As I look around the Internet for information on building EFHW UnUns, I see the ratios of 49:1 and 64:1 appear quite often. I get that these are the squares of 7:1 (21:3 or 14:2) and 8:1 (24:3 or 16:2) toroid windings, so I so know how the numbers are derived. What I have yet to see is someone make an UnUn with a 22:3 (7.3:1) or 23:3 (7.7:1) secondary to primary turn ratio, which would give a 54:1 or 59:1 UnUn ratio, respectively. I also see a fairly broad range for impedance values of an EFHW antenna as ranging from 2500-6000 ohms at the feedpoint, with 3000-5000 ohms being a more widely quoted range, so I get the fact that by the time that you reduce the impedance of the antenna on the transmitter side of the UnUn that it's "close enough" to 50 ohms that it doesn't much matter whether you're using a 49:1 or 64:1. I guess the question that pops up in my puny little brain is why our community mainly uses whole integer values for turn ratios. Does it give better results at the UnUn, or is it for a different reason, perhaps being that the math is just that much easier?

Look at it this way, your feed line is 50 ohms nominal. A ratio of 1 represents 50 ohms, 2500 ohms /50 = 50. That is like saying 50 to 1. You have to convert the antenna feed impedance down to 50 ohms. . 49 x 50 = 2450 ohms. 64 x 50 = 3200 ohms antenna feed impedance. Most end feds are in that range so either 49 or 64 may work depending on the installation. Make sense? You can't normally work to a tenth of a ratio due to any variables that might be present. If it had to be that precise, there would be little usable bandwidth before the SWR goes out of usable limits as you move in frequency so the transforming unit has to be broad banded.

I'm not sure that I understand your answer. You seem to be saying that the antenna will have a narrower bandwidth if the turn ratio contains fractions. Would you please explain why that would be?

I use 3:23 for my 80m EFHW (used on 80, 40, 20, 15) unun. Works well with a 150pF cap across input. 200kHz of 80m centred on 3.650 and all of the higher bands at <1:1.5. As per advice I use 2:16 for shorter 40m EFHW (used on 40-10) Like you I'm keen to hear from experts if there's a reason fractional ratios like this should be avoided.

KM3F gave an excellent response and pretty much explains it. To add to it: A simple center fed horizontal dipole, in free space, is about 72 ohms. Now install that same dipole in your back yard about 16 feet in the air and depending on the gr ground conductivity, this value will change. Next go from a horizontal dipole to an inverted vee, again the feed point impedance will change. What I’m getting to is, a HWEF erected in your back yard is not guaranteed to have a fixed value of 3200 ohms on all band or even any band. It’s a variable. It may in fact be 3200 ohms on one band and different on other bands. Just like using 50 ohm coax on a 72 ohm center fed dipole, where its feed point value changes, so does the feed point change on a HWEF. There is no law that says you MUST use either a 49 or 64 to 1 UnUn. Barry, KU3X

None that I can see. Suppose we build the transformer the way I like to build them. I wind a three turn primary out of heavy wire. I wind a secondary out of smaller diameter wire (because the current in the secondary is only about 20% of that in the primary), and I connect the two windings in series, so that the secondary impedance (relative to 50 Ohms) is: Z=50*((3+s)/3)^2, where s is the number of turns on the secondary winding. If s=18, then we have the familiar 50:2450 Ohm (1:7 turns ratio) transformer. Next, I use the antenna modeler to find the required wire lengths such that if fed with the s=18 turns transformer, the swr(50) looking into the primary side of the transformer is 1. Here is the free space model: Now, I show what happens to the Z (and Swr50) at the transformer primary as s is varied from 12 turns to 22 turns. The Z column shows the transformer's secondary impedance in Ohms (based on 3turn primary), all other aspects of the antenna model remaining the same... Clearly, the design will tolerate anything from s= 15 to 21 secondary turns. The wire lengths can be optimized after you pick a turns ratio to restore the Swr50 back to 1. For example, with s=15 (1800 Ohms), the optimum wire lengths would be 4.61 and 61.91ft, respectively. The biggest impact on the performance of these antenna remains the length of the short wire3. In a real antenna, wire3 is replaced with CM current flowing down coax! If you do not properly choke the CM current at the appropriate distance from the transformer, that can have a huge impact on the swr of the antenna, an impact much, much larger than changing the transformer ratio...

WK7L, your getting the "Ratio" mixed up with 'math fractional division'. They are both stated the same way but you need to think Ratio for the application being discussed. For example: Standing Wave Ratio is a ratio of any two values. Such as an antenna impedance of 200 ohm referred to a 50 ohm reference is a 4 to 1 ratio or 200/50 = 4 as a ratio. Only the name changes. If you are only dealing with numbers as pure fractions, then 200 divided by 50 is still 4 'without any reference'. Reference is the key difference between the two uses. Further, any number that results in a division that = 4 is the same answer....4. It could be 2000/500 still = 4. SWR: 50/25 also =2. If an antenna feed impedance is 25 ohms and >>referenced<< to 50 ohms, is still a ratio of 2. NOT 12.5. In this case the numbers are inverted for SWR use and not for fractional use. The reason the numbers are reversed is an Antenna can have an impedance below/less than 50 ohm reference we use. It's how you use the numbers with reference to 50 ohms when talking about matching impedances from one level to another either above 50 or below the 50 reference value. . Hope you have a picture of Ratio difference from straight fractional use of the numbers. Wait until you ask about the j value included in a full Impedance measurement! Your question was a good one for us to help with. There is more but lets let it at this for now. Good luck.

Those are actually both compromises...In the latest ARRL antenna book, it suggests that 64:1 is a better choice, and I concur. The average "end fed zepp" has a feed point resistance of about 3500 ohms. 3500/64=54.7 ohms....a pretty good compromise.

OH....and the whole integer "perfect square" ratios are easier to create with transmission line methods. Jerry Sevick DID show how to get non-perfect-square ratios, but those always require a "Texas Two-step" somewhere. A "pure" transmission line transformer will always be a perfect square (and an integer)

You seem to confirm my initial thought which is that there's really nothing wrong with 22 or 23 turns instead of 24. I appreciate your extra commentary on SWR because after I posted this originally I did realize that the turns ratio does affect SWR for the same length of antenna. I hadn't intended to propose using the turns ratio as a way to tune the antenna, but it appears that some folks may have taken it that way. Thanks for helping to clarify that!