HF Yagi Antennas (2-6 Element)

Introduction

This page has a variety of calculators that can be used to calculate dimensions for practical antennas for 6, 10, 11, 12, 15, 17 and 20 Meter Yagi Antennas. While you may not have the space for a large array, there is a lot to be gained from simple, 2 and 3 Element arrays. Yes, I do include 11 meters. While it is not a ham band, a 2 or 3 element yagi for this band would provide better communication than strapping on a amplifier.

All of the equations used on this page are based on the Basic Wavelength Formula, which is shown on the right. But that is quite a bunch of numbers to remember, so the formula is approximated, as shown under the heading the Approximate Wavelength Formula.

But we are really only interested in a "1/2 wavelength" for use as a dipole element. So the formulas would be adjusted, as shown on the right under 1/2 Wavelength Formula.

That is assuming an antenna in "free space". There are velocity effects of the length/diameter ratio, end capacitive effects, and effects due to external objects. All of these things can change the actual length of a half-wavelength dipole. These things generally cause the length to be shortened anywhere between 3% and 7% giving us the formula under 1/2 Wavelength Formula (Adjusted).

For the purposes of this web page, I will be using a slightly different formula that takes the length/diameter ratio into account.

The designs presented on this page are what William Orr, W6SAI, refers to as "pretuned" arrays. By that he means that, the formulas used will create a yagi design that can be adjusted while the antenna is on the ground, and then placed in operation, without the need for re-tuning. Adjustments to the parasitic elements, made after the antenna is in place, could yield a slight improvement in F/B Ratio, but rarely produces any increase in Gain. Its best to simply settle for reasonable Gain and F/B Ratio figures. With the designs produced on this page there will be a F/B Ratio of approximately 12 dB, for two element arrays and 20 dB for three element arrays.

The original information on these antennas did not include data for the WARC bands (12 meters and 17 meters) and only included US Imperial dimensions (feet and inches). I have expanded on this to include Metric dimensions and information for the WARC bands. If you want to design for a frequency that is different than the ones I provide, you can use the frequency that is closest to your needs and then use my web page on Antenna Scaling. Making small changes in the element lengths, without changing the element diameters, will not cause a problem. The antenna will still perform well.

You might notice that the drawings only show the Driven Element as solid element, the same as the parasitic elements. While the Driven Element requires a matching device, it is not shown to keep the drawings uncluttered. For information on the matching device, see the section at the bottom on Impedance Matching. The Driven Element is marked with a Center Line (℄) that can be used as a reference point in the section on Impedance Matching.

2-Element Yagi Array

A minimalist Yagi will have only two elements. It would have a Driven Element and either a parasitic Reflector, or a parasitic Director.

It may seem that adding a single parasitic Reflector would be better than adding a single parasitic Director. But it turns out that, adding a single parasitic Director offers slightly higher Gain and slightly better Front/Back Ratio. But the real advantage of using a parasitic Director, as opposed to a parasitic Reflector, is boom length. The spacing required for a parasitic Director is much less than the spacing required for a parasitic Reflector.

That being said, the calculator only deals with a Two Element Yagi that consists of a Driven Element and a parasitic Director.

With the spacing shown, the 2-Element yagi will exhibit 4.8 dBd of Gain on 6 and 10 Meters and 5.3 dBd of Gain on 11 to 20 Meters. The Front/Back Ratio will be about of about 12 dB on 6 thru 20 Meters. Of particular importance is the feed impedance. The impedance at the feed point will be around 20-30 Ohms, indicating that a matching device will be necessary to match the feed point to 50 Ω coaxial cable (see below).

The calculator will specify 1.5 inch tubing for 10 and 20 meters and 1 inch tubing for the other bands. The larger diameters are used to insure that the reactance of the array elements remain low at frequencies removed from the design frequency. Smaller diameter elements could be used, like heavy gauge wire, but the useful bandwidth will decrease. With smaller diameter elements the calculated lengths will still be valid.

The dropdown selector for Frequency may seem limited but the frequencies available should provide for sufficient bandwidth on all the bands. , select the frequency of interest. The reason for the increased element size on those bands is operating bandwidth. The larger diameter elements increase the 2:1 SWR bandwidth. You could certainly use a smaller or larger tubing, or even wire, but the elements would need to be scaled a bit so that the resonent point stays the same. My calculator for Frequency/Diameter/Length Scaling can be used for this purpose. Using the driven element as a focal point, the Direction of Maximum Signal is to the right, away from the director.

3-Element Yagi Array

The next step up from a Two-Element Yagi is the Three-Element Yagi. This antenna contains one Driven element plus two parasitic elements, a Reflector and a Director. The Reflector is located on one side of the Driven element and the Director is located on the other side of the Driven Element. The Direction of Maximum Signal is then outward, on the Director side of the yagi

The calculator on the right illustrates the Three-Element Yagi. It shows the relationship between the elements.

In the space provided on the top right, enter the center frequency for your proposed 3-element Yagi antenna. Then just click your mouse anywhere on the the page. The details of the 3-element Yagi antenna will be calculated using the equations above, and then annotated on the drawing.

Impedance Matching

The nominal feed impedance of a dipole feed element, in free space, would be around 72 Ω. But the close proximity of parasitic elements causes the feed impedance of the dipole to be reduced to around 20 Ω. You could split the element at the center and feed it directly with coax, but the SWR would be pretty bad across the band. So a better method of feeding the antenna is with a matching device. There are a variety of matching devices that can be used (see my web page on Yagi Matching). But if you intend to feed the antenna with common 50 Ω coax, a good choice would be either a Gamma Match or Omega Match.

The drawing on the right shows the essential elements of a Gamma Match. The Gamma Rod is just that. A metallic rod that is mounted parallel to the Driven Element, left or right of center. In general, the Gamma Rod should be about 1/4 the diameter of Driven Element and should be spaced about 4 times the diameter of the Driven Element. The outer end of the Gamma Rod is shorted to the Driven Element with a strap. Initially, it is good to make the strap adjustable. For the shorter rods, a piece of plexiglass at each end should be sufficient to keep the rod stable. For the longer rods, you might want to add a few plexiglass spacers along the length, to keep the spacing consistent. The Resonating Condenser is usually a variable capacitor. This can be mounted in a small plastic box to keep the weather out. Once the adjustable strap and capacitor are set there shouldn't be any more adjustments needed.

Band	C_MAX	L 2-El.	L 3-El.	S	D1	D2
6	25 pF	12" (0.304 m)	14" (0.355 m)	3" (76.2 mm)	1" (25.4 mm)	3/16 (4.7625 mm)
10	45 pF	20" (0.508 m)	24" (0.609 m)	4" (101.6 mm)	1-1/2 (38.1 mm)	1/4 (6.35 mm)
11	50 pF	24" (0.609 m)	28" (0.711 m)	4" (101.6 mm)	1" (25.4 mm)	1/4 (6.35 mm)
12	60 pF	27" (0.685 m)	30" (0.762 m)	4" (101.6 mm)	1" (25.4 mm)	1/4 (6.35 mm)
15	70 pF	30" (0.762 m)	36" (0.914 m)	5" (127 mm)	1" (25.4 mm)	3/8 (9.525 mm)
17	100 pF	35" (0.889 m)	42" (1.066 m)	5" (127 mm	1" (25.4 mm)	3/8 (9.525 mm)
20	130 pF	40" (1.016 m)	48" (1.219 m)	6" (152.4 mm)	1-1/2 (38.1 mm)	1/2 (12.7 mm)

The table on the right provides values for a matching network that will match 50 Ω coax to the antennas defined on this web page. These values are just approximate, but should get you very close to your goal.