Yagi Antenna Design NIST

NBS TECHNICAL NOTE 688

NATIONAL BUREAU OF STANDARDS

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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 c a r r i e d out by the Nat ional Bureau of Standards a t antenna t e s t ranges located i n S t e r l i n g , V i r g i n i a , and a t Table Mountain near Boulder, Colorado.

These measurements were c a r r i e d out by the Antenna Research Section o f the Radio System D i v i s i o n , Nat iona l Bureau of Standards.

i i i

CONTENTS

1. INTRODUCTION . 2. METHOD OF MEASUREMENT

3. RESULTS . 3.1 E f f e c t o f Re f lec to r Spacing on Measured Gain . 3.2 E f f e c t o f D i f f e r e n t Equal Length D i rec to rs and Spacing on Heasured Gain

f o r D i f f e ren t Yagi Lengths

Ef fec t o f D i f f e r e n t Diameters and Lengths o f Directors on Heasured Gain

E f fec t o f t he S ize o f a Support ing Boom on the Optimum Length o f a P a r a s i t i c Element .

3.3

3.4

3.5 E f f e c t o f Spacing and Stacking o f Yagi Antennas on Rea l izab le Gain

Page

1

1

1

2

2

6

6

6

3.6 Measured Rad ia t ion Pat te rns o f D i f f e r e n t Length Yagi Antennas 6

4. DESIGNING THE YAGI ANTENNA 16

5 . CONCLUS IONS 21

6. ACKNOWLEDGMENTS . 2.1 7. REFERENCES . 21

L I S T OF TAGLES and FIGURES

Table 1. Optimized Lengths of P a r a s i t i c Elements f o r Yagi Antennas o f S ix D i f f e ren t Lengths . 7

F igure 1. Gain i n dB o f a Dipole and Re f lec to r f o r D i f fe ren t Spacings Between Elements 3

Figure 2. Arrangement o f Three Re f lec t i ng Elements Used With the 4.21 Yagi . 3 F igure 3. Photograph o f the Tr igona l Re f lec to r Experimental Set-Up Used With

the 4.21 Yagi 4

F igure 4. Gain o f a Yagi as a Funct ion o f Length (Number of D i rec to rs ) fo r D i f f e r e n t Constant Spacings Between Girectors o f Length Equal t o 0.3822, . 4

F igure 5. Gain o f a Yagi as a Funct ion o f Length (Number of D i rec to rs ) fo r D i f f e r e n t Constant Spacings Between Directors o f Length Equal t o 0.4111 . 5

F igure 6. Gain o f a Yagi as a Function o f Length (Number of D i rec to rs ) fo r D i f f e r e n t Constant Spacings Between Directors o f Length Equal t o 0.4242, . 5

V

Figure 7.

Figure 8.

i

F igure 9.

i

F igure 10.

F igure 11.

f i gu re 12.

Figure 13.

F igure 14.

F igure 15.

Figure 16.

Figure 17.

F igure 18.

Figure 19.

F igure 20.

Figure 21.

Comparison o f Gain o f D i f f e r e n t Length Yagis Showing the Re la t ionsh ip Between D i rec to rs Optimized I n Length t o Y ie ld Haximum Gain and D i rec to rs of Optimum Uniform Length . 8 Measured Gain Vs D i rec to r Length o f a 1.251 Yagi Antenna Using Three D i rec to rs o f D i f f e r e n t Length and Diameter Spaced 0.351 . 8 , Yagi Antenna Design Data Showing the Relat ionship Between Element Diameter t o Wavelength Ra t lo and Element Length f o r D i f f e r e n t Antennas

?

9

Graph Showing the E f f e c t o f a Support ing Boom on Length o f Elements . - 10 Gain o f an Array o f Yagis, Stacked One Above the Other and i n Broadside, as a Function o f Spaclng . 1 1 Gain o f an Array of Two Sets o f Stacked Yagis Spaced 1.61 as a f u n c t i o n of Hor izontal Distance Between Them . 11 Radiat ion Patterns o f a D ipo le and Ref lec to r With 0.21 Spacing . 12 Radiat ion Patterns o f a 3-Element, 0.41 Long Yagi . 12 Radiat ion Patterns of a 5-Element, 0.81 Long Yagi . 13 Radiat ion Patterns of a 6-Element, 1.21 Long Yagi . 13 Radiat ion Patterns o f a 12-Element, 2.21 Long Yagi . 14 Radiat ion Patterns o f a 17-Element, 3.21 Long Yagi . 14 Radiat ion Patterns o f a ls-Element, 4.21 Long Yagi . 15 Use o f Design Curves i n Determining Element Lengths of 0.8X Yagi Considered in Example 1 18

Use o f Design Curves i n Determining Element Lengths o f 4.21 Yagi Considered in Example 2 20

Y A G I ANTENNA DESIGN

Peter P. V iezbicke

Th is repor t presents data, using modeling techn ques, f o r the optimum design o f d i f f e r e n t length Yagi antennas. This in fo rmat ion i s presented i n graph ica l form t o f a c i l i t a t e the design o f p r a c t i c a l leng th an ennas--from 0.ZX t o 4.2A long--for operat ion i n the HF, VHF, and UHF frequency range. d i f f e r e n t antenna parameters on r e a l i z a b l e ga ln were a l s o i nves t i ga ted and the r e s u l t s a re presented. o f two o r more antennas t o provide a d d i t i o n a l gain.

