the use of a ring array as a skip range antenna

Tillman, Patton, Blakely, and Schultz: Skip Range Antenna

CONCLUSION

Laboratory performance tests of the sextuple MFSsystem clearly indicate the inherent superiority ofMFS over FSK for the transmission of teletype infor-mation under white and impulse type noise conditions.The performance of the standard FSK system with thecomb input filter was found to be approximately 2decibels better than the same system with the standardinput filter. Since the effective bandwidth of the combfilter is approximately the same as the bandwidth ofthe sextuple MFS input filter, it can be seen that theMFS system is about 4 decibels better than the FSKsystem with equivalent pre-detection bandwidths, This

improvement is mainly due to a reduction of bandwidthwhich is permissible with the greater pulse duration inthe MFS system. This greater pulse duration is achievedwithout a reduction in the speed of transmission of in-formation. A slight additional improvement results fromthe simpler code used by the MFS system. Theoreticalgains have been satisfactorily verified.

ACKNOWLEDGMENTThe authors wish to recognize Messrs. D. R. Meier-

diercks, F. Picus, and W. Posner, for considerable aidin the theoretical and experimental efforts. The workdescribed in this paper was sponsored by the U. S.Air Force under Contract AF33(038)-22536.

The Use of a Ring Array as a Skip Range Antenna *J. D. TILLMANt, MEMBER, IRE, W. T. PATTONt, MEMBER, IRE, C. E. BLAKELYt, AND

F. V. SCHIJLTZt, SENIOR MEMIER, IRE

Summary-The problem involved here is the development of ashore antenna for shore-to-ship communications at distances from40 to 500 miles. The difficulty at these distances is due to interfer-ence between ground-wave and sky-wave modes of propagation.

The propagation factors involved are considered and it is shownthat (1) A frequency less than 3.3 mc should be used, (2) The groundwave should be used during the day and (3), The sky wave shouldbe used at night.

An azimuthally omnidirectional antenna is described which con-sists of vertical monopoles equally spaced around the circumferenceof a circle. The antenna can be excited in either of two ways, one ofwhich concentrates the radiated energy along the ground for usewith the ground wave, and the other of which gives maximum radia-tion at a polar angle of 30 degrees and a null in the ground plane foruse with the skywave. The results of model tests at 30 mc and at1,200 mc are given. Results of calculations showing the expectedcoverage for noon and midnight are included.

INTRODUCTIONT IS THE purpose of this paper to describe anantenna system to be used to transmit signalsover the range from 40 to 500 miles. This antenna

is intended primarily for shore-to-ship communication,so that the ground paths involved will consist mainlyof sea water. Reliable operation for 24 hours each dayand for any season or geographical location is required.

Communication into the region within 500 miles ofthe transmitter is characterized by severe fading. Thisfading is the result of interference between ground-waveand sky-wave fields which are of the same order ofmagnitude over part of the region. The zone in whichthis severe fading and interference occurs is normallyabout 100 miles across, and is located at about 200

* Original manuscript received June 17, 1955, revised manuscriptreceived, August 8, 1955. The research reported in this paper hasbeen sponsored by the Bureau of Ships, Dept. of the Navy.

t Electrical Engineering Dept., University of Tennessee, Knox-ville, Tenn.

miles from the transmitter at night, and at about 600miles during the day. The question of obtaining an ade-quate signal-to-noise ratio is the same for this systemas for any other, and the principal problem is one ofeliminating interference between ground-wave and sky-wave modes of propagation. This is accomplished bythe use of an antenna which can be excited in either oftwo ways:

1. A ground-wave phasing which gives a patternconcentrating the radiated energy along the sur-face of the earth for communication via the groundwave.

2. A sky-wave phasing which eliminates any groundwave by means of a null at zero degrees elevationangle and concentrates the radiated energy aboutan elevation angle of 60 degrees for communica-tion via the sky wave.

In each case the radiation pattern is omnidirectionalin azimuth. The ground-wave phasing is used to com-municate during the day and for distances of less thanabout 200 miles at night. The sky-wave phasing is usedat night for distances greater than about 100 miles.

