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NBS TECHNICAL NOTE 688

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

Yagi Antenna Design

NEW BOOK SHELF

JAN 3 1 1977


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NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 was established by an act of Congress March 3, 1901.The Bureau's overall goal is to strengthen and advance the Nation's science and technologyand facilitate their effective application for public benefit. To this end, the Bureau conductsresearch and provides: (1) a basis for the Nation's physical measurement system, (2) scientificand technological services for industry and government, (3) a technical basis for equity in trade,and (4) technical services to promote public safety. The Bureau consists of the Institute forBasic Standards, the Institute for Materials Research, the Institute for Applied Technology,the Institute for Computer Sciences and Technology, and the Office for Information Programs.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the UnitedStates of a complete and consistent system of physical measurement; coordinates that systemwith measurement systems of other nations; and furnishes essential services leading to accurateand uniform physical measurements throughout the Nation's scientific community, industry,and commerce. The Institute consists of the Office of Measurement Services, the Office ofRadiation Measurement and the following Center and divisions:

Applied Mathematics Electricity Mechanics Heat Optical Physics Centerfor Radiation Research: Nuclear Sciences; Applied Radiation Laboratory Astrophysics 2Cryogenics 2 Electromagnetics - Time and Frequency 2 .

THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading toimproved methods of measurement, standards, and data on the properties of well-characterizedmaterials needed by industry, commerce, educational institutions, and Government; provides

advisory and research services to other Government agencies; and develops, produces, anddistributes standard reference materials. The Institute consists of the Office of StandardReference Materials, the Office of Air and Water Measurement, and the following divisions:

Analytical Chemistry Polymers Metallurgy Inorganic Materials ReactorRadiation Physical Chemistry.

THE INSTITUTE FOR APPLIED TECHNOLOGY provides technical services to promotethe use of available technology and to facilitate technological innovation in industry and

Government; cooperates with public and private organizations leading to the development oftechnological standards (including mandatory safety standards), codes and methods of test;

and provides technical advice and services to Government agencies upon request. The Insti-tute consists of the following divisions and Centers:

Standards Application and Analysis Electronic Technology Center for ConsumerProduct Technology: Product Systems Analysis; Product Engineering Center for BuildingTechnology: Structures, Materials, and Life Safety; Building Environment; Technical Evalua-

tion and Application Center fo r F ire Research: Fire Science; Fire Safety Engineering.THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts researchand provides technical services designed to aid Government agencies in improving cost effec-tiveness in the conduct of their programs through the selection, acquisition, and effective

utilization of automatic data processing equipment; and serves as the principal focus within

the executive branch for the development of Federal standards for automatic data processing

equipment, techniques, and computer languages. The Institute consists of the following

divisions:

Computer Services Systems and Software Computer Systems Engineering Informa-tion Technology.

THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination andaccessibility of scientific information generated within NBS and other agencies of the FederalGovernment; promotes the development of the National Standard Reference Data System and

a system of information analysis centers dealing with the broader aspects of the National

Measurement System; provides appropriate services to ensure that the NBS staff has optimumaccessibility to the scientific information of the world. The Office consists of the following

organizational units:

Office of Standard Reference Data Office of Information Activities Office of TechnicalPublications Library Office of International Relations Office of InternationalStandards.

1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address

Washington. DC. 20234.- Located at Boulder. Colorado 80302.


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Yagi Antenna Design

Peter P. Viezbicke

Time and Frequency DivisionInstitute for Basic StandardsNational Bureau of StandardsBoulder, Colorado 80302

*t* T 0F o r

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U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, SecretaryEdward 0. Vetter, Under SecretaryDr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued December 1976


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NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 688Nat. Bur. Stand. (U.S.), Tech Note 688, 27 pages (December 1976)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1976

For sale by the Superintendent of Documents, US Government Printing Office, Washington, DC. 20402(Order by SD Catalog No. C13. 46:688) Price 65 cents (Add 25 percent additional for other than U.S. mailinj


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FOREWORD

This work was carried out by the NationalBureau of Standards at antenna test rangeslocated in Sterling, Virginia, and at TableMountain near Boulder, Colorado.

These measurements were carried out by theAntenna Research Section of the Radio SystemDivision, National Bureau of Standards.

