theta was set to 90 degrees. The Forward Phi was set to 0 degrees. The Backward Theta was set to 90 degrees. The Backward Phi was set to 180 degrees. Both “d-Phi”s were set to 5 degrees. Finally, I clicked the "Generate" button. After a little while, the DOS screen and the "Status" screen disappeared to be replaced with the "Pattern (F4)" and "Imp. / SWR / Gain (F5)" screens.
On the main menubar of the "Imp. / SWR / Gain (F5)" screen, I selected "Show/Forward gain", to see if the Total Forward Gain curve for the 473 to 695 MHz UHF band was about what I expected. There were no surprises. It was a pretty flat gain curve. The lowest gain of 12.5 dBi occurred at 473 MHz and the highest gain of 14.1 dBi occurred at 665 MHz. It was really nice. Until very recently, I thought this gain curve was the most important characteristic of a modeled antenna and that it provided an excellent way to compare different antenna geometries. Now, I hear this curve is really the "Raw Gain" curve and perhaps it could be adjusted using a few other estimates available in the 4NEC2 output to build a "Net Gain" curve. Using the “Net Gain” curve should provide even more realistic comparisons. Is that true?
Next, I started Excel on top of 4NEC2 and opened an empty spreadsheet. I labeled a few columns with the following titles: Frequency, Channel, Raw Gain, Zo, Zr, Zi, FP Gain, Net Gain and Delta. I switched back to 4NEC2's "Imp. / SWR / Gain (F5)" screen and selected "Plot/Forw-gain" from the main menubar. An information box appeared to tell me that "wGnuPlot.exe was not found... ". I clicked the OK button to acknowledge the message. 4NEC2 scheduled Notepad to show me all the beautiful data it had copied into the Plot.txt file for the wGnuPlot application. I closed Notepad.
The Plot.txt file structure is very simple and can be easily imported into an Excel spreadsheet. On my computer, the Plot.txt file lives in the C:\4nec2\plot folder.
I switched back to Excel and imported the Plot.txt into a new spreadsheet. I copied the numbers in the Frequency column and paste them to my first spreadsheet just under the Frequency column label. I repeated the process for the Total Gain numbers and pasted them just under the "Raw Gain" column label. I closed the Plot.txt spreadsheet. I switched back to 4NEC2's "Imp. / SWR / Gain (F5)" screen and selected "Plot/R-in (real)" from the main menubar. 4NEC2 overwrote the Plot.txt file with this new data and complained as before when it could not schedule wGnuPlot.exe. I think the "R-in (real)" data corresponds to the real part of antenna's complex impedance (Zr). So as above, I imported it into a new spreadsheet, copied the data in "Real-in (real)" column and pasted it just under the Zr label in my first spreadsheet. I switched back to 4NEC2's "Imp. / SWR / Gain (F5)" screen and selected "Plot/X-in (imag)" from the main menubar. 4NEC2 overwrote the Plot.txt file with this new data and complained as before when it could not schedule wGnuPlot.exe. I think the "X-in (imag)" data corresponds to the imaginary part of antenna's complex impedance (Zi). So again, I imported it into a new spreadsheet, copied the data in the "X-in (imag)" column and pasted it just under the Zi label in my first spreadsheet. I populated the Channel and Zo columns. I built the "FP Gain" and "Net Gain" formulas based on Autofils’ suggestion to ericball and populated those two columns. I built a Delta Gain column which is nothing more than the difference between the "Net Gain" and the "Raw Gain". Finally, I added some documentation above the table and cleaned things up a bit. The spreadsheet text follows:
"Net Gain" Calculations for the Gray Hoverman 12 Antenna
Frequency (MHz) vs. Total Net Horizontal Gain Estimates (dBi)
Geometric Design Data Taken from Elvis Gump's Drawing (6 Gage Wire)
Data extracted from 4nec2's plot files using 300ohm's cut and paste method
"Net Gain" calculated using Autofils' method outlined below
NetGain = RawGain+10*log(Feed-pointGain)
where Feed-point Gain = 4*Zr*Zo/((Zr+Zo)^2+Zi^2)
The [10*log(base10)] converts to decibels, and Feed-point Gain is less than 1, since there is a loss.
Zo = characteristic Impedance for the transmission line connected to the antenna ( Zo=300 for the GH)
Zr = real part of antenna's complex impedance at a specific frequency
Zi = imaginary part of antenna's complex impedance at a specific frequency
RawGain = Gain output given by 4nec2 at the specific frequency
Delta = Net Gain - Raw Gain
Freq Ch Raw Zo Zr Zi FP Net Delta
(MHz) No. Gain Ohms Ohms Ohms Gain Gain Gain
473 14 12.58 300 116.705 -204.150 0.650 10.71 -1.87
479 15 12.72 300 116.756 -168.820 0.693 11.13 -1.59
485 16 12.83 300 119.062 -138.807 0.733 11.48 -1.35
491 17 12.94 300 123.117 -112.943 0.770 11.81 -1.13
497 18 13.03 300 128.585 -90.478 0.804 12.08 -0.95
503 19 13.11 300 135.215 -70.918 0.834 12.32 -0.79
509 20 13.18 300 142.789 -53.934 0.861 12.53 -0.65
515 21 13.24 300 151.099 -39.297 0.884 12.71 -0.53
521 22 13.30 300 159.936 -26.830 0.904 12.86 -0.44
527 23 13.35 300 169.089 -16.379 0.921 12.99 -0.36
533 24 13.40 300 178.348 -7.788 0.935 13.11 -0.29
539 25 13.44 300 187.516 -0.888 0.947 13.20 -0.24
545 26 13.49 300 196.420 4.509 0.956 13.30 -0.19
551 27 13.53 300 204.926 8.608 0.964 13.37 -0.16
557 28 13.57 300 212.940 11.629 0.971 13.44 -0.13
563 29 13.61 300 220.422 13.786 0.976 13.50 -0.11
569 30 13.65 300 227.380 15.287 0.980 13.56 -0.09
575 31 13.69 300 233.868 16.314 0.984 13.62 -0.07
581 32 13.73 300 239.981 17.015 0.987 13.67 -0.06
587 33 13.77 300 245.844 17.500 0.989 13.72 -0.05
593 34 13.82 300 251.610 17.836 0.991 13.78 -0.04
599 35 13.86 300 257.444 18.033 0.993 13.83 -0.03
605 36 13.91 300 263.528 18.057 0.995 13.89 -0.02
611 37 13.95 300 270.041 17.805 0.996 13.93 -0.02
617 38 14.00 300 277.158 17.103 0.998 13.99 -0.01
623 39 14.05 300 285.040 15.702 0.999 14.04 -0.01
629 40 14.09 300 293.803 13.242 0.999 14.09 0.00
635 41 14.14 300 303.492 9.244 1.000 14.14 0.00
641 42 14.18 300 314.013 3.089 0.999 14.18 0.00
647 43 14.21 300 325.039 -5.986 0.998 14.20 -0.01
Please take a look at this procedure and please run a few spot checks of the "Net Gain" calculations. I need to know how to work through a problem by hand before I can automate the process.
Yikes!!! The editor stripped out all of the tabs in the spreadsheet table. That's not nice. Stuff Happens... LOL... Just Stay Out of the Stuff Storms!!!
Thank you,
DTV Student