Broadband Qasi-Taper Hlelcal An+,emias
The Ivan A. GJeý..tiag Laboratories"40% The Aerospace Corperstbl
144 El Segundo, Calif. 903kb
30 September 197?
~~ ~P.O. cox 92960, Worldwal w-taI enter-~~ Los Angeles. Ca. 9 0009
This report was submitted by The Aerospace Corporation, El Segundo,
CA 90245, under Contract F04701-75-C-0076 with the Space and Missile
Systems Organization, Deputy for Advanced Space Programs, P. 0. Box 92960,
Worldway Postal Center, Los Angeles, CA 90009. It was reviewed and
approved for The Aerospace Corporation by A. H. Silver, Director,
Electronics Research Laboratory, and H. F. Meyer, Director, FLTSATCOM
Program Office.
This report has been reviewed by the Information Office (01) and is
releasable to the National Technical Information Service (NTIS). At NTIS,
it will be available to the general public, including foreign nations.
This technical report has been reviewed and is approved for publica-
tion. Publication of'this report does not constitute Air Force approval of
the report's findings or conclusions. It is published only for the exchange
and stimulation of ideas.
MichaeL E McDonald, Brton, Col, USAFProject Engineer Project Engineer
YFOR THE COMMANDER
white b0ti
Nd T S. McCARTMEY, Brig/ * F RU 3tftSystem Program DirectorYLTSATC System frogram -. eAWIuty for $Paco CaMMwL1cAtts systa
1 9
t-,~-(A
UJNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE (Wh~en Does Entered)
I9)REPORT DOCUMENTATION PAGE READ INSTRUCTIONS
R~~ ~ ~ GEO UOVT ACCESSION NO. 3. RECIPIENT'S
C TALOG NUMBER
4 ~ ~ E R-77-172 JBF ECO P TNG OR
4~ J'~'" ~ ~S. TYPE OF RE~R AD AN Q AS-TAPER HELICAL Julinal~
A. ATHOR(i)NU ERs
j. L. /Wong 0H. E. King j 7t7 7
9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASKAREA A WORK UNIT NUMBERS
The Aerospace CorporationEl Segundo, Calif. 90245
iI. CONTROLLING OFFICE NAME AND ADDRESS , 2 1rUM;Q
Space and Missile Systems Organization ( 32 SepUM * 777Air Force Systems Command 13. 'NUMBER OF PAGESLos Angeles, Calif. 90009 30
14. MONITORING AGENCY NAME & A=DIESS~fifdifferent fram CoptroliQt Office) 15. SECURITY CLASS. (of this report)
Unclassified$~ IS&. DECLASSIFICATION/OOWNGRADINGSCHEDULE
16. DISTRIBUTION STATEMENT (ot this Report)
t Approved for public release; distribution unlimited.17. DISTRIBUTION STATEMENT (of the abstract enteredin Block 20, Ifidliforent free, Report)
10. SUPPLEMENTARY NOTES
Ill. KEY WOROS (Ccritinue an rev.erse side ft neceeemy and identify by block num~ber)
Tapered He1>,ý Quasi-Taper HelixUniform Helix Conical HelixNon-Uniform Helix
0. STAT(miie, eee. eI e.e n dat ybekwbe.A unique approach is described for widening the bandwidth of a helical antennawith improved gain, pattern, and axial ratio characteristics. The antenna maybe described as a non-uniforni or quasi-taper helix, which consists of a corn-.bination of uniform and tapered helix sections. Measured patterns, gain, axialratio, and VSWR for variouc helical antenna configurations are presented andcompared. It is shown that a non-uniform, quasi-taper helix can provide anoperating bandwidth twice that of a convent-,onal uniform -diameter helix.
FORtM 143NCASFE
,.4A CCJAPUTs CLASSIFICATION arTHIS PAGEz (Vhnb"t X"4e04d0
UNCLASSIFIED19CURITY CLASSIFICATION OFF THIS PAOZfVhmVale flafti,0mD)Ill. KEY WORDS (Continued)
20. AIISTRlACT (Continued)
4UN LASSIFIED
PREFACE
The authors wish to thank the FLTSATCOM Program Office,
especially H. F. Meyer, Director, and P. J. Parszik for their interest
and support of this antenna development. Thanks also go to G. G. Berry,
L. U. rrown, H. B. Dyson, B. A. Jacobs, 0. L. Reid, and J. T. Shaffer
for constructing and testing of the various antennas.
