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"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
 

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At this point in time, I am operating in the "Brut Force" mode. I have not explored the Symbols (SY) card yet. I barely have the discipline to stay away from it.
Although the geometry editor is okay to use, you really should use the NEC editor and start using symbols so 4nec2 does all of the calculations. Just be aware that if you go back and change the file using the geometry editor that you will lose all of the symbols.
I think you and ericball were saying the data presented in 4nec2's "Forward Gain" chart is really "Raw Gain" data. It is not necessarily the effective gain delivered by the antenna. There are additional factors (SWR, etc, etc) that could heavily influence what a very nearby tuner sees. I think you are saying, "Net Gain" vs Frequency plots are the proper modeling method to compare different antenna geometries.
4nec2 models transmission, not reception. And although you can use "reciprocity" theories to get from one to the other, there are differences. When transmitting, any energy reflected by impedance mismatches goes back to the transmitter where it is reflected back to the antenna. This is what SWR measures. But in receiving antenna the energy is reflected back through the antenna and radiated.

See http://www.digitalhome.ca/forum/showthread.php?p=767012#post767012 for my take on 4nec2 optimization.
 

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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.
You really should strive to get it to 1.0 (0 db). (otherwise, you have to remember in your head to do the subtraction or addition to a lot of channels) Its not that hard to do to get it perfect after a few times. And after a while, you quickly learn which way to adjust up or down. I dont change the number of segments until changing the wire radius doesnt do the trick. I just change the wire radius from the drop down box in Geometry Editor. That usually does it. If it doesnt, then I manually input a wire radius that is between gauge sizes.
 

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4nec2 models transmission, not reception. And although you can use "reciprocity" theories to get from one to the other, there are differences.
I thought about that. So that would mean modeling with 4nec2s advanced features over various ground types and conditions would be pretty much an exercise in futility for receiving, as the transmitter that is actually transmitting is far away. So modeling in a "free space" environment is the only way to go.
 

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Another Question about "Net Gain"

Hi Folks,

I am re-doing Experiment 1 and trying to apply Autofils' suggestions. Its a whole lot of work to calculate the "Net Gain". LOL... now I understand why Autofils wanted somebody to step up and write some code to parse 4NEC2's frequency sweep output files.

The other day, I outlined a procedure as I understand it to take the 4NEC2 "Raw Gain" data and a few other data items to calculate "Net Gain" data:

Autofils in an earlier post wrote:

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
I forgot to ask about the Characteristic Impedance or Zo term. Autofils said, "Zo = characteristic Impedance for the transmission line connected to the antenna ( Zo=300 for the GH)". I remember the old flat 300 ohm twin lead in wire. Today, the usual practice is to connect a 300 ohm to 75 ohm "Balum" transformer immediately to the antenna and run 75 ohm coax cable down to the TV tuner.

Also somewhere in my readings, I believe I remember a basic dipole antenna has a Characteristic Impedance of about 72 ohms, a basic bowtie antenna has a Characteristic Impedance of about 75 ohms and a basic folded dipole has Characteristic Impedance of about 300 ohms. Where did thing this Characteristic Impedance thing come from and why does a Gray Hoverman design have a Characteristic Impedance of 300 ohms? Why isn't it say 100 or 200 ohms?

Thanks,
DTV Student
 

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Today, the usual practice is to connect a 300 ohm to 75 ohm "Balum" transformer immediately to the antenna and run 75 ohm coax cable down to the TV tuner.
Correct, the antenna is 300 ohms and the coax cable is 75 ohms and the balun is in a 4:1 ratio. Thats the set standard for residential tv antennas. So use Zo = 300. At least maybe until 75 ohm to 75 ohm 1:1 baluns become commonplace. At 75 ohm characteristic impedance, you still need a balun to go from balanced to unbalanced line. Hence the name "balun". (baluns can also be made from coax cable, but theyre tricky for the average person to make)

Also somewhere in my readings, I believe I remember a basic dipole antenna has a Characteristic Impedance of about 72 ohms, a basic bowtie antenna has a Characteristic Impedance of about 75 ohms and a basic folded dipole has Characteristic Impedance of about 300 ohms. Where did thing this Characteristic Impedance thing come from and why does a Gray Hoverman design have a Characteristic Impedance of 300 ohms? Why isn't it say 100 or 200 ohms?
A dipole has a Characteristic Impedance of about 72 ohms, until you put on directors or reflectors, then it changes. Same thing for the bowtie, and most bowties are 4 ganged which changes the impedance drastically. The reason all these antennas are 300 ohm, is because thats the set standard (probably because in the orig old days, the folded dipole ruled and making twin lead lower than 300 ohms was too tricky for the manufacturing of the day. Were lucky they didnt settle on the wide 600 ohm standard which was easier to make consistantly, heh) So the goal is to design your antenna for 300 ohms so everything fits. At least until the next, if ever, standard.
 

