To preemptively dispel any of the common misunderstandings, here are a few facts about the 3 wire dipole:
1) It is not a fan dipole, or a fat dipole. It is not a linear loaded dipole, a "cobra," or a "cage" dipole.
2) The feedline does not radiate in any manner similar to a G5RV.
3) The feedline does not radiate because it is balanced and feeds a balanced load.
4) There is negligible mismatch between the load and the feed.
5) A 1:1 balun at the feed point is unnecessary and an improper choice of baluns.
6) It's not a loop antenna. So a 75 ohm coax matching section is just plain wrong.
7) It is not, and can not be fed directly with coax. If it were there would be a 9:1 or 12:1 mismatch at the antennas natural resonant frequency which would be a disaster. (Unless you've got some 450ohm coax laying around!)
Now that we know what math validates our real world experience, we can see that a folded dipole isn't necessarily confined to 2 wires, a 3 works too. What about 4? Lets modify our formula again remembering to account for the concept we validated: "by a factor of the number of wires"
Feeding a 4 wire dipole with 450 ohm ladder line, we modify our formula to: Za=16Zt*Zd over Zt+4Zd
Working this formula gives you the values 518400 from the top and 738 from the bottom. 518400/738=702 ohms.
In a perfect world, when divided by the 50 ohms your radio expects to see, a 14:1 balun and presents almost exactly 50 ohm match to your radio. But good luck finding such an animal. A 16:1 balun though, still gives the radio 44 ohms of impedance, for an SWR of better than 1.3:1 and is likely your best commercially available option.
A 5 wire version would work too. Just modify the formula to Za=25Zt*Zd over Zt+5Zd, To save you the effort: You'll need a 20:1 transformer balun.
You may have noticed feed line impedance is a factor in our formula. What happens to our multi-wire folded dipoles if we use 600 ohm feed line? Using our new found knowledge, lets do the math!
For the 3 wire, only this time using 600 ohm feed:
9Zt*Zd over Zt+3Zd
(600*3 to the 3rd)*72=388800
388800/816=476 ohms in free space.
476 ohms at resonance is not the best possible match to 600 ohm feed line in free space, but still presents very passable SWR better than 1.5:1.
The 4 wire version, using the 600 ohm feed:
16Zt*Zd over Zt+4Zd
(600*4 to the 4th)*72=691200
691200/816=847 ohms...still a passable match for a 16:1 transformer balun.
Since 847/50=16.9 a 16.9:1 balun would be ideal, but there is no such thing and dipoles aren't quite 72 ohms in real life. In reality, the difference comes out as nearly negligible.
There is good news! The impedance changes with respect to near by objects...of chief concern here, the ground. At 1/8 wavelength in elevation the ~440 ohm 3 wire version in practice becomes much closer to 375 ohms. So, why not feed it with 1/8th wavelength of 600 ohm feed and a 9:1 balun? 375/9=A perfectly respectable 42 ohm match to your radio. This may be the best option for those of us obsessed with the best possible match, but can't get a 40 meter 3 wire up higher than 60 feet.
Simply put: mismatch matters. All that power has to go somewhere. The worse the SWR is, the less that power radiates as RF and the more it leaves the system in some way or another, mostly in the form of heat, either in the feed line or the tuner or in the tuner by canceling reactance in some way, not as RF at the antenna like we want. Yes, it is true that when the wave returns from the end of the wire it sees the finals of your radio as simply another end of the wire and heads back the other direction back up the wire again for another chance at being radiated like we want, but much of it is lost with each pass up and down the system. This is not new and 100% of the power eventually does go somewhere. The question is where and how much of it gets there?
Antenna tuners are a good solution to always running your radio with in it's design parameters at just about any frequency you wish to operate, especially the automatic kind if protecting the radio is of primary concern. Good solution right? Protect the radio and operate on any and all bands! SWEET! This magic box really isn't magic. Though it is a novel solution for part of the problem, it's not a cure-all. The problem with them is they don't tune the antenna, they tune the antenna system. That high mismatch is still present and the waves of energy still go back and forth from end. No big deal right? Except that the tuner brings everything in line by dissipating a significant portion of the returned energy in any form possible that is not the RF that we want. It does this in order to fool the radio. The higher the mismatch apparent at the tuner, the more energy leaves as "other" from that magic box every time that RF wave turns around and heads back up the wire for another try at being your next DX contact. To get a "good" SWR with a tuner you could easily put 100 watts from your radio into your antenna system only to lose 60, 70, 80, or 99.9(!) watts before the rf leaves the shack. Yes you can work different bands safely now, but at what cost?