- -
CONTENTS
PREAC IT DUTO.............................................5I
II. GENERAL DESCRIPTION................................7
III. VSWRGCHARACTERISTICS................................. 9
IV. PATTERNS AND GAIN . ........................ 13
A. UniiformnHelix.................................... 1t3
B. Tapered-End Helix................................... i3
C. Continuously Tapered Helix........................... 23D. Quasi -Taper Helix...................................23
V. CONCLUSIONS...........................................35
REFERENC ES................................................ 37
K* .3. -JIMvi
FIGURES
1. VSWR of Two 18-Turn Helices: Uniformly Wound andLast Two Turns Wound on a Tapered Diameter ........... 10
2. VSWR of a Seven-Turn Uniform Helix and the Same Helixwith Two Additional Turns on a Tapered Diameter ......... ii
3. Gain and Axial Ratio Characteristics of a ConventionalUniformly Wound 18-Turn Helix ..................... 14
4. Radiation Patterns of an 18-Turn Uniform Helix .......... 15
5. Halfpower Beamwidth and Gain-Beamwidth Product of an18-Turn Uniformly Wound Helix ..................... 17
6. Gain and Axial Ratio Characteristics of an 18-Tt .n tUni-formly Wound Helix with a Two-Turn Tapered-End Section . . 18
7. Radiation Patterns of an 18-Turn Uniform Helix with aTwo-Turn Tapered-End Section ..... 0 ................... 19
8. Halfpower Beamwidths and Gain-Beamwidth Products of an18-Turn Uniform Helix with a Two-Turn Tapered-EndSection ......................... ............. 22
9. Gain and Axial Ratio Characteristics of a 17.64-TurnConical Helix ....... . ...... ................... 24
10. Radiation Patterns of a 17.64-Turn Conical Helix ............ 25
It. Halfpower Beamwidth and Gaint-BeimwLdth Product of a17.64-Turn Conical Helix . . . . . . . .................. 26
12. Basic Dimensions of a Non-Uniform Diameter Helix ....... 28
13. Gain and Axial Ratio Characteristics of a Non-UniformDiameter Helix ........... 29
14. Radiation Patterns of a 17.64-Turn Non-Uniform DiameterHelix ....................................... 30
15. Halfpower Beamwidth and Gain-Beamwidth Product of a17.64-Turn Non-Uniform Diameter Helix ............... 31
16. Gain and Axial Ratio Characteristics of a Non-Uniform 6 KHelix Consisting of Eight-Turn Uniformly Wound +9.64-Turn Continuous Taper ........ . .... . ............. 33
-4- '
I..
I. INTRODUCTION
Helical antennas are generally constructed with a uniform diameter
[Ref. 1] or a tapered diameter [Refs. 2, 3]. The helical gain characteristics
over a wide bandwidth are not readily available in the literature, The pur-
pose of this report is to describe the characteristics of a non-uniform helix
and to demonstrate how the bandwidth of a conventional uniform (constant
diameter) helix can be extended by the use of non-uniform helical structures.
The non-uniform helix consists of multiple uniform-diameter helical sections
that are joined together by short, tapered transitions. With a non-uniform
helix, it is possible to shape the gain vs frequency response to provide
either enhanced gain at selected frequencies or a near-flat gain response
over a broad bandwidth.
The non-uniform helix antenna was developed for operation in the 290
to 400 M.%z band (- 1.4:1 frequency ratio) with optimum gain characteristics
I'at the low-frequency.end. A conventional helix, which provides an effective
operating bandwidth of approximately 25%, could not meet the desired gain
performance characteristics. This report describes the results of 3/8-scale
(773 to 1067 MHz) experiments made on a variety of helix antenna configura-
tions including uniform, tapered, and non-uniform diameters.
i '-5-
,j1 i .... ' 4
11. GENERAL DESCRIPTION
Most of the experimental helices were wound with thin copper strips
0. 468-in. wide. The plane of the strip (wide dimension of strip) was wound
orthogonal to -he helix axis, similar to a "slinky". Helices wound with
round conductors or with metall.ic tapes (wound such that the plane of the
tape is parallel to the helix axis) yielded similar results as experimentally
verified by the authors. The "strip" approach was chosen because of me-
chanical convenience and ease of construction. It was found that an accurate
helix could be made by properly joining a series of loops. The mean cir-
cumference of each loop was made equal to the length of one helical turn or,
equivalently, the mean diameter of each loop was made equal to VDM + (S/TT
where DM is the mean diameter of the helix and S is the spacing between turns
(p.\tch). In the tapered portions of the helix the average taper diameter of
each turn was selected for DM. Styrofoam forms were cut to the desired
mean helix diameter and slitted with a razor blade to the desired helical
path. Each loop was joined end-to-end (butt joint) and soldered together
with an overlapping strap. The loops are then inserted into the slitted foam.
