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Communications Research Cenfre

B EVERAGE ANTENNAS FOR HF COMMUNI~ATIONS, DIRECTION FINDING AND OVER-THE-HORIZON RADARS by

1. litva and B.J. Rook

DEPARTM ENT 0 F CO MMUNICAT IONS MINISTER E DES COMMUNICATIONS

CRC REPORT NO. 1282

This work was sponsored by the Department of National D~fence,R w m h and Development Branch under Project No. 28-03-24, Task ACN35321 and 3x28.

CANADA

OTTAWA, AUGUST 1976

C O M M U N I C A T I O N S

R E S E A R C H

C E N T R E

DEPARTMENT OF COMMUNICATIONS CANADA

BEVERAGE ANTENNAS FOR HF COMMUNICATIONS, DIRECTION FINDING AND OVER-THE-HORIZON RADARS by

J . Litva and B.J. Rook

(Radio and Radar Branch)

. Received July I976 Ptrblished August I976

CRC REPORT NO. 1282

TELS REPORT NO. 37

OTTAWA

This work was sponsored by the Department of National Defence, Research and Development Branch under Project No. 28-03-24. Task ACN35321 and 35C28. CAUTION The use of this information i s permitted subject to recognition of proprietary and patent tights.

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TABLE OF CONTENTS ABSTRACT .

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................................ 1 . INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Description o f the Beverage Antenna . . . . . . . . . . . . . . . 1.2 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Motivation f o r CRC Work . . . . . . . . . . . . . . . . . . . . . 1.4 Preview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . SITING OF BEVERAGE ANTENNAS . . . . . . . . . . . . . . . . . . . . . 2.1 Siting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Homogeneity o f the Ground . . . . . . . . . . . . . . . . . . . . 2.3

2.4

2.5

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Measurement o f Ground Constants 2.3.1 F i e l d Intensity Versus Radial Distance 2.3.2 Beverage Antenna Parameters 2.3.3 L i s t i n g o f Soil Types Deduced from Field Intensity and Antenna Measurements . . . . . . . . . . . . . . . . . . Theoretical Attenuation. Impedance and Phase Velocity . . . . . Debert Measurements . . . . . . . . . . . . . . . . . . . . . . .

3 . BEVERAGE ANTENNA PARAMETERS . . . . . . . . . . . . . . . . . . . . . 3.1 Design Parameters . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Efficiency of Beverage Antennas . . . . . . . . . . . . . . . . . 3.3 Radiation Patterns . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Individual Beverage Element . . . . . . . . . . . . . . . 3.3.2 Beverage Pair Antenna . . . . . . . . . . . . . . . . . . 3.4 Isolation Between Beverage Elements . . . . . . . . . . . . . . . 3.5 Phase Centre o f Beverage Elements . . . . . . . . . . . . . . . . 3.6 Low Frequency Beverage Antenna . . . . . . . . . . . . . . . . . 3.7 +Surface Wave Gain of Beverage Antennas . . . . . . 3.7.1 Theoretical Expression . . . . . . . . . . . 3.7.2 Measured Surface Wave Gain . . . . . . . . . 3.8 Theoretically Derived Values of Surface Wave Gain .

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2 2 2 3 4 5

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9 9 11 13 14 14 18 18 21

22 22 24 26 26 27 27 27 29 31

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....................... .......................... ......................... . ............... ........ .............. ................... ................. ........ .................. ........................ .......... 5 . CONCLUSIONS AND RECOMMENDATIONS . . . . . . . . . . . . . . . . . . . 5.1 S i t i n g of HF Antenna . . . . . . . . . . . . . . . . . . . . . . 5.2 Beverage Antenna Parameters . . . . . . . . . . . . . . . . . . . 5.3 Beverage Antenna Systems . . . . . . . . . . . . . . . . . . . . 5.4 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 . ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 . REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

BEVERAGE ANTENNA SYSTEMS 4.1 Introduction 4.2 Rosette Arrays 4.2.1 Cambridge Bay Rosette Array 4.2.2 Rosette Array as a Communications Antenna 4.2.3 Rosette Array as a DF Antenna 4.3 Cambridge Bay Linear Array 4.3.1 Description of the Array 4.4 Linear Phased Beverage Arrays for Communications 4.4.1 I n i t i a l Considerations 4.4.2 Beverage Array a s a Point-to-Point Communications Antenna. 4.4.3 Efficiency of a Linear Beverage Array

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APPENDIX I APPENDIX I1

.Theoretical Curves f o r Attenuation. C h a r a c t e r i s t i c

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Impedance and Velocity Ratio

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31 31 32 32 32 33 34 34 35 35 37 38 42 42 42 43 43 44 45 89

.Theoretical Curves f o r Azimuthal Beamwidth. Vertical

. . . . . . . . . . . . 97 Surface Wave Gain . . . . . . . . . 122

Beamwidth. Gain. and Take-Off Angle APPENDIX 111 .Theoretical Curves f o r APPENDIX IV

.An Analysis of the Beverage Antenna and I t s Applications

t 6 Linear Phased Arrays . . . . . . . . . . . . Section 1 .Analysis of the Beverage Antenna . Section 2

. . . . . . 125 . . . . . . 126 .The Effects of Ground on the Beverage Antenna Radiation Pattern . . . . . . . . . . . . . . 134

Section 3 .Determination of the C h a r a c t e r i s t i c Impedance (Z, ) and the Complex Propagation Constant (y) 137

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4 Radiation Fattern o f a Linear Array. . . . . . . 5 - 'Primary' Grating Lobes. 6 - Beam Steering. . . . . . . . . . . . . . . . . . 7 Amplitude Weighting. 8 - Azimuthal Bearing Errors Caused by Linear Array on Sloping Ground Section 9 - Radiation Pattern Formation as a Function o f the Radial Distance R. Section Section Section Section Section

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142 149 151 160 166 169

BEVERAGE ANTENNAS FOR HF COMMUNICATIONS, DIRECTION FINDING AND OVER-THE-HORIZON RADARS by J . Litva and B . J .

sv //A

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Rook

ABSTRACT

d e t a i l e d d e s c r i p t i o n i s given of t h e experimental and t h e o r e t i c a l r e s u l t s o b t a i n e d from a study o f t h e Beverage antenna. The r e s u l t s show t h a t t h i s antenna is u s e f u l as a r e c e i v i n g antenna i n t h e h i g h frequency r a n g e because it is h i g h l y d i r e c t i v e l a r g e l y frequency independent, has a low take- off a n g l e and i s r e l a t i v e l y inexpensive t o c o n s t r u c t . Since t h e e l e c t r i c a l p r o p e r t i e s of t h e ground o v e r which HF a n t e n n a s may be s i t u a t e d w i l l a f f e c t t h e i r performance, a novel t e c h n i q u e i s d e s c r i b e d , which u t i l i z e s a s i n g l e Beverage elerient t o determine t h e s e p r o p e r t i e s . Comprehensive Beverage a n t e n n a engineering- design- data have been c a l c u l a t e d and t a b u l a t e d i n a r e a d i l y a c c e s s i b l e format f o r t h e communications e n g i n e e r . Beverage a n t e n n a s are shown t o b e e f f e c t i v e elements o r " b u i l d i n g blocks" f o r HF antenna systems, such as r o s e t t e and l i n e a r antenna a r r a y s . These have a p p l i c a t i o n t o HF d i r e c t i o n f i n d i n g , over- the- horizon r a d a r and p o i n t - t o - p o i n t communication systems .(I I t is shown t h a t a Beverage l i n e a r a r r a y system h a s s u f f i c i e n t g a i n a t h i g h frequency t h a t it may be used i n t h e t r a n s m i t t i n g a s w e l l as t h e r e c e i v i n g mode. A l i s t i n g of a computer program is included which can be used t o c a l c u l a t e a l l n e c e s s a r y d e s i g n parameters of e i t h e r s i n g l e Beverage a n t e n n a s or a r r a y s of Beverage antennas.

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1.