Key words: Yagi.

The e f f e c t s of

F i n a l l y , supplemental data a re presented on the s tack ing

Antenna, d i rec to r , d r i ven element, ga in , r a d i a t i o n pa t te rn , r e f l e c t o r ,

1. INTRODUCTION

The Yagi-Uda antenna 111, commonly known as the Yagi, was invented i n 1926 by D r . H. Yagi I t s con f igura t ion normally cons i s t s o f a number of d i r e c t o r s and r e f l e c t o r s and Shintaro Uda.

t h a t enhance r a d i a t i o n i n one d i r e c t i o n when p roper l y arranged on a suppor t ing s t ruc tu re .

Since i t s discovery, a l a rge number of repo r t s have appeared i n the l i t e r a t u r e r e l a t i v e t o the analysis, design, and use of the Yagi antenna [2, 3 , 4, 5 , 6 , 7, 8, 91. However, l i t t l e o r no data seem t o have been presented regarding how p a r a s i t i c element diameter, element length, spacings between elements, support ing booms o f d i f f e r e n t c ross sec t iona l area, var ious r e f l e c t o r s , and o v e r a l l leng th a f f e c t measured gain.

This r e p o r t presents the r e s u l t s of extens ive measurements c a r r i e d o u t by the Nat ional Bureau o f Standards t o determine these e f f e c t s and g ives graph ica l data t o f a c i l i t a t e the design of d i f f e r e n t length antennnas t o y i e l d maximum gain. I n addition., des ign c r i t e r i o n i s a l so presented on stacking--one above the o ther and i n a columnar con f igu ra t i on . gain i s g iven i n decibels (de) r e l a t i v e t o a d i p o l e (reference antenna) a t t he same he igh t above ground as the t e s t (Yagi) antenna.

The

2. METHOD OF MEASUREMENT

The measurements were ca r r i ed o u t a t the NBS antenna range when i t was loca ted a t S t e r l i n g , V i r g i n i a , and a t Table Mountain, Colorado, a f t e r the antenna research group was relocated t o Colorado. The antenna under t e s t was used as a rece iv ing antenna and was loca ted approximately 320 meters from a ta rge t t ransmi t te r and antenna. The t r a n s m i t t i n g antenna was located a t a height above ground so tha t the rece iv ing antennas were i l l um ina ted a t g raz ing angles. The Yagi under t e s t was mounted 3X (wavelength) above ground and i t s ga in was compared t o a reference d ipo le antenna located approximately 5X to one s ide and a t the same he igh t as the t e s t antenna. Each antenna was matched p rec i se l y t o 50 ohms and switched a l t e r n a t e l y t o an a t tenuator and associated rece iv ing and de tec t i ng equipment loca ted i n a nearby wooden b u i l d i n g . constant rece iver output l eve l , l i n e losses t o each were measured and compensated f o r i n a r r i v i n g a t f i n a l values o f gain. The values o f ga in were reproduc ib le to w i t h i n 0.2 dB over the per iod when measurements were being c a r r i e d ou t . measured i n a forward d i r e c t i o n compared to the maximum response of a d i p o l e a t the same height above ground and are bel ieved accurate t o w i t h i n 0.5 dB. i s o t r o p i c source, the values must be increased by 2.16 dB.

A l l measurements were conducted a t a modeling frequency o f 400 MHz.

I n comparing the a t tenuator readings o f t he two antennas t o produce a

The values presented are those

i f referenced t o an

3. RESULTS

The r e s u l t s o f the measurements c a r r i e d ou t i n t h i s study are presented i n g raph ica l form. dimensions w i t h maximum gain f o r the con f igu ra t i on under cons idera t ion . these t e s t s was t o determine the fo l low ing :

They are intended t o provide a simple means of designing a Yagi antenna of p r a c t i c a l The purpose o f

i

a.

b. E f f e c t o f d i f f e r e n t equal length d i r e c t o r s , t h e i r spacing and number on

E f f e c t o f r e f l e c t o r spacing on the g a i n of a d i p o l e antenna

r e a l i z a b l e ga in

E f f e c t o f d i f f e r e n t diameters and lengths o f d i r e c t o r s on r e a l i z a b l e ga in c.

d. E f f e c t o f the s i ze o f a support ing boom on the o p t i m u m length o f p a r a s i t i c e 1 emen t s

e.

f. Measured r a d i a t i o n patterns o f d i f f e r e n t Yagi con f igura t ions

E f f e c t o f spacing and stacking o f antennas on ga in

3.1 EFFECT OF REFLECTOR SPACING ON MEASURED GAIN

These t e s t s as w e l l as a l l others were c a r r i e d out on a non-conducting p lex ig lass boom mounted 31 above ground. and 3.4, a l l p a r a s i t i c elements were cons t ruc ted of 0.63 cm (one-fourth inch) diametcr aluminum tubing. was a half-wave fo lded d ipo le matched t o 50 ohms us ing a double-stub tuner.