A constant pitch spacing of 3.2 in. was selected, although a constant
angular pitch provides similar electrical characteristics as verified by ex-
perinments (by the authors). The helix was backed by a cavity, 11. 25-in.
diameter X 3. 75-in. high, which is a reasonable physical size, to reduce
backlobe radiation and enhance the forward gain. A metallic center tube
(I. 125-in. diameter), which provided mechanical support, was used in all
the helix models. The total length of the helix = NS + LF, where N = number
of helix turns at a spacing S, and LF = feed strap length (the distance above
the cavity plate where the first turn of the helix starts).
-7-
i p,
I1. VSWR CHARACTERISTICS
The VSWR of all the antennas discussed herein is less than 1.5:1 over
the test frequency range from 650 to 1100 MHz (except for the uniform helix)
when a microstrip matching transformer is used. The transformer is placed
on the cavity surface and it is tapered from 50 ohm at the coax input port to
approximately 140 ohms at the helix feed point.
The solid-line curve of Fig. I is for a 18-turn uniform helix with a
4. 59-in. diameter aad a 12. 50 pitch angle (3. 2-in. spacing between turns).
By tapering the last two turns to a 2.98-in. diameter and maintaining a 3.2-in.
spacing between turns, the dashed-line curve shows a considerable improvement
in VSWR. The resonant region (C/ X > 1. 1) found in the uniform helix disap-
peared in the tapered-end helix. The VSWR characteristics for all the non-
uniform helices in the subsequent discussions are similar to that of the tapered-
end helix curve.
The characteristic change in VSWR by tapering the end also holds for
a shorter helix as shown in Fig. 2. The solid-line curve is for a 7-turn uni-
form helix with a 5.28 in. diameter and a 10.920 pitch angle (3. 2-in. spacing
between turns). By adding two additional turns and tapering the helix diameter
to 4. 13-in. diameter (with the same 3.2-in. spacing between turns), a signifi-
cant reductioa in VSWR over a wide frequency band was observed as shown by
the dashed curve. Also, it is noted that the low frequency characteristics are
essentially unchanged with a cutoff at -- 534 MHz, corresponding to C/ X - 0. 75,where C is the circumference of the 5.28-in. diameter helix. The low fre-
quency cutoff characteristics agree well with theoretical predictions [Refs. 1,- 6].
-9-
0468 STRIP WIDTH12.5 PITCH I. - 6
0459 STRIP WIDTH 2.98 I 6.4.5D 3.2 ,---------- 2 TUCRNS•
~458D T N
-132
,I5S 125. PICH " --. 1 S18 TURN'S " •5.3
16 TURNS
1 111.5 x3.75H CAVITY
- UNIFORM --- 16T(4.59D)+2T TAPER
CIRCUMFERENCE, C/X0.8 0.9 1.0 1.1 1.2 1.3I . I I I t I
2.50144 • RUN 2, GRAPH I8144 RUN 3, GRAPH 2
2UNIFORM HELIX
TAPERED END1.5
1.0600 700 800 900 1000 1100
FREQUENCY, MHz
Fig. 1. VSWR of Two 18-Turn Helices: Uniformly Woundand Last Two Turns Wound on a Tapered Diameter
-10-
-1144 IUN li
N 1424)4P% 4.13rj.j -i 7 L5.28 D F. - 6.4a 09~ ------ 5.280 D ~ -7 TURNS 10.9
22.65 7 TURNSS =3.2 _ I 22.65
VS 3.2 2z L2Cl. 2 5 D x 3.75 H CAVITY
UNIFORM 7T (5.28D) + 2T TAPER
FREQUENCY, MHz
Fig. 2. VSWR of a Seven-.Turn Uniform Helix and the SameHelix with Two Additional Turns on a TaperedDiameter62
