NBS TECHNICAL NOTE 688
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
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for Applied Technology, the Institute for Computer Sciencej and Technology. the office for Information Programs, and the
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THE INFOR BASIC STANDARDS provides the central basis within the Unitui States of a complete anii c o d t ent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes
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oratory Astrophysics'
- Electricity - Mechanics - Heat - Optical Physics - Center for Radiation Research - L*b.
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a
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lME INSITNTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts research and provides technical services
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THE OFFICE FOR INFORMATION PROCRAMS promotes optimum dissemination and accessibility of scientific information generated within NBS; 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 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
Officeof Information Activities
m c e of International Standards
Office of International Relations.
- Office of
Technical Publications
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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.), T e c h N o t e 688, 27 pages ( D e c e m b e r 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 4 6 688) Price 65 Cents (Add 25 percent additional for other than U S mailing)
FOREWORD
T h i s work was c a r r i e d out by the N a t i o n a l
Bureau o f Standards a t antenna t e s t ranges
l o c a t e d i n S t e r l i n g , V i r g i n i a , and a t T a b l e
Mountain near Boulder, Colorado.
These measurements were c a r r i e d out by t h e
Antenna Research Section o f the Radio System
D i v i s i o n , N a t i o n a l Bureau of Standards.
iii
CONTENTS
Page
.
1.
INTRODUCTION
2.
METHOD OF MEASUREMENT
3.
RESULTS
1
1
.
1
.
3.1
E f f e c t o f R e f l e c t o 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 r e c t o r s and Spacing on Heasured Gain
f o r D i f f e r e n t Yagi Lengths
2
3.3
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 Heasured Gain
6
3.4
E f f e c t o f t h e S i z e o f a Supporting Boom on t h e Optimum Length o f a
P a r a s i t i c Element
6
3.5
E f f e c t o f Spacing and S t a c k i n g o f Yagi Antennas on R e a l i z a b l e Gain
6
3.6
Measured R a d i a t i o n P a t t e r n s o f D i f f e r e n t Length Yagi Antennas
6
2
.
4.
D E S I G N I N G THE YAGI ANTENNA
16
5.
CONCLUS IONS
21
6.
ACKNOWLEDGMENTS
7.
REFERENCES
.
2.1
.
21
L I S T OF
Table 1.
F i g u r e 1.
TAGLES
and FIGURES
Optimized Lengths o f P a r a s i t i c Elements f o r Yagi Antennas o f S i x
D i f f e r e n t Lengths
7
Gain i n dB o f a D i p o l e and R e f l e c t o r f o r D i f f e r e n t Spacings Between
Elements
3
.
F i g u r e 2.
Arrangement o f Three R e f l e c t i n g Elements Used With t h e 4.21 Yagi
F i g u r e 3.
Photograph o f t h e T r i g o n a l R e f l e c t o r Experimental Set-Up Used With
t h e 4.21 Yagi
F i g u r e 4.
.
4
4
Gain o f a Yagi as a F u n c t i o n o f Length (Number of D i r e c t o r s ) f o r
D i f f e r e n t Constant Spacings Between D i r e c t o r s o f Length Equal t o
0.4111
5
Gain o f a Yagi as a Function o f Length (Number of D i r e c t o r s ) f o r
D i f f e r e n t Constant Spacings Between D i r e c t o r s o f Length Equal t o
.
0.4242,
5
.
F i g u r e 6.
3
Gain o f a Yagi as a F u n c t i o n o f Length (Number of D i r e c t o r s ) f o r
D i f f e r e n t Constant Spacings Between G i r e c t o r s o f Length Equal t o
0.3822,
F i g u r e 5.
.
V
Figure
7.
Comparison o f Gain o f D i f f e r e n t Length Yagis Showing t h e R e l a t i o n s h i p
Between D i r e c t o r s Optimized I n Length t o Y i e l d Haximum Gain and
D i r e c t o r s o f Optimum Uniform Length
8
Measured Gain Vs D i r e c t o r Length o f a 1.251 Yagi Antenna Using Three
D i r e c t o r s o f D i f f e r e n t Length and Diameter Spaced 0.351
8
.
F i g u r e 8.
.
i
Figure
9.
i
?
Yagi Antenna Design Data Showing t h e R e l a t i o n s h i p Between Element
Diameter t o Wavelength R a t l o and Element Length f o r D i f f e r e n t Antennas
9
.-
10
F i g u r e 10.
Graph Showing t h e E f f e c t o f a Supporting Boom on Length o f Elements
F i g u r e 11.
Gain o f an Array o f Yagis, Stacked One Above the Other and i n Broadside,
as a Function o f Spaclng
11
Gain o f an Array o f Two Sets o f Stacked Yagis Spaced 1.61 as a f u n c t i o n
o f H o r i z o n t a l Distance Between Them
11
f i g u r e 12.
.
.
.
12
F i g u r e 13.
R a d i a t i o n P a t t e r n s o f a D i p o l e and R e f l e c t o r With 0.21 Spacing
F i g u r e 14.