With the except ion o f measurements s ta ted i n sect ions 3 . 3

The dr iven element used i n the Yagi as w e l l as i n the reference d ipo le

The g a i n o f a d i p o l e and r e f l e c t o r combination for d i f f e r e n t spacings between the two elements i s shown i n f i g u r e 1 . Maximum measured ga in was 2.6 dB and was r e a l i z e d a t a spacing of 0.21 behind the dipole. measurements. However, f o r the d i f f e r e n t Yagi con f igu ra t i ons the r e f l e c t o r l eng th was opt imized t o y i e l d maximum gain. r e f l e c t o r con f igu ra t i on shown i n f i g u r e 2.

This r e f l e c t o r spacing was used i n a l l subsequent

An a d d i t i o n a l 0.75 dB gain was r e a l i z e d using the

Although t h i s arrangement was used on ly on t h e 4.21 long Yagi, comparable bene f i t s would be r e a l i z e d w i t h other antenna lengths. A photograph of the experimental set-up f o r t h i s con f igu ra t i on i s shown i n f i gu re 3 .

Various arrangements and spacings o f r e f l e c t o r elements were tes ted on the 4.21 Yagi using the d r i l l e d p lex ig lass support as shown. The r e f l e c t i n g elements were arranged i n shapes o f p lane r e f l e c t i n g surfaces, parabolas and corner r e f l e c t o r s . d i f f e r e n t shaped s o l i d r e f l e c t i n g surfaces placed a t var ious distances behind the d r i ven element were a l s o used. O f the combjnations tested, the one shown i n f i g u r e 2 y ie lded the l a rges t increase i n gain over tha t of the s i n g l e r e f l e c t i n g element.

In add i t i on ,

3.2 EFFECT OF DIFFERENT EQUAL LENGTH DIRECTORS AND SPACiNG ON MEASURED GAIN FOR DIFFERENT YAGI LENGTHS

These measurements were conducted us ing the same non-conducting boom as mentioned i n the preceding sect ion. was 0.4821 i n l eng th and spaced 0.21 behind the d r i v e n element. elements was 0.00851 (0.25 inches = 0.63m).

The dr iven element cons is ted o f a x/2 fo lded d ipo le ; t he r e f l e c t o r The diameter of a l l

The ga in o f t h e Yagi was measured as a f u n c t i o n of antenna length (number of d i r e c t o r s ) f o r d i f f e r e n t equal length d i rec to rs and spacing between them. The d i r e c t o r lengths were var ied from 0.304X t o 0.4231 and spacings f rom 0.011 t o 0.401. The Yagi length, measured from the d r i ven element t o the l a s t d i r e c t o r , was va r ied from an o v e r a l l l eng th o f 0.2x to 10.2X. The r e f l e c t o r i n a l l cases was f i xed . . Although many measurements were c a r r i e d ou t , on l y those r e s u l t s and associated graphs a r e presented tha t show the e f f e c t s o f these parameters on measured gain.

Figures 4, 5, and 6 show the r e l a t i v e ga in of a Yagi as a func t i on o f length fo r

Figure 4 shows tha t fo r r e l a t i v e l y shor t d i r e c t o r s a t a spacing o f 0.3X, d i f f e r e n t spacings between d i rec to r elements us ing d i r e c t o r lengths o f 0.3821, 0.4111, and 0.424A. the ga in o f the Yagi increased t o a maximum value o f 14.5 dB when the antenna length was increased t o approximately 101. Note, however, t h a t as the spacing between elements was

2

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2 5 W e 1

-e- --*

-T DE R E F L E C T O R 21 : I f , I , +,

s -05 .10 1 5 2 0 .25 3 0 .35A

SPACING, S , OF REFLECTOR BEHIND DRIVEN ELEMENT

F I G . 1 G A I N I N dB OF A DIPOLE AND REFLECTOR FOR DIFFERENT SPACINGS BETWEEN ELEMENTS

0- L R 3

- OIRECTORS- 0 L R 3

D R I V E N 1 E L E H E NT

R E F L E C T O R L E N G T H S

L R 1 = LR2 = 0 . 4 5 5 1 L R 3 = 0 . 4 7 3 1 F R E Q = 4 0 0 M H z

0 . 2 7 1

L R 2 0

[ L E N G T H S NOT CORRECTED FOR B O O M OR SUPPORT T H I C K N E S S ]

F I G . 2 ARRANGEMENT OF THREE REFLECTING ELEMENTS USED WITH THE 4.2X YAGI

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I I I I 1 I I I I

w > U 3 m I J L L I i La x u a-

on Y

c z

Y - > - w .--- 4 0

F I G . 3 PHOTOGRAPH OF THE TRIGONAL REFLECTOR EXPERIMENTAL SET-UP USED WITH THE 4 .2X YAGI

0 .3X S P A C I N G 0 . 4 X S P A C I N G 1 4

12 0

9 e

Q 0 . 2 X S P A C I N G .* 0.06X S P A C I N G Q 9

, d 9a

0 .3X S P A C I N G 0 . 4 X S P A C I N G 1 4

9 e

12

Q 0 . 2 X S P A C I N G

o . 1 o x S P A C I N G

F I G . 4 GAlN OF A YAGI AS A FUNCTION OF LENGTH (NUMBER OF DIRECTORS) FOR DIFFERENT CONSTANT SPACINGS BETWEEN DIRECTORS OF LENGTH EQUAL TO 0.3821