INTRODUCTION

1.1 DESCRIPTION OF THE BEVERAGE ANTENNA A Beverage antenna i s a non- resonant broadband antenna which h a s been used and t e s t e d over t h e frequency range 3 t o 30 MHz. I t c o n s i s t s of a long w i r e (Figure 1 ) s t r e t c h e d h o r i z o n t a l l y above t h e ground and i s , i n essence, a l o s s y t r a n s m i s s i o n l i n e w i t h t h e ground a c t i n g as t h e conductor f o r t h e r e t u r n c u w e n t . Its c h a r a c t e r i s t i c impedance i s approximately 400-600 ohms. The antenna i s terminated i n i t s c h a r a c t e r i s t i c impedance a t one end, v i a a ground screen, and t h e r e c e i v e d s i g n a l i s taken from t h e o t h e r end through a t r a n s f o r m e r , one s i d e of which i s connected t o ground v i a a n o t h e r ground s c r e e n . The transformer i s used t o match t h e 400-600 ohm impedance of t h e antenna t o a s t a n d a r d 50-ohm c o a x i a l c a b l e . The d i r e c t i o n of t h e beam, o r maximum s e n s i t i v i t y of t h e a n t e n n a t o r a d i o s i g n a l s , i s toward t h e terminated end. The dimensions of HF Beverage antennas are a s follows; t h e i r l e n g t h s vary from 50 t o 150 m and t h e i r h e i g h t s above ground v a r y from 0 . 3 t o 3 m. T y p i c a l l y though, t h e i r l e n g t h and h e i g h t are r e s p e c t i v e l y about 110 m and 1 . 5 m.

The behaviour of t h e Beverage antenna can most e a s i l y be described i n t h e r o l e of a r e c e i v i n g antenna. One imagines t h e antenna subdivided i n t o elements of e q u a l l e n g t h , each of which i s a f f e c t e d by a d i r e c t and i n d i r e c t r a y emanating from a r a d i o t r a n s m i t t e r . The r e s u l t i n g h o r i z o n t a l component of t h e e l e c t r i c a l f i e l d o u t s i d e each element i s t h e v e c t o r sum of t h e horiz o n t a l components a s s o c i a t e d w i t h t h e two r a y s . The r e s u l t a n t e l e c t r i c - f i e l d component f o r each element w i l l induce an a l t e r n a t i n g v o l t a g e i n t h a t element. The elements can now b e thought of as c o n t a i n i n g RF g e n e r a t o r s , which cause RF c u r r e n t s t o flow t h a t are a t t e n u a t e d a t t h e r e c e i v e r t e r m i n a l s i n proport i o n t o t h e d i s t a n c e of t h e antenna element from t h e r e c e i v e r . The energy a r r i v i n g a t t h e terminated end i s absorbed and d i s s i p a t e d by t h e t e r m i n a t i n g r e s i s t o r ; t h e magnitude of t h e c u r r e n t a t t h e r e c e i v i n g end i s t h e v e c t o r sum of t h e c u r r e n t s generated by each imaginary g e n e r a t o r , delayed i n phase and a t t e n u a t e d i h amplitude i n p r o p o r t i o n t o t h e d i s t a n c e of t h e g e n e r a t o r from t h e r e c e i v i n g end of t h e antenna.

1.2

PREVIOUS WORK

The i n i t i a l developmental work performed w i t h t h e Beverage antenna w a s c a r r i e d o u t by H.H. Beverage p r i o r t o 1923. H e t e s t e d t h e antenna on a t r a n s o c e a n i c c i 5 c u i t using l o n g waves i n t h e frequency range 1 2 t o 42 KHz and found t h a t w i t h antenna l e n g t h s of approximately one wavelength (7 t o 25 km) t h e antenna w a s e f f e c t i v e i n reducing i n t e r f e r e n c e and s t a t i c because of i t s d i r e c t i v e n a t u r e . This work w a s f i r s t r e p o r t e d i n a n e a r c l a s s i c a l paper by Beverage, e t . a l (1923). T r a v e r s et a l . d i d e x t e n s i v e t h e o r e t i c a l and experimental r e s e a r c h w i t h t h e Beverage antenna from 1961 t o 1967. Their work i s documented i n a s e r i e s of r e p o r t s , w i t h l i m i t e d d i s t r i b u t i o n , submitted t o t h e U . S . Navy. A b r i e f u n c l a s s i f i e d summary of t h e i r work appeared i n Martin e t a l . (1965).

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The work of Travers e t al. c o n s i s r e d of t h e f i r s t e x t e n s i v e a p p l i c a i o n of t h e a n t e n n a f o r r e c e p t i o n a t HF f r e q u e n c i e s . I n t h e c o u r s e of t h e i r work they concluded t h a t t h e a n t e n n a w a s an e f f e c t i v e low c o s t element w i t h h i g h d i r e c t i v i t y t h a t worked o v e r good a s w e l l a s poor s o i l throughout t h e complete band from 1 t o 3 0 MHz. They found i t t o b e non- resonant o v e r a t l e a s t a f i v e o c t a v e frequency r a n g e when i t s l e n g t h w a s g r e a t e r t h a n one- half wavelengtp, and impedance t o be p r i m a r i l y r e s i s t i v e and f l a t over t h e HF band. Numerous t h e o r e t i c a l antenna r a d i a t i o n p a t t e r n s w e r e c a l c u l a t e d f o r v a r i o u s a n t e n n a l e n g t h s , h e i g h t s , s o i l c o n d i t i o n s , r a d i o wave p o l a r i z a t i o n s and e l e v a t i o n a n g l e s - o f - a r r i v a l . They a l s o concluded t h a t due t o i t s d i r e c t i v e n a t u r e , t h e antenna w a s n o t o n l y u s e f u l f o r r e c e p t i o n b u t a l s o f o r t r a n s m i s s i o n e i t h e r singly o r arrayed. E x t e n s i v e developmental work w a s a l s o performed by Travers e t a l . i n HF d i r e c t i o n f i n d i n g u s i n g l a r g e numbers of Beverage a n t e n n a c o n f i g u r e d i n r o s e t t e a r r a y s of v a r i o u s dimensions. I n one 360" r o s e t t e a r r a y , f o r example, t h e elements were 120 m i n l e n g t h and s e p a r a t e d by 10". The s t a n d a r d d e v i a t i o n i n a n g l e - o f - a r r i v a l of 402 bea.rings t a k e n on sky-wave s i g n a l s "of chance" was I n a n o t h e r i n s t a l l a t i o n , a 72" rosette a r r a y w i t h r e p o r t e d t o be 3 . 8 " . elements 300 m i n l e n g t h s e p a r a t e d by 2" y i e l d e d a s t a n d a r d d e v i a t i o n f o r 408 b e a r i n g s of 1.04" . Some developmental work h a s been performed by t h e s t a f f of Rome A i r Development C e n t e r (RADC) a t t h e i r Dexter, N.Y. a n t e n n a s i t e . T h i s h a s been d i r e c t e d towards d e v e l o p i n g an e f f e c t i v e over- the- horizon (OTH) r a d a r a n t e n n a . A number of l i n e a r phased a r r a y s have been c o n s t r u c t e d and t e s t e d i n b o t h t h e r a d a r receive and t r a n s m i t modes. A two- dimensional a r r a y i s c u r r e n t l y b e i n g e v a l u a t e d and i s b e i n g used t o d e v e l o p and t e s t a d a p t i v e a r r a y t e c h n i q u e s . Their i n i t i a l work p r e - d a t e s t h a t performed by CRC. D i s c u s s i o n s between CRC and RADC p e r s o n n e l were h e l d p r i c - t o C R C ' s embarking on t h e HF a n t e n n a program d e s c r i b e d i n t h i s r e p o r t .

