Javascript® Electronic Notebook by Martin E. Meserve 2 and 3 Element Yagi Matching
As the title indicates, this page lists several different matching devices that can be used to match your antenna to your chosen feed line. Often the preferred feed line is unbalanced, low impedance coaxial cable (50/75 Ω), but some operators prefer using balanced feed line, like Ladder Line (75/300/450 Ω).
Some of the information on this page comes from a book written by William I. Orr, W6SAI called the Beam Antenna Handbook, 5th Edition. Its a fairly old book (1967) and I have taken some of the drawings from that book and regenerated/expanded/updated them. The original drawings only contained US/Imperial dimensions and equations plus it used some very outdated references, like MC (Mega Cycle) updated to MHz. I have also crossed the information with more current books, like the ARRL Antenna Handbook, 18th edition. Often the information was the same, but in some cases, it was slightly different. In many cases I also included a built in calculator that can be used to to generate information for your specific needs.
is specifically for creating a matching device that will allow you to use 50/75 Ω coax or 75/300/450 Ω Ladder Line with the 2 Element Yagi and 3 Element Yagi designs presented on this site, that have feed impedances between 18 and 22 Ω. The matching approaches can be used with any antenna. However, you need to be aware of the radiation resistance of your antenna. All matching techniques do not work, under all situations.
While this matching device is included, it may not be a good choice.
The T-Match incorporates resonating capacitors (variable) in each leg, to tune out the reactance of the T-Rods. The far ends of the T-Rods use adjustable metal straps to connect the T-Rods to the driven element. While the diagram shows that this is for matching high impedance, 300 Ω, balanced feed line, the matching network can also be used for matching low impedance, 75 Ω, balanced feed line. The length of the T-Rods, the spacing from the driven element, and the ratio of the diameter of the T-Rods to the driven element determine the impedance transformation.
The equations that are shown on the diagram generate US/Imperial dimensions. The calculator (above right) provides dimensions in both US/Imperial and Metric. In general, the T-Rods should be about 1/4 the diameter of the driven element (D2 = D1/4) and should be spaced away from the driven element by a distance equal to four times the diameter of the driven element (S = 4×D1). The length of the each T-Rod will be about 12% of the driven element, for a 300 Ω match and 9% for a 72 Ω match.
For example, the driven element for a 10 Meter 2-element yagi, designed for center frequency of 28.75 MHz, would be 16' 6-1/4" (4.974 m) in length (λ/2 (ft) = 471/FMHz) and would have diameter (D1) of 1-1/2" (38.1 mm). For a 300 Ω match, the T-Rods should be 0-3/8" (9.5 mm) in diameter (D2) and 1' 11-3/4" (604.3 mm) in length. The T-Rod spacing (S), from the center of the driven element to the center of the T-Rod, would be 6" (152.4 mm). The variable capacitors required for the match would be 210/F(MHz), or 7 pF.
For a 72 Ω match, assuming the same driven element, the T-Rods should be 0-3/8" (9.5 mm) in diameter (D2) and 1' 5-7/8" (453.2 mm) in length. The T-Rod spacing (S), from the center of the driven element to the center of the T-Rod, would be 6" (152.4 mm). The variable capacitors required for the match would be 210/F(MHz), or 7 pF
The λ/2 balun transformer consists of a λ/2 loop of coaxial cable. The shields of the feed line and the loop are connected together and then bonded to the center of the driven element. The center conductor of the feed line is attached to the center conductor of one side of the λ/2 loop, and to one side of the balanced driven element. The center conductor on the other side of the λ/2 loop ties to the remaining side of the balanced driven element.
Note: The calculated Balun Length dimension is only for the shielded section of the coax loop. Make sure you add some extra length for connecting to the feed points.
The Gamma Match is effectively one half of a T-Match and is used to match your balanced antenna driven element, to unbalanced coaxial cable. It is probably the most comonly used matching device. It only uses a single Gamma Rod and a single series resonating capacitor, but the general characteristics of the T-Match apply to the Gamma Match.
Because the Gamma Match is unbalanced, the outer shield of the coaxial cable is connected (grounded) to the center of the driven element. Physically, using a solid driven element uncomplicates the possible mounting problems that split elements may provide.
Using the dimension shown in the drawing, the capacitor has a capacitance of approxiately 15 pF per inch, engaged. The Gamma Rod setting is determined by the placement of the outer clamp. The Gamma resonating capacitor is then adjusted by loosening the inner clamp and moving the position of the outer aluminum tube. Two of these Coaxial Gamma Matches can be employed back-to-back to construct a Coaxial T-Match.
The drawing on the right shows that, a similar multiplication of the feed point resistance can be had by connecting the ends of three half wave dipoles (one split at the center) together. In this case, the feed point resistance will be increased to about 630 Ω and can still be connected to a balanced transmission line. Again, this assumes that all of the wires (tubes) are the same diameter. This can be expanded to more λ/2 dipoles, with the feed point resistance being equal to 70 × N2, where N = Number of wires.