-Ii-
IV. PATTERNS AND GAIN
A. UNIFORM [IELIX
Figure 3 shows the gain and axial ratio characteristics of a 18-turn
uniformly wound helix, 4. 59-in. diameter. By defining the bandwidth as
the 2 dB points (from gain maximum) of the gain curve, the frequency ratio
becomes 970/770 or 1.26:1. Also, note that for C/X < I ýhe gain slope
varies approximately as f 4 , where f = frequency. Representative patterns
using a rotating linearly polarized source ark shown in Fig. 4. The half-
power beamwidths (HPBW) and the gain-beamwidth products (GO 2, where
9 = HPBW) are shown in Fig. 5. Note that the HPBW is approximately in-
versely proportional to f2 for C/ X < 1. 1 while the gain is proportional to
f for C/
CIRCUMFERENCE, C/X
0.8 0.9 1.0 1.1 1.2 1.317 11 1.. 1 1 1 .1C17 C44 RUN 2GRAPHS I 6
8 24 74
17 5* PITICH
16 4SRWII/
15- 118 TURNS
14 s12 wiDUbCH CAVITY /
afIf
Ur PEAK GAIN
12/
11o
3
10 AXIAL RATIO g2
•I ' :
FREQUENCY, MHz
INV "PAKGI
3 Gi aon
UnifrmlyWAuIAL RAT~iO- H2lix
-14-"
122* 120 1ww 5 ~ 13r 1w 20
Wi. .RaitinPatterns of anttr 11TiUifr ei
AII
', ,tr Ii S ,0 l P.tt., 21
302-
'-1
120 -16- 1010
IsLeJI 1 9r 1
CIRCUMFERENCE, C/A0.8 0.9 1.0 1.1 1.2 1.3
50 I ' 40,000
12Y PITCHI0.450 STRIP WIDTH
4.56
HPBW18 TURNS
CO4 0 G 2 -30,000~
1126 0 C.7 AVITY
cc
'U
30-20,000
HPBW-8
20..,....- 10,000800 0 80 goo90 1000 1100
FRE(EIUENCY, MHz
Wi.5. Ha14powsr BoamwidtbL and Gain-Boamwidth
- Product mfa 4.8,vTkum Uniformly Wound
A.1
14
17 C144 R6N 3 II
04NB STRIP *rn1H
16 4~I t 6
32 ~ 3
122
11501R1AT
102AXIAL RATIO
1% 00 700 800 Bo0 1000 1100~FREQUENCY, MHz
119. 6. GALn &ad Axial R~atio Char'acteristics of ma
iB8- Tur TjdfUomly Wound Helix with a
Two-Tpu Toee-a Ssctuou
P m
dB A 44 -Run 0 /
Pater 0G 1 t-2
-67 7
30'3
1122e~5 1A20T
Fig. 7. Radiation ~Pattern. 27 a 8TriUnfrn~ex
9-6-7
Lo 300 30'___
'-4 14
b9 ,
6000 60- 65100
Fig. 7. RaitoMaten fani uzUnfr ei
-20-... 10
va50r 130 1.tt., 1310II
IF0 130 90, 900go
Fig 7 Rditin Pttrn o a i-Tun niorMHliwith a20 TwoTur Tapre E1dSeci'
30
101
60 55,000
Q.4 STIW WION
2 Tom.
55 50,000~T32
1Ur PTCH1
S45 40,000 • .
50 % 35,0001
0 LU2A5 30,00030 36 5,000
1 1
I 's I
25 *20,000
20 L . , ' - 15.000600 700 800 900 1000 1100
FREQUENCY, MHz
Fig. 8. Halfpower Beamnwldths and Galn-BeamwidthProducta of an 18-Turn Uniform Helix with aTwo-Turn Tapered-End Section
It should be pointed out that the primary purpose of the present study
was to optimize the gain of the helical antenna in the lower portion of the
773 to 1067 MHz band without substantial gain degradation in the upper por-
tion of the band. Thus, the measurements performed for all the helices
investigated in the present study cover this frequency range, which may
exceed the theoretical limits for an axial mode uniform helix [Refs. 1, 4-6].
For a uniform helix with a 4. 59-in. diameter and a 12. 5 pitch angle, reason-
able antenna performance can be expected from 650 to 1025 MHz, which cor-
respond approximately to 0. 8 < C/A < 1. 125. Beyond this frequency range
severe pattern distortion and gain degradation would result as can be evident
from Figures 3, 4, 6 and 7.