Tuners are part of the solution to getting a good match between the radio and the antenna system, but not the solution.
Mismatch in the antenna system matters because energy can not be created or destroyed, it can only change forms. So why not conserve it by transforming it to what you need to start with, thereby reducing the mismatch? Minus the 9:1 transformer balun for the 450 ohm 3 wire dipole, 64% of the power would be lost in one form or another. The tuner would have to get rid of 64% of the power in system to make the SWR appear good at the radio. Now take that tuner and move off the band you designed the antenna/feed system for...Full power into a 10,000 ohm load! Yikes! The mismatch is still there...unless we transform it.
A balun of the proper ratio minimizes losses period.
Hand in hand with minimizing losses, when stepping impedance down, transformation baluns make the job of the tuner easier by reducing the mismatch it has to work with to effect a match. This is why the 4:1 current balun is the most common, It effectively expands the range of the tuner by transforming the mismatch to 1/4 what it would otherwise be with almost no losses in the process but not down so far as to exceed the tuners limits when stepping impedance UP is needed. The 4:1 is just a happy medium and it applies to, and works well with the broadest range of products and possibilities...and it's a little vanilla. (But, I like vanilla!)
Check this out though, (and this is what I was working up to) by knowing what the actual mismatch is on each band for your given antenna system at the point you intend to feed it from, you can choose different baluns of different ratios to transform the impedance up, or down as needed to keep more of that power on the feed line/antenna where it will do the most good. Feeding your antenna with a properly installed run of ladder line is an excellent choice in this regard, losses will be negligible even against tremendous mismatch. Coax tends to be "lossy" under high SWR conditions. Reputable balun manufacturers recommend not using it in conditions exceeding 5:1 SWR. (DX Engineering) That may be overly cautious, nevertheless, choosing to use the minimum amount necessary of the highest quality you can afford in the lowest SWR portion of your system would be a smart choice.
I do not mean to imply that coax is "bad" in any way, just that coax and ladder line have different properties to consider in both use and installation. Placing the best coax you can afford between the radio or tuner and the balun is the best place. The reason for this is the SWR swings will be least (stepped down by some ratio, remember), and by it's very nature it will be least susceptible to the influence of nearby equipment. It simply just is a better choice for use on the shack side of the system. While the ability to reject locally generated noise, and tolerate high power, high SWR, while having low losses and there is little to upset the balanced nature, makes ladder line the best choice for the bulk of your system outside the shack.
Minimizing the load/loss on the tuner to virtually nil, could be easy if not for the added expense of more equipment outside the window of the shack and things to switch around with every band change.
In radio, as with elsewhere, nothing is free. Your antenna will still be the wrong size to work as good as it could, when driven far from it's design, but intentionally transforming the impedance to minimize losses at the tuner is a good thing and a step in the right direction towards a better more effective shack. Many HAMS already do this with a 4:1 and generic dipoles and give it little thought and work all bands all over the world. With a little more thought they might also remember they are not chained to the trusty 4:1 and their losses could be less.
Baluns do indeed have loss, but not nearly like that of inductor coils at the antenna and the loss is only in that a balun is a real world device that must connect with your antenna system with a connector of some sort. Losses in the balun itself can only be considered as negligible in comparison to the 9 or 12 or 16 or 25 fold reduction in mismatch that must otherwise be dissipated.
In short, SWR is an indication of all system losses as measured at a specific point, usually at the radio. Mismatch refers only to the antenna side of the system to the feed point discounting any transformation methods. Mismatch matters and a folded dipole of any variety needs a transformer balun to normalize the impedance mismatch to that of a standard dipole. The radio expects to see a 50 ohm resistive load and it is best to meet this requirement as nearly as possible on the frequency you intend to drive the antenna before you even consider adding a tuner to the system to fine tune the SWR.
Folded dipoles of any variety do not work on even harmonics of the design frequency. Nor do they work on the 2nd fundamental. The electric/magnetic fields tend to cancel each other out. A folded dipole of around 16-16 .5 megahertz will present a nearly a 0/infinity ohm load around 4mhz (80 meters) and similarly a 0/infinity ohm load around 32-ish megahertz (and every other even harmonic). The upside is the SWR will be flat enough it will work 17, and 20 meter bands just nearly perfectly and the 3rd harmonic, 6 meters also with very little effort.