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OK, I've got Wine installed on linux, and 4NEC2 installed on Wine. I deviated slightly from the FAQ, by giving Wine a 1280x1024 "desktop". 4NEC2 has problems finding its help files, but works otherwise. I can get to the help files manually. What directory do Windows users start in, and are there any environment variables to set?

I'm confused about the co-ordinate system, I think that X and Y are cartesian co-ordinates. I assume Z is from the screen pointing at me? I'm also having trouble following the first example. Are there any tutorials on the web?
 

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What directory do Windows users start in, and are there any environment variables to set?
In C:\4nec2. I believe the help files are in theC:\4nec2\exe directory. After starting the program, you can go into Settings on the main screen to set your preferences, ie length and wire units (metric or US and can change back and forth) and characteristic impedence.

The first thing to do is to go thru the _GetStart.txt file and follow the lessons.

Also on Arie Voors site, download the pdf files and read the 4 part series on A Beginners Guide to Modeling with NEC by Cebrik. This will help give you perspective and are the best tutorials available.


I'm confused about the co-ordinate system, I think that X and Y are cartesian co-ordinates. I assume Z is from the screen pointing at me?
The above A Beginners Guide to Modeling with NEC tutorial will clear everything theoretical up. Its a convention. The Z coordinate is up and down. The Y coordinate is left and right (port and starboard). The X coordinate is front to back of the antenna, plus pointing to front (towards the transmitting station), minus going to the rear. Life is easier when everyone uses these same conventions.
 

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A dipole has a Characteristic Impedance of about 72 ohms, until you put on directors or reflectors, then it changes. Same thing for the bowtie, and most bowties are 4 ganged which changes the impedance drastically. The reason all these antennas are 300 ohm, is because thats the set standard (probably because in the orig old days, the folded dipole ruled and making twin lead lower than 300 ohms was too tricky for the manufacturing of the day. Were lucky they didnt settle on the wide 600 ohm standard which was easier to make consistantly, heh) So the goal is to design your antenna for 300 ohms so everything fits. At least until the next, if ever, standard.
I'm glad it's 300 ohm imagine trying to get a decent match to 75 ohm directly with a wide band antenna like TV.

If your feed point impedence goes from 150 to 600 ohm with a 300 ohm antenna it's still only a 2:1 mismatch ratio at worst. But with 75 ohm you only have a 38 - 150 ohm window.

Full wave single bowties are more in the 600 - 900 ohm range.
 

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Hi Folks,


I forgot to ask about the Characteristic Impedance or Zo term. Autofils said, "Zo = characteristic Impedance for the transmission line connected to the antenna ( Zo=300 for the GH)".
DTV Student
DTV Student,

Here is a very quick note about antenna impedance and Zo of the connecting down-lead.

1. Antenna Impedance

The NEC2 engine calculates the RawGain and the antenna's complex impedance at a single frequency, where the antenna's impedance (Za) is given by two parts, the real and imaginary values.
( The real part is resistive; the imaginary part can be either capacitance or inductance)
If you are familiar with the "j" operator for complex numbers, then...
Za = Zr + jZi or Za = Zr - jZi.

The magnitude of the antenna's impedance is SqRt (Zr^2 + Zi^2)

When you do a sweep like 450 to 700 Mhz, step 10; the NEC2 engine calculates the Raw gain and antenna Zr and Zi for each of the frequencies defined in the sweep. ( Take a look at the F8 output and you see this).

So the antenna's impedance is a fixed property of the design....what you see as the antenna's impedance is what you get...

If you model a folded dipole, you'll see an antenna impedance of 300 ohms at the resonant frequency.
If you model a simple "straight" dipole with two elements, you see an antenna impedance of 72 - 75 ohms at the resonant frequency.