PROPAGATION CONSIDERATIONSThe antenna is to be used for a particular communica-

tion link, so that rather specific antenna requirementscan be determined by a consideration of propagationfactors. The important considerations are

1. Skip distance.2. Ground-wave intensity-to-sky-wave intensity ra-

tio.3. Signal-to-noise ratio.Since the reason for investigating these factors is to

establish criteria for the design of the antenna, themethods of computing sky-wave field intensities and

1955 1655

PROCEEDINGS OF THE IRE

skip distances given in CRPL Circular No. 4621 areconsidered to be sufficiently accurate. This circularalso contains noise data which are adequate for thispurpose. Ground wave field intensities can be found byusing well known methods.2 These factors must be usedto select an operating frequency and to determine therequired vertical radiation pattern of the antenna.

For daytime the use of a frequency near two mega-cycles per second is indicated, as both sky-wave inter-ference and noise go through a minimum with respectto frequency in this range. The use of frequencies belowabout one megacy,cle per second is undesirable at nightbecause a large number of fairly strong multi-hop sky-wave modes are excited simultaneously, and inter-mode interference is correspondingly severe. A furtherundesirable factor is the excessive size of the requiredantenna structure at these relatively low frequencies.An upper limit on the nighttime frequency can be setby stipulating that the skip distance must never exceedthe distance that can be covered by the ground wave ifthere is no sky-wave interference. This insures coverageby one mode or the other. These distances for a sunl-spot minimum are plotted against frequency in Fig. 1,and it is seen that the highest frequency that may beused for all conditions is 3.3 megacycles per secoind.This frequency will be used for all following calculationsin this paper.

J800 ._.</

z600X_:+1 ^34 9 r

U- CUNP NVAVE RANG

2s00 - <- X

0 2 3 4 5 6 7 8 9FREQUENCY IN MC

Fig. 1 -Skip distance and ground wave range vs frequency. Theground-wave range is for a 5-kilowatt transmitter located 2 milesfrom a straight coast, and is based on no interfering sky wave.

Calculatioins of relative ground-wave and sky-wavefield intensities show that for daytime conditions iono-spheric absorption reduces sky-wave interference to apoint where the ground-wave communication is satis-factory without requiring a pattern greatly sharper thanthat of a quarter-wave monopole. At night the sky waveis relatively unabsorbed, and is strong enough to over-ride noise at distances greater than about 100 milesfrom the transmitter. To reduce the ground-wave

1 "Ionospheric Radio Propagation," U. S. Dept. of Commerce,Nat. Bur. Standards Circ. No. 462; June, 1948.

2 "Ground Wave Field Intensities," Signal Corps PropagationUnit, Tech. Rep. No. 3; June 1949.

intensity sufficiently so that it will not interfere with thesky wave requires a Inull in the antenna pattern at theground plane, thus eliminating the ground wave. Thisnull must exist for all azimuth angles or the region ofinterference-free coverage will be a inarrow wedge-shaped area. This in turn implies that the azimuthalradiation pattern at all polar angles be omnidirectionial,unless excessively complicated antennas are used. Maxi-mum radiation should be at about a 60-degree elevationiangle, corresponding to a 1-FIOP-F2 distance of about200 nautical miles, thus concentrating the field in thedesired area. The region out to the poinlt where the skywave is strong enough to override noise must be coveredvia the ground wave. Since the sky wave is relativelystrong at night, the ground-wave phasing of the antennashould concentrate the enregy along the surface asmuch as possible to keep initerference to a miiiinium.

THE ANTENNA SYSTEM

The antenna requiremenits set out above can be miietby an array of vertical elements equally spaced arounidthe circumference of a circle. The use of such ani arrayto obtain patterns haviing little radiation at high angleswas proposed by Chireix,' by Hansen and Hollings-worth,4 and, in a somewhat different form, by Page.5This array can also be excited in such a way as to givethe pattern desired for sky-wave communication.

It is shown in the Appendix that the pattern of suchan array of quarter-wave monopoles is given by

cos (Cosac2-on-i0 ---.