R a d i a t i o n P a t t e r n s o f a 3-Element,
0.41 Long Yagi
.
12
F i g u r e 15.
R a d i a t i o n P a t t e r n s o f a 5-Element, 0.81 Long Yagi
.
13
F i g u r e 16.
R a d i a t i o n P a t t e r n s o f a 6-Element,
.
13
F i g u r e 17.
R a d i a t i o n P a t t e r n s o f a 12-Element, 2.21 Long Yagi
.
14
F i g u r e 18.
R a d i a t i o n P a t t e r n s o f a 17-Element, 3.21 Long Yagi
F i g u r e 19.
R a d i a t i o n P a t t e r n s o f a ls-Element, 4.21 Long Yagi
F i g u r e 20.
Use o f Design Curves i n Determining Element Lengths of 0.8X Yagi
Considered i n Example 1
18
Use o f Design Curves i n Determining Element Lengths o f 4.21 Yagi
Considered i n Example 2
20
F i g u r e 21.
1.21 Long Yagi
,
.
.
14
15
Y A G I ANTENNA DESIGN
Peter P. V i e z b i c k e
T h i s r e p o r t presents data, using modeling techn ques, f o r t h e optimum design
o f d i f f e r e n t l e n g t h Yagi antennas. T h i s i n f o r m a t i o n i s presented i n g r a p h i c a 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 l e n g t h an ennas--from 0.ZX t o 4.2A
long--for o p e r a t i o n i n t h e HF, VHF, and UHF frequency range. The e f f e c t s o f
d i f f e r e n t antenna parameters on r e a l i z a b l e g a l n were a l s o i n v e s t i g a t e d and t h e
r e s u l t s a r e presented. F i n a l l y , supplemental d a t a a r e presented on t h e s t a c k i n g
o f two o r more antennas t o p r o v i d e a d d i t i o n a l gain.
Key words:
Yagi.
Antenna, d i r e c t o r , d r i v e n element, g a i n , r a d i a t i o n p a t t e r n , r e f l e c t o r ,
1.
INTRODUCTION
The Yagi-Uda antenna 111, commonly known as t h e Yagi, was i n v e n t e d i n 1926 by D r . H. Yagi
I t s c o n f i g u r a t i o n normally c o n s i s t s o f a number o f d i r e c t o r s and r e f l e c t o r s
and S h i n t a r o 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 r o p e r l y arranged on a s u p p o r t i n g s t r u c t u r e .
Since i t s discovery, a l a r g e number of r e p o r t s have appeared i n t h e l i t e r a t u r e r e l a t i v e
t o t h e a n a l y s i s , 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 r e g a r d i n g how p a r a s i t i c element diameter,
element l e n g t h , spacings between elements, s u p p o r t i n g booms o f d i f f e r e n t c r o s s s e c t i o n a l
area, v a r i o u s r e f l e c t o r s , and o v e r a l l l e n g t h a f f e c t measured g a i n .
T h i s r e p o r t presents t h e r e s u l t s of e x t e n s i v e measurements c a r r i e d o u t by t h e N a t i o n a l
Bureau o f Standards t o determine these e f f e c t s and g i v e s g r a p h i c a l d a t a t o f a c i l i t a t e t h e
I n addition., d e s i g n c r i t e r i o n
design o f d i f f e r e n t l e n g t h antennnas t o y i e l d maximum gain.
i s a l s o presented on stacking--one above t h e o t h e r and i n a columnar c o n f i g u r a t i o n . The
g a i n i s g i v e n i n d e c i b e l s (de) r e l a t i v e t o a d i p o l e ( r e f e r e n c e antenna) a t t h e same h e i g h t
above ground as t h e t e s t (Yagi) antenna.
2.
METHOD OF MEASUREMENT
The measurements were c a r r i e d o u t a t t h e NBS antenna range when i t was l o c a t e d 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 t h e antenna research group was
r e l o c a t e d t o Colorado. A l l measurements were conducted a t a modeling frequency o f 400 MHz.
The antenna under t e s t was used as a r e c e i v i n g antenna and was l o c a t e d approximately
320 meters from a t a r g e t t r a n s m i t t e r and antenna. The t r a n s m i t t i n g antenna was l o c a t e d a t
a h e i g h t above ground so t h a t the r e c e i v i n g antennas were i l l u m i n a t e d a t g r a z i n g angles.
The Yagi under t e s t was mounted 3X (wavelength) above ground and i t s g a i n was compared t o
a r e f e r e n c e d i p o l e antenna l o c a t e d approximately 5X t o one s i d e and a t t h e same h e i g h t as
t h e t e s t antenna.