It is a multi-wire folded dipole! At it's natural resonant frequency a 3 wire folded dipole represents approximately a 450-600ohm load depending on wavelengths in elevation. Making a near perfect 1:1 match to either 450 or 600 ohm feedline, which is then transformed with either a 9 or 12:1 balun for direct feed to the radio. For just the same reasons as you would use a 4:1 or 6:1 transformer balun and t.v. twin lead for a standard 300 ohm folded dipole.
To describe the behavior of the "power formula" as it applies to the regular folded dipole the formula Za=Zt*Zd overZt+2Zd fits the bill and is well available from all regular folded dipole sources.
Za= Antenna impedance
Zt= Transmission line impedance
Zd= Dipole impedance
With the 3 wire folded dipole though, to validate our presumption that impedance changes by a factor of the number of wires is the determining factor we can change the well known formula to account for the 3rd wire. We change it so the formula becomes: Za=9Zt*Zd over Zt+3Zd.
In the top portion of the equation, per our assumption we modify the top to 450*3 to the 3rd * 72. (The 450 came from the impedance value of the feed line we intend to use.) And like the standard folded dipole, on the bottom of the equation, we modify it to, the 450 ohm ladder line and the 72 ohm dipole accounted for the number of times it is present in the design. In this case, 3 times on account of 3 wires in this design.
For a 3 wire, multiwire folded dipole in freespace this formula gives 429.5 ohms at resonance. Which is very close to real world empirical data.
It's not magic, it's just not common...and it works REALLY well.
To understand why the impedance of a regular folded dipole changes, we must first understand how the impedance of a regular dipole works. To do this we must take a look at the "power formula" found in any electrical study book.
P=(I*I) * R, this can be rewritten as R = P / (I*I).
Let's say you were to key your radio and try to put 100 watts to any standard dipole and the current was 1.2 amps, solving for resistance would be as simple as R = 100 / (1.2*1.2), which is the same as R = 100 / 1.44, which is 69.44 ohms. Math is math and we just discovered what we already knew; the standard dipole is about 70 ohms.
In the folded dipole, however the wires are in parallel and the current must be divided equally between the two wires of each half. The total current in each half hasn't changed and and the total power has not changed, so what does change?
All things being equal the resistance is the only thing that can change. Since we have 2x the wires on each half, the current must be half on each wire of the original 1 wire design and the resistance must double for each segment of each half for a total change of 4 times the original. From this, we can infer that the impedance changes by a factor of the number of wires.
The formula now is Resistance = 100watts / (.6*.6). The ".6" being half the current in each wire of the standard common dipole design. This is the same as R = 100 /.36, which of course is a resistance of 277.77 ohms, 4 times the total resistance normal dipole antenna. Our presumption seems correct.
The simple answer is efficiency.
The longer answer: Efficiency is a ratio. Efficiency is radiated power divided by input power.
It will always be less than 100% for all antennas. For omnidirectional antennas this is simple, but for directional (gain) antennas it will exceed 100 percent in the direction of radiation. This number will be counteracted in directions of non-radiation (the nulls in your radiation pattern) but efficiency is nevertheless an antennas most important characteristic and can never exceed 100% in total. The less "ideally" sized the antenna the more inefficient an antenna will be compared to one that is nominally sized.
Efficiency is only nebulously related to "resonance" in that impedance mismatch is one of it's effects. "Efficiency" and a "good match" are frequently confused terms shrouded in mystery. As an extreme but possible real world scenario: Operating on 160 meters while mobile may be possible, the system may be said to be "resonant" a perfect 1:1 SWR (A good match, wo-hoo!) It can be done with out a tuner even, given loading coils, resistors, a capacity hat and healthy dose of voodoo, but the antenna itself will radiate virtually nothing. It is inefficient. A tiny fraction of a watt effective radiated power would be a reasonable expectation…
To explain this: the total efficiency (Et) of an antenna equals the loss due to impedance mismatch (Ml) times the antennas radiation efficiency (Er), (from the equation above, which in turn is dependent on radiation resistance, reactance and conductivity of the material the antenna is made from.) For now, efficiency=
Et=Ml * Er
A good properly sized antenna in free space can be nearly 100% efficient, radiating nearly 100% of it's power in the form of RF and reflecting almost 0 energy back at the source. The ideal 1.0:1! Sadly though such a thing is not possible due to conductivity losses is real world material, and anything near by the radiator that may absorb RF. Real world antennas with compromises, can usually achieve ~80-90% efficiency quite easily. Quite a bit more given ideal circumstances. It is the rest of the system, the losses on the reflected power (losses going up the feed line to the antenna, and an equal loss coming back), in combination with what is actually radiated, and what we intentionally get rid of that can makes it seem like we have a good theoretical 100% perfect match.
