# Formula to calculat e Feedline length

Discussion in 'Antennas, Feedlines, Towers & Rotors' started by AB2UI, Jul 3, 2012.

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1. ### AB2UIGuest

I have searched in a number of places and I am seeing answers that contradict each other. What I am looking for is a simple formula to calculate the optimum length of 300 ohm ladder line to a dipole. I have seen some sites saying the feed-line should be a 1/2 wavelength of your dipole (not sure how to calculate that if the dipole is used for multiple bands) then I read a website that said that the feed-line length must never be equal to 1/2 wavelength of the frequency the dipole is cut for.

So, with that said, can anyone please provide me with a formula so I can redo the feed-line length's to my two dipoles and get the optimal length so it is an easy match for my tuner and I do not have huge losses in the cable.

At this point my ladder line terminates into two baluns outside of my house then there is a 50' or so run of coax to my radio. I am thinking of running the ladder-line through the sill of my basement window and run the ladder line through the basement, through a hole in the floor and then place the balun within a foot or two from my rig.

Also, if someone can provide me with a formula to calculate loss in the feed-line that can be used for both ladder line and coax. It's OK, if the formulas are a bit complex as long as all the variables to enter into the formula are clearly defined.

This would be a huge help to me.

P.S. If I'm only putting out 100 watts and I do end up running the ladder line along the rafters in the roof of my antenna, will I have any issues of RF interference inside of the house? This has always been my main concern and is the reason I always left he baluns outside and ran coax into the house to the rig.

Thanks,

2. ### PD7MAAHam MemberQRZ Page

There is a French prog. named Levy that showes the antenna length and the feedline in cm.
http://sites.estvideo.net/f5imv/levy.html
Works fine
Shows also the radiation patern.One dipole leg is on the left so the feeder is on the right side.

have fun
John

Last edited: Jul 3, 2012
3. ### N9XVHam MemberQRZ Page

The idea of "optimum length" is based on the principle of a 1/2-wave length of transmission line's ability to "mirror" the antenna impedance back to the input end of the line at whatever the resonant frequency is. For a multiband dipole fed with a single transmission line, the "usefulness" of this principle falls away because the impedance of the antenna will range according to the frequency applied to it.

You said your feedline terminates into two baluns, and then to a single run of coax? Why two baluns?

The "usefulness" of ladder line does come into play here because at HF ladder line is for all "practical" purposes lossless.

With coax, you can determine the matched feedline loss. Then take into account additional loss due to swr. Bam! there's a snapshot of what the coax is doing. Do the same thing for the ladder line, and there's a snapshot of what the ladder line is doing. All of this is only relative to a specified frequency! For a resonant antenna operating at a single specified frequency, the calculations aren't too difficult.

Thankfully, W2DU has done a spectacular job of laying it out for us,

IN LINE DUE TO REFLECTIONS AND SWR

and

POWER RELATIONSHIPS ON MISMATCHED
TRANSMISSION LINES

Find anything this gentleman ever wrote and study it dutifully!!!

For any of this to truly "mean" ANYTHING, you would need to know the impedance of your antenna. The only real way to know that is with an analyzer. The antenna analyzer looks at the phase angle between voltage & current at the point where it's inserted. Which is why a 1/2-wavelength transmission line can be useful when analyzing the antenna, it will mirror the antenna impedance back to the analyzer and allow you "harness" the magnitude of antenna impedance. It's resistive & reactive component and the associated phase angle. Of course this all changes with frequency. Eventually you reach a point (when changing the frequency) where the 1/2-wavelength line is no longer a 1/2-wavelength and it's ability to mirror the impedance falls away! Also, too many multiples of a 1/2-wavelength line will mush or "washout" the mirroring effect. I've modeled this in TLdetails and it seems around 10 multiples or so, the mirroring effect is just about nil.

There are some really great transmission line programs out there, and the one I like best is from AC6LA,

TLdetails

with his program you can enter exact antenna impedance (your analyzed value), and choose a multitude of feedline and shave lengths down to fractions of an inch and impedances down to within an ohm etc. It's really worth the time investment to get comfortable with this program as if your using a simple calculator.

The fact that ladder line (parallel feedlines etc) is nearly lossless at HF, allows it to more efficiently re-radiate the reflected energy due to the SWR. The ladder line allows you to "approach" the condition of NO losses due to additional losses in the feedline. ALL of the reflected energy WOULD be re-radiated if not for the losses in the feedline as the energy travels back and forth between antenna and transmitter.
SWR does absolutely no harm to the transmitter, it's the phase angle or "de-tuning" of the final amplifier stage. The PA stage tries to deliver too much current when not enough voltage is there to produce it!