1.3

MOTIVATION FOR CRC WORK

O r i g i n a l l y , t h e m o t i v a t i o n f o r c o n d u c t i n g developmental work on Beverage a n t e n n a s came from a CRC r e q u i r e m e n t f o r a h i g h l y d i r e c t i o n a l OTH r a d a r receive a n t e n n a w i t h a 360" a z i m u t h a l c a p a b i l i t y . T h i s a n t e n n a w a s t o be s i t e d a t Cambridge Bay, N.W.T. and was t h e r e f o r e r e q u i r e d t o w i t h s t a n d extreme c l i m a t i c c o n d i t i o n s . A thorough s e a r c h of commercially a v a i l a b l e HF antennas revealed t h e following general shortcomings:

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they w e r e p r o h i b i t i v e l y expensive;

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t h e i r i n s t a l l a t i o n w a s expensive because i t required s p e c i a l i z e d p e r s o n n e l and equipment;

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t h e y had l a r g e moving s t r u c t u r e s which c o u l d prove t o b e troublesome i n low A r c t i c t e m p e r a t u r e s ;

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t h e i r d i r e c t i v i t y g a i n s were l i m i t e d t o a b o u t 1 0 dB and t h e i r a z i m u t h a l beamwidths w e r e a t l e a s t 60 d e g r e e s ;

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t h e y r e q u i r e d e x t e n s i v e ground s c r e e n s ; t h e i r maintenance r e q u i r e m e n t s w e r e q u i t e s u b s t a n t i a l and t h e r e f o r e expensive.

4 I t w a s d e c i d e d , on t h e b a s i s of t h e e n c o u r a g i n g r e s u l t s of e a r l y r a d i a t i o n p a t t e r n measurements of Beverage a n t e n n a s , t h a t a r o s e t t e a r r a y of 24 Beverage a n t e n n a s ( e l e m e n t s ) b e i n s t a l l e d a t Cambridge Bay, N.W.T. The elements of t h e rosette a r r a y w e r e phased i n p a i r s , g i v i n g 1 2 f i x e d beams, which could b e s e l e c t e d w i t h a remotely o p e r a t e d e l e c t r i c a l s w i t c h l o c a t e d a t t h e c e n t r e of t h e a r r a y . This c o n f i g u r a t i o n of Beverage e l e m e n t s r e s u l t e d i n a n i n e x p e n s i v e h i g h l y d i r e c t i o n a l HF a n t e n n a which had a low p h y s i c a l p r o f i l e , and i n a d d i t i o n , c o n t a i n e d no moving p a r t s . The Cambridge Bay r o s e t t e a r r a y w a s , n e e d l e s s t o s a y , found t o b e a n e f f e c t i v e OTH r a d a r r e c e i v i n g a n t e n n a . T$e s u c c e s s r e a l i z e d i n t h i s a p p l i c a t i o n p o i n t e d t o t h e u s e of Beverage a n t e n n a s a s " b u i l d i n g b l o c k s " f o r w i d e - a p e r t u r e i n e x p e n s i v e HF a n t e n n a s . These would f i n d u s e i n HF communications, OTH r a d a r s and HF d i r e c t i o n f i n d i n g systems. The Beverage a n t e n n a ' s a t t r a c t i v e n e s s stems from i t s h i g h d i r e c t i v i t y and wide bandwidth c h a r a c t e r i s t i c s , and of utmost importance, i t s s i m p l i c i t y and low c o s t . It w a s d e c i d e d t h a t a thorough knowledge of i t s p a r a m e t e r s w a s r e q u i r e d t o a l l o w f o r o p t i m i z a t i o n of i t s performance i n v a r i o u s c o n f i g u r a t i o n s . The m o t i v a t i o n t h e n f o r t h e a n t e n n a work t h a t h a s t a k e n p l a c e a t CRC s i n c e 1971 h a s been, s i m p l y , t o d e r i v e a complete d e s c r i p t i o n of t h e t e c h n i c a l p a r a m e t e r s of t h e a n t e n n a and t o d e t e r m i n e , by t e s t i n g , i t s p o t e n t i a l a s a n HF a n t e n n a . With t h i s i n mind t e s t s and e v a l u a t i o n s have been performed i n t h r e e d i s t i n c t a r e a s : namely, communications, d i r e c t i o n f i n d i n g and r a d a r . E x t e n s i v e measurements have been performed on i n d i v i d u a l Beverage e l e m e n t s and compared w i t h r e s u l t s d e r i v e d by u s i n g t h e o r e t i c a l developments t h a t have been p u b l i s h ed elsewhere. Comprehensive e n g i n e e r i n g d a t a have been c a l c u l a t e d and t a b u l a t e d i n a r e a d i l y a c c e s s i b l e and u s a b l e f o r m a t . These can b e used by t h e communications e n g i n e e r t o e f f e c t i v e l y d e s i g n HF Beverage a n t e n n a s y s t e m s . Techniques have been developed which p e r m i t comprehensive a s s e s s m e n t s of antenna s i t e s . F i n a l l y , a computer program w a s developed, based i n l a r g e measure on t h e t h e o r e t i c a l work performed a t t h e South West Research I n s t i t u t e (SWRI). T h i s g i v e s CRC a c a p a b i l i t y f o r c a l c u l a t i n g p a r a m e t e r s f o r e i t h e r s i n g l e Beverage e l e m e n t s o r a r r a y s of Beverage e l e m e n t s .

1.4

PREVfEW

T h i s r e p o r t g i v e s a summary of t h e e x p e r i m e n t a l and t h e o r e t i c a l d a t a t h a t have been accumulated and developed, r e s p e c t i v e l y , a t t h e Communications Research C e n t r e s i n c e J u l y 1971 a t which t i m e some e x p l o r a t o r y measurements were performed on a Beverage a n t e n n a e r e c t e d a t H a l l Beach, N.W.T. Because,of t h e l a r g e wavelengths e x h i b i t e d by HF r a d i o waves, t h e ground on which HF a n t e n n a s a r e e r e c t e d must be c o n s i d e r e d an i n t e g r a l p a r t of t h e s e a n t e n n a s . T h e r e f o r e , p r o p e r t i e s of t h e ground must be t a k e n i n t o c o n s i d e r a t i o n when a t t e m p t i n g t o d e t e r m i n e t h e performance of HF a n t e n n a s . With t h i s i n mind t e c h n i q u e s a r e o u t l i n e d i n S e c t i o n 2 f o r measuring ground p a r a m e t e r s f o r s i t i n g of Beverage o r o t h e r HF a n t e n n a s , by t h e e r e c t i o n of a s i n g l e Beverage element and measurement of i t s e l e c t r i c a l p a r a m e t e r s . The e f f e c t of t h e e l e c t r i c a l p r o p e r t i e s of t h e ground on t h e a n t e n n a ' s impedance, g a i n , current- wave v e l o c i t y , current- wave a t t e n u a t i o n , take- off a n g l e , e t c . , i s d i s c u s s e d i n c o n s i d e r a b l e d e t a i l . I t i s shown t h a t any one of t h e s e readily- measured p a r a m e t e r s can b e used t o d e r i v e t h e e l e c t r i c a l p a r a m e t e r s of t h e ground.

5

Once t h e e l e c t r i c a l p a r a m e t e r s of t h e ground t o be used are known, p r e c i s e e n g i n e e r i n g of Beverage a n t e n n a s c a n b e accomplished by r e f e r r i n g t o d a t a g i v e n i n Appendix 11. I t c o n s i s t s of t h e o r e t i c a l c u r v e s which g i v e t h e f o l l o w i n g Beverage a n t e n n a p a r a m e t e r s ; a z i m u t h a l beamwidth, v e r t i c a l beamw i d t h , power g a i n and v e r t i c a l take- off a n g l e . These a r e g i v e n f o r a wide range of antenna g e o m e t r i e s ( l e n g t h and h e i g h t ) and ground p a r a m e t e r s . An e x t e n s i v e comparison i s a l s o made of t h e o r e t i c a l l y d e r i v e d and measured a n t e n n a parameters t o d e f h e t h e p r e c i s i o n and c o n f i d e n c e l e v e l s t h a t c a n b e assigned t o the t h e o r e t i c a l curves. 0

'