I i


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CONTENTS

1. INTRODUCTION

2. METHOD OF MEASUREMENT

3. RESULTS

3.1 Effect of Reflector Spacing on Measured Gain

3.2 Effect of Different Equal Length Directors andfor Different Yagi Lengths

Spac ng on Measured Gain

3.3 Effect of Different Diameters and Lengths of Directors on Measured Gain

3.4 Effect of the Size of a Supporting Boom on the Optimum Length of a

Parasitic Element ..........3.5 Effect of Spacing and Stacking of Yagi Antennas on Realizable Gain

3.6 Measured Radiation Patterns of Different Length Yagi Antennas

k. DESIGNING THE YAGI ANTENNA

5. CONCLUSIONS

6. ACKNOWLEDGMENTS ....7. REFERENCES

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LIST OF TABLES and FIGURES

Table 1. Optimized Lengths of Parasitic Elements for Yagi Antennas of SixDifferent Lengths ..........

Figure 1. Gain in dB of a Dipole and Reflector for Different Spacings BetweenElements ...........

Figure 2. Arrangement of Three Reflecting Elements Used With the k.2X Yagi

Figure 3. Photograph of the Trigonal Reflector Experimental Set-Up Used Withthe k.2\ Yagi

Figure k. Gain of a Yagi as a Function of Length (Number of Directors) for

Different Constant Spa. igs Between Directors of Length Equal to0.382X .

Figure 5- Gain of a Yagi as a Function of Length (Number of Directors) forDifferent Constant Spacings Between Directors of Length Equal to0.41 U .

Figure 6. Gain of a Yagi as a Function of Length (Number of Directors) forDifferent Constant Spacings Between Directors of Length Equal toO.klkX .-...


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Figure 7.

Figure 8.

Figure 9-

Figure 10.

Figure 1 1

.

Figure 12.

Figure 13.

Figure ]k.

Figure 15.

Fi gure 16.

Figure 17.

Figure 18.

Figure 19.

Figure 20.

Figure 21

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Comparison of Gain of Different Length Yagis Showing the RelationshipBetween Directors Optimized in Length to Yield Maximum Gain andDirectors of Optimum Uniform Length .......Measured Gain Vs Director Length of a 1.25A Yagi Antenna Using ThreeDirectors of Different Length and Diameter Spaced 0.35A.

Yagi Antenna Design Data Showing the Relationship Between ElementDiameter to Wavelength Ratio and Element Length for Different Antennas

Graph Showing the Effect of a Supporting Boom on Length of Elements

Gain of an Array of Yagis, Stacked One Above the Other and in Broadsas a Function of Spacing ......Gain of an Array of Two Sets of Stacked Yagis Spaced 1 .6X as a functof Horizontal Distance Between Them .....Radiation Patterns of a Dipole and Reflector With 0.2A Spacing

Radiation Patterns of a 3~Element, 0.k\ Long Yagi

Radiation Patterns of a 5-Element, 0.8A Long Yagi

Radiation Patterns of a 6-Element, 1.2A Long Yagi

Radiation Patterns of a 12-Element, 2.2X Long Yagi

Radiation Patterns of a 17-Element, 3.2X Long Yagi

Radiation Patterns of a 15 - Element, 4.2X Long Yagi

Use of Design Curves in Determining Element Lengths of 0.8X YagConsidered in Example 1 .......Use of Design Curves in Determining Element Lengths of h.2X YagConsidered in Example 2

.......

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YAGI ANTENNA DESIGN

Peter P. Viezbicke

This report presents data, using modeling techniques, for the optimum design

of different length Yagi antennas. This information is presented in graphical

form to facilitate the design of practical length antennas--f rom 0.2A to k.2X

long--for operation in the HF, VHF, and UHF frequency range. The effects of

different antenna parameters on realizable gain were also investigated and the

results are presented. Finally, supplemental data are presented on the stacking

of two or more antennas to provide additional gain.

Key words: Antenna, director, driven element, gain, radiation pattern, reflector,

Yagi.

1 . INTRODUCTION

The Yagi-Uda antenna [1], commonly known as the Yagi, was invented in 1926 by Dr. H. Yagiand Shintaro Uda. Its configuration normally consists of a number of directors and reflectorsthat enhance radiation in one direction when properly arranged on a supporting structure.

Since its discovery, a large number of reports have appeared in the literature relativeto the analysis, design, and use of the Yagi antenna [2, 3, 4, 5, 6, 7, 8, 9], However,little or no data seem to have been presented regarding how parasitic element diameter,element length, spacings between elements, supporting booms of different cross sectionalarea, various reflectors, and overall length affect measured gain.

This report presents the results of extensive measurements carried out by the NationalBureau of Standards to determine these effects and gives graphical data to facilitate thedesign of different length antennnas to yield maximum gain. In addition, design criterionis also presented on stacki ng--one above the other and in a columnar configuration. Thegain is given in decibels (dB) relative to a dipole (reference antenna) at the same heightabove ground as the test (Yagi) antenna.