2,(w t+no) )

where each of the m elements has a current l/rm, andthere is a progressive phase difference 27rn/m betweenadjacent elements. Jn(x) is the Bessel function of thefirst kind of order n. The angles 0 and 4 are showni inFig. 7. The use of (1) assumes that m is larger than thecritical value specified in the Appendix. In (1) choosen = 0. A null in the ground plane (at 0=900) can thenbe obtained by setting 27rp/X equal to any root of Jo(x)=0. The smallest radius giving this null is p=0.383X.See pattern for this case in Fig. 2 (opposite). Inspectionshows that this pattern meets the requirements for thesky-wave phasing. Since the phase difference betweenadjacent elements is 27rn/m, and n = 0, all of the currentsare in phase for this method of excitatioin.To obtain a vertical pattern giving better sky-wave

suppression than given by the elements of the array,it is necessary that 27rp/X be less than the value of xfor the first maximum of Jn(x). This insures thatJ.1(27rp/X sin 0) is a monotone increasing function of 0.

3 H. Chireix, "Antennes a rayonnement zenithal reduit," L'OndeElect., vol. 15, pp. 440-456; July, 1936.

4 W. W. Hansen and L. M. Hollingsworth, "Design of 'flat-shoot-ing' antenna arrays," PROC. IRE, Vol. 27, pp. 137-143; Feb., 1939.

6 H. Page, "Ring aerial systems," Wireless Eng., vol. 25, pp. 308-315: October, 1948.

1656 November


For p=0.383X, this requires that n_2. In an antennaof this size a value of n> 3 leads to undesirable super-

gain characteristics.6 Then the value of n = 3 is the bestfor the present purpose. This pattern is also shown inFig. 2.

f3

-40

10 20 30 40 50 60 70 &0POLAR ANGLE IN DEGREES

Fig. 2-Vertical pattern of a single-ring array of quarter-wavemonopoles with a radius of 0.383 wavelength.

Eq. (18) in the Appendix can be used to fix m. Nineelements are needed for p = 0.383 X and n = 3. Gains maybe calculated by the method due to Page.7 For n = 0, thegain is 5.94 decibels, and for n=3 it is 2.57 decibels.

EXPERIMENTAL VERIFICATION

A model of the antenna was constructed and testedat 1,200 mc. Azimuthal patterns at a number of polarangles were obtained for both methods of excitation bymeans of a pattern recorder. Vertical patterns were ob-tained by point-by-point measurements. Experimentaldata together with calculated values are shown in Figs.3-6 on the following page. The agreement with theoryis seen to be quite good.

6 L. J. Chu, "Physical Limitations of Omnidirectional Antennas,"MIT Tech. Rep. No. 64, pp. 11-21; May, 1948.

7H. Page, "Radiation resistance of ring aerials," Wireless Eng.,vol. 25, pp. 102-109, April, 1948.

The final antenna will consist of nine folded mono-poles equally spaced about the circumference of a circle.At 3.3 mc, the radius of the circle is 114 feet, and theelements are 75 feet high. It is planned to feed the ele-ments with coaxial cables emanating from the center ofthe ring where the matching and phasing network areto be located. The antenna was also modeled at 30 mc toinvestigate these lumped circuit driving networks. Thisstudy showed that each phasing of the antenna couldbe excited by a network containing three T-sections,and that the current in each element could be set towithin the required tolerance without undue difficulty.

PROPAGATION CALCULATIONS

The probable ranges that can be covered usingthis antenna have been calculated. These calculationsare based on a required signal-to-noise ratio of 10decibels and a 10-decibel separation of ground-waveand sky-wave modes of propagation, both of which areadequate for teletype. Allowance has been made forfading, assuming a Rayleigh distribution for the sky-wave field intensity. The calculations were made for atransmitter power of 3 kw and an over-all efficiency of50 per cent. The antenna was considered to be locatedtwo nautical miles inland from a straight coast line.Ranges for noontime conditions are shown in Table I

TABLE IRANGES IN NAUTICAL MILES AT NOON FOR A SINGLE-RINGARRAY LOCATED Two MILES FROM A STRAIGHT COAST

Calculations are based on 3 kw transmitter and a frequency of 3.3 mc.

Azimuth Noise Noise Noise Noise Noiseangle Grade 1 Grade 2 Grade 3 Grade 4 Grade 5

0 690 690 690 560 430

30 670 670 670 550 420

60 560 560 560 490 360

and for midnight in Table II. The data in Table II are

the range using the ground-wave phasing, and the innerand outer limits of coverage using the sky-wave phasing.