I t i s shown t h a t t h e performance of a s i n g l e Beverage e l e m e n t , as a r e c e i v e antenna i n t h e HF band, i s n o t degraded by i t s low e f f i c i e n c y ( - 2 % ) . T h i s i s due t o t h e p r e s e n c e of a t m o s p h e r i c and g a l a c t i c n o i s e a t HF f r e q u e n c i e s making t h e HF environment i n h e r e n t l y n o i s y . S e c t i o n 4 d e a l s w i t h r o s e t t e and l i n e a r phased a r r a y s u s i n g Beverage a n t e n n a s as b a s i c b u i l d i n g b l o c k s . R e s u l t s a r e g i v e n of e v a l u a t i o n s performed on a number of p r o t o t y p e Beverage a r r a y s used as d i r e c t i o n f i n d i n g and communications a n t e n n a s . These have been developed and c o n s t r u c t e d by CRC d u r i n g t h e c o u r s e of t h e work d e s c r i b e d i n t h i s r e p o r t . Both t h e i r t h e o r e t i c a l and measured e l e c t r i c a l p a r a m e t e r s a r e g i v e n i n t h i s s e c t i o n . It i s a l s o shown i n S e c t i o n 4 t h a t a l i n e a r phased a r r a y of Beverage a n t e n n a s c a n be e f f e c t i v e l y used n o t only a s a point- to- point communications r e c e i v e a n t e n n a , b u t a l s o a s a t r a n s m f ' a n t e n n a . Although t h e e f f i c i e n c y of a s i n g l e element i s o n l y a b o u t 1 . 5 2 , I d s u l t i n g i n an a n t e n n a w i t h a power g a i n of 0 dBi, an i n c r e a s e i n e f f i c i e n c y a u e t o a r e d u c t i o n i n ground l o s s e s c a n be r e a l i z e d by p h a s i n g a number of a n t e n n a e l e m e n t s t o g e t h e r . It i s e x p e c t e d t h a t an e f f i c i e n c y of 25% c a n b e r e a l i z e d i n p r a c t i c e , which t h e n p e r m i t s f a b r i c a t i o n of communications a n t e n n a s w i t h power g a i n s of a b o u t 15-18 dBi. The performance of t h e s e a n t e n n a s s u r p a s s e s i n many i n s t a n c e s , t h a t of c l a s s i c a l a n t e n n a s . Furthermore t i e y c a n b e i n s t a l l e d and m a i n t a i n e d a t an antenna s i t e a t a f r a c t i o n of t h e c o s t of c l a s s i c a l a n t e n n a s . The m a j o r i t y of t h e t h e o r e t i c a l development used i n t h i s r e p o r t i s g i v e n I i n Appendix I V . E q u a t i o n s a r e d e r i v e d which p e r m i t t h e c a l c u l a t i o n of a l l p e r t i n e n t e l e c t r i c a l p a r a m e t e r s f o r Beverage e l e m e n t s . A l a t e r s e c t i o n of Appendix I V g i v e s e q u a t i o n s which c a n b e used t o c a l c u l a t e r a d i a t i o n p a t t e r n s of l i n e a r phased a r r a y s . F i n a l l y , a l i s t i n g i s g i v e n of t h e computer program used t o c a l c u l a t e t h e e l e c t r i c a l p a r a m e t e r s of b o t h s i n g l e Beverage e l e m e n t s and a l s o l i n e a r phased a r r a y s of Beverage a n t e n n a s .

,

2. 2.1

S I T I N G OF BEVERAGE ANTENNAS

SITING

The e l e c t r i c a l p r o p e r t i e s of t h e ground o v e r which a Beverage a n t e n n a o r any HF a n t e n n a i s e r e c t e d a f f e c t i t s e l e c t r i c a l p a r a m e t e r s and t h e r e b y i t s performance. I t i s of p a r t i c u l a r importance t h a t t h e ground s u r r o u n d i n g Beverage a n t e n n a a r r a y s b e chosen t o b e as i s o t r o p i c and homogeneous as p o s s i b l e t o e n s u r e t h a t t h e r a d i a t i o n p a t t e r n s of t h e i n d i v i d u a l a n t e n n a s a r e

6 symmetrical, s i m i l a r and n o t skewed i n azimuth. V a r i a t i o n s i n t h e e l e c t r i c a l p r o p e r t i e s of t h e ground w i l l t e n d t o d e g r a d e t h e r a d i a t i o n p a t t e r n s of a n t e n n a a r r a y s a n d i n p a r t i c u l a r Beverage a r r a y s .

The e l e c t r i c a l p a r a m e t e r s of t h e ground a t Cambridge Bay, N . W . T . , a r e deduced from a number of independent Beverage a n t e n n a p a r a m e t e r measurements. These a r e d e s c r i b e d i n d e t a i l i n S e c t i o n 2.3. A t o p o g r a p h i c a l map of t h e s i t e showing t h e l o c a t i o n of b o t h t h e r o s e t t e and l i n e a r Beverage a n t e n n a a r r a y s i s g i v e n i n F i g u r e s 2 and 3 . The numerous l a k e s i n t h e v i c i n i t y of t h e s e afltennas s u g g e s t s t h a t t h e ground a t t h i s s i t e i s n o t l i k e l y t o b e e i t h e r i s o t r o p i c o r homogeneous. I n g e n e r a l , t h e t e r r a i n , a l t h o u g h r e l a t i v e l y f l a t , i s i n t e r s p e r s e d w i t h h i l l s . The e l e v a t i o n of t h e r o s e t t e and l i n e a r Beverage a n t e n n a a r r a y s above sea l e v e l r e s p e c t i v e l y w a s a p p r o x i m a t e l y 100 and 50 ft. The r o s e t t e a n t e n n a a r r a y w a s s i t e d n e a r t h e c r e s t of a h i l l whereas t h e l i n e a r a n t e n n a a r r a y w a s s i t e d i n a n a d j a c e n t low- lying area.

2.2

HOMOGENEITY OF THE GROUND

Two t y p e s of measurements were performed a t Cambridge Bay t o d e t e c t any h e t e r o g e n e i t y i n t h e ground s u r r o u n d i n g t h e Beverage r o s e t t e a n t e n n a a r r a y . The p o s i t i o n of t h e r o s e t t e a r r a y i s shown i n t h e t o p o g r a p h i c a l map g i v e n i n F i g u r e 2 . The f i r s t c o n s i s t e d of f i e l d i n t e n s i t y measurements i n t h e v i c i n i t y of a X / 4 monopole. They were made on t h e ground w i t h a f i e l d i n t e n s i t y meter. The r a n g e of t h e meter from t h e monopole w a s 610 m t h r o u g h o u t , and i t s azimuth w a s incremented i n 15" s t e p s . The monopole was e x c i t e d by a 9.5 MHz one- watt s o u r c e and w a s l o c a t e d a t t h e g e o m e t r i c a l c e n t r e of t h e a r r a y . R e s u l t s a r e g i v e n i n F i g u r e 4 of t h e measurements which were made on 26 J u l y 1972 and 26 September 1972. The f i r s t measurement w a s made p r i o r t o t h e i n s t a l l a t i o n of t h e r o s e t t e a n t e n n a a r r a y , w h i l e t h e l a t t e r w a s made f o l l o w i n g i t s i n s t a l l a t i o n . They b o t h i n d i c a t e t h a t t h e ground w i t h i n a 610 m r a d i u s of t h e r o s e t t e a n t e n n a a r r a y i s r e l a t i v e l y homogeneous i n a z i m u t h , a l t h o u g h t h e r e are s m a l l p e r t u r b a t i o n s p r o b a b l y caused by t h e s m a l l l a k e s and h i l l s i n t h e v i c i n i t y of t h e a r r a y . For example, peaks i n s i g n a l l e v e l i n F i g u r e 4 o c c u r a t a z i m u t h s of 1 2 0 ° , 240" and 300". F i g u r e 2 i n d i c a t e s t h a t t h e s e c o r r e s p o n d c l o s e l y t o a z i m u t h s where a t l e a s t p a r t of t h e ground between t h e monopole and d e t e c t o r i s covered w i t h water. It i s of some i n t e r e s t t o n o t e t h a t t h e i r r e g u l a r i t i e s a p p e a r i n g on t h e c u r v e f o r 26 J u l y a l s o a p p e a r on t h e c u r v e f o r 26 September. The f i e l d i n t e n s i t y l e v e l measured on 26 September w a s r o u g h l y 5 dB g r e a t e r t h a n t h a t measured on 26 J u l y , which w a s c o n t r a r y t o e x p e c t a t i o n s s i n c e t h e e l e c t r i c a l p a r a m e t e r s of t h e ground i n t h e A r c t i c a r e u s u a l l y c o n s i d e r e d t o d e t e r i o r a t e d u r i n g t h e w i n t e r s e a s o n . However, t h e increase is e a k i l y explained i f i t i s a t t r i b u t e d t o a decrease i n t h e e f f e c t i v e d i s t a n c e o f p r o p a g a t i o n due t o a n enhancement of t h e c o n d u c t i v i t y of t h a t p o r t i o n of t h e p a t h covered w i t h Beverage a n t e n n a s and t h e i r copper ground screens. The second t y p e of measurement w a s performed i n t h e a i r w i t h a n a i r An a i r b o r n e measurement of t h e f i e l d i n t e n s i t y e m i t t e d by a d i p o l e w a s made on 19 August 1974. The monopole w a s l o c a t e d s l i g h t l y n o r t h e a s t of t h e r o s e t t e array f o r t h i s measurement. Its l o c a t i o n i s g i v e n i n F i g u r e 3 . An improved XELEDOP t e c h n i q u e (Barnes, 1965) w a s employed t o make t h e

craft.

measurements.