2. Transmission Line - Characteristic Impedance

The transmission line is used to interconnect the antenna to your receiver.
Standard transmission lines used for TV antennas are either the old standard 300 ohm twin-line or 75 ohm coax. If the antenna's impedance is 300ohm, then you must connect a 4:1 balun at the antenna feed-point, if you are using 75 ohm coax down-lead ( 300 to 75 ohm).

In the case of the GH, the antenna's impedance is typically 300 ohm, but it does vary over the UHF band... look at the Z plot.
You want to match the antenna's impedance to the characteristic impedance (Zo) of the transmission line to simply minimize SWR losses.
If you want to understand transmission lines, take a look at the Radio Amateur's Handbook...they describe it very well...check your local libaray.


Now 4nec2 allows you to specify the characteristic impedance of the transmission line from the main window, via "Char-Impedance" under the settings tab.

Once you have run a sweep, you can change that value and re-examine the SWR plot with the new value when you re-click on the SWR plot....give it a try !!


Note re Net Gain Calculation:

The task of calculating Net gain, was greatly simplified when 300ohm noted that the table values of all the parameters ( RawGain, Zr and Zi) are available under plot (see http://www.digitalhome.ca/forum/showpost.php?p=781674&postcount=208 ), so all you have to do is copy and paste into a spreadsheet....easy as pie !!!
 

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OK, I'm working my way through the examples. I still have some issues with Notepad for viewing. Otherwise 4NEC2 is up and running under Wine. A few "concept" questions...
  1. The antenna is located at Y = 0. Is the TV station assumed to be in the "plus Y" or "minus Y" direction?
  2. Are there any "standard numbers" to use for the UHF TV band assuming co-ax cable? I'm talking stuff like
    • default voltage-source
    • wire-conductivity
    • load
    • impedance
    • diameter/radius
    • "speed of electricity" in a wire (as a fraction of "c")
    • ground, etc, etc
 

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Welcome to the Modeler's Corner

Walter,

Welcome aboard!

I am a Newbie too. Many of the more experienced modelers can answer your questions. It takes a little while to get your arms around 4NEC2. "A Beginner's Guide to Modeling with NEC" (Parts 1 through 4) by L. B. Cebik is a great place to start. This tutorial and a few other goodies can be found at

http://wireless.ictp.it/school_2005/download/nec2/ .

You might also be wondering about the frequencies used by TV broadcasters. Here is some information I picked up a few months back that might be helpful:

Frequencies of Terrestrial Television Channels

All television stations in the United States of America broadcasting terrestrial signals are licensed by the Federal Communications Commission. The FCC assigns the maximum power and center frequency of each channel. Every channel is limited to a 6 MHz bandwidth, or ±3 MHz about its center frequency.

The older VHF television channels, 2 through 13, were broken up into three contiguous bands. Channels 2 through 4 operated between 54 MHz and 72 MHz. Channels 5 through 6 operated between 76 MHz and 88 MHz. Channels 7 through 13 operated between 174 MHz and 216 MHz. Channels 2 through 6 are often referred to as the VHF-LO band and channels 7 through 13 as the VHF-HI band.

Sometime later, the FCC allocated frequencies 470 MHz through 884 MHz in the UHF band, to channels 14 through 82. The frequencies used by channels 70 through 82 were reassigned as the demand for cell phone communication grew. Early in 2009, the FCC will also reallocate the frequencies used by channels 52 through 69.

The center frequency of each channel can be calculated as following:

Channels 2 through 4: Frequency in MHz = (6 X Channel Number) + 45

Channels 5 through 6: Frequency in MHz = (6 X Channel Number) + 49

Channels 7 through 13: Frequency in MHz = (6 X Channel Number) + 135

Channels 14 and above: Frequency in MHz = (6 X Channel Number) + 389

Example: Calculate the Wavelength (λ) of Channel 32.

Center Frequency = (6 X 32) + 389 = 581 MHz
Frequency Band = (581 - 3) through (581 + 3) MHz = 578 through 584 MHz

Wavelength of 578 MHz = 300/578 meters = 0.519031 meters
Wavelength of 578 MHz = 300/578 meters X 39.37 in/meter = 20.4343 inches

Wavelength of 584 MHz = 300/584 meters = 0.513699 meters
Wavelength of 584 MHz = 300/584 meters X 39.37 in/meter = 20.2243 inches


Good Luck and Keep Plugging Away,
DTV Student
 

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GH Driver Array - Modeling Experiments - Part 4

Hi Folks,

Experiment #1 (Revisited)

Purpose of Experiment:

To observe what happens to the Net Horizontal Gain, Raw Horizontal Gain and Standing Wave Ratio vs. Channel Number curves as the feedpoint gap distance is changed from 0.5 inches to 5.0 inches in steps of 0.5 inches for several families of the Gray Hoverman Driver Array Assembly.