4

Y > U 3

u- CLO

= 4' 2 - L7

R

W on I-

L w - w - w +-I 4 0 2 a

, , / G A I N O F D I P O L E AND R E F L E C T O R

1 2

10

8

6

0 . 1 X S P A C I N 4

. 3 X S P A C I N G

0 . 4 a SPACING

W I

0.30~ SPACING

4 ' a S P A C I N G . 0.35A S P A C I N G

'1 0 . 4 X \ \ . - I I I I 1 I I I I I I J 7 0 1 2 3 4 5 6 7 8 9 10

ADD 0 . 2 ~ FOR R E F L LENGTH OF ANTENNA I N U A V E L E N G T H S

FIG. 6 GAIN OF A YAGI AS A FUNCTION OF LENGTH (NUMBER OF DIRECTORS) FOR DIFFERENT CONSTANT SPACINGS BETWEEN DIRECTORS OF LENGTH EQUAL TO 0.4241

5

1

I

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decreased, an o s c i l l a t o r y wave p a t t e r n r e s u l t e d wherein t h e max shorter Yagi l e n g t h and var ied between a maximum and minimum va was changed. As the length o f the d i r e c t o r s was increased, the pa t te rn were a l s o enhanced together w i t h a reduc t ion i n gain as

mum gain occurred a t a ue as the length of the Yagi v a r i a t i o n s i n the wave shown i n f i g u r e s 5 and 6 .

The curves presented i n f i g u r e 7 show a comparison o f r e a l zed ga in vs Yagi leng th up t o 4.21 for antennas us ing d i r e c t o r s o f equal leng th and those optimized i n length. optimized length conf igura t ions the ga in increased from 0.5 dB f o r the 2.2A antenna t o approximately 1.5 dB fo r the 4.2X Yagi.

For the

Table 1 g ives d e t a i l s o f antenna parameters f o r the

3.3 EFFECT OF DIFFERENT DIAMETERS AND LENGTHS OF DIRECTORS ON MEASURED G A I N

This e f f e c t was determined by measuring the ga in o f d i f f e r e n t Yagi con f igura t ions for d i f f e r e n t d i r e c t o r lengths of var ious diameters. Curves showing the r e s u l t s of measurements car r ied ou t on the 1.251 long Yagi are g iven i n f i g u r e 8. As expected, the maximum ga in f o r the d i f f e r e n t combinations remained unchanged. The l a r g e r diameter elements y i e l d e d maximum gain a t shor te r lengths w h i l e the smal le r d iameter elements y ie lded maximum ga in a t cor re - spondingly g rea ter lengths. Results o f a s e r i e s of measurements, n o t i n g these e f f e c t s , were car r ied o u t on the d i f f e r e n t leng th Yagis and, together w i t h r e s u l t s presented i n Table 1 , a set o f design curves was produced and i s presented i n f igure 9 . basic design c r i t e r i o n o f the Yagi antenna and a r e v a l i d over a large frequency range prov ided t h e selected element diameter t o wavelength r a t i o d/X f a l l s w i t h i n the l i m i t s shown.

These data p rov ide the

3.4 EFFECT OF THE S I Z E OF A SUPPORTING BOOM ON THE OPTIMUM LENGTH OF A PARASIT IC ELEMENT

Round and square suppor t ing booms of d i f f e r e n t cross-sect-ion area were employed i n Yagi antennas o f d i f f e r e n t lengths t o determine what e f f e c t the boom diameter had on the optimum length o f the p a r a s i t i c elements. resul ts . The e f f e c t o f a round suppor t ing boom on the length o f a p a r a s i t i c element i s represented by t h e curve i n f igure IO. T h i s experimental response can be used i n app ly ing the boom c o r r e c t i o n f o r the f i n a l Yagi design.

The round and square booms y i e l d e d s i m i l a r

3.5 EFFECT OF SPACING AND STACKING OF Y A G I ANTENNAS ON REALIZABLE G A I N

As shown i n f i g u r e 1 1 , a d d i t i o n a l g a i n i s r e a l i z e d when antennas are stacked one above the o t h e r or i n broadside. N o t o n l y i s ga in increased but the beamwidth i s reduced appreciably depending upon the c o n f i g u r a t i o n employed.

F igure 11 (A) shows the e f f e c t s o f s tack ing two antennas, one above the o ther . These responses show s i m i l a r mutual e f f e c t s between t w o seven-element Yagis and between two f i f teen-e lement Yagis. A t c lose spacing, approximately O.Bh, the gain was reduced due t o h igh mutual impedance e f f e c t s but increased t o a maximum o f 2.5 dB as the spacing was increased t o approximately 1.61. S i m i l a r e f f e c t s were measured w i t h the combination shown i n f i g u r e 1 1 (B). Maximum gain i n t h i s case was r e a l i z e d w i t h the two antennas spaced a t approximately 2.01.