7

A XELEDOP i s a s h o r t d i p o l e antenna u i t h an HF t r a n s m i t t e r l o c a t e d a t i t s t e r m i n a l s . Antenna p a t t e r n measurenents a r e made by towing t h i s package behind an a i r c r a f t . Since t h e package used a t Cambridge Bay c o n s i s t e d of a ' s h o r t d i p o l e antenna and a n HF r e c e i v e r a t i t s t e r m i n a l s r a t h e r t h a n a t r a n s m i t t e r i t was c a l l e d a RELEDOP.

e

The amplitude of t h e f i e l d s r a d i a t e d by t h e monopole antenna w a s measured w i t h an a i r c r a f t and t h e XELEDOP package and t h e d a t a w e r e r e l a y e d t o a c h a r t recorder l o c a t e d i n t h e a i r c r a f t . The a i r c r a f t towing t h e RELEDOP flew a t an a l t i t u d e of 10,000 f t . (3.05 km) and a c o n s t a n t range of 8 nm (14.8 km) from a ground based r a d a r s i t u a t e d n e a r t h e monopole. The e l e v a t i o n angle- of- arrival of a r a y j o i n i n g t h e d e t e c t o r and t h e monopole w a s 11.6'. The r e s u l t s of a measurement made a t 9.75 MHz are shown i n F i g u r e 5 t o g e t h e r w i t h t h e measured p a t t e r n of a Beverage p a i r antenna. More w i l l be s a i d of t h e Beverage p a i r antenna measurement a t a l a t e r t i m e . The accuracy of t h e s e f i e l d i n t e n s i t y measurements w a s determined p r i m a r i l y by t h e accuracy t o which t h e a i r c r a f t could b e k e p t a t a range of 8 nm from t h e t r a c k i n g r a d a r . This v a l u e w a s 20.1 nm. S i n c e t h e r e l a t i v e change i n f i e l d i n t e n s i t y E a t t h e a i r c r a f t due t o t h i s v a r i a t i o n i n range 1: i s given by E-tAE1 + A- r= 1 + -0.1 E r 8

-

i t follows t h a t t h e accuracy of t h e measurement w a s 20.1 dB. The p h y s i c a l s e p a r a t i o n of t h e monopole and t h e t r a c k i n g r a d a r caused a s y s t e m a t i c e r r o r i n t h e measurements. T h i s e r r o r i s e a s i l y c o r r e c t e d by u s i n g t h e i n v e r s e r e l a t i o n s h i p between f i e l d i n t e n s i t y and range.

An example of t h e accuracy of t h e measurements i s provided i n F i g u r e 5 by t h e v a r i a t i o n i n t h e level of t h e background s i g n a l . The l e v e l was approximately 0.8 dB g r e a t e r a t an azimuth of 125' than a t an azimuth of 305". The f a d a r used t o t r a c k t h e a i r c r a f t with t h e RELEDOP w a s n o t c o l l o c a t e d w i t h t h e monopole, as mentioned b e f o r e , b u t r a t h e r , w a s l o c a t e d i n "D" t r a i n which w a s a d i s t a n c e of 0.41 nm from t h e monopole, on a r a d i a l whose azimuth w a s 125". Therefore, a t an azimuth of 1 2 5 O t h e a i r c r a f t w a s 0.82 nm f u r t h e r from t h e monopole than when i t s azimuth w a s 305". This would b e expected t o produce a v a r i a t i o n of 0.85 dB i n t h e measured f i e l d i n t e n s i t y , which i s i n c l o s e agreement with what w a s measured. I t t i s of i n t e r e s t t o n o t e t h a t t h e v a r i a t i o n i n t h e f i e l d r a d i a t e d by t h e monopole antenna and which i s a t t r i b u t a b l e t o v a r i a t i o n s i n t h e topography of t h e land ir, t h e v i c i n i t y of t h e antenna i s less than 0.5 dB. This r e s u l t i s s u r p r i s i n g because t h e t e r r a i n s l o p e s down from t h e monopole f o r azimuths between 20 and 200°, whereas f o r azimuths between 240 and 20° t h e t e r r a i n n o t only i s rougher, b u t t h e monopole i s somewhat obscured by t h e crest of t h e h i l l on which i t i s s i t u a t e d . A t t h e s e azimuths one would e x p e c t , both s c a t t e r i n g of t h e e l e c t r o m a g n e t i c energy and some o b s c u r a t i o n of t h e monopole by t h e c r e s t of t h e h i l l .

".

.

