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VHF/UHF Yagi Antenna Design Help
by Martin E. Meserve

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This is intended to go into a little more detail on the VHF/UHF Yagi Design program. The design program is long enough without being choked with detailed explanations.

The design program is best suited for antennas in the VHF, UHF, and Microwave frequencies because lower frequency antennas, that have gains between 11.8 to 21.6 dBd, tend to be physically impractical. For example, a yagi antenna for 50 MHz would have elements that are around 8 - 10 feet (2.5 - 3 M) long. For a 3 or 4 element antenna the overall size would not be excessive and would be practical. But, this would only get you limited gain.

If you wanted, say, 12 dBd of Gain, it would require 10 elements. This would make the boom 2.3 wavelengths (44.9 feet, 13.695 M) long. That may not be very practical.

Even though the program specifies a gain between 11.8 to 21.6 dBd, you can still specify a smaller gain, like 6 dBd. You may get a warning when the dimensions are displayed, but, the design should still be accurate. However, in order to prevent the program from performing needless calculations the upper limits are protected. You can not calculate an antenna with a specified Gain in excess of 21.6 dBd or a specified Boom Length in excess of 39 Wavelengths.

Design Frequency

A bandwidth of 7% of the center frequency, at the -1 dB forward-gain points, is typical for yagis designed here. The Design Frequency should be this center. Also, the Design Frequency should be limited to the VHF, UHF, and Microwave frequencies. Use the Select box, next to the the Design Frequency entry box, to specify the frequency dimensions in Mega Hertz (MHz) or Giga Hertz (GHz).

All internal calculations are performed in Wavelengths and converted to the various dimensions for output, as necessary. Some of the equations and conversion that I use are listed to the right.



Gain/Boom Length

You can define you antenna with a required Gain or Boom Length. If you enter a required Gain, the program will calculate the necesary Boom Length. Conversly, if you enter a required Boom Length, the program will calculate the possible Gain. Specifying a Boom Length is useful when you have stock lengths of boom material or length restrictions. The Boom Length can be specified in inches, millimeters, or Wavelenghts.

The Gain of a Yagi style antenna is directly proportional to Boom Length. This is because longer booms allow for more Director elements, and hence, higher Gain. Current indications are that doubling a Yagi's boom length will result in a maximum theoretical gain increase of about 2.6 dB. In practice, the increase will be a little less due to construction errors.

Gains are specified in dBd (dB Gain over a Dipole). This is different than dBi (dB Gain over Isotropic). An Isotropic radiator is considered to be omni directional (radiates equally in all directions) and has 0 dB gain ,whereas a Dipole is considered to have 2.1 dBi. So when you specify an antenna with 12 dBd, for example, you are also specifying an antenna with 14.1 dBi.

Boom Length is calculated from Gain using:

Conversly, Gain is calculated from Boom Length using:

Reflector and Director Spacing

The default Reflector spacing is 0.2 Wavelengths behind the Driven element. Spacings between 0.15 and 0.2 Wavelengths are valid and have little effect on the foward Gain. However, the Reflector spacing can affect the feed impedance. It may be useful to make the Reflector element spacing adjustable in order to obtain a better match on the Driven element.

DL6WU designs generally use the 0.2 Wavelength Reflector spacing and the ARRL designs use the 0.15 Wavelength Reflector spacing. You can select either spacing or any other spacing between them, in 0.01 Wavelength increments.

One place where adjusting the Reflector spacing may be useful is, if you have a boom of fixed length. By reducing the Reflector spacing you may be able to fit another Director on the Boom.

An example of this is a antenna designed for 440 MHz on a Boom with a fixed length of 1000 mm (1 Meter). If a 0.2 Wavelength spacing is used only 5 Director elements will fit on the boom for an effective Gain of 9.732 dBd. However, should you reduce the Reflector spacing to 0.16 Wavelengths, 6 Director elements will fit on the boom for an effective Gain of 10.483 dBd. This is not a very big Gain increase (0.75 dBd) and will be much less for longer boom lengths, but it may be useful.

The default Director element spacing is calculated from an array that gradually increases from about 0.65 wavelengths, for the first driven element, to 0.4 wavelengths for element 14 and beyond. A user can select the spacing defined by DL6WU or the ARRL and they only differ for the first 3 driven elements.

