688 NBS TECHNICAL NOTE NATIONAL BUREAU OF STANDARDS The National Bureau of Standards' 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 technology and facilitate their effective application for public benefit TO thk end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific rad technological services for industry and government, (3) a technical basis for equity in trade. and (4) technical services to pro. mote public safety. Tbe Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, &e Institute for Applied Technology, the Institute for Computer Sciencej and Technology. the office for Information Programs, and the Office of Experimental Technology Incentives Program. THE IN- FOR BASIC STANDARDS provides the central basis within the Unitui States of a complete anii codt- ent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes tial services leading to accurate and uniform physical measurements throughout the Nation's scientific community, indw, and commerce. The Institute consists of the Office of Measurement Services, and the following center and divisions: - - - - - - Applied Mathematics Electricity Mechanics Heat Optical Physics Center for Radiation Research L*b. - - - oratory Astrophysics' Cryogenics' Electromagnetics' Time and Frequency'. TKE INSTITUTE FOR MATERIALS RESEARCE conducts materials research leading to improved methods of mCBdufe ment, standards, and data on the properties of wellcharacterized materials needed by industry, commerce, educational insti- tutions, and Government provides advisory and research services to other Government agenaes; and develops, produas, and distributes standard reference materials. The Institute conskts of the Office of Standard Reference Materials, the.Otticc of Air and Water Measurement, and the following divisions: - - - - - Analytical Chemistry Polymers Metallurgy Inorganic Materials Reactor Radiation Physical Chemistry. THE INSTITUTE FOR APPLIED TECHNOLOGY provides technical services developing and promoting the w of avail- able technology; cooperates with public and private organizations in developing technological standards, codes, and tat metb- ods; and provides technical advice semces, and information to Government agencies and the public. The Institute consists of the following divisions and centers: - - Standards Application and Analysis Electronic Technology Center for Consumer Product Technology: Product - Systems Analysis; Product Engineering Center for Building Technology: Structures, Materials. and Safety; Building - Environment; Technical Evaluation and Application Center for Fire Research: Fire Science; Fire Safety Engineering. lME INSITNTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts research and provides technical services designed to aid Government agencies in improving cost effectiveness in the conduct of their programs through the selection, acquisition, and effective utikation of automatic data processing equipment; and serves as the principal focus wtlh the exec- utive branch for the development of Federal standards for automatic data processing equipment, techniques, and computer languages. The Institute consist of the following divisions: - - - Computer Services Systems and Software Computer Systems Engineering Information Technology. TAE OFFICE OF EXPERIMENTAL TECHNOLOGY ln(lCENTIYES PROCRAM seeks to affect public policy and proas to facilitate technological change in the private sector by examining and experimenting with Government policies and prac- tica in order to identify and remove Government-related barriers and to correct inherent market imperfections that impede the innovation prous. THE OFFICE FOR INFORMATION PROCRAMS promotes optimum dissemination and accessibility of scientific informa- tion generated within NBS; promotes the development of the National Standard Reference Data System and a system of in- formation analysis centers dealing with the broader aspects of the National Measurement System; provides appropriate Serkcs to ensure that the NBS staff has optimum accessibility 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 Technical Publications - mce of International Standards Office of International Relations. Yagi Antenna Design Peter P. Viez bicke Time and Frequency Division Institute for Basic Standards National Bureau of Standards Boulder, Colorado 80302 U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary Edward 0. Vetter, Under Secretary Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director Issued December 1976 NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 688 Nat. 