A combination o f the above two c o n f i g u r a t i o n s us ing spacings as shown y i e l d e d an add i t iona l 2.5 dB gain and a corresponding reduc t ion i n beamwidth. For example, four 0.8; Yagi antennas, appropr ia te ly stacked, spaced and fed i n phase y ie lded a gain o f 14.2 dB r e l a t i v e t o a d i p o l e located a t the same h e i g h t above ground. I n cont ras t , a combination o f four 4.2). Yagi antennas y ie lded a ga in o f 19.6 dB r e l a t i v e t o a d ipo le , as shown by the graph i n f i g u r e 12.

3.6 MEASURED R A D I A T I O N PATTERNS OF DIFFERENT LENGTH Y A G I ANTENNAS

Radiat ion pa t te rns measured i n the E ( h o r i z o n t a l - s o l i d curves) and H (ver t ical-dashed curves) planes f o r d i f f e r e n t Yagi designs a r e presented i n f igures 13 through 19. The

6

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TABLE 1 . OPTIMIZED LENGTHS OF P A R A S I T I C ELEMENTS

FOR YAGI ANTENNAS OF S I X DIFFERENT LENGTHS

G A I N RELATIVE TO HALF-WAVE D I P O L E I N d B

DESIGN CURVE (SEE FIG. 9)

7.1 9.2 10.2 12.25 13.4 1 4 . 2

(A) (B) ( c ) (6) (D)

ELEMENT DIAMETER = 0.0085

f = 400 MHz REFLECTOR SPACED 0.21 BEHIND DRIVEN ELEHENT

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Q - n w 1 4 -

LL 1 3 - a

a

> U 3

-I

I

0 t W

1 1 -

DIRECTOR LENGTHS OPTIMIZED FOR ElAXlMUM GAIN ( S E E T A B L E 1 )

N = NUMBER OF D I R E C T O R S S = S P A C I N G BETWEEN D I R E C T O R S ( R E F L E C T O R SPACED 0.21 ON A L L ANTENNAS)

p

I = 1 S.0.2A ,

7 I I I 1

F I G . 7 COMPARISON OF GAIN OF DIFFERENT LENGTH YAGIS SHOWING THE RELATIONSHIP BETWEEN DIRECTORS OPTIMIZED I N LENGTH TO Y I E L D MAXIMUM G A I N AND DIRECTORS OF OPTIMUM UNIFORM LENGTH

w

1 . o 2.0 3.0 4.0 5.0

OVERALL LENGTH, I N WAVELENGTHS, OF DIFFERENT YAG IS

-1 0 b

0.32 Un

0.16 un t 0.08 cm DIAMETER 1 in. - 2.5.5 cn

Q u I I I I I J

1 1 1 2 13 14 1 0

LENGTH OF DIRECTORS I N INCHES

F I G . 8 MEASURED G A I N VS DIRECTOR LENGTH OF A 1.251 YAGI ANTENNA USING THREE DIRECTORS OF DIFFERENT LENGTH AND DIAMETER SPACED 0.351

1- Ln

--I-- 7

S H 1 9 N 3 1 3 A V M N I S l N 3 W 3 1 3 30 H 1 9 N 3 1

9

. 0 c1

I- U a I I- Cs r W 2 W w U 3

0 I-

= W I- W

U c(

n I- z W aI W

a W I- W x U w n 8- z W x W v ) A U W Z r

Z W UI- W Z Z U I- W I - m r

W

U W I Y mu- L w

n a

o n I-- u o 2 Y W =I c

w

W i 3 IZ I-W -I

W ZI- W Z 2ZW O E I W v)d

W

I-J Z W U> d

i

0 pr) 0

In N 0

0 (u 0

u)

0 F

0

0 c

m 0 0

Y SlN3W313 3I l ISWWd A0 H13N31 W n W l U O N I 3SW3t13NI

v)

5 W II W J W

LL 0

I I- c3 z W

z 0

x 0 0

a z

m

- z 0 a. P 3 v)

a LL 0 i- V W L LL W

W I t- c3 z - z I v)

I P Q

c3

0 c

W LL -

10

f

3 - t-- 5

F I G . 11 G A I N OF AN ARRAY OF YAGIS, STACKED ONE ABOVE THE OTHER AND I N BROADSIDE, AS A FUNCTION OF SPACING

m TI

3 - - 22

5

0

w

QIPI-

2 -

0- 7 E L E M E N T Y A G I ANTENNAS 1 - -+ 15 E L E M E N T Y A G I ANTENNAS

I I 1

(L -I

I a

20

19

18

1 7

m -0

-

-

-

-

4 . 2 X L O N G r 1 1 5 E L E M E N T Y A G I

d h = 2 L S P A C I N G S = 1.6X AND H E I G H T h = 2 . 0 X C O N S T

f I I 3 . 0 I 1 . o 2 . 0 0

HORIZONTAL SPACING, H I N WAVELENGTHS, BETWEEN STACKED YAGIS

F I G . 12 GAIN OF AN ARRAY OF TWO SETS OF STACKED YAGIS SPACED 1 . 6 1 AS A FUNCTION OF HORIZONTAL DISTANCE BETWEEN THEM

11

I - .. .