8 The s e c o n d -i s t h e s u p e r i o r of t h e two t e c h n i q u e s used a t Cambridge Bay f o r determining t h e homogeneity o f t h e ground. This stems from i t s c l o s e s i m u l a t i o n of a skywave c o n f i g u r a t i o n . The f i r s t t e c h n i q u e measures t h e e f f e c t of t h e ground on t h e e l e c t r o m a g n e t i c wave which p r o p a g a t e s from t h e v e r t i c a l monopole d i r e c t l y t o t h e d e t e c t o r . The s t r e n g t h of t h e s i g n a l i s p r o p o r t i o n a l p r i m a r i l y t o t h e c o n d u c t i v i t y of t h e ground over which t h e wave propagates. V a r i a t i o n s i n t h e s t r e n g t h of t h e s i g n a l can b e a t t r i b u t e d t o v a r i a t i o n s i n t h e e l e c t r i c a l c o n d u c t i v i t y of t h e ground. I n t h e second technique, t h e signal a t t h e d e t e c t o r c o n s i s t s of a d i r e c t r a y n o t a f f e c t e d by t h e ground and a r e f l e c t e d wave whose amplitude and phase i s a f u n c t i o n of f i e e l e c t r i c a l parameters of t h e ground. T h i s dependence can b e observed i n F i g u r e s 6 and 7 where 1 0 MHz r e f l e c t i o n c o e f f i c i e n t s are given f o r seven types of ground. This l a t t e r technique a l l o w s one, i n p r i n c i p l e , t o deduce t h e ground r e f l e c t i o n c o e f f i c i e n t i n t h e v i c i n i t y of t h e source-monopole antenna and t h e r e f o r e t h e e l e c t r i c a l ground parameters. It i n e f f e c t i n t e g r a t e s t h e p r o p e r t i e s of t h e ground over a r e g i o n approximately t h e s i z e of one f r e s n e l zone, which f o r a 1 0 MHz monopole antenna r e c e i v i n g e l e c t r o m a g n e t i c energy a t an e l e v a t i o n a n g l e of s a y 11.6", i s an e l l i p s e whose dimensions are 780 by 160 meters. The t o t a l area c o n t a i n e d w i t h i n t h i s e l l i p s e i s 2 3 . 6 a c r e s , approximately t w i c e t h e area covered by t h e r o s e t t e antenna a r r a y shown i n F i g u r e 3 . C l e a r l y , t h e second t e c h n i q u e i s s u p e r i o r t o t h e f i r s t f o r probing ground homogeneity, simply because i t employs a geometry which i s a c l o s e r approximation t o t h a t used when HF skywaves are used f o r communications, d i r e c t i o n f i n d i n g o r OTH r a d a r s . I n F i g u r e 3 a compass r o s e h a s been drawn c o n c e n t r i c w i t h t h e l o c a t i o n of t h e monopole used f o r t h e a i r b o r n e tests. The dashed c i r c l e d e f i n e s t h e o u t e r edge of t h e f i r s t F r e s n e l zone a t 1 0 MHz. The bottom curve (binary curve) i n F i g u r e 5 i s i n t e n d e d t o i n d i c a t e t h e l o c a t i o n of t h e l a k e s w i t h i n t h e a r e a d e s c r i b e d by t h e c i r c l e i n F i g u r e 3. It w a s d e r i v e d from Figure 3, f i r s t l y , by drawing r a d i a l s , a t a p p r o p r i a t e azimuthal i n c r e m e n t s , from t h e c e n t r e of t h e c i r c l e t o i t s circumference. I f t h e r a d i a l w a s found t o p a s s over a l a k e contained w i t h i n t h i s c i r c l e i t w a s a s s i g n e d t h e number "one". On t h e o t h e r hand, i f i t d i d n o t i t w a s a s s i g n e d t h e number z e r o . I n t h e bottom graph i n F i g u r e 5 t h e s e numbers are p l o t t e d a g a i n s t t h e i r azimuths. The dashetl l i n e s i n F i g u r e 5 a t t e m p t t o show t h a t t h e r e i s a c o r r e l a t i o n between t h e measured v a r i a t i o n i n t h e monopole's t e r m i n a l v o l t a g e and t h e l o c a t i o n of t h e l a k e s c o n t a i n e d w i t h i n t h e c i r c l e i n F i g u r e 3 . The c o r r e l a t i o n i s p a r t i c u l a r l y good f o r azimuths between 234 and 286" where a s u b s t a n t i a l p o r t i o n of a r e l a t i v e l y l a r g e l a k e i s i n t h e f i r s t F r e s n e l r e g i o n of t h e monopole antenna. The c o r r e l a t i o n a t o t h e r azimuths i s n o t as w e l l defined due t o t h e d i f f i c u l t y of d e c i d i n g where, i n terms of t h e i r e f f e c t on t h e r e f l e c t e d r a y , t h e l a k e s e f f e c t i v e l y start and s t o p and a l s o t h e d i f f i c u l t y of matching t h e p e r t u r b a t i o n s i n t e r m i n a l v o l t a g e t o t h e c o r r e c t l a k e . Nevert h e l e s s , t h e good agreement i n F i g u r e 5 between t h e azimuths a t which p e r t u r b a t i o n occur on t h e f i e l d i n t e n s i t y curve and t h e azimuths a t which t h e b i n a r y curve h a s a v a l u e of 1 s u g g e s t s a high d e g r e e of c o r r e l a t i o n between t h e p e r t u r b a t i o n s and t h e presence of l a k e s . F i g u r e 5 provides an example t h e r e f o r e of t h e c h a r a c t e r i s t i c s e x h i b i t e d by p e r t r u b a t i o n s c a u s e d by ground which i s n o t homogeneous and i n p a r t i c u l a r i t demonstrates t h e i r r e l a t i v e magnitudes.

.)

9

2.3

MEASUREMENT OF GROUND CONSTANTS

The ground parameters at Cambridge Bay were derived independently from five measurements which are described in detail and are as follows:

.'

-

measurement of the amplitude of the field radiated by a monopole as a function of radial distance from the monopole;

-

measurement of the input impedance of a Beverage antenna as a function of frequency ;

- measurement of

the phase velocity of a current-wave on a Beverage antenna as a function of frequency;

-

measurement of the attenuation of a current-wave on a Beverage antenna as a function of frequency;

-

measurement of the gain of a Beverage antenna at 9 MHz.

Four of the five methods involve measurements of Beverage antenna parameters. The first was included to serve as a check on the accuracy of the remaining four. They will be discussed individually, and in particular, it will be shown that Beverage antenna parameters can be used to find the electrical constants of the ground beneath the antenna. The ground parameters can then be used to derive certain other essential electrical parameters of the Beverage antenna using a computer program developed at CRC and which is based in part on theoretical work described by Travers et a1 (1964). This program and the theoretical development on which it is based are described in complete detail in Appendix IV. The program can be used to calibrate gain and azimuthal radiation patterns of arrays of Beverage antennas for a given elevation angle.

2.3.1

Field I n t e n s i t y Versus Radial Distance

A measurement of field intensity versus distance from a monopole antenna excited with a 9.75 MHz transmitter was made on 18 August 1974. The location of the monopole is shown in Figure 3 . The radial along which the measurements were made coincided with a road which ran to the north-west of the monopole. The results are shown plotted in Figure 8 with two theoretical curves derived from a Sommerfeld analysis of ground-wave propagation (Terman, Electronic and Radio Engineering, p. 804, 1955) for average ground (wet) and poor ground. Their conductivities and dielectric constants are given in Table I, which lists the electrical parameters of nine distinct and identifiable t$pes of earth. There is good agreement between the theoretical curve for poor ground and the experimental results of 18 August 1974. The field intensity measurements made on 26 September 1972 and 26 July 1972 are also included. These were previously given in greater detail in Figure 4. Average values are plotted with error bars showing the range of the variation in the measurements due to inhomogeneities in the ground.

10 TABLE i Eorth Conductivity Converstion Toble (With Typical Dielectric Constants) (A fter Trovers et 01, 1964) Resistivity Conductivity

1 -

(0)

U

Type of Earth

emu (Abmho cm)

esu (statmho cm)

Dielectric constant (Typical)

(mho-meter)

* Sea Water

5 x lo-"

4.5 x

Sea Water

3 x lo-11

Wet Rich Soil

3 x 10lS

Average Soil (Wet)

1 x

Average Soil (Dry1

3 x 10-14

Poor Soil

1x

10-l~

(Dry)

3x

10-15

Dry Sand

i x

9x

D r y Granite (Subsurface)

1 x 10-l*

900

10-13

5

.2

81

2.7 x 10"

3

.33

81

2.7 x 10'

.03

33

15 - 16

.01

1 00

10 - 25

333

10- 15

1o'O

9 x lo7 2.7 x lo'

9 x lo6

3

10-3

1 x 10-3

1 o3

10

Poor Soil

2.7 x lo6 105

3

10-4

3.3

1x 10-~

1o4

10-7

1 07

lo3

8 5 Probably

1 pv/m. I f t h e r o s e t t e a r r a y were t o improve t h e c o n d u c t i v i t y of t h e ground so t h a t i t w a s e q u i v a l e n t t o t h a t of w e t r i c h s o i l w i t h t h e d i e l e c t r i c c o n s t a n t remaining u n a l t e r e d t h e f i e l d s t r e n g t h of 0.152 km would i n c r e a s e t o Thus a n improvement i n c o n d u c t i v i t y of t h e f i r s t 0.152 km 119.8 dB > 1 pv/m. of a 0.610 km p a t h of t h i s magnitude i s s u f f i c i e n t t o i n c r e a s e t h e s i g n a l l e v e l measured a t a d i s t a n c e of 0.152 km and a l s o 0.610 km from t h e monopole by 7 . 2 dB. T h i s i s s u f f i c i e n t t o a c c o u n t f o r t h e d i s c r e p a n c y between t h e measurements made on 26 September and 26 J u l y 1972.

I t may b e concluded t h a t t h e ground i n t h e v i c i n i t y of t h e r o s e t t e a r r a y corresponds on t h e a v e r a g e t o a v e r a g e ground ( d r y ) . Measurements show i n a d d i t i o n t h a t i t v a r i e s between poor ground and a v e r a g e ground ( w e t ) .

2.3.2

Beverage Antenna Parameters

( a ) Impedance Measurements: Impedance measurements were made a s a f u n c t i o n of f r e q u e n c y on seven of t h e twenty- four Beverage a n t e n n a s c o n t a i n e d i n t h e Cambridge Bay r o s e t t e a n t e n n a a r r a y . The a v e r a g e of t h e s e seven measurements i s p l o t t e d as a dashed c u r v e i n each of t h e f o u r diagrams g i v e n i n F i g u r e 10. The q u a s i - p e r i o d i c n a t u r e of t h e e x p e r i m e n t a l c u r v e i n d i c a t e s a s t a n d i n g wave c o n d i t i o n on t h e Beverage a n t e n n a s which s u g g e s t s t h a t t h e antennas were n o t t e r m i n a t e d i n t h e i r c h a r a c t e r i s t i c impedances.