Each antenna was matched p r e c i s e l y t o 50 ohms and switched a l t e r n a t e l y
t o an a t t e n u a t o r and associated r e c e i v i n g and d e t e c t i n g equipment l o c a t e d i n a nearby
wooden b u i l d i n g . I n comparing t h e a t t e n u a t o r readings o f t h e two antennas t o produce a
constant r e c e i v e r output l e v e 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 g a i n were r e p r o d u c i b l e to w i t h i n 0.2 dB
over t h e p e r i o d when measurements were being c a r r i e d o u t . The v a l u e s p r e s e n t e d a r e those
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 t h e same
h e i g h t above ground and a r e b e l i e v e d accurate t o w i t h i n 0.5 dB.
i f r e f e r e n c e d t o an
i s o t r o p i c source, t h e values must be increased by 2.16 dB.
3.
RESULTS
The r e s u l t s o f the measurements c a r r i e d o u t i n t h i s study a r e presented i n g r a p h i c a l
form. They a r e intended t o p r o v i d e a simple means o f designing a Yagi antenna of p r a c t i c a l
dimensions w i t h maximum gain f o r t h e c o n f i g u r a t i o n under c o n s i d e r a t i o n . The purpose o f
these t e s t s was t o determine the f o l l o w i n g :
a.
E f f e c t o f r e f l e c t o r spacing on t h e g a i n of a d i p o l e antenna
b.
E f f e c t o f d i f f e r e n t equal l e n g t h d i r e c t o r s , t h e i r spacing and number on
realizable gain
c.
E f f e c t o f d i f f e r e n t diameters and l e n g t h s o f d i r e c t o r s on r e a l i z a b l e g a i n
d.
E f f e c t o f t h e s i z e o f a supporting boom on t h e o p t i m u m l e n g t h o f p a r a s i t i c
e 1 ement s
e.
E f f e c t o f spacing and stacking o f antennas on g a i n
f.
Measured r a d i a t i o n patterns o f d i f f e r e n t Yagi c o n f i g u r a t i o n s
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 l e x i g l a s s
With t h e e x c e p t i o n o f measurements s t a t e d i n s e c t i o n s 3 . 3
and 3.4, a l l p a r a s i t i c elements were c o n s t r u c t e d of 0.63 cm ( o n e - f o u r t h inch) diametcr
The d r i v e n element used i n t h e Yagi as w e l l as i n t h e r e f e r e n c e d i p o l e
aluminum tubing.
was a half-wave f o l d e d d i p o l e matched t o 50 ohms u s i n g a double-stub tuner.
boom mounted 31 above ground.
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 t h e two
elements i s shown i n f i g u r e 1 . Maximum measured g a i n was 2.6 dB and was r e a l i z e d a t a
spacing of 0.21 behind the dipole. This r e f l e c t o r spacing was used i n a l l subsequent
measurements. However, f o r the d i f f e r e n t Yagi c o n f i g u r a t i o n s t h e r e f l e c t o r l e n g t h was
o p t i m i z e d t o y i e l d maximum gain. An a d d i t i o n a l 0.75 dB g a i n was r e a l i z e d u s i n g t h e
r e f l e c t o r c o n f i g u r a t i o n shown i n f i g u r e 2.
Although t h i s arrangement was used o n l y on t h e 4.21 long Yagi, comparable b e n e f i t s
would be r e a l i z e d w i t h o t h e r antenna lengths.
A photograph o f t h e experimental set-up f o r
t h i s c o n f i g u r a t i o n i s shown i n f i g u r e 3 .
i
Various arrangements and spacings o f r e f l e c t o r elements were t e s t e d on t h e 4.21 Yagi
u s i n g t h e d r i l l e d p l e x i g l a s s support as shown. The r e f l e c t i n g elements were arranged i n
In a d d i t i o n ,
shapes o f p l a n e r e f l e c t i n g surfaces, parabolas and c o r n e r 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 p l a c e d a t v a r i o u s d i s t a n c e s behind t h e d r i v e n
element were a l s o used. O f the combjnations t e s t e d , t h e one shown i n f i g u r e 2 y i e l d e d t h e
l a r g e s t increase i n g a i n over t h a t of the s i n g l e r e f l e c t i n g element.
3.2
EFFECT OF DIFFERENT EQUAL LENGTH DIRECTORS AND
SPACiNG ON MEASURED GAIN FOR DIFFERENT YAGI LENGTHS
These measurements were conducted u s i n g t h e same non-conducting boom as mentioned i n
t h e preceding s e c t i o n . The d r i v e n element c o n s i s t e d o f a x/2 f o l d e d d i p o l e ; t h e r e f l e c t o r
was 0.4821 i n l e n g t h and spaced 0.21 behind t h e d r i v e n element. The diameter o f a l l
elements was 0.00851 (0.25 inches = 0.63m).
The g a i n o f t h e Yagi was measured as a f u n c t i o n of antenna l e n g t h (number o f d i r e c t o r s )
f o r d i f f e r e n t equal l e n g t h d i r e c t o r s and spacing between them. The d i r e c t o r l e n g t h s were
v a r i e d from 0.304X t o 0.4231 and spacings f r o m 0.011 t o 0.401.