Az imu t ha 1

m U

aJ m c 0 n

-0 aJ N v

tu E 0 z

ngl e , degrees

POLE AND REFLECTOR WITH 0.2x SPACING

m U

01 ln C 0 P #I W QI.

D W N

..

-8-

7

E 0 z

-

_ _ . .

i- --

I 1 - _ - - - - ! I

i I A-

F

,'-\ c;:

Azimuthal Angle, degrees

FIG. 16 RADIATION PATTERNS OF A 6-ELEMENT. 1 .21 LONG YAGI

13

m U

13 0, N -I- -

TI al N

i


FIG. 1 7 R A D I A T I O N PATTERNS OF A 12-ELEMENT, 2.21 LONG YAGI


F I G . 18 RADIATION PATTERNS OF A 17-ELEHENT. 3.2x LONG YAGI

14

I . . _II-- -a e . - ---T--------- ' . . - . . . .. . . . -~ - . - - ~ ~ -

I

FIG. 19 RADIATION PATTERNS OF A 15-ELEMENT, 4.21 LONG YAGI

15

i

I

element) are presented i n f i g u r e 13. 1 1 l 0 respecdively. measured 57 i s i n the order o f 24 dB, wh i l e the r a d i a t i o n to the rea r was on ly 8 dB down from t h a t i n the forward d i rec t i on .

The 3-dB E and H plane beanwidths measured 66' and The beanwidth of the 3-element 0.4X antenna, as shown i n f i gu re 14,

and 72' i n the E and H planes respec t ive ly . The E plane, f ron t - to -s ide r a t i o

The rad ia t i on pa t te rn o f the 5-element 0.81 Yagi presented i n f i g u r e I 5 i s charac ter ized by a 3 dB beamwidth o f 48' and 56' i n the E and H planes respec t i ve l y . f ron t - to -s ide r a t i o remained comparable t o the 3:element antenna; however, the f r o n t - t o - back r a t i o was improved considerably and measured 15 dB. I n r a d i a t i o n pa t te rns o f 6, 12, 17 and 15-element Yagis as shown i n f igures 16 through 19, the beamwidths became progres- s i v e l y smaller as was expected w i t h increased gain.

The E plane,

4. DESIGNING THE YAGI ANTENNA

To f a c i l i t a t e the design o f an antenna o f p r a c t i c a l dimensions and y e t r e a l i z e maximum gain, re fe r t o the curves shown i n f i g u r e 9. These data were developed from r e s u l t s o f model measurements c a r r i e d o u t a t 400 HHz using elements o f d i f f e r e n t diameters. those curves are presented which w i l l enable the user t o design t h e 0.4, 0.8, 1.2, 2.2, 3.2 and 4.2h long Yagis t h a t y i e l d gains o f 7.1, 9.2, 10.2, 12.3, 13.4 and 14.2 dB respec- t i v e l y over t h a t o f a d ipo le mounted a t the same he igh t above ground.

Only

I n designing a Yagi antenna, the fo l l ow ing bas ic in fo rmat ton i s requ i red and, o f course, w i l l depend upon ind i v idua l requirements.

1.

2.

Frequency of operat ion, f (wavelength, h )

Antenna gain required, G (dB)

3.

4.

Careful considerat ion should a l so be given t o se lec t i on o f t h e diameter o f the elements and boom a t the wavelength o r frequency o f operat ion. Th is i s important s ince smaller diameter and l i g h t e r mater ia ls can be used a t the higher frequencies i n con t ras t t o la rger and heavier mater ia ls needed f o r support a t the lower frequencies. Note a l s o tha t the selected element diameter-to-wavelength r a t i o s used in the des ign o f the chosen antenna must f a l l w i t h i n the l i m i t s shown.

Diameter o f p a r a s i t i c elements (d i rec to rs - re f l ec to rs ) used i n cons t ruc t ion , d/A

Diameter of support ing boom used i n cons t ruc t ion , D/x

I f maximum gain i s t o be rea l i zed using the data presented, i t i s essent ia l to follow

TO

The f i r s t considers the des ign o f a 5-element,

very c lose ly the procedure described here. In add i t i on , the element lengths should be measured and cu t t o a to lerance o f about 0.0031 w i t h respect t o t h e ca l cu la ted values. a i d the user i n the design o f t h i s antenna and t o f a m i l i a r i z e him i n use of the design data, two s p e c i f i c examples are presented. 0.81 Yagi; the second example presents a step-by-step procedure for the design of a 15- element, 4.21 Yagi. operate a t a frequency o f 50.1 MHz i n the amateur r a d i o band and y i e l d a gain o f 9.2 dB r e l a t i v e t o a dipole. The elements s h a l l be constructed of 2.54 cm (1 in.) diameter aluminum tubing w i t h the boom o f 5.08 cm (2 in.) diameter aluminum tub ing .