C. CONTINUOUSLY TAPERED HELIX
A continuously tapered helix (literally known as conical helix) with a
constant pitch spacing of 3.2 in. was tested. 1lhe helix consists of 17.64 turns
7 with a 5. 32-in. diameter at the base and 2. 98-in. diameter at the top as shownin the sketch of Fig. 9. The peak gain is slightly lower than the uniform helix
but the axial ratio and sidelol. characteristics are improved as can be seen
from Figures 9 and 10. The HPBW and gain-beamwidth product a,- shown
in Fig. 11. It is interesting to note that the high and low frequency limits are
approximately determined by the mean circumference of the helix. The gain
peaks at a frequency where the mean circumference is approximately 1. 05 X.
However, the gain-frequency response broadens considerably with substantial
increase in gain at the high frequency end. For example, Fig. 9 shows the
gain v.ries + I dB from 820 to 1120 MHz, a 1. 37:1 frequency ratio compared
with 1. Z6:l for a uniform helix.
D. QUASI- TAPER ~4
As mentioned previously, the purpose of the present study wAs to develop
a helical anteun capable of oper&tiUo from 773., to 1067 MHz with optimum gain
characteristics in the lower portion of the band. The' uniform helix and the ta-
pered-end hs4Ix wo$e foono a4m of nm.tiag the gain-bandwidth re-
.bLb'2 . :•
17 'RN1 3
C144 RN1GRAWH 31-3510 1 74
16
32~15
Q.*B STRP P
1411t250i3.16CAVMrYPE KG I
Zi13
12
11
lBa
~~-AýAMA PIATIO IL
600 700 800 1110 1180m~ SXftUEtf~j MI1z
rý-- o O~A A Ail &U htaovs
308 0 dB A144 '"I
10 10 ,
62L10 ,.0. w12 012 1 2 I 0- 4-
190 go" 190
1 20 1 50 130 1 5 1100 S ' 1 0 5
-. 10 A 10
60. 60 \\w w6/0V20I3\06
A90 q0
900 J1 t 9i
WIDTH F- 174TUN
455.176 UN
-~~ ,juu~t
32.D
31~
••.--HPW c0 -=
56S~
S40 40,00(0 -
=:E 83' 13,0WIOTI
25 25 , x 3.7 K I C. [ ...
4000 30,006
FREQUENCY, MHz
Fig. i 1. H.]alfpow'er Ban~iwdth and Gain-Beamwidtb Product
cia& 17o.64-turn C•=lc&1Hl iUx
G'.
30- -30,000 ;R- -
700 Bo 900 100 110
quirements. The continuously tapered helix provided broader frequency
coverage with increased gain at the high frequency end, but the gain-band-
width was still less than desired. In this section, the characteristics of a
non-unifcrm or quasi-taper helix are discussed.
A non-uniform helix can be made in various forms. It may be con-
structed with two or more uniform helix Lections of different diameters or
a combination of uniform and tapered sections. Figure 12 shows a typical
non-uniformn helix consisting of principally two uniform-diameter sections -
5. 28 and 4. 13 inches. The helix is described as a 7-turn helix (5. 28 D) +
Z 2-turn taper (5.28 D to 4. 13 D) + 6.64-turn (4.13 D) + 2-turn end taper
(4. 13 D to Z. 98 D), A constant pitch spacing of 3. 2-in. was maintained in
all four helical sections. During the experimental phase a parametric study
,• made by varying the number of turns, the diameters of the helices, and
the lengths of the tapered transition region. It was found that an antenna can
be synthesized to yield a specified gain-frequency response.
/ Figure 13 illustrates the gain response for the non-uniform helix con-
figuration of Fig. 12. This helix was optimized as desired over the low fre-
quency region, with a gain of 14. 7 + 0. 4 dB from 773 to 900 MHz and re -
mained relatively flat (14.05 + 0.25 dB) from 900 to 1067 MHz. The gain
is constant within + I dB over a frequency ratio f min = 1.55
(710 to 1100 MHz) as compared to 1.26 for a uniform helix. The axial ratio* 1is < 1 dB. The beam shape and sidelobe characteristics are considerably
improved over those of a uniform helix as illustrated in Fig. 14. It is inter-
esting to note that the high frequency cutoff is not limited by the larger, 5.28-
in. diameter helical section (C/ X % 1.55 at 1100 MHz) but rather by the
smaller, 4. 13-in. diameter helical section (C / X 1.21 at 1100 MHz). The
HPBW and GO2 plots are depicted in Fig. 15. Note that the beamwidth re-
mains relatively constant, 330 + 30 over the 773 to 1067 MHz test frequency
range.