The Yagi l e n g t h , measured
from t h e d r i v e n element t o the l a s t d i r e c t o r , was v a r i e d from an o v e r a l l l e n g t h 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 x e d . . Although many measurements were c a r r i e d o u t ,
o n l y those r e s u l t s and associated graphs a r e presented t h a t show t h e e f f e c t s o f these
parameters on measured gain.
F i g u r e s 4, 5, and 6 show the r e l a t i v e g a i n o f a Yagi as a f u n c t i o n o f l e n g t h f o r
d i f f e r e n t spacings between d i r e c t o r elements u s i n g d i r e c t o r l e n g t h s o f 0.3821, 0.4111,
and 0.424A. F i g u r e 4 shows t h a t f o r r e l a t i v e l y s h o r t d i r e c t o r s a t a spacing o f 0.3X,
t h e g a i n o f t h e Yagi increased t o a maximum v a l u e o f 14.5 dB when the antenna l e n g t h was
increased t o approximately 101. Note, however, t h a t as t h e spacing between elements was
2
*--
-e-
W
2
5
W
-T
:If
e
1
DE
REFLECTOR
21
-05
+,
,
,
I
.10
15
s
20
.25
30
.35A
SPACING, S, OF REFLECTOR BEHIND DRIVEN ELEMENT
FIG.
1
G A I N I N dB OF A DIPOLE AND REFLECTOR FOR
DIFFERENT SPACINGS BETWEEN ELEMENTS
0-L R 3
-
0
OIRECTORS-
LR3
DRIVEN
ELEHE NT
0.271
1
REFLECTOR LENGTHS
L R 1 = LR2 = 0 . 4 5 5 1
LR3 = 0 . 4 7 3 1
FREQ = 4 0 0 MHz
0
LR2
[ L E N G T H S NOT CORRECTED FOR BOOM OR SUPPORT T H I C K N E S S ]
FIG. 2
ARRANGEMENT OF THREE REFLECTING ELEMENTS USED W I T H THE
3
4.2X
YAGI
i
FIG. 3
PHOTOGRAPH OF THE TRIGONAL REFLECTOR EXPERIMENTAL
SET-UP USED WITH THE 4 . 2 X YAGI
!
0.3X SPACING
0.4X
14
12
SPACING
0
w
>
U
e
3I J
m
L L I i
La
a-
Q
x u
.*9
9
Q
0.2X SPACING
0.06X S P A C I N G
Y
on
o.1ox SPACING
c
z
Y-
’,
.-->
-w
d
9a’
40
K
FIG. 4
I
I
I
I
1
I
I
I
I
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
12
>
Y
10
U
3
.3X SPACING
8
W
on
I-
L
w-
6
0 . 4 a SPACING
w
- w
+-I
40
2a
0.1X SPACIN
4
u-
CLO
,,/GAIN
=
4
'
L
7
O F D I P O L E AND R E F L E C T O R
2R
W
I
0 . 3 0 ~SPACING
'
4
a
'1 \. \0.4X
SPACING
II
0.35A S P A C I N G
.
I
I
1
I
I
I
I
I
I
J
1
ADD 0 . 2 ~
FOR R E F L
2
3
4
5
6
7
8
9
10
7 0
LENGTH O F ANTENNA I N U A V E L E N G T H S
FIG. 6 GAIN O F A YAGI A S A FUNCTION O F LENGTH (NUMBER OF DIRECTORS)
FOR DIFFERENT CONSTANT SPACINGS BETWEEN DIRECTORS OF LENGTH
EQUAL TO 0.4241
5
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 v a r i e d between a maximum and minimum va
was changed. As the l e n g t h o f the d i r e c t o r s was increased, the
p a t t e r n were a l s o enhanced together w i t h a r e d u c t i o n i n g a i n as
mum g a i n occurred a t a
ue as t h e l e n g t h o f t h e Yagi
v a r i a t i o n s i n t h e wave
shown i n f i g u r e s 5 and 6 .
j
The curves presented i n f i g u r e 7 show a comparison o f r e a l zed g a i n vs Yagi l e n g t h up
t o 4.21 for antennas u s i n g d i r e c t o r s o f equal l e n g t h and those optimized i n l e n g t h . For t h e
optimized l e n g t h c o n f i g u r a t i o n s t h e g a i n increased from 0.5 dB f o r t h e 2.2A antenna t o
T a b l e 1 g i v e s d e t a i l s o f antenna parameters f o r t h e
approximately 1.5 dB f o r t h e 4.2X Yagi.
1
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 t h e g a i n o f d i f f e r e n t Yagi c o n f i g u r a t i o n s for
Curves showing the r e s u l t s o f measurements
d i f f e r e n t d i r e c t o r l e n g t h s o f v a r i o u s diameters.
c a r r i e d o u t on t h e 1.251 l o n g Yagi a r e g i v e n i n f i g u r e 8. A s expected, t h e maximum g a i n f o r
t h e 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 s h o r t e r lengths w h i l e t h e s m a l l e r d i a m e t e r elements y i e l d e d maximum g a i n a t c o r r e spondingly g r e a t e r 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
c a r r i e d o u t on t h e d i f f e r e n t l e n g t h Yagis and, t o g e t h e r 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 p r e s e n t e d i n f i g u r e 9 . These d a t a p r o v i d e t h e
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 l a r g e frequency range p r o v i d e d
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.