I n the f i r s t example, consider the design o f a 0 . 8 ~ Yagi antenna t o

GIVEN: Frequency 50.1 HHz, X = 597 cm. (235 in.) Element Diameter, d = 2.54 cm. (1 i n . )

d/h = 0.0042

Boom diameter , D = 5.1 cm. (2 i n . ) D/X = 0.0085 Element spacing = 0.21 = 119 cm. (47 in . ) Overal l leng th 2 0.81 = 478 cm. (188 in . )

16

STEP 1:

STEP 2:

STEP 3:

STEP 4:

STEP 5:

Plot the lengths of the parasitic elements obtained from Table 1 for 0.81 long Yagi on the corresponding curve In figure 9. For clarlty, these curves are reproduced in figure 20. Establish points LD = L , L , LR and determine

1 O3 D2 the parasitic element lengths for d/X = 0.0085.

Thus LD = Lo3 = 0.4281 1

L - 0.4241 LR = 0.4821

D2

For our design, where the element diameter to wavelength ratio d/X - 0.0042, plot and establish this point on the director curve and indicate by a check

mark (4.

For the same d/1 ratio, determine the uncompensated length of the reflector LR - 0.4851. With a pair of dividers, measure the distance along the curve between the initial points 0 , = D

point established in Step 2 downward along the curve and determine the uncompensated length of director L

From the foregoing, the uncompensated parasitic element lengths for the 50.1 MHz Yagi are:

This is the uncompensated director length of D1 = D = 0.442X. 3

to D2 determined i n Step 1 . Transpose this distance from the 3

= 0.4381. O2

L = 0.438X

LR = 0.4851

D2

To these values, a correction must be added to compensate for the boom diameter. Refer to figure 10. For a boom diameter-to-wavelength ratio O/X = 0.0085, determine the fractional increase in wavelength by which each of the parasitic elements must be increased. From the chart this length = 0.0051. Thus, for this design the exact lengths of the parasitic elements should be measured and cut to the following lengths.

= L = 0.4421 + 0.0051 = 0.4471 = 267 cm. O3

L = 0.4381 + 0.0051 = 0.4431 = 264.5 cm.

= 0.4851 + 0.005X = 0.490X = 293 cm. O2

LR The driven element is designed so that the Yagi can work either into a 50 or 200 ohm load

impedance. Precise matching to 50 ohms can be accomplished by using a double-stub tuner connected into the feed line.

For a 50 ohm impedance, a folded dipole and a quarterwave balun can be employed.

17

!

SHlSN313AVM N I SlN3W313 30 H19N31

18

I f the antenna i s designed w i t h a 200 ohm balanced input impedance, then the dr iven element should be designed t o provide an impedance step-up r a t i o o f 12. t i on , a X/2 balun s e c t i o n and stubs can be used t o p rov ide proper impedance transformat ion

For t h i s conf igura-

and matching. OtHer matching methods can a lso be employed such as Gamma o r T match [ l o , 1 1 , 121.

As a second example, cons ider the design of a 4.2h long Yagi t o p rov ide a ga in of 14.2 d8 r e l a t i v e t o a d i p o l e t o operate on 827 HHz i n the center o f TV Channel 73. For the cons t ruc t i on o f t h i s antenna l e t us select and use a 1/2-inch diameter boom w i t h 3/16-inch diameter elements u s i n g t h i n w a l l brass tubing.

GIVEN:

STEP 1:

STEP 2:

STEP 3:

STEP 4:

STEP 5:

Frequency 827 HHz, A - 36.34 cm. (14.3 in . ) Element diameter, d

d/X = 0.013

Boom diameter, D = 1.27 cm. (1/2 i n . )

D/X = 0.035

Element spacing

Overa l l leng th = 4.2A = 152 cm. P l o t t h e lengths of p a r a s i t i c elements from Table 1 for the 4.21 long Yagi on

the corresponding curve i n f i g u r e 9. For c l a r i t y , these curves a r e reproduced and presented i n f i g u r e 21. Es tab l i sh po in ts LD = L 02* L ~ 3 * - * L ~ l and locate t h e p a r a s i t i c element lengths on the curve as i n the prev ious example f o r the

d/A = 0.0085 case.

For our p a r t i c u l a r design, however, where the element d iameter t o wavelength

r a t i o d/X = 0.013, p l o t and es tab l i sh t h i s p o i n t on the 4 . Z - long Yagi curve and i n d i c a t e t h i s s t a r t i n g po in t w i t h a check (4. d i r e c t o r l eng th of D1 = D2 = 0.4141.

For t h e same d/X r a t i o , determine the uncompensated l eng th o f the r e f l e c t o r ,

LR = 0.473X; from curve D, f i gu re 21.

With t h e use o f a p a i r of d iv iders , e s t a b l i s h and measure t h e distance be-

tween the p o i n t s D1 = D2 t o D Transpose t h i s d i s tance from the i n i t i a l (4 mark downward along the d i r e c t o r curve and determine LD

Measure the d is tance from D1 = D2 t o D4.

i n i t l a l (4 p o i n t and determine length o f D4 = 0.3951.

determine remaining d i r e c t o r lengths.