*

Two t h e o r e t i c a l c u r v e s of i n p u t impedance a r e a l s o i n c l u d e d i n each of t h e diagrams o f F i g u r e 1 0 , one f o r a Beverage a n t e n n a t e r m i n a t e d i n 390 ohms and t h e o t h e r f o r a Beverage a n t e n n a t e r m i n a t e d i n i t s c h a r a c t e r i s t i c impedance. The g r a p h s a r e f o r f o u r d i f f e r e n t t y p e s of s o i l c o n s i s t i n g of poor s o i l , a v e r a g e s o i l ( d r y ) , a v e r a g e s o i l (wet) and w e t r i c h s o i l . I n a l l c a s e s t h e a n t e n n a ' s h e i g h t above ground i s 1 meter.

.

A comparison of t h e a m p l i t u d e and p h a s e s of t h e p e r t u r b a t i o n s on t h e e x p e r i m e n t a l c u r v e and t h e t h e o r e t i c a l c u r v e f o r a 390 R t e r m i n a t i o n , s u g g e s t s c l o s e s t agreement o c c u r s f o r a v e r a g e s o i l ( d r y ) and a v e r a g e s o i l (wet). From t h e s e i n p u t impedance measurements one c o n c l u d e s t h a t t h e s o i l type a t Cambridge Bay, i n terms of i t s e l e c t r i c a l p a r a m e t e r s i s l o c a t e d between, 01 = 3 x € 1 = 1 2 and 0 2 = lo-', 2 = 1 7 , where t h e v a l u e s o f € a r e medians of t h o s e l i s t e d i n T a b l e I .

(b) Attenuation Measurements: One o f t h e Beverage a n t e n n a p a i r s i n t h e r o s e t t e a r r a y w a s e x c i t e d w i t h an RF g e n e r a t o r a t a number of f r e q u e n c i e s between 5.8 and 23.7 MHz. The r e s u l t i n g a m p l i t u d e of t h e current- wave on one

12 of the wires was measured with a current probe, as a function of distance from the feed point. In Figure 11 the relative amplitude of the current versus the distance from the feed point is shown for the various test frequencies. The attenuation constant for the Beverage element was derived from these curves and is also plotted as a function of frequency in Figure 11. The attenuation constant increases monotonically with increasing frequency. Theoretical values of current-wave attenuation on a Beverage antenna whose height above ground is one meter are given in Figure 12 for average soil Jdry), average soil (wet) and wet rich soil. The experimental curve for Cambridge Bay is superimposed in each graph so that a comparison can be readily made between the experimental and theoretical curves. The best a reement occurs for ground parameters for average soil (wet); namely, 0 = 1 0 ' mho/m and € = 17.0.

P

(c) Measurement of Phase Velocity: The termination of one of the Beverage antennas in the Cambridge Bay rosette array was replaced with a "short". The antenna was then excited with an RF generator at frequencies of 5, 10, 15 and 20 MHz. The short circuit caused an RF current standing wave condition on the antenna. A current probe was used to locate current-wave nodes which were numbered consecutively, starting from the terminated end. The measurements are plotted in Figure 13 in terms of distance of the nulls from the terminated end as a function of their assigned numbers. The wavelength of the current-wave is readily derived from the slopes of the straight lines. The velocity of the wave is then calculated and the ratios of the current-wave velocities and the speed of light are plotted in Figure 14. Theoretical values of current-wave velocity ratios are given for antenna heights between 0.3 and 3.0 meters and for average soil (dry), average soil (wet) and wet rich soil. The agreement in Figure 14 between the experimental and theoretical curves is not sufficiently close to allow for an unambiguous selection of the ground types. Further measurements need to be made to resolve the discrepancy between the theoretical and experimental values of current-wave velocity.

(d)' Measurement of Beverage Pair Gain: A derivation of the Beverage pair gain, based for the most part, on the data in Figure 5 is as follows:

- gain of Beverage pair antenna with respect to (w.r.t.) the monopole antenna at an elevation angle of 11"

- Beverage pair cable losses

-

monopple antenna cable losses

- net gain of Beverage pair w.r.t. monopole antenna

-

gain of monopole antenna w.r.t. isotropic (assuming average soil wet) at 11" elevation angle

6 dB 5 dB

7.5 dB 3.5 dB -1 dB

- gain

of monopole antenna w.r.t. isotropic (assuming poor soil) at 11" elevation angle

-5 dB

- gain of Beverage pair w.r.t. isotropic (assuming average soil wet) at elevation angle of 11"

2.5 dB1"

I

13

-

g a i n of Beverage p a i r w . r . t .

i s o t r a p i c (assuming poor

soil) a t e l e v a t i o n a n g l e of 11"

-

g a i n of Beverage p a i r a n t e n n a a t nose w . r . t .

-

g a i n of Beverage antenna w . r . t .

Beverage p a i r antenna

gain of Beverage antenna w . r . t . average s o i l - wet)

i s o t r o p i c (assuming

g a i n of Beverage antenna w . r . t . soil)

i s o t r o p i c (assuming poor

*

-1.5 dBi g a i n a t 11"

No dB

- 3 dB -0.5 dBi - 4.5 dBi

The t h e o r e t i c a l gain of a Beverage antenna whose h e i g h t above ground i s 1 meter and l e n g t h i s 100 meters i s given i n Figure 2 1 . Its v a l u e a t 10 MHz i s - 3 . 4 dBi and is e s s e n t i a l l y c o n s t a n t f o r ground t y p e s between poor s o i l (dry) and w e t r i c h s o i l . The g a i n of a monopole, on t h e o t h e r hand, v a r i e s from +5 dBi f o r p e r f e c t ground t o -1 d B i f o r average s o i l (wet) and f i n a l l y -5 d B i f o r poor s o i l . Agreement between t h e t h e o r e t i c a l g a i n of a Beverage antenna and t h a t deduced from t h e Cambridge Bay measurements o c c u r s only i f i t i s assumed t h a t t h e monopole a t Cambridge Bay w a s s i t u a t e d on s o i l which f e l l between average s o i l w e t and poor s o i l . From t h e Beverage p a i r g a i n measurements, t h e r e f o r e , i t can b e concluded t h a t t h e ground t y p e a t Cambridge Bay i s roughly average s o i l ( d r y ) . The g a i n of a Cambridge Bay Beverage p a i r w a s measured p r e v i o u s l y u s i n g a 9 MHz d i p o l e suspended from a b a l l o o n a t a d i s t a n c e of 0.488 km from t h e c e n t r e of t h e r o s e t t e a r r a y ( L i t v a and Stevens, 1973). The f i e l d a t t h e c e n t r e of t h e a r r a y w a s measured w i t h a f i e l d i n t e n s i t y meter and i n a d d i t i o n a measurement w a s made of t h e v o l t a g e a t t h e t e r m i n a l s of a Beverage p a i r antenna. From t h e s e i t was concluded t h a t t h e g a i n of t h e Beverage p a i r w a s 0 dBi, s u g g e s t i n g t h e gain of an i n d i v i d u a l element t o be -3 dBi, which i s i n c l o s e agreement w i t h t h e t h e o r e t i c a l g a i n . This r e s u l t t e n d s t o l e n d support t o t h e argument made above f o r deducing ground parameters a t Cambridge Bay from a measurement of t h e g a i n of a Beverage p a i r antenna w i t h r e s p e c t t o t h e g a i n of a X/4 monopole antenna.

2.3.3

Listing o f Soil Types Deduced from Field Intensity and Antenna Measurements

Table I1 g i v e s a l i s t i n g of s o i l t y p e s deduced from two d i s t i n c t types of measurements performed a t Cambridge Bay. The f i r s t c o n s i s t of measurements of t h e f i e l d i n t e n s i t y of ground waves r a d i a t e d by X/4 monopole a n t e n n a s . The second c o n s i s t e d of measurements of t h o s e e l e c t r i c a l parameters o f ' B e v e r a g e antennas which a r e a f u n c t i o n of t h e s o i l t y p e beneath t h e antenna.