3.4
THE OPTIMUM LENGTH OF A P A R A S I T I C ELEMENT
I
!
EFFECT OF THE S I Z E OF A SUPPORTING BOOM ON
i
1
Round and square s u p p o r t i n g 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 t h e boom diameter had on t h e
The round and square booms y i e l d e d s i m i l a r
optimum l e n g t h o f the p a r a s i t i c elements.
r e s u l t s . The e f f e c t o f a round s u p p o r t i n g boom on t h e l e n g t h o f a p a r a s i t i c element i s
represented by t h e curve i n f i g u r e IO. T h i s experimental response can be used i n a p p l y i n g
the boom c o r r e c t i o n f o r t h e f i n a l Yagi design.
3.5
!
!
1
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 a r e stacked one
above t h e o t h e r or i n broadside. N o t o n l y i s g a i n increased b u t t h e beamwidth i s reduced
appreciably depending upon t h e c o n f i g u r a t i o n employed.
!
F i g u r e 11 (A) shows the e f f e c t s o f s t a c k i n g two antennas, one above t h e o t h e r . 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 t e e n - e l e m e n t Yagis. A t c l o s e spacing, approximately O.Bh, the g a i n was reduced due t o
h i g h mutual impedance e f f e c t s b u t increased t o a maximum o f 2.5 dB as t h e 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 g a i n 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 t h e above two c o n f i g u r a t i o n s u s i n g spacings as shown y i e l d e d an
a d d i t i o n a l 2.5 dB g a i n and a corresponding r e d u c t i o n i n beamwidth. For example, f o u r 0.8;
Yagi antennas, a p p r o p r i a t e l y stacked, spaced and f e d i n phase y i e l d e d a g a i n o f 14.2 dB
r e l a t i v e t o a d i p o l e l o c a t e d a t t h e same h e i g h t above ground.
I n c o n t r a s t , a combination
o f four 4.2). Yagi antennas y i e l d e d a g a i n o f 19.6 dB r e l a t i v e t o a d i p o l e , as shown b y 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
R a d i a t i o n p a t t e r n s measured i n t h e E ( h o r i z o n t a l - s o l i d curves) and H ( v e r 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 i g u r e s 13 through 19. The
6
;
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
DIPOLE I N d B
7.1
9.2
DESIGN CURVE
(SEE F I G . 9)
(A)
(B)
10.2
12.25
13.4
14.2
(c)
(6)
(D)
ELEMENT DIAMETER = 0.0085
f = 400 MHz
REFLECTOR SPACED 0.21 BEHIND DRIVEN ELEHENT
?
-n
Q
w
DIRECTOR LENGTHS OPTIMIZED
FOR ElAXlMUM GAIN ( S E E T A B L E 1 )
14-
>
U
3
LL
-I
13-
a
I
a
0
t
11
W
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
1 .o
2.0
3.0
4.0
5.0
OVERALL LENGTH,
FIG.
7
I N WAVELENGTHS, OF DIFFERENT YAG IS
COMPARISON OF G A I N OF DIFFERENT LENGTH Y A G I S SHOWING THE
R E L A T I O N S H I P BETWEEN DIRECTORS O P T I M I Z E D I N LENGTH TO Y I E L D
MAXIMUM G A I N AND DIRECTORS OF OPTIMUM UNIFORM LENGTH
w
-1
0
b
0.32 Un
Q
u
1 in.
I
I
10
I
I
I
11
12
13
-
‘t
0.16 un
0.08 cm DIAMETER
2.5.5 cn
J
14
LENGTH OF DIRECTORS I N INCHES
FIG.
8
MEASURED G A I N VS DIRECTOR LENGTH OF A 1 . 2 5 1 Y A G I ANTENNA
U S I N G THREE DIRECTORS OF DIFFERENT LENGTH AND DIAMETER
SPACED 0.351
7
1- --I-Ln
a
W
IW
x
U
w
n
8-
z
W
x
Wv)
A U
W
Z
Z
r
W
UIW
Z
ZU
I-
.
WI-
mr
W
0 na
c1
U
W
I-
I
Y
U mu-
a
L w
on
I
w
C
s
u
o
2 Y
W
W
I- I--
r
2 =I
W
c
w
W i 3
3
I-W
-I
U IZ
0 W
I- ZI-
=
W
I-
I
W
W
Z
2ZW
O E
W
v)d
W
U
c
(
n
I-
z
W
aI
W
I-J
Z
W
U>
d
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
v)
5
W
II
W
J
W
LL
0
I
Ic3
z
W
z
0
x
0
0
m
a
z
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
i
0
c
-
W
LL
Y
0
In
0
u)
pr)
N
(u
F
0
c
0
0
0
0
0
m
0
0
‘SlN3W313 3IlISWWd A0 H13N31 W n W l U O N I 3SW3t13NI
10
t--
3-
5
m
QIPI-
TI
5
3-
22
20- 7 E L E M E N T Y A G I ANTENNAS
-+ 15 E L E M E N T Y A G I ANTENNAS
1I
0
FIG.