Figure 1: The Gray Hoverman Driver Array Assembly



In Figure 1, the length of wire number 17 corresponds to the feedpoint gap distance; wire numbers 2 through 7 and 10 through 15 represent the zigzag elements; and wire numbers 1, 8, 9 and 16 make up the stub elements.


Methods and Materials:

See Experiment 1 for background information.

There was a lively discussion following the posting of Experiment 1. The experienced antenna modelers made a few suggestions and helped me to get a better understanding of several confusing issues. An antenna has many characteristics which affect performance. The novice is tempted to look for just a single number. “Gain” is the obvious choice. Later, the novice learns that “Gain” varies with frequency. Nothing is simple. He replaces the single number with a “Gain” response curve across the frequencies of interest. He searches the web for more information. There is plenty. Most of it is too advanced or specific to amateur radio operators. He stumbles into the world of antenna modeling using 4NEC2. Suddenly, he has the means to drown himself with data… but oh… what an opportunity to learn. I am learning to swim again.

While exploring the Geometric Editor, I eased into a nasty habit of looking at the “Horizontal Forward Gain” frequency sweep plot and totally ignoring all others. I simply had no idea what charts, like the “Standing Wave Ratio” plot, were trying to tell me. The learning curve is long and steep.

The “Forward Gain” data displayed by 4NEC2 is sort of what might happen in a perfect world, that is, if no impedance mismatches occurred across the frequencies of interest. Impedance mismatches lead to additional signal losses and are indirectly reflected in the “Standing Wave Ratio” data.

The “Forward Gain” data plotted by 4NEC2 is often called the “Raw Gain”. It should be modified to include the affects of impedance mismatches. Autofils calls the modified data… “Net Gain”, and calculates it from the impedance data provided by 4NEC2 as follows:

NetGain = RawGain+10*log(FeedPointGain)
where FeedPointGain = 4*Zr*Zo/((Zr+Zo)^2+Zi^2)

The [10*log(base10)] part of the calculation converts to decibels, and FeedPointGain is less than 1, since there is a loss.

Zo = characteristic Impedance for the transmission line connected to the antenna (Zo=300 for the Gray Hoverman antenna)
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

In Experiment 1, I only provided frequency sweeps of the “Raw Gain”. I am back tracking to include the “Net Gain” and “Standing Wave Ratio” charts. The ranges of the stub length and the feed point gap have been increased slightly. The stub lengths vary from 2.0 inches to 7.0 inches in steps of 1.0 inch and feed point gap distances vary from 0.5 inches to 5.0 inches in steps of 0.5 inches. As before, I decided to keep the zigzag element lengths fixed at 7.07 inches in order to keep the total count of modeling files down to a reasonable number.

The sixty NEC files were separated into the following six family groupings:

H01 - 7.07in ZigZags - 2in Stubs - 0.5in Gap.nec
H02 - 7.07in ZigZags - 2in Stubs - 1.0in Gap.nec
H03 - 7.07in ZigZags - 2in Stubs - 1.5in Gap.nec
H04 - 7.07in ZigZags - 2in Stubs - 2.0in Gap.nec
H05 - 7.07in ZigZags - 2in Stubs - 2.5in Gap.nec
H06 - 7.07in ZigZags - 2in Stubs - 3.0in Gap.nec
H07 - 7.07in ZigZags - 2in Stubs - 3.5in Gap.nec
H08 - 7.07in ZigZags - 2in Stubs - 4.0in Gap.nec
H09 - 7.07in ZigZags - 2in Stubs - 4.5in Gap.nec
H10 - 7.07in ZigZags - 2in Stubs - 5.0in Gap.nec

H11 - 7.07in ZigZags - 3in Stubs - 0.5in Gap.nec
H12 - 7.07in ZigZags - 3in Stubs - 1.0in Gap.nec
H13 - 7.07in ZigZags - 3in Stubs - 1.5in Gap.nec
H14 - 7.07in ZigZags - 3in Stubs - 2.0in Gap.nec
H15 - 7.07in ZigZags - 3in Stubs - 2.5in Gap.nec
H16 - 7.07in ZigZags - 3in Stubs - 3.0in Gap.nec
H17 - 7.07in ZigZags - 3in Stubs - 3.5in Gap.nec
H18 - 7.07in ZigZags - 3in Stubs - 4.0in Gap.nec
H19 - 7.07in ZigZags - 3in Stubs - 4.5in Gap.nec
H20 - 7.07in ZigZags - 3in Stubs - 5.0in Gap.nec