For a multiband antenna, you COULD have multiple "ideal lengths" for multiple frequencies Vs multiple impedances corresponding to all of this, but as you can see - it;s simply not practical or necessary. Just use the ladderline & balun as you are. Be sure your using a good broadband balun. The tuner will tune it, add coffee and enjoy!

Running ladder line along the rafters shouldn't be an issue as long as they are not near metal. I would still "stand them off" if you can to minimize humidity & moisture effects. Long term heat effects might be a bigger concern. My underside of my roof deck (upper attic area near rafters) easily reaches 130 to 140 degrees F in the peak of summer! A few years of that would truly put the ladder line to the test insulation wise anyway!

Kevin

Last edited: Jul 3, 2012
4. ### G3TXQHam MemberQRZ Page

Does anyone know which of the various TL programs has a good model for 300 Ohm ladderline?

Steve G3TXQ

5. ### N9XVHam MemberQRZ Page

TLdetails does, and you can even create your own feedline.

6. ### W5DXPHam MemberQRZ Page

The work that I have done on this subject is based on parallel feedlines (twinlead, ladder-line, and open-wire). I used EZNEC to generate the information and the feedlines in EZNEC are assumed to be lossless. The optimum feedpoint impedance is assumed to be at a current maximum, low impedance point, which is not necessarily the lowest loss point but is the point that will give the lowest SWR without a tuner. Lengths that are close to that point will usually work with internal autotuners. Here is that graph generated from EZNEC based on the length in WL of the dipole and feedline:

http://www.w5dxp.com/majic.gif

As one can see, the relationship is not linear. I came up with a curve-fitted formula for this relationship and it is available in BASIC for download on this web page.

The feedline wavelength formula, curve-fitted to EZNEC results is:

fedlinwl = .25 - (TAN(2.5 * (dipwl - 1))) / 12.02

Where the dipole wavelength (dipwl) is normalized between 0.5WL and 1.5WL.

Also available on that page is a graphic, IMAXGRAF.EXE, that will allow one to change the length of the dipole while displaying the optimum lengths of feedline up to 150' for single frequencies in each phone band. That DOS program will run under XP but requires DOSBox for later versions of Windows. I have updated that program for my own use. The new update calculates the optimum lengths for both band edges so the display is somewhat busy with twice the number of dots. For what its worth, the harder to read but with more information version is available at:

http://www.w5dxp.com/IMAXGRA2.EXE

If anyone chooses to use this version, let me know what you think. Here's an example of the IMAXGRAF.EXE display screen for a ZS6BKW 90' antenna. Note the grouping of current maximum points around a ladder-line length of 40'.

File size:
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7. ### K8JDHam MemberQRZ Page

According to this diagram My 90 ft dipole with 50 ft of 300 ohm line (length in package I had) should work best on 15M but I never have been able to make a contact on 15M, it works best, for me, on 40/30/20M ! WHY?

http://www.w5dxp.com/IMAXGRA2.EXE
If anyone chooses to use this version, let me know what you think. Here's an example of the IMAXGRAF.EXE display screen for a ZS6BKW 90' antenna. Note the grouping of current maximum points around a ladder-line length of 40'.[/QUOTE]

8. ### G3TXQHam MemberQRZ Page

I don't see 300 Ohm ladderline as an option in my version 2.0 of TLDetails; I see "Generic 300 ohm tubular", but that's a quite different "animal".

Yes I can enter a bespoke cable, but where are the parameters for 300 Ohm ladderline? I've not been able to find any.

Steve G3TXQ

9. ### WB2UAQHam MemberQRZ Page

Steve,
I measured the Zo of various samples of 300 twin lead. The stuff is not well controlled. The Zo I measured (determined) was from 230 ohms to close to 300 ohms. Maybe this is the reason why TL has no characteristics for generic 300 Ohm line. The worst case was "300" ohm line from JSC. It is pretty tough but is was at about 230 ohms. I am using it since last November and it is has held up well scrapping against tree branches as it has a thick ribbon of insulation and heavier guage stranded copper. I use the pulse gen, scope and small variable resistor method to determine Zo. I found it to be the best method as I don't need to worry about baluns and their impact on measurements when using unbalanced test equipment (my equip is ancient bridges of various types). 73, Pete

10. ### W5DXPHam MemberQRZ Page

Google the MUF (maximum useable frequency). We have been in the low of the sunspot cycle headed for a high so 21 MHz, in the recent past, has been above the MUF. But the best is yet to come.

http://en.wikipedia.org/wiki/Maximum_usable_frequency

11. ### W5DXPHam MemberQRZ Page

I've used it for years. As far as I can tell, its VF is closer to 0.8 than it is to 0.9 and its Z0 is about 280 ohms. If someone wants to test 1/2WL at a certain frequency, that should be a relatively easy thing to do with an MFJ-259B.

