**Coaxial Cable Twelfth-wave Transformer
Construction**

Several members of a local club and I engaged in a discussion on how best to match 75 ohms to 50 ohms for a feed line from a dipole. Various matching transformers for the feedpoint were identified, but one, for example, was a quintifilar-wound one, and I didn’t want to get into that. The wire thickness and toroid size for QRO (100 watt) operation would mean thick wire and a fairly large, and somewhat expensive toroid (I like free solutions, or nearly so, anyway). I did some research and found a very simple solution for matching a 75 Ohm dipole feed line to a 50 Ohm line to the transmitter. The solution is based on an article on Darrel Emerson, AA7FV’s website at https://www.cv.nrao.edu/~demerson/cs/twelfth.htm. Darrel states that this is a summary of the article published in QST for June 1997. He references an original article published in 1961, "A Convenient Transformer for Matching Coaxial Lines" in Electronic Engineering, Vol. 33, pp 42-44.

Since the information first appeared on this web site, I found an article by **Arnie Coro, CO2KK** in CQ VHF in the July 1997 issue titled, "Yes, All My Coax Cables are 75 Ohm (and everything works OK!)" More on Arnie's article later.

Why bother, you say, to match 75 to 50 ohms? Well, one
reason is that I have several of the old Heathkit single-band
transceivers, and the maximum SWR rating is 1.5:1. Those boatanchor rigs
use sweep tube finals, and the output is not the familiar Pi net, rather
an L-network (only one capacitor, not the "Plate" and "Load" caps found in
a Pi network). Modern transistor-PA rigs are designed to be connected to 50 ohm loads. Okay, so why use 75 ohm coax at all? That's easy: **extremely low cost and lower loss**. The 75 to
50 Ohm transformation was of particular interest to me because I had some
quad-shielded, direct-bury RG-6/U 75 ohm stuff with an attenuation of 1.6
dB at 55 MHz and 4.15 dB @400MHz, slightly better than the larger and heavier Belden
8237 RG-8/U. I wanted to use as much of the RG-6 as possible and run the last
few feet into the shack with a 50 Ohm type coax. High quality RG-6/U can be
obtained very cheaply, and sometimes free, from cable installers who have
tail ends they can't use.

The 12th-wave technique is similar in concept to using a quarter-wave matching section of
coax that has a characteristic impedance between between two impedances. The 12th-wave matching technique uses two
twelfth-wave sections, one of 50-Ohms and one of 75-Ohms, in the feedline of halfwave dipole. A dipole's center-feedpoint impedance
is typically about 72 Ohms at the center, if it is a flat-top, and depending on the height above ground and the frequency. Again, the advantage of using 75 ohm coax for the feedline is lower losses, especially at high HF and VHF and UHF frequencies with a long feedline. Consider 2 cases: If 50-Ohm coax is used as the feedline, the mismatch is at the antenna feedpoint. If 75 Ohm coax is used as the feedline, the mismatch is at the transmitter. In the first case, an antenna tuner/transmatch could reduce the SWR seen by the transmitter, but it would not reduce the standing wave on the feedline. In the second case, the transmatch would match the transmitter to the feedline, and there would not be a mismatch between the 75-Ohm feedline and the dipole. **A 12th-wave matching section precludes the need for a transmatch** for a single band dipole antenna (or, for example, a 6-meter beam, if the beams' matching device (hairpin, etc.) is adjusted to 75 ohms instead of 50 ohms.)

The matching sections can be inserted at the shack end of the feedline to take advantage of the 1:1 match of the dipole and the 75-Ohm coax and its lower loss in the long run down to near the shack. Then comes the 2 transformer sections, and the final section of 50-Ohm coax enters the shack and connect to the rig. The two matching sections are one of 75 Ohms, and the other of 50 Ohms. The 12th-wave matching method is a very good solution for a single-band antenna.

The 2 matching sections must take into account the velocity factor of each type of coax. At 28.470, using (arbitrarily) a type of RG-59A/U foam which has a velocity factor of 0.83 and RG-58/U at 0.66 Vf, the matching section lengths are 28.0 inches of RG-59A/U and 22.3 inches of RG-58/U. If the Vf's of the two lines are the same, the matching section lengths will be the same. The velocity factors of the main feed line sections themselves are irrelevant as far as the matching sections are concerned.