H21 - 7.07in ZigZags - 4in Stubs - 0.5in Gap.nec
H22 - 7.07in ZigZags - 4in Stubs - 1.0in Gap.nec
H23 - 7.07in ZigZags - 4in Stubs - 1.5in Gap.nec
H24 - 7.07in ZigZags - 4in Stubs - 2.0in Gap.nec
H25 - 7.07in ZigZags - 4in Stubs - 2.5in Gap.nec
H26 - 7.07in ZigZags - 4in Stubs - 3.0in Gap.nec
H27 - 7.07in ZigZags - 4in Stubs - 3.5in Gap.nec
H28 - 7.07in ZigZags - 4in Stubs - 4.0in Gap.nec
H29 - 7.07in ZigZags - 4in Stubs - 4.5in Gap.nec
H30 - 7.07in ZigZags - 4in Stubs - 5.0in Gap.nec

H31 - 7.07in ZigZags - 5in Stubs - 0.5in Gap.nec
H32 - 7.07in ZigZags - 5in Stubs - 1.0in Gap.nec
H33 - 7.07in ZigZags - 5in Stubs - 1.5in Gap.nec
H34 - 7.07in ZigZags - 5in Stubs - 2.0in Gap.nec
H35 - 7.07in ZigZags - 5in Stubs - 2.5in Gap.nec
H36 - 7.07in ZigZags - 5in Stubs - 3.0in Gap.nec
H37 - 7.07in ZigZags - 5in Stubs - 3.5in Gap.nec
H38 - 7.07in ZigZags - 5in Stubs - 4.0in Gap.nec
H39 - 7.07in ZigZags - 5in Stubs - 4.5in Gap.nec
H40 - 7.07in ZigZags - 5in Stubs - 5.0in Gap.nec

H41 - 7.07in ZigZags - 6in Stubs - 0.5in Gap.nec
H42 - 7.07in ZigZags - 6in Stubs - 1.0in Gap.nec
H43 - 7.07in ZigZags - 6in Stubs - 1.5in Gap.nec
H44 - 7.07in ZigZags - 6in Stubs - 2.0in Gap.nec
H45 - 7.07in ZigZags - 6in Stubs - 2.5in Gap.nec
H46 - 7.07in ZigZags - 6in Stubs - 3.0in Gap.nec
H47 - 7.07in ZigZags - 6in Stubs - 3.5in Gap.nec
H48 - 7.07in ZigZags - 6in Stubs - 4.0in Gap.nec
H49 - 7.07in ZigZags - 6in Stubs - 4.5in Gap.nec
H50 - 7.07in ZigZags - 6in Stubs - 5.0in Gap.nec

H51 - 7.07in ZigZags - 7in Stubs - 0.5in Gap.nec
H52 - 7.07in ZigZags - 7in Stubs - 1.0in Gap.nec
H53 - 7.07in ZigZags - 7in Stubs - 1.5in Gap.nec
H54 - 7.07in ZigZags - 7in Stubs - 2.0in Gap.nec
H55 - 7.07in ZigZags - 7in Stubs - 2.5in Gap.nec
H56 - 7.07in ZigZags - 7in Stubs - 3.0in Gap.nec
H57 - 7.07in ZigZags - 7in Stubs - 3.5in Gap.nec
H58 - 7.07in ZigZags - 7in Stubs - 4.0in Gap.nec
H59 - 7.07in ZigZags - 7in Stubs - 4.5in Gap.nec
H60 - 7.07in ZigZags - 7in Stubs - 5.0in Gap.nec

A ZIP file named "Exp 01 Revisited - Antenna Geometry Files.ZIP" in the Yahoo group "AntennaModelingExperiments" contains these files. The URL is http://groups.yahoo.com/group/AntennaModelingExperiments/files/Gray%20Hoverman%20Designs/Experiment%2001%20-%20Revisited/Antenna%20Geometry%20Files/

These files can also be generated by editing the SY cards containing the Stub (S) and Feed Point Gap (FPG) variables in the following listing:


CM Driver Assembly for a Gray Hoverman Antenna (6 Gage Wire)
CM Reflector Not Included
CM 7.07 inch Zig Zags, 6.0 inch Stubs, 4.0 inch Feed Point Gap
CM All linear measurements below are expressed in inches
CM All angular measurements below are expressed in degrees
CE
SY Z = 7.07107 'Zig Zag Element's Length in Inches
SY S = 6.0 'Stub Element's Length in Inches
SY FPG = 4.0 'Feed Point Gap in Inches
SY WR = 0.081011 'Wire Radius in Inches
SY ZW = Z*cos(45) 'Zig Zag Element's Width in Inches
SY ZH = Z*sin(45) 'Zig Zag Element's Height in Inches
GW 1 21 0 (FPG/2)+ZW 3*ZH 0 (FPG/2)+ZW+S 3*ZH WR
GW 2 21 0 FPG/2 2*ZH 0 (FPG/2)+ZW 3*ZH WR
GW 3 21 0 (FPG/2)+ZW ZH 0 FPG/2 2*ZH WR
GW 4 21 0 FPG/2 0 0 (FPG/2)+ZW ZH WR
GW 5 21 0 FPG/2 0 0 (FPG/2)+ZW -ZH WR
GW 6 21 0 (FPG/2)+ZW -ZH 0 FPG/2 -2*ZH WR
GW 7 21 0 FPG/2 -2*ZH 0 (FPG/2)+ZW -3*ZH WR
GW 8 21 0 (FPG/2)+ZW -3*ZH 0 (FPG/2)+ZW+S -3*ZH WR
GW 9 21 0 -((FPG/2)+ZW) 3*ZH 0 -((FPG/2)+ZW+S) 3*ZH WR
GW 10 21 0 -(FPG/2) 2*ZH 0 -((FPG/2)+ZW) 3*ZH WR
GW 11 21 0 -((FPG/2)+ZW) ZH 0 -(FPG/2) 2*ZH WR
GW 12 21 0 -(FPG/2) 0 0 -((FPG/2)+ZW) ZH WR
GW 13 21 0 -(FPG/2) 0 0 -((FPG/2)+ZW) -ZH WR
GW 14 21 0 -((FPG/2)+ZW) -ZH 0 -(FPG/2) -2*ZH WR
GW 15 21 0 -(FPG/2) -2*ZH 0 -((FPG/2)+ZW) -3*ZH WR
GW 16 21 0 -((FPG/2)+ZW) -3*ZH 0 -((FPG/2)+ZW+S) -3*ZH WR
GW 17 13 0 -FPG/2 0 0 FPG/2 0 WR
GS 0 0 0.0254
GE 0
GN -1
EK
EX 0 17 7 0 1 0
FR 0 0 0 0 585 0
EN


A horizontal frequency sweep was produced for each of the above NEC files using 4nec2’s Generate (F7) function. The following parameters were used: Resolution: 5 degrees; Frequency Start: 473 MHz; Frequency Stop: 695 MHz; Frequency Step: 6 MHz; Forward Theta: 90 degrees; Forward Phi: 0 degrees; Forward delta-Phi: 5 degrees; Backward Theta: 90 degrees; Backward Phi: 180 degrees; and Backward delta-Phi: 5 degrees. The 473 to 695 MHz range with steps of 6 MHz was selected to produce points which fell in the center frequencies of each UHF channel from 14 through 51.

As each frequency sweep was completed, “Standing Wave Ratio” (S W R), “Raw Gain” (Forw-gain), “Real Impedance” (R-in (real)) and “Imaginary Impedance” (X-in (imag)) data were transferred to Excel worksheets for calculating the “Net Gain” and plotting the “Net Gain”, “Raw Gain” and “Standing Wave Ratio” data.

At http://www.digitalhome.ca/forum/showthread.php?t=83772&page=7 , Post 101, you will find a procedure for transferring the data and calculating the “Net Gain” data. This manual method can be used to build the “Net Gain”, “Raw Gain” and “Standing Wave Ratio” plots for a small number of models, but it is mind numbing, error prone and woefully inadequate for comparing more than twenty models. A utility to parse the NEC2 engine’s output file and build a table similar to the procedure results noted above would be very helpful.