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, U S Government Printing Office, Washington. D C 20402 (Order by SD Catalog No C13 46 688) Price 65 Cents (Add 25 percent additional for other than U S mailing) FOREWORD This work was carried out by the National Bureau of Standards at antenna test ranges located in Sterling, Virginia, and at Table Mountain near Boulder, Colorado. These measurements were carried out by the Antenna Research Section of the Radio System Division, National Bureau of Standards. iii CONTENTS Page . 1. INTRODUCTION 1 2. METHOD OF MEASUREMENT 1 . 3. RESULTS 1 . 3.1 Effect of Reflector Spacing on Measured Gain 2 3.2 Effect of Different Equal Length Directors and Spacing on Heasured Gain for Different Yagi Lengths 2 3.3 Effect of Different Diameters and Lengths of Directors on Heasured Gain 6 3.4 Effect of the Size of a Supporting Boom on the Optimum Length of a . Parasitic Element 6 3.5 Effect of Spacing and Stacking of Yagi Antennas on Realizable Gain 6 3.6 Measured Radiation Patterns of Different Length Yagi Antennas 6 4. DESIGNING THE YAGI ANTENNA 16 5. CONCLUS IONS 21 . 6. ACKNOWLEDGMENTS 2.1 . 7. REFERENCES 21 LIST OF TAGLES and FIGURES Table 1. Optimized Lengths o.f Parasitic Elements for Yagi Antennas of Six Different Lengths 7 Figure 1. Gain in dB of a Dipole and Reflector for Different Spacings Between Elements 3 . Figure 2. Arrangement of Three Reflecting Elements Used With the 4.21 Yagi 3 Figure 3. Photograph of the Trigonal Reflector Experimental Set-Up Used With the 4.21 Yagi 4 Figure 4. Gain of a Yagi as a Function of Length (Number of Directors) for Different Constant Spacings Between Girectors of Length Equal to . 0.3822, 4 Figure 5. Gain of a Yagi as a Function of Length (Number of Directors) for Different Constant Spacings Between Directors of Length Equal to . 0.4111 5 Figure 6. Gain of a Yagi as a Function of Length (Number of Directors) for Different Constant Spacings Between Directors of Length Equal to 0.4242, . 5 V Figure 7. Comparison of Gain of Different Length Yagis Showing the Relationship Between Directors Optimized In Length to Yield Haximum Gain and . Directors of Optimum Uniform Length 8 Figure 8. Measured Gain Vs Director Length of a 1.251 Yagi Antenna U.s ing Three Directors of Different Length and Diameter Spaced 0.351 8 , i ? Figure 9. Yagi Antenna Design Data Showing the Relationship Between Element Diameter to Wavelength Ratlo and Element Length for Different Antennas 9 . - Figure 10. Graph Showing the Effect of a Supporting Boom on Length of Elements 10 Figure 11. Gain of an Array of Yagis, S.ta cked One Above the Other and in Broadside, as a Function of Spaclng 11 figure 12. Gain of an Array of Two Sets of Stacked. Yagis Spaced 1.61 as a function of Horizontal Distance Between Them 11 . Figure 13. Radiation Patterns of a Dipole and Reflector With 0.21 Spacing 12 . Figure 14. Radiation Patterns of a 3-Element, 0.41 Long Yagi 12 . Figure 15. Radiation Patterns of a 5-Element, 0.81 Long Yagi 13 . Figure 16. Radiation Patterns of a 6-Element, 1.21 Long Yagi 13 . Figure 17. Radiation Patterns of a 12-Element, 2.21 Long Yagi 14 . Figure 18. Radiation Patterns of a 17-Element, 3.21 Long Yagi 14 . Figure 19. Radiation Patterns of a ls-Element, 4.21 Long Yagi 15 i Figure 20. Use of Design Curves in Determining Element Lengths of 0.8X Yagi Considered in Example 1 18 Figure 21. Use of Design Curves in Determining Element Lengths of 4.21 Yagi Considered in Example 2 20 YAGI ANTENNA DESIGN Peter P. Viezbicke This report presents data, using modeling techn ques, for the optimum design of different length Yagi antennas. This information is presented in graphical form to facilitate the design of practical length an ennas--from 0.ZX to 4.2A long--for operation in the HF, VHF, and UHF frequency range. The effects of different antenna parameters on realizable galn 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 111, commonly known as the Yagi, was invented in 1926 by Dr. H. Yagi and Shintaro Uda. Its configuration normally consists of a number of directors and reflectors that 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 relative to the analysis, design, and use of the Yagi antenna [2, 3, 4, 5, 6, 7, 8, 91. 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 sectional area, various reflectors, and overall length affect measured gain. This report presents the results of extensive measurements carried out by the National Bureau of Standards to determine these effects and gives graphical data to facilitate the design of different length antennnas to yield maximum gain. In addition., design criterion is also presented on stacking--one above the other and in a columnar configuration. The gain is given in decibels (de) relative to a dipole (reference antenna) at the same height above ground as the test (Yagi) antenna. 