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 - _