The matching sections are placed in the feed line between the 75-Ohm and 50-Ohm feed line sections, reversed in order. In other words, the 75 ohm feed line from the dipole down to near the the shack end, then the 50-Ohm 12th-wave matching section, and then the 75-Ohm 12th-wave matching section, and from there, the 50-Ohm feed line to the transmitter. The matching section pair does not actually have to be at any particular position in the overall feed line. Putting the matching section near the entrance to the shack would be more convenient for adjustment and maintenance of the connectors. Any length of 50 and 75 Ohm lines can be used for the main feed line sections; the matching section pair is simply inserted between them. The SWR bandwidth is very broad, similar to a quarter-wave matching system. Any ratio of coaxial feed lines may be matched this way, but the author points out that 10:1 may be a recommended practical limit.

For 75 to 50 ohm matching, the SWR bandwidth chart shows an almost linear progression from the design frequency to plus 150%. Plus or minus 10 % is about 1.1:1, 20% is about 1.2:1. etc. Of course, at plus or minus 50% of the match frequency, where the SWR is 1.5:1, one might as well just be using the 75 ohm line direct to the transmitter.

If you are
**even reasonably close to the target frequency, there is a real benefit**.
For example, assume a frequency, say 50.4 MHz, for the 1:1 SWR target
frequency for cutting the lengths of matching cables. At 110% of 50.4
(55.44 MHz), and 90% (45.36 MHz), the SWR has only risen to 1.1:1. At
lower frequencies, the numerical bandwidth for the 10% is more limited.
On 80, with the 1:1 SWR frequency selected at 3.750 Mhz, the 1.1:1 SWR
limits are 3.375 and 4.125, but that is the whole 80 meter
band! Note that this does not mean the bandwidth of the antenna is changed or made more broadband, rather the match of the feedline is very good over a wide frequency range.

**Coax connectors/adapters and Construction**

One thing I wondered about was the availability of coax fitting adapters to join the four line sections. AA7FV’s summary doesn't mention connectors; his drawings simply show them connected as tubular sections with lines for the center and shields. Simply soldering the sections together with addition of appropriate insulation would work. For RG-6 and RG-58 or RG-8X, BNC connectors are a good choice. The original design for BNC at Bell Labs included interconnectablity of 75 ohm and 50 ohm BNC connectors. They are different with respect to radius from the center pin and shield, and also the thickness of the dielectric. It is common to find suppliers of BNC connectors for CCTV using 50 ohm BNCs for 75 ohm RG-59 or RG-6 rather than the less common 75 ohm versions. In an earlier paragraph, I mentioned that one of my feedlines is RG-6 quad shield. Quad shield is a larger diameter than regular RG-6. Since the application for twelth-wave transformer matching requires direct interfacing or 50 ohm and 75 ohm coax, it matters little, if at all, if BNC connectors or adapters are 50 or 75 ohm. F female to male BNC adapters are available, or all-BNC for the connectors can be used, with double-male adapters used for the junctions. I initially made my own homebrew adapters using F double male connectors soldered to BNC male PC Board connectors, using flux and solder paste suitable for aluminum soldering. The photos show this process. I used my homebrew F-to-BNC connector for my first "transformed" feedline. On the feedline end, I used a compression type quad shield size F male. I simply use all BNC crimp connectors (and regular RG-6 cable) for new feedlines. The connectors should be sealed against the environment, or course.

Arnie, CO2KK's application in his CQ VHF article used 50-ohm RG-213 and 75-ohm RG-11/U and employed PL-259 male connectors and mating barrel connectors for the connections. Those can also be used with the smaller cables with the proper reducers. The jacket on the RG-6 feedline to the antenna and the RG-6 matching section might have to be cut and only the bare shield slipped into the reducer. I haven't tried that, but I will.

The following photos show the sequence for assembly of the connectors. Photo 7 shows a connector between two sections. Click on a photo to enlarge.

F female and BNC Female |
Two Connectors Fitted |
Connectors Soldered |
Resistance Check |

Epoxy Applied |
Heatshrink Applied |
Connector in Feed Line |

**Calculation Spreadsheet**

To avoid having to do the math, which involves arctangents and the like, I developed a spreadsheet which is downloadable from this website. The spreadsheet includes a diagram of how the matching sections are placed in the feed line, so that the person doing the calculation entries have something to refer to.