0.381X, L t o LD = 0.3771. ' 8 13

To these values a co r rec t i on must be added t o compensate f o r boom diameter.

Again, r e f e r t o f i g u r e 10.

0.035, determine the f r a c t i o n a l amount by which each element must be

increased t o compensate f o r boom. From the curve, determine t h i s length =

0.0261.

Thus, t o r e a l i z e maximum gain from t h i s antenna, measure and cu t the

p a r a s i t i c elements t o the fo l low ing lengths:

- 0.48 cm.

= 0.3081 = 11.2 cm.

1

Th is i s the uncompensated

3' = 0.4091.

3 Transpose t h i s d is tance from

S i m i l a r l y ,

= 0.3911, LD = 0.385X, L = LD5 6 DJ

For a boom diameter-to-wavelength r a t i o D/X =

19

0 0 0 0 0 0 0 0 0 0 0 0 0 0

SH13N313AVM N I S l N 3 W 3 1 3 30 H19N31

20

= L = 0.414X + 0.026X = 0.440X = 16.0 cm. O2

I

I

I

L = 0.4091 + 0.0261 = 0.4351 = 15.8 cm.

L = 0.3951 + 0.026X = 0.4211 = 15.3 cm.

L = 0.391h + 0.0261 = 0.4171 = 15.1 cm.

L = 0.3851 + 0.0261 = 0.4111 = 14.9 cm.

L = 0.3811 + 0.0261 = 0.407X = 14.8 cm.

D3

D4

D5

D6

D J ,= 0.3771 + 0.026X = 0.4031 = 14.6 cm. L -

'8 LD13 LR = 0.4731 + 0.0261 = 0.4991 = 18.1 cm.

The d r i ven element can be o f a v a r i e t y o f designs and w i l l depend upon

ind i v idua l requirements. I t i s usua l l y measured and c u t to one-hal f

wavelength less a shortening f a c t o r t o compensate f o r end-ef fects and

matched t o the c h a r a c t e r i s t i c impedance of the feed l i n e .

5. CONCLUSIONS

The data presented i n t h i s repo r t prov ide the necessary in format ion for the design o f Yagi antennas ranging i n length from 0.21 t o 4.2X. antennas t o y i e l d maximum ga in f o r seven d i f f e r e n t design conf igurat ions. s tack ing o f antennas, s ide by s ide and one above the o t h e r - - a l l fed i n phase--provides an a d d i t i o n a l g a i n up to 5.2 dB over t h a t of the s i n g l e ar ray.

These data a l l o w the user t o design In add i t i on ,

6. ACKNOWLEDGMENTS

The author wishes t o extend s incere apprec iat ion t o Wi l l i am Gorboczieski f o r h i s a s s i s t - ance i n t h e f a b r i c a t i o n of t e s t set-ups and i n ca r ry ing out of t h e measurements. Also, s ince re apprec ia t i on and thanks t o A l v i n Wilson f o r p rov id ing t h e r a d i a t i o n pat terns.

7. REFERENCES

[l] Shintaro, U., and Yasuto, H., Yagi-Uda Antennas (Sasoki P r i n t i n g and Publ ish ing Co., Ltd., Senda, Japan, 1954).

[2] Mai l loux, R. J., The long Yagi-Uda array, IEEE, Trans. Antennas and Prop., AP-14, pp. 128-137 (Mar. 1966).

[3 ] Barbano, N., Log pe r iod i c Yagi-Uda ar ray , IEEE, Trans. Antennas and Prop., AP-14, pp. 235-238 (Mar. 1966).

[ 4 ] Th ie le , G. A., Analysis Y Yagi-Uda type antennas, IEEE, Trans. Antennas and Prop. AP-17, pp. 24-31 (Jan. 1969).

[SI Emerson, J., Arranging Yagi antennas f o r p o s i t i v e r e s u l t s , Broadcast Engineering, No. 5 , pp. 32-40 (May 1971).

[6] Shen, L., D i r e c t i v i t y and bandwidth of single-band and double band Yagi arrays, I E E E , Trans. Antennas and Prop., AP-20, pp. 178-180 (Nov. 1972).

21

[7] Cheng, 0. K . , and Chen, C. A., Optimum element spacings for Yagi-Uda arrays, I E E E , Trans. Antennas and Prop., AP-21, pp. 615-623 (Sept. 1973). I

[8] Chen, C. A . , and Cheng, 0 . K., Optimum element lengths for Yagi-Uda arrays, IEEE, Trans. Antennas and Prop., AP-23, pp. 8-15 (Jan. 1975).

191 Nose, K . , Crossed Yagi antennas for circular polarizatlon, QST, pp. 21-24 (Jan. 1973).

[lo] Healey, 0. J., 1 1 1 , An examination of the G m Match, QST, pp. 11-15 (Apr. 1969). [ l l ] Nose, K . , Adjustment of Gamma-matched parasitic beams, QST, pp. 44-46 (Mar. 1958).

!

[I21 The Radio Amateur's Handbook, Fifty Second Ed. (AH Radio Relay League, 1976). i

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