TABLE IIRANGES IN NAUTICAL MILES AT MIDNIGHT FOR A SINGLE-RING ARRAY LOCATED Two MILES FROM A STRAIGHT COAST

Calculations are based on 3 kw transmitter and a frequency of 3 mc.

Azimuth Antenna Noise Noise Noise Noise Noiseangle phasing Grade 1W Grade 2W Grade 3W Grade 4 .Grade 5

G 204 204 204 204 204

0 40 61 91 148 N

1000+ 930 630 420 N

G 195 195 195 195 195

30 40 61 91 148 N

l ,/ ~~~~1000+ 930| 630 420 N

G 165 165 165 165 165

60 N0 61 91 148 NS

1000+ 930 630 420 ~~~~~N

1955 1657


0 10 20 30 40 50 60 70 80

POLAR ANGLE IN DEGREES

Fig. 3-Measured and calculated vertical patterns of a single-ringarray of quarter-wave monopoles with a radius of 0.383 wave-length and n=0.

-40

0 10 20 30 40 50 60 70 80

POLAR ANGLE IN DEGREES

Fig. 4-Measured and calculated vertical patterns of a single-ringarray of quarter-wave monopoles with a radius of 0.383 wave-length and n = 3.

Fig. 5-Measured and calculated horizontal pattern at 0=30 degrees Fig. 6-Measured and calculated patterns of a single-ring array ofof a single-ring array of quarter-wave monopoles with a radius of quarter-wave monopoles with a radius of 0.383 wavelength and0.383 and n=0. n =3.

The letter N is used to indicate that a signal-to-noiseratio of 10 decibels does not exist at any point in the0-to-500-mile region. Calculations were also carriedout for a large number of other cases. These include:

1. Sporadic E-mode present.2. Ionospheric absorption abnormally high.3. Twilight conditions.4. Arctic ionospheric and noise conditions.

In each case the results are acceptable.

CONCLUSIONSThe antenna system described in this paper appears

to offer a method of obtaining reliable shore-to-shipcommunication over distances of less than 500 mileswithout the customary fading caused by interferencebetween ground-wave and sky-wave fields. This ab-sence of interference is quite valuable where extremeaccuracy of reception of the transmitted signal is re-

quired.

1658 November

"I

z

CL

19coI11

Z

0ccnI

z4xli

41


APPENDIX

DERIVATION OF THE EXPRESSION FOR THE ARRAYFACTOR

A plan view of the m element array is shown in Fig.7. Establish a spherical co-ordinate system, with thepolar axis perpendicular to the plane of the circle, andchoose 4 = 0 through element m. Let the radius of thecircle be 7. To obtain patterns of the type desired letthe current in the ith element be

27rni= - -i.

m (5)

The summation in (4) has been investigated by Sten-zel8 for n=0 and m even, by Chireix,9 for n0 and meven, and by Page'0 for n=0 and m even or odd. Ageneral development follows that holds for each ofthese cases and also for n 5O and m odd. We mustinvestigate

S

SIm = E f,i(z cos 17i-nt1i)i=l

(6)(2)

where n is any positive integer or zero. There is thus a

uniform progressive phase shift between adjacent ele-ments, with n complete cycles of phase shift around thering. The field from the ith element is proportional to

l=Io jt+(27rn/m)i+27rp/Xsin ecos (4-(27rIm)i)]m

(3)

This may be expanded in a series of Bessel functions,"giving

Jo(z)m m oo

SM= ° e-in ti7+2 E , e-in7i[(-1) k cos 2kqJ2k(Z)m i=1 i=1 k=1

+j(- 1) k-l cos (2 k-1)XOJ2k,_(Z) ]. (7)

Each term of (7) may be considered separately. Let

I mSi = -Ex-ijn,7Jo(z),

m ial2 m oo

S2 = -- 1e-jnij(-1) k COS 2 kiJ2k(z),M i-=l kl1

(8)

(9)