2. METHOD OF MEASUREMENT

The measurements were carried out at the NBS antenna range when it was located atSterling, Virginia, and at Table Mountain, Colorado, after the antenna research group wasrelocated to Colorado. All measurements were conducted at a modeling frequency of 400 MHz.The antenna under test was used as a receiving antenna and was located approximately320 meters from a target transmitter and antenna. The transmitting antenna was located ata height above ground so that the receiving antennas were illuminated at grazing angles.The Yagi under test was mounted 3^ (wavelength) above ground and its gain was compared toa reference dipole antenna located approximately 5A to one side and at the same height asthe test antenna. Each antenna was matched precisely to 50 ohms and switched alternatelyto an attenuator and associated receiving and detecting equipment located in a nearbywooden building. In comparing the attenuator readings of the two antennas to produce aconstant receiver output level, line losses to each were measured and compensated for in

arriving at final values of gain. The values of gain were reproducible to within 0.2 dBover the period when measurements were being carried out. The values presented are thosemeasured in a forward direction compared to the maximum response of a dipole at the sameheight above ground and are believed accurate to within 0.5 dB. If referenced to anisotropic source, the values must be increased by 2.16 dB.

3. RESULTS

The results of the measurements carried out in this study are presented in graphicalform. They are intended to provide a simple means of designing a Yagi antenna of practicaldimensions with maximum gain for the configuration under consideration. The purpose ofthese tests was to determine the following:


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a. Effect of reflector spacing on the gain of a dipole antenna

b. Effect of different equal length directors, their spacing and number onreal izable gai n

c. Effect of different diameters and lengths of directors on realizable gain

d. Effect of the size of a supporting boom on the optimum length of parasiticel ements

e. Effect of spacing and stacking of antennas on gain

f. Measured radiation patterns of different Yagi configurations

3.1 EFFECT OF REFLECTOR SPACING ON MEASURED GAIN

These tests as well as all others were carried out on a non-conducting plexiglassboom mounted 3A above ground. With the exception of measurements stated in sections 3.3and 3-^, all parasitic elements were constructed of 0.63 cm (one-fourth inch) diameteraluminum tubing. The driven element used in the Yagi as well as in the reference dipolewas a half-wave folded dipole matched to 50 ohms using a double-stub tuner.

The gain of a dipole and reflector combination for different spacings between the twoelements is shown in figure 1. Maximum measured gain was 2.6 dB and was realized at aspacing of 0.2A behind the dipole. This reflector spacing was used in all subsequentmeasurements. However, for the different Yagi configurations the reflector length wasoptimized to yield maximum gain. An additional 0.75 dB gain was realized using thereflector configuration shown in figure 2.

Although this arrangement was used only on the ^4 . 2X long Yagi, comparable benefitswould be realized with other antenna lengths. A photograph of the experimental set-up forthis configuration is shown in figure 3.

Various arrangements and spacings of reflector elements were tested on the k.2\ Yagiusing the drilled plexiglass support as shown. The reflecting elements were arranged inshapes of plane reflecting surfaces, parabolas and corner reflectors. In addition,different shaped solid reflecting surfaces placed at various distances behind the drivenelement were also used. Of the combinations tested, the one shown in figure 2 yielded thelargest increase in gain over that of the single reflecting element.

3.2 EFFECT OF DIFFERENT EQUAL LENGTH DIRECTORS AND

SPACING ON MEASURED GAIN FOR DIFFERENT YAGI LENGTHS

These measurements were conducted using the same non-conducting boom as mentioned inthe preceding section. The driven element consisted of a A/2 folded dipole; the reflectorwas 0.^82X in length and spaced 0.2A behind the driven element. The diameter of allelements was 0.0085A '(0.25 inches = 0.63cm).

The gain of the Yagi was measured as a function of antenna length (number of directors]for different equal length directors and spacing between them. The director lengths werevaried from 0.304A to 0.423A and spacings from 0.01A to 0.40X. The Yagi length, measuredfrom the driven element to the last director, was varied from an overall length of 0.2A to10. 2X. The reflector in all cases was fixed. Although many measurements were carried out,only those results and associated graphs are presented that show the effects of theseparameters on measured gain.

Figures k, 5, and 6 show the relative gain of a Yagi as a function of length fordifferent spacings between director elements using director lengths of 0.382A, 0.^1 IX,and O.kmX. Figure h shows that for relatively short directors at a spacing of 0.3X,the gain of the Yagi increased to a maximum value of 14.5 dB when the antenna length wasincreased to approximately 10A. Note, however, that as the spacing between elements was


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