Results and Conclusions:

The “Net Gain”, “Raw Gain” and “Standing Wave Ratio” vs. Channel plots for each family grouping are shown below:

H01 – H10 Family, 7.07 inch Zig Zags, 2 inch Stubs:











Please Continue At... GH Driver Array - Modeling Experiments - Part 5
 

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GH Driver Array - Modeling Experiments - Part 9

Experiment #1 (Revisited) Continued (Last Page)

H51 – H60 Family, 7.07 inch Zig Zags, 7 inch Stubs:











Note the vertical scales on the “Net and Raw Horizontal Gain” plots. They all run from 5 to 12 dBi to provide better separation between the curves. This was especially appropriate for the H41 – H50 and the H51 – H60 families. Their “Raw Horizontal Gain” curves almost blurred together using the more traditional scale of 0 to 12 dBi.

In Experiment 1, for a Gray Hoverman Driver Array with zigzag element lengths in the 7 inch neighborhood and with stub element lengths in the 3 to 6 inch range, it appeared that the feed point gaps between 0.5 and 3.0 inches had very little affect on the “Raw Horizontal Gain” across the UHF DTV band. The big picture is not nearly so clear after accounting for the mismatched impedance losses as seen in the “Net Horizontal Gain” plots.

The “Standing Wave Ratio” plots are confusing at first sight. For a perfect model, the curve would be a flat line with SWR values equal to 1 across all frequencies of interest. Models with SWR values between 1 and 2 have only modest signal losses due to impedance mismatches. Models with SWR data between 2 and 3 have higher signal losses due to impedance mismatches, but may still prove to be useful models. Models with SWR values greater than 3 need to be improved. In this study, the better SWR plots seem to be those that oscillate slightly between SWR values of 1.5 and 2.5, for example the H41 – H50 family with feed point gaps in the 2.5 inch to 5.0 inch range. The H51 – H60 family also looks promising over this range. Unfortunately, its “Horizontal Gain” plots both fall off rapidly for channels above 45.

Feed point gap distances certainly have a larger impact on “Net Gain” than one might expect from looking at only the “Raw Gain” plots. Unfortunately, 4NEC2 does not directly provide a “Net Gain” option. The end user can get a warm fuzzy feeling about a particular model without calculating and plotting the “Net Gain” data by looking at both the “Standing Wave Ratio” and “Raw Gain” plots. One search strategy for promising models might be to look for models with the lowest “Standing Wave Ratio” values and the highest “Raw Gain” across the frequencies of interest. Then, after finding an interesting neighborhood, calculate and plot the “Net Gain” to get a better picture of the expected performance.

Your encouragement, comments and suggestions are always appreciated.

Thank you,
DTV Student
 

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A few "concept" questions...
The antenna is located at Y = 0. Is the TV station assumed to be in the "plus Y" or "minus Y" direction?

No, "Y" is your left and right by convention. The TV station assumed to be in the "plus X" or "minus X" direction by convention. And Z is up and down.

Are there any "standard numbers" to use for the UHF TV band assuming co-ax cable? I'm talking stuff like
default voltage-source - Leave at default values, its for transmitting. (but some number is required for input)

wire-conductivity - Depends on what metal type youre using, the LD card type 5 is the input for it. The 4nec2 help file has various types of metals listed in the reference section. Also when choosing the LD card in the NEC editor, there is a drop down box.

load - Leave at default, also for transmitting. (but some number is required for input)


impedance - Set Characteristic Impedance in Settings to 300 ohms for TV antennas.

diameter/radius - Depends on what your using, the GW "wire description card" is its input. Can also be entered in Geometry Edit.

"speed of electricity" in a wire (as a fraction of "c") - Velocity factor. Also taken care of in LD card type 5 for the antenna wire when metal type is specified.

And for transmission line velocity factors, thats specified if and when you want to custom model it for your home, not really necessary for basic antenna design. Common tv coax is 75 ohms, twin lead is 300 ohms. The specific cable manufacturer is the best place to get exact velocity factor numbers, but general numbers can be found by googling or looking in the Channel Master catalog under RG6, RG6 Quad, RG59, 300 ohm twin lead types.

ground, etc, etc - Model in "free space" environment, GN card, -1 type. Near ground effects are mainly going to apply for transmission, I believe. Near ground types and effects absord the radiated power of many watts in transmission, whereas in receiving we're dealing in tiny micro-volts by the time the signal gets here.

I dont understand your problem with Notepad. Are you saying you cant cut and paste ?
 
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