Boom Correction, Boom Type, Mounting, and Dimensions

The type of Boom, metalic or non-metalic, and the method of mounting the elements effects the length of the antenna array elements. Close proximity of a metalic boom to the antenna array elements causes a shortening effect which raises it's operating frequency. Lowering the operating frequency back to the design frequency would require the elements to be lengthened. If the elements are actually bonded to the metalic boom, as opposed to being insulated from the boom by grommets, even more of an effect is realized.

The precise amount, to lengthen the elements by, is based on the design frequency and the relationship of the Boom Diameter to the design frequency, in Wavelength.

The following equation describes this relationship for Boom Diameters less than, or equal to, 0.055 × Wavelength. This yields the percentage of Boom Diameter which must be added to element lengths. BC equals the Boom Correction and BD_WL is the boom diameter, in wavelengths.

BC = 733 × BD_WL × (0.055 - BD_WL) - 504 × BD_WL × (0.03 - BD_WL)

Selecting Metal Boom (Bonded) means that a Metal Boom is used and the elements pass through and are physically Bonded to it. This is not a good choice unless the elements are welded to the boom. Otherwise, air currents can cause vibration of the antenna elements which in turn will cause the mounting holes to widen and the elements will get loose. Loose vibrating elements can introduce noise into the signal.

Selecting Metal Boom (Insulated) - means that a Metal Boom is used and the elements pass through it, however, they are insulated from the boom. This is usually done with rubber grommets. When this is the case, the calculated Boom Correction is divided by two.

Selecting Non-Metallic Boom means that a materal other than Metal is used for the boom, i.e. wood, plastic, etc., or a Metal Boom is used but the elements are mounted on insulators, above or below the boom, such that the metal-to-metal spacing is greater than the boom radius.

NOTE - The last option means that there will be no correction made for the influence of the boom and that any Boom Diameter that is entered, will not be used in the calculation of the element lengths. If in doubt, select the first or second option and you can review your decision later.

You can choose to accept the Boom Correction listed in the select boxes or set your own value. You can return to the program calculated value at any time by clicking on the Init BC button.

Element Diameters

For these designs, the diameter of the Driven and Parasitic elements should be limited to between 0.001 and 0.02 wavelengths.

The spacing of the Reflector element is fixed at 0.2 wavelengths, for all designs. However, this value is not carved in stone and can be anything from 0.15 to 0.2 wavelengths. In the ARRL Examples, listed at the bottom of the main page, a 0.15 wavelength Reflector spacing is used.

The spacing of the Director elements along the boom is calculated from a Exponential curve for the first 13 elements and then remains constant at 0.4 wavelengths for elements 14 through N.

As with the Reflector spacing, the ARRL Examples use a slightly modified equation for calculating the spacing, from one element to the next.

Element Spacing from Previous Element (wavelengths)

Ele

Spacing

Ele

Spacing

Ele

Spacing

Ele

Spacing

1

0.061

2

0.112

3

0.156

4

0.194

5

0.226

6

0.253

7

0.277

8

0.297

9

0.314

10

0.329

11

0.341

12

0.352

13

0.361

14

0.369

15

0.376

16

0.381

17

0.386

18

0.390

19

0.394

20

0.397

21

0.400

22

0.402

23

0.404

24

0.405

25

0.407

26

0.408

27

0.409

28

0.410

29

0.411

30

0.411

31

0.412

32

0.412

33

0.413

34

0.413

35

0.413

36

0.414

37

0.414

38

0.414

39

0.414

40

0.414

Viewing the Design and Sample Designs

On the Yagi Design web page, this section provides you with a way of collecting all of the design information into one single page. This gives you a better overview and is easier to read than skipping back and forth on the design page.

You can start up the design viewer at the start of your work and leave it up throughout. It will not update on it's own, but, all you need to do is press the view button and all the latest information is displayed.

These are antenna designs from The ARRL Antenna Book, 18th Edition. They were designed using a method similar to the one in this web page, however, the element spacing and length curves are slightly different. That being said, don't expect to design an antenna, with this program, that exactly matches the ARRL designs.

The director spacings gradually increases until a constant spacing of about 0.4 Wavelengths is reached. The director lengths start out longest with the first director and then decrease in length. This method of construction results in a wide gain bandwidth. A bandwidth of 7% of the center frequency at the -1 dB forward-gain points is typical for these yagis.