The efficiency of the antenna itself specifically here is what I'm talking about. Due to the impedance mismatch in the radiator you have caused by design considerations (read: compromises,) an undersized, improperly oriented, and/or poorly located antenna can easily be down 20 db for an efficiency of 1%! It's no wonder you need a matching network to do "something" with all this "antenna unhappiness." Actual system efficiency can only go down from here depending how we deal with the mismatch.
Each element of an antenna can be considered as a resistor of a a certain value at a given frequency. When designing a center fed dipole antenna, the builder usually shoots for a value of about 70 ohms. This value is variable depending on how far from the center it is fed, but that is beside the point. In an electrical circuit, the value of resistors in series combine lowering current and increasing losses in a commutative manner, resistors in parallel are distributive in nature. Trap dipoles are constructed as resistors in series, each trap, connection and wire segment. However well designed and constructed, the losses add with each additional set of components. It follows then that 2,3,4,5 or however many resistors we chose, constructed in parallel, the current and resistive resistance will divide and associated losses will decrease. All things being equal, as the antennas impedance increases by a factor of the number of wires, the radiation resistance for the circuit in total must change accordingly to some equivalent value. Here's the part we care about: MORE WIRES MEANS MORE RADIATION!
A single dipole has a resistive component of about 72 ohms. Two 72 ohm dipoles in parallel have a resistive component of 36 ohms, 3 wires of 24 ohms, 4 wires a resistive component of 18 ohms, and 5 wires, 14.4 ohms. This is the root cause of the changes in the "folded dipole impedance formula." This is also why impedance transformation (normalization at the entrance of the system) becomes such a big deal with the multi-wire dipole, we don't want to lose the efficiency gains made by having a parallel radiation circuit.
Power, current and resistance are all in relation to each other, in RF though resistance is more complex than we might suspect at first due to our association which ohms law and DC circuits. There is a great deal of complicated literature about the subject with supporting math that can be taxing for non-math professionals. In the previous paragraph the values stated are only the resistive component of a more in-depth math problem caused by alternating current that we need to understand before we can simply claim more wires=more radiation.
Radiation resistance, resistance due to losses caused by the conductivity of the material, and either reactance or capacitance of an antenna at a given frequency all must be factored in to our understanding of Ohm's law and how it applies here. Simply stated though, the stronger the input impedance and the less reactance that must be tuned out, the stronger the electromagnetic field will be disturbed and ultimately more power will be radiated. My favorite explanation is here: https://en.wikipedia.org/wiki/Radiation_resistance
Using the Wikipedia explanation P=(I*I)R, and using our example from the beginning of the article, Power is calculated as P=(I*I)*R, 100 email@example.com amps current=1.44*69.44 ohms of resistance.
We can determine the radiation resistance as R =P over (I*I)
For a standard dipole radiation resistance is the same as the resistive component of it's impedance because it is a special situation at a given point. There is no reactance to figure in to the equation. As we go up or down in frequency capacitance or reactance enter into the equation and the simplicity quickly disintegrates. For now though:
For a standard folded dipole at design frequency radiation resistance is 277 ohms 277=100/(.6*.6)
For a 3 wire dipole at design frequency radiation resistance is 625 ohms 625=100/(.4*.4)
For a 4 wire dipole at design frequency radiation resistance is 1111 ohms 1111=100/(.3*.3)
Finally for a 5 wire design at design frequency, radiation resistance is 1736 ohms 1736=100/(.24*.24)
The radiation resistance is only one component of our multi-wire dipole but it is useful to know that as the number of wires increases radiation resistance, and thus antenna efficiency also increases. There is a better connection with the œther.