11
1
I
G A I N OF AN ARRAY OF YAGIS, STACKED ONE ABOVE THE OTHER
AND I N BROADSIDE, AS A FUNCTION OF SPACING
w
20
-
19
-
18
-
17
-
(L
-I
a
r“1
4 . 2 X LONG
1 5 ELEMENT
YAGI
I
f
d
h = 2L
m
S P A C I N G S = 1.6X AND
H E I G H T h = 2.0X CONST
-0
f0
I
I
I
1 .o
2.0
3.0
HORIZONTAL SPACING, H I N WAVELENGTHS, BETWEEN STACKED Y A G I S
F I G . 12
G A I N OF AN ARRAY OF TWO SETS OF STACKED Y A G I S SPACED 1 . 6 1
AS A FUNCTION OF HORIZONTAL DISTANCE BETWEEN THEM
11
I
-
.. .
Az imu tha 1 ngl e , degrees
POLE AND REFLECTOR WITH 0.2x SPACING
m
U
aJ
m
c
n
0
-0
aJ
N
v
tu
E
0
z
I
1-_---I
!
i
I
A
-
-\',
c;:
m
U
..
01
l
n
C
0
P
-
#I
W
QI.
D
W
N
-8-
__
7
. .
E
0
z
--
i
-
F
Azimuthal Angle, degrees
F I G . 16
RADIATION PATTERNS OF A 6-ELEMENT.
13
1 . 2 1 LONG YAGI
m
U
i
13
0,
N
-I-
Azimuthal Angle, degrees
FIG. 1 7
R A D I A T I O N PATTERNS OF A 12-ELEMENT,
2.21 LONG YAGI
TI
al
N
Azimuthal Angle, degrees
F I G . 18
RADIATION PATTERNS OF A 17-ELEHENT.
3.2x LONG YAGI
14
. .
-
. .
. ..
.
.
.
-~ -
.
-
-
~
~
- ---T---------
e
'
.
-
I
..
-a
_
I
I
-
I
FIG. 19
RADIATION PATTERNS OF A 15-ELEMENT,
15
4.21 LONG YAGI
element) are presented i n f i g u r e 13. The 3-dB E and H plane beanwidths measured 66' and
1 1 l 0 respecdively. The beanwidth of t h e 3-element 0.4X antenna, as shown i n f i g u r e 14,
measured 57 and 72' i n t h e E and H planes r e s p e c t i v e l y . The E p l a n e , f r o n t - t o - s i d e r a t i o
i s i n the order o f 24 dB, w h i l e t h e r a d i a t i o n to t h e r e a r was o n l y 8 dB down from t h a t i n
the forward d i r e c t i o n .
The r a d i a t i o n p a t t e r n o f the 5-element 0.81 Yagi presented i n f i g u r e I 5 i s c h a r a c t e r i z e d
by a 3 dB beamwidth o f 48' and 56' i n t h e E and H planes r e s p e c t i v e l y . The E plane,
f r o n t - t o - s i d e r a t i o remained comparable t o t h e 3:element
antenna; however, t h e f r o n t - t o back r a t i o was improved c o n s i d e r a b l y and measured 15 dB.
I n r a d i a t i o n p a t t e r n s o f 6, 12,
17 and 15-element Yagis as shown i n f i g u r e s 16 through 19, t h e beamwidths became p r o g r e s s i v e l y smaller as was expected w i t h increased gain.
4.
DESIGNING THE YAGI ANTENNA
To f a c i l i t a t e t h e 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, r e f e r t o the curves shown i n f i g u r e 9. These d a t a 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 u s i n g elements o f d i f f e r e n t diameters. Only
those curves a r e presented which w i l l enable t h e 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 respect i v e l y over t h a t o f a d i p o l e mounted a t t h e same h e i g h t above ground.
I n designing a Yagi antenna, the f o l l o w i n g b a s i c i n f o r m a t t o n i s r e q u i r e d and, o f
course, w i l l depend upon i n d i v i d u a l requirements.
i
I
1.
Frequency o f o p e r a t i o n , f (wavelength, h )
2.
Antenna g a i n required, G (dB)
3.
Diameter o f p a r a s i t i c elements ( d i r e c t o r s - r e f l e c t o r s )
4.
Diameter o f s u p p o r t i n g boom used i n c o n s t r u c t i o n , D/x
used i n c o n s t r u c t i o n , d/A
Careful c o n s i d e r a t i o n should a l s o be g i v e n t o s e l e c t i o n o f t h e diameter o f the
T h i s i s important s i n c e
elements and boom a t t h e wavelength o r frequency o f o p e r a t i o n .
smaller diameter and l i g h t e r m a t e r i a l s can be used a t t h e h i g h e r frequencies i n c o n t r a s t
t o l a r g e r and heavier m a t e r i a l s needed f o r support a t t h e lower frequencies.