12. ### N9XVHam MemberQRZ Page

You can "set" the desired parameters in the User Defined option 1, 2 and 3.

13. ### G3TXQHam MemberQRZ Page

The 300 Ohm cable I have here works out to have a matched loss of 0.7dB/100ft@30MHz - marginally worse than a good quality coax like LMR400; and that's when it's dry. Yet we continue to hear that "ladderline is virtually lossless at HF"

I can do most of the measurements myself, but being lazy was hoping that someone might have a full set of parameters that would plug into TLDetail, or Owen's (VK1OD) calculator.

73,
Steve G3TXQ

14. ### G3TXQHam MemberQRZ Page

Of course - so, what are K0, K1 and K2 for a commercial 300 Ohm ladderline?

73,
Steve G3TXQ

15. ### G3TXQHam MemberQRZ Page

Duplicate post

16. ### AB2UIGuest

I have the MFJ to analyze the SWR of the antenna but I have been told by fellow hams that it will not be accurate trying to do any measurements against an EDZ for 20 M since the antenna is not truly resonant at 20 M. (as opposed to cutting a dipole exactly for 14.100 Mjz for example and feeding it directly with 50 ohm coax.

17. ### N9XVHam MemberQRZ Page

From the website ac6la.com,

(K0 is associated with the DC resistance of the conductors which is a constant for any given line type. K1 is associated with the "skin effect" or "high frequency" resistance of the conductors which varies in proportion to the square root of frequency. K2 is associated with the dielectric loss which varies directly with frequency.)

The analyzer should be accurate for the given scenario.

At a specified frequency, the antenna impedance is x, the resistive component is x, the reactive component is x. The SWR is whatever it is for that set of data. An analyzer that only analyzes resonant antennas isn't much of an analyzer. As long as your working within the given limits of the instrument, there shouldn't be any question of accuracy.

The matched loss is a different animal than additional loss due to SWR, particularly high SWR as would be expected from a "multi-band" antenna fed with a single feedline. That's where the "fork in the road" is between the two types of lines. A better choice would be a 600-ohm line with even greater efficiency regarding the SWR loss dilemma. The parallel feedline out performs the coax when SWR (high SWR) comes into play. Two parallel #12 wires about 6-inches apart is the best way to single-feed a multiband antenna as far as the SWR losses are concerned. It gets back to what is the goal of the antenna, relatively simple multi-band operation that's reasonably efficient? Or, the absolute perfectly resonant antenna with an exact impedance match with no reactive component and highly efficient? The latter WILL likely happen at one particular frequency!

18. ### W5DXPHam MemberQRZ Page

Maybe LMR400 is also "virtually lossless" at HF compared to RG58?

19. ### N9XVHam MemberQRZ Page

Well I guess he didn't like the answers he was getting here, he started another thread with the exact same question

20. ### G3TXQHam MemberQRZ Page

It's interesting to "unpick" why ladderline losses tend to be lower than coax losses when feeding a multiband doublet.

At HF, feedline losses are almost entirely "copper losses" and therefore are dependent on the wire's RF resistance and the current it is flowing. The centre conductor and braid of a coax like RG213 have similar RF resistance to a couple of #12 wires, so that's not the explanation. What changes dramatically between coax and ladderline in this application is the current flowing, and that's largely a function of the Zo of the line.

If we assume the feedpoint impedance of a doublet might vary from as little as 50 Ohms to as much as 4000 Ohms on the different bands, choosing a Zo of SQRT(50*4000)=447Ohms limits the SWR excursions to 9:1 at worst; but using 50Ohm coax gives us SWRs ranging from 1:1 to 80:1.

So, it's not so much that coax is worse than ladderline at handling high SWR; it's that the coax's Zo is not well "matched" to the range of impedances presented by the doublet, and consequently the range of SWRs is much greater.

Steve G3TXQ