Links for understanding the math-y end of things when our simplicity has flew the coup feel free to check these links:
If you followed the links provided in the buttons above, this will not be news to you. But for the rest of us: Reactance is imaginary. Reactance or capacitance affect efficiency. Capacitance is caused by an antenna that is too short. Reactance is caused by an antenna that is the wrong size for a given frequency. Also as no surprise, capacitors or inductors can be used to fool an antenna/antenna system into behaving electrically longer or shorter than it really is. The reactance kind of resistance is typically denoted with an uppercase X and is a factor of our total impedance, usually denoted with a capital Z. Fudging the value of either the inductance or reactance by switching capacitors or inductors in to or out of the antenna system is the method by which an antenna tuner operates.
Solving for X (reactance,) is not as complicated as it first seems Z=R+jX
Whereas: Z is impedance
R is the Resistance
X is the Reactance
j is the square root of -1
Working the equation is not exceptionally complicated either. But it can easily be obtained by direct measurement with any antenna analyzer. This being the primary difference between an analyzer and a simple SWR bridge. Both capacitive Xc and inductive Xl figure into total reactance. Given by: X=Xl - Xc
It is worth noting that, though always positive in value Xc always makes a negative contribution to reactance. Adding capacitance will fool your radio into thinking an antenna shorter than it really is as it's value is always less than 0.
The reactance is said to be inductive if, X=>0 as is the case for using a center fed dipole on a frequency longer in wave length than the antenna. Using a 15 meter dipole on 10 meters, for example. There is a lot of inductance there drawing current from your radio. Capacitance must be added to cancel out the inductance and is easily done so by simply adding a variable capacitor at the feed point.
If there is no reactance, reactance equals 0. When X=0, the impedance is purely resistive, as is the case for a truly resonant center fed dipole at design frequency.
When reactance is greater than 0, X=<0, the reactance is said to be capacitive as is the case for using our center fed dipole on a frequency shorter than the antenna. Using a 10 meter dipole on 15 meters, for example, the antenna is too short and is said to be very capacitative. Inductance must be added to an electrically short antenna to cancel out it's capacitative nature...that large coil on the mobile antenna you want to use on 160 meters.
Incidentally, This is why a tuner will tune a load of many thousand ohms quite easily, adding a large amount of physically small capacitors into the circuit is easy. The tuner has a difficult time with a load of a couple of ohms, however, because inductors are large cylindrical coils of wire. There is physical space considerations to be made in the design of any real world product and a large amount of current with very little resistance to contend with. Both of these combine to form an engineering challenge reaching a point of practicality. Any reasonable tuner will have a lower limit of 4 or 5 ohms or so.
I only mention Reactance in that it is a component of our total impedance that must be understood. It works in the same manner as a parallel circuit as we would expect any resistive value to. When system losses through both radiation and ohmic losses in the form of heating from coils, traps, capacitors, inductors etc, are greater than the reactance, efficiency will suffer. Even if you could cancel out the reactance, little power would be radiated from a load that is a couple of ohms.
Fortunately, (coming full circle here), with radiation resistance being characteristically high for folded dipoles and given their parallel circuit design, resistive resistance and reactive resistance in relation to total impedance tends scale more slowly, thus useable bandwidth for a given antenna tends to be fairly wide and efficiency tends to remain higher across a broader range of frequencies.
Having said all of this, I have learned a great deal on this particular antenna project. I make no guarantee as to the accuracy of the information provided here, as it only reflects my understanding as of right now at the time of this writing. There is no liability expressed or implied by this web page or myself in any manner. You are a responsible grown-up of unknown location, presumably on Earth. What you do with this information is up to you, should you choose to do anything at all. If I have missed anything, or you have any corrections or additional information, please, I am all ears. I want to know if my understanding can be improved in some way. Advanced math such as calculus or trigonometry is a mystery to me. Algebra is as far as I got in our education system and as such, is all that is represented here. I tend to think I am in the majority on this point and have done my best to present the information in a clear, concise, conversational manner so as to best illustrate the concepts as understood. There is a great deal of theory that can be figured, but for non-professionals, little of that matters in relation to what can actually be measured in the real world for Amateur purposes. Besides, direct measurement and experimentation often times is easier and the learning to be gained like is that much more meaningful for it. If anyone has access to EZNEC or some other modeling program...Please, contact me via QRZ.com I would like to see how the modeled performance compares to the explanation on this page.
Thank you for taking the time to read my thoughts on the multi-wire dipole.