2. METHOD OF MEASUREMENT The measurements were carried out at the NBS antenna range when it was located at Sterling, Virginia, and at Table Mountain, Colorado, after the antenna research group was relocated 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 approximately 320 meters from a target transmitter and antenna. The transmitting antenna was located at a height above ground so that the receiving antennas were illuminated at grazing angles. The Yagi under test was mounted 3X (wavelength) above ground and its gain was compared to a reference dipole antenna located approximately 5X to one side and at the same height as the test antenna. Each antenna was matched precisely to 50 ohms and switched alternately to an attenuator and associated receiving and detecting equipment located in a nearby wooden building. In comparing the attenuator readings of the two antennas to produce a constant 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 dB over the period when measurements were being carried out. The values presented are those measured in a forward direction compared to the maximum response of a dipole at the same height above ground and are believed accurate to within 0.5 dB. if referenced to an isotropic 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 graphical form. They are intended to provide a simple means of designing a Yagi antenna of practical dimensions with maximum gain for the configuration under consideration. The purpose of these tests was to determine the following: a. Effect of reflector spacing on the gain of a dipole antenna b. Effect of different equal length directors, their spacing and number on realizable gain 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 parasitic e 1 emen ts 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 plexiglass boom mounted 31 above ground. With the exception of measurements stated in sections 3.3 and 3.4, all parasitic elements were constructed of 0.63 cm (one-fourth inch) diametcr aluminum tubing. The driven element used in the Yagi as well as in the reference dipole was 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 two elements is shown in figure 1. Maximum measured gain was 2.6 dB and was realized at a spacing of 0.21 behind the dipole. This reflector spacing was used in all subsequent measurements. However, for the different Yagi configurations the reflector length was optimized to yield maximum gain. An additional 0.75 dB gain was realized using the reflector configuration shown in figure 2. Although this arrangement was used only on the 4.21 long Yagi, comparable benefits would be realized with other antenna lengths. A photograph of the experimental set-up for this configuration is shown in figure 3. Various arrangements and spacings of reflector elements were tested on the 4.21 Yagi i using the drilled plexiglass support as shown. The reflecting elements were arranged in shapes of plane reflecting surfaces, parabolas and corner reflectors. In addition, different shaped solid reflecting surfaces placed at various distances behind the driven element were also used. Of the combjnations tested, the one shown in figure 2 yielded the largest 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 in the preceding section. The driven element consisted of a x/2 folded dipole; the reflector was 0.4821 in length and spaced 0.21 behind the driven element. The diameter of all elements was 0.00851 (0.25 inches = 0.63m). 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 were varied from 0.304X to 0.4231 and spacings from 0.011 to 0.401. The Yagi length, measured from the driven element to the last director, was varied from an overall length of 0.2x to 10.2X. 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 these parameters on measured gain. Figures 4, 5, and 6 show the relative gain of a Yagi as a function of length for different spacings between director elements using director lengths of 0.3821, 0.4111, and 0.424A. Figure 4 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 was increased to approximately 101. Note, however, that as the spacing between elements was 2 *-- -e- W 2 5 : I f -T W e 1 DE REFLECTOR 21 , , + , s I -05 .10 15 20 .25 30 .35A SPACING, S, OF REFLECTOR BEHIND DRIVEN ELEMENT FIG. 1 GAIN IN dB OF A DIPOLE AND REFLECTOR FOR DIFFERENT SPACINGS BETWEEN ELEMENTS 0- LR3 - 0 OIRECTORS- LR3 0.271 1 DRIVEN ELEHE NT REFLECTOR LENGTHS LR1 = LR2 = 0.4551 LR3 = 0.4731 FREQ = 400 MHz 0 LR2 [LENGTHS NOT CORRECTED FOR BOOM OR SUPPORT THICKNESS] FIG. 2 ARRANGEMENT OF THREE REFLECTING ELEMENTS USED WITH THE 4.2X YAGI 3