Note a l s o
t h a t the selected element diameter-to-wavelength r a t i o s used i n t h e d e s i g n o f t h e chosen
antenna must f a l l w i t h i n t h e l i m i t s shown.
I f maximum g a i n i s t o be r e a l i z e d u s i n g t h e d a t a presented, i t i s e s s e n t i a l to follow
very c l o s e l y t h e procedure described here.
In a d d i t i o n , t h e element l e n g t h s should be
measured and c u t t o a t o l e r a n c e o f about 0.0031 w i t h respect t o t h e c a l c u l a t e d values.
TO
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 t h e design
data, two s p e c i f i c examples a r e presented. The f i r s t considers t h e d e s i g n o f a 5-element,
0.81 Yagi; t h e second example presents a step-by-step procedure for t h e design o f a 15element, 4.21 Yagi.
I n t h e f i r s t example, consider t h e design o f a 0 . 8 ~Yagi antenna t o
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 g a i n o f 9.2 dB
r e l a t i v e t o a d i p o l e . The elements s h a l l be c o n s t r u c t e d of 2.54 cm (1 in.) diameter
aluminum t u b i n g w i t h t h e boom o f 5.08 cm (2 in.) diameter aluminum t u b i n g .
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.
Overall l e n g t h
2
(47 i n . )
0.81 = 478 cm. (188 i n . )
16
STEP 1:
Plot the lengths of the parasitic elements obtained from Table 1 for 0.81 long
Yagi on the corresponding curve In figure 9.
reproduced in figure 20.
For clarlty, these curves are
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
D2
-
0.4241
LR = 0.4821
STEP 2:
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
STEP 3:
STEP
4:
(4. This is
the uncompensated director length of D1 = D = 0.442X.
3
-
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 to D2 determined i n Step 1 . Transpose this distance from the
3
point established in Step 2 downward along the curve and determine the uncompensated length of director L
= 0.4381.
O2
From the foregoing, the uncompensated parasitic element lengths for the 50.1 MHz
Yagi are:
L
= 0.438X
D2
LR = 0.4851
To these values, a correction must be added to compensate for the boom diameter.
STEP
5:
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 para-
From the chart this length = 0.0051.
Thus, for this design the exact lengths of the parasitic elements should be
sitic elements must be increased.
measured and cut to the following lengths.
= 0.4421
= L
+ 0.0051 = 0.4471 = 267 cm.
O3
= 0.4381 + 0.0051 = 0.4431 =
L
264.5 cm.
O2
= 0.4851 + 0.005X = 0.490X = 293 cm.
LR
The driven element is designed so that the Yagi can work either into a 50 or 200 ohm load
impedance. For a 50 ohm impedance, a folded dipole and a quarterwave balun can be employed.
Precise matching to 50 ohms can be accomplished by using a double-stub tuner connected into
the feed line.
17
!
SHlSN313AVM N I SlN3W313 30 H 1 9 N 3 1
18
I f the antenna i s designed w i t h a 200 ohm balanced i n p u t impedance, then the d r i v e n
element should be designed t o p r o v i d e an impedance step-up r a t i o o f 12. For t h i s c o n f i g u r a t i o n , a X/2 b a l u n s e c t i o n and stubs can be used t o p r o v i d e proper impedance t r a n s f o r m a t i o n
and matching.
OtHer matching methods can a l s o be employed such as Gamma o r T match [ l o , 1 1 ,
121.
As a second example, c o n s i d e r the design o f a 4.2h long Yagi t o p r o v i d e a g a i n o f 14.2
d8 r e l a t i v e t o a d i p o l e t o o p e r a t e on 827 HHz i n t h e c e n t e r o f TV Channel 73. For the
c o n s t r u c t i o n o f t h i s antenna l e t us s e l e c t 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:
Frequency 827
HHz, A
Element diameter, d
d/X
STEP 1:
--
36.34 cm.
(14.3
in.)
0.48 cm.
= 0.013
Boom diameter, D
= 1.27 cm. (1/2 i n . )
D/X
= 0.035
Element spacing
= 0.3081 = 11.2 cm.
Overall length
=
4.2A = 152 cm.
P l o t t h e l e n g t h s o f p a r a s i t i c elements from Table 1 for t h e 4.21 l o n g Yagi on
t h e corresponding curve i n f i g u r e 9.
For c l a r i t y , t h e s e curves a r e reproduced
-
E s t a b l i s h p o i n t s LD = L 0 2 * L ~ 3 ** L ~ l and l o c a t e
1
and presented i n f i g u r e 21.
t h e p a r a s i t i c element lengths on t h e c u r v e as i n t h e p r e v i o u s example f o r the
d/A = 0.0085 case.
STEP 2:
F o r our p a r t i c u l a r design, however, where t h e element d i a m e t e r t o wavelength
r a t i o d/X = 0.013,
p l o t and e s t a b l i s h t h i s p o i n t on t h e 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 p o i n t w i t h a check
(4.