-27-
0.468 STRIP WIDTH 6
2.980 -j_ _
4 2 TURNS
4.130D=13.860 ----•" , q---
6.64 TURNS
I"- 1 j | 21.25
S =3.2 (constant) wmf S
5.2800=10-920~~*47 TURNS
Mwumft.ý22.65
I--
11.250x3.5H CAVITY
Fig. 12. Aa&sic D .zmuiausQo a. Non-Utiorra M)am ter Hm)4z
0 468 SI Nil' WUi) 111
'U ~'TURNS4130
a -13 W654 Iums~ '212
15 v
~226
14
CC~13
12
102
-. FREQUENCY. MH2,
l 4g 13. Galni an~d Ax~al Ratio Cb~iacte#4s0s of &() pI n~qfQ2r Diamnetet Hei~x
30- 00
W44
113
K0s
It-
IIImm W!P -r1 w w
0.468 STJ WIDTH
2A80
22T
4.13 0
C-- na
25 20,000
1-1
Em 40 '
2 5,0 i$:r- ý
cmi
I ~Another example of a non-.uniform helix is shown in Fig. 16. Thishelix was constructed hy tapering the top 10. 64 turns of the helix of Fig. 12,which results in a helix consisting of a uniform section (5. 28-in, diameter)
I plus a tapered section from 5.28 to 2.98-in, diameter. As shown in Fig. 16,I the + 1. 1 dB gain bandwidth is wider than the non-uniform helix of Fig. 13,but the gain at the high frequency end iai lower.
...... ...
17 (:1 44 Ith 1to 1 74
16Tmdh
1L to W
CAIT .,-MEASURED PEAK GAIN
12
10
so10 700 *0 , 900 1000 110,0i&QUNCY. Miz
1.16. Ckda and A~sla U~tio dzaractesultics of a Nba-Uwio~
low
y OIv
V. CONCLUSIONS
The uniqueness of a non-uniform helix antenna has been demonstrated.
Such an approach yields wider bandwidths in gain, pattern, and axial ratio
as compared to the conventional uniform-diameter helix. The non-uniform
helix can also provide a means to synthesize an antenna to attain a specified
gain-frequency response. A continuously tapered diameter helix does not have
this flexibility nor the bandwidth of the non-uniform (quasi-taper) helix. The
following table provides a comparison of the + I dB gain bandwidth for the
various helical antennas:
Frequency Range with Frequency RatioType of Helix + I dB Gain Variation ~rnax / min~
Uniform 770 - 970 MHz 1. 26:1
Tapered-End 770 - 980 MHz 1. 27:1
Continuous Taper 820 - 1120 MHz 1. 37:1
Quasi-Taper 710 - 1100 MHz 1. 55:1
I---~ra a-,_-,_
REFERENCES
J. . D. Kraus, Antemias, McGraw-Hill Book Co., New York (1950),Ch. 7.
Z. J. S. Chatterjee, "Radiation Field of a Conical Helix,," J. Appi1. Phy2..24, 550-559 (May 1953).
3. H. S. Barsky, "Broadband Conical Helix Antennas, ' 1959 IRE NationalConvention Record, Part 1, 138-146.
4. T. S. M. Maclean and R. G. Kouyouanjian, "The Bandwidth of HelicalAntennas, " IRE Transactions on Antennas and Propag~ation. AP-7,S12ecial Supplement, S379-S386 (December 1959).
5. T. S. M. Maclean and W. E. J. Farvis, "The Sheath-Helix Approachto the Helical Aerial, " Proc. lEE 109, Part C548-555 (1962).
6. T. S. M. Maclean, "An Engineering Study of the Helical Aerial,"Proc. IEEE 110, 112-116 (January 1963).
( ')7. D. 3. Angelakos and D. Kajfez, "Modifications on the Axial-ModeHelical Antenna," Proc. IEEE 55., 558-559 (April 1967).
0 - _