2 m oo

S3 = Ei-nj(- 1) ''- cos (2k 1)ifJ2kl(Z). (10)m i=l k=l

Now in each case these sums reduce to geometric pro-

gressions. The first is

1 m

SI E JO(z)t-jnEj (27rnj m) %

m i-1

( ) e-jn4 Ej(27rnlm)im

Jo(z) sin nrnj(n+l/m)n

m sin (7rn/m)(11)

If M>n, which is the only practical case, and n5O, S5=0. If n=O, S,=Jo(z). Thus,

S, {Jo(z) n = 0

n 5 0.(12)

For S2 we obtain, by reversing the order of summation,and by a simple algebraic manipulation, that

Fig. 7 View of a single-ring array lying in the r, c, 0 = 0 degplane of a spherical co-ordinate system.

The array factor is then found by summing Ei frorto m. This gives

I0 m= _-0 t+n0) E ((zcosr7jl7j)mr=n

where

2,xpz = -sin

x

rrees

:n 1

1 °° mn=2 -£> ( 1) J2k(Z) Ej [Ej(2k-n)OEf(n-2k) (2r/ m) i

m k=l i=l

+ e-j(2k+n)OEj(n+2k) (2ir/ m) i] (13)

S2 may now be expanded by the use of the expression(4) for the sum of a geometric progression, giving

8 H. Stenzel, "Uber die richtcharakteristik von in einer EbeneAngeordneten Strahlern," Electr. Nachr. Technik, vol. 6, pp. 165-181;May, 1929.

9 Chireix, loc. cit.10 Page, loc. cit.11 G. N. Watson, "Theory of Bessel Functions," Cambridge Uni-

versity Press, Cambridge, England, pp. 22-23; 1944.

Ii =-ei(wt+(27rn/m)i)m

1955 1659


1 XS2=- 2, (- 1) kJ2k(Z)

m k_1Fk sin (n-2k)irfiE(2k-n)Ej(:m+lIm)(n -21k)rL sin (n-2k) r/m

+ E-j(2k+n),Ej(m+l/rn)(nf(n+2k) r sin (n+2k)7-sin (n+2k)7r/mj

In (14) n and m are integers and k takes on only integralvalues. Then the only values of k which give rise tononzero terms are those for which

Imr-n Imr-nk=-- or k =-o

2 2

There are four cases: n odd, m odd; n even, m odd;n odd, m even; and n even, m even. The algebra foreach of these cases is straightforward but tedious andwill not be given here. The summation for S3 can becarried out in the same way as for S2. When this isdone, the result obtained by adding Si, S2, and S3 is thesame for all four cases although different terms comefrom Si, S2, and S3 for each case. The final expressionfor the array factor is

E = jnjlojn (isin E) 3(cot±nO)

+Io Z{ k en-nJkm -(sin 0) irwt±(n-km)41]

+ jk ~ ~27rp . 0 jw4(mnOFor+nJk+n sin ti re e(15)

For n=, this reduces to

/2grp \jwE = IoJo -r sin A l/i tX/

00 ~~~~/2irp+ 2Io t Z jk; COSSkmJk.f V-sinf) .

k-l1(16)

The azimuthal pattern at polar angle 0 will be circu-lar if

(14)(17)Jm-n sin N<< Jn -sin

where terms for k > 2 are neglected because of the rapiddecrease of Jk(x) with increasing k. The peak-to-peakvariation in the pattern in db is

/2irp \ /2rp \AJnI-sin0 + ;Jm-n -sinGVAR= 20 log . (18)

/J 2; sin 0\ ¢- _ 2sin0w\

If n 0, (18) is valid for m even, but if m is odd the termfor k= 1 is in quadrature with the principal term aind

VAR= 10 log-

23rp ] [ /2ip 2

o -= sin 1+ fil1 sino[ L \X

[Jo sin

(19)

If m is large enough so that the use of (18) or (19)shows that the azimuthal patterni is essentially a circle,the term for k = 1 can also be neglected and

E = jnIoJn 7Psin 0)Ei t+n4) (20)

This is the expression for the patterin of an array ofisotropic radiators, and must be multiplied by the ex-pression for the pattern of the individual elements toobtain the equation of the final pattern.

C~AD

1660 -November

the use of a ring array as a skip range antenna

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