T h i s i s t h e uncompensated
d i r e c t o r l e n g t h of D1 = D2 = 0.4141.
STEP 3:
F o r t h e same d/X r a t i o , determine t h e uncompensated l e n g t h o f t h e r e f l e c t o r ,
LR =
STEP 4:
0.473X;
from curve D, f i g u r e 21.
With t h e use o f a p a i r of d i v i d e r s , e s t a b l i s h and measure t h e d i s t a n c e between t h e p o i n t s D1 = D2 t o D
3'
Transpose t h i s d i s t a n c e from t h e i n i t i a l
(4
= 0.4091.
mark downward along the d i r e c t o r c u r v e and determine LD
3
Measure t h e d i s t a n c e from D1 = D2 t o D4.
initlal
(4 p o i n t
Transpose t h i s d i s t a n c e from
and determine l e n g t h o f D4 = 0.3951.
= 0.3911,
d e t e r m i n e remaining d i r e c t o r lengths.
LD5
0.381X, L
to
'8
LD
Similarly,
LD = 0.385X,
6
L
=
DJ
= 0.3771.
13
To these values a c o r r e c t i o n must be added t o compensate f o r boom diameter.
STEP 5:
For a boom diameter-to-wavelength r a t i o D/X =
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, d e t e r m i n e t h i s l e n g t h =
0.0261.
Thus,
t o r e a l i z e maximum g a i n from t h i s antenna, measure and c u t t h e
p a r a s i t i c elements t o the f o l l o w i n g l e n g t h s :
19
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
0
0
0
= L
+ 0.026X
= 0.414X
= 0.440X = 16.0 cm.
O2
= 0.4091 + 0.0261 = 0.4351 = 15.8 cm.
L
D3
= 0.3951 + 0.026X = 0.4211 = 15.3 cm.
L
D4
= 0.391h + 0.0261 = 0.4171 = 15.1 cm.
L
D5
I
= 0.3851 + 0.0261 = 0.4111 = 14.9 cm.
L
D6
= 0.3811 + 0.0261 = 0.407X = 14.8 cm.
L
DJ
L
=, 0.3771 + 0.026X = 0.4031 = 14.6 cm.
-
'8
LD13
LR = 0.4731 + 0.0261 = 0.4991 = 18.1 cm.
The d r i v e n element can be o f a v a r i e t y o f designs and w i l l depend upon
I
i n d i v i d u a l requirements.
I t i s u s u a l l y measured and c u t t o o n e - h a l f
wavelength l e s s a s h o r t e n i n g f a c t o r t o compensate f o r e n d - e f f e c t s and
matched t o t h e c h a r a c t e r i s t i c impedance o f t h e feed l i n e .
5.
I
CONCLUSIONS
The d a t a presented i n t h i s r e p o r t p r o v i d e t h e necessary i n f o r m a t i o n f o r t h e d e s i g n o f
Yagi antennas r a n g i n g i n l e n g t h from 0.21 t o 4.2X.
These d a t a a l l o w t h e user t o design
antennas t o y i e l d maximum g a i n f o r seven d i f f e r e n t design c o n f i g u r a t i o n s .
In addition,
s t a c k i n g o f antennas, s i d e by s i d e 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 t o 5.2 dB over t h a t of t h e s i n g l e a r r a y .
6.
ACKNOWLEDGMENTS
The a u t h o r wishes t o extend s i n c e r e a p p r e c i a t i o n t o W i l l i a m Gorboczieski f o r h i s a s s i s t Also,
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 c a r r y i n g out of t h e measurements.
s i n c e r e a p p r e c i a t i o n and thanks t o A l v i n Wilson f o r p r o v i d i n g t h e r a d i a t i o n p a t t e r n s .
7.
[l] S h i n t a r o , U., and Yasuto, H.,
Ltd., Senda, Japan, 1954).
REFERENCES
Yagi-Uda Antennas (Sasoki P r i n t i n g and P u b l i s h i n g Co.,
IEEE, Trans. Antennas and Prop.,
AP-14,
Log p e r i o d i c Yagi-Uda a r r a y , IEEE, Trans. Antennas and Prop.,
pp. 235-238 (Mar. 1966).
AP-14,
[ 2 ] M a i l l o u x , R. J . , The long Yagi-Uda a r r a y ,
pp. 128-137 (Mar. 1966).
[ 3 ] Barbano, N.,
[ 4 ] T h i e l e , G. A.,
Analysis Y Yagi-Uda t y p e antennas,
pp. 24-31 (Jan. 1969).
[SI
I E E E , Trans. Antennas and Prop. AP-17,
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.
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 a r r a y s , I E E E ,
Trans. Antennas and Prop.,
AP-20, pp.
178-180 (Nov. 1972).
21
5,
[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 o f the G
m Match, QST, pp. 11-15 (Apr. 1969).
[ l l ] Nose, K . , Adjustment o f 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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