The s o i l type a t Cambridge Bay i s s e e n i n Table I1 t o v a r y between poor s o i l and average s o i l (wet). I t i s n o t homogeneous, b u t , i f i t i s t o b e c l a s s i f i e d w i t h one l a b e l , t h e one t h a t b e s t d e s c r i b e s i t i s average soil ( d r y ) , w i t h t h e f o l l o w i n g e l e c t r i c a l p a r a m e t e r s , (5 = 3 x mho/m and €= 12. The agreement shown i n Table I1 between t h e s o i l types deduced from t h e v a r i o u s measurements l i s t e d i n Table I1 i s reasonably good. This t e n d s t o c o r r o b o r a t e t h e e f f e c t i v e n e s s of t h e CRC Beverage computer program i n c o r r e c t l y p r e d i c t i n g Beverage antenna p a r a m e t e r s , when t h e ground parameters a r e known.

--

c

~

14 TABLE It Listing of Soil Types Derived from Measurements at Cambridge Bay

Technique

I

Field Intensity

Type of Soil poor soil (wet)

- average soil

u (mho/m) 10-3

-

10-2

E: (Air = 1) 10 - 17

II Antenna Measurements

* average soil (dry) average soil (wet)

3 x 10-3 lo-*

12

(b) Attenuation

average soil (wet)

1 o-2

17

(c) Phase Velocity

lnconclusive

(d) Gain

average soil (dry)

3 x 10-3

12

Average

average soil (dry)

3x

12

(a) Impedance

Inconclusive

103

17 Inconclusive

Only the current-wave phase velocity was found to be problematic in that the evidence it provided regarding the soil type at Cambridge Bay was inconclusive. Further work is required to resolve the discrepancy between the measured and theoretical values.

2.4 THEORETICAL ATTENUATION, IMPEDANCE AND PHASE VELOCITY Theoretical values are given in Appendix I of attenuation, characteristic impedance and phase velocity of Beverage antennas with heights above ground varying between 0 . 3 and 3 . 0 meters and for seven types of soil. The ground constants vary from u = lo”, € = 2 (Dry Granite, substrate) to u = lo’*, € = 17 (Average soil, wet). These data can be used in the design and engineerivg of Beverage antenna systems. Once an antenna site is selected, the ground parameters need first to be determined, either by a measurement of signal strength as a function of distance from a monopole, or by a measurement of the attenuation of a current-wave on a temporary Beverage antenna. The value of the terminating resistor can be obtained from the curves of characteristic impedance given in these figures. The attenuation curves can be used to determine the power dissipation requirements of the terminating resistor for Beverage antennas used for transmitting. In Chapter 3 it will be seen that following a determination of the ground constants at the chosen antenna site the theoretical radiation patterns can be derived. The antenna can then be engineered to optimize the take-off angle, beamwidth, directivity and power gain within the constraints imposed by the type and quantity of the available real estate.

2.5

DEBERT MEASUREMENTS

The procedures given in Section 2.4 for determining ground parameters to facilitate derivation of antenna parameters will be demonstrated by means

of an example. The antenna i n t h i s example is a n eight- element Beverage a r r a y c u r r e n t l y b e i n g used as a communication antenna a t Debert, N.S. These r e s u l t s presented h e r e w i l l a l s o p r o v i d e a f u r t h e r t e s t of t h e CRC Beverage antenna computer program. The Beverage a r r a y a t Debert c o n s i s t s of Beverage elements whose l e n g t h s a r e 110 m and whose h e i g h t above ground v a r y between 0.73 and 2 . 9 m because of v a r i a t i o n s i n topography. The average h e i g h t of t h e elements i n t h e a r r a y i s 1.8 m. Most of t h e measurements r e p o r t e d h e r e w e r e made on element 81 whose h e i g h t v a r i e s between 0.73 and 1.55 m w i t h an average v a l u e of 1.13 m. 0

A composite measurement of t h e i n p u t impedances of t h e eight- elements of t h e Debert a r r a y i s given i n F i g u r e 1 5 ( a ) . Each element w a s terminated i n i t s c h a r a c t e r i s t i c impedance (Z,). The magnitude of Z, w a s obtained by measuring t h e i n p u t impedance of each a n t e n n a , a t c e r t a i n f r e q u e n c i e s , and varying t h e v a l u e of i t s t e r m i n a t i n g r e s i s t o r u n t i l t h e a n t e n n a ' s i n p u t impedance w a s equal t o t h e v a l u e of t h e r e s i s t o r . The v a l u e of t h e i n p u t impedance a t which t h i s agreement occurred w a s t a k e n as t h e c h a r a c t e r i s t i c impedance of t h e element. The measured v a l u e s i n F i g u r e 1 5 ( a ) are f a i r l y c o n s t a n t over t h e frequency range 2 - 1 7 MHz, s u g g e s t i n g t h a t t h i s procedure f o r determining t h e c h a r a c t e r i s t i c impedance is v a l i d . Above 1 7 MHz a " f a l l o f f " i n impedance i s e v i d e n t on a l l t h e elements.

The measured d a t a i s compared w i t h a t h e o r e t i c a l curve d e r i v e d f o r a Beverage element s i t u a t e d on average s o i l ( w e t ) w i t h a h e i g h t above ground of 2 m. The s o i l type w a s o b t a i n e d from a c o n s i d e r a t i o n of Figure 16(d) and w i l l be d i s c u s s e d i n more d e t a i l l a t e r . There i s r e a s o n a b l y good agreement between t h e t h e o r e t i c a l and e x p e r i m e n t a l v a l u e s i n F i g u r e 1 5 ( a ) . The measured i n p u t impedance of element f l t e r m i n a t e d i n i t s c h a r a c t e r i s t i c impedance i s given i n Figure 1 5 ( b ) . The e x p e r i m e n t a l curve i s compared h e r e w i t h t h e o r e t i c a l curves f o r average s o i l ( d r y ) , average s o i l (wet) and w e t r i c h s o i l . Although reasonably good agreement e x i s t s , t h e i n p u t impedance of t h e Beverage antenna i s a weak f u n c t i o n of t h e s o i l t y p e and t h e r e f o r e does not a l l o w f o r a unique s e l e c t i o n of s o i l type.

'

Open c i r c u i t and s h o r t c i r c u i t i n p u t impedance measurements of element These measurements w e r e made a t f r e q u e n c i e s f o r which t h e i n p u t impedance of t h e element w a s r e a l when s h o r t c i r c u i t e d . The curve f o r c h a r a c t e r i s t i c impedance i n Figure 1 6 ( a ) w a s d e r i v e d from t h e d a t a contained i n F i g u r e s 1 5 ( c ) and (d) w i t h t h e e x p r e s s i o n

f l are given i n Figure 1 5 ( c ) and (d):

zo where

=

JzoCZSC

Zoc = open c i r c u i t impedance Zsc = c l o s e d c i r c u i t impedance

Z,

I =

c h a r a c t e r i s t i c impedance

The average v a l u e of c h a r a c t e r i s t i c impedance determined i n t h i s manner and shown i n Figure 1 6 ( a ) i s 480 52.

.

16 A p l o t of s h o r t c i r c u i t resonance number f o r element i"1 is given a s a function of frequency i n Figure 1 6 ( b ) . These curves were obtained by consecu t i v e numbering of t h e d a t a p o i n t s i n Figure 1 5 ( c ) and then p l o t t i n g t h e number a s s o c i a t e d with each resonance p o i n t a g a i n s t t h e frequency a t which t h e resonance occurred. The phase v e l o c i t y r a t i o (n) of t h e current-wave on This expression was t h e antenna can b e determined from t h i s graph using (2). derived by using t h e f a c t t h a t t h e number of half- wavelengths of t h e currentwave on t h e antenna i n c r e a s e s by one when t h e frequency is increased from one resonance p o i n t t o t h e n e x t

n = -211 mc n = phase v e l o c i t y r a t i o

where

11 = l e n g t h of t h e antenna m = s l o p e of t h e curve i n Figure 16(b)

c = v e l o c i t y of l i g h t of t h e phase v e l o c i t y r a t i o f o r ' e l e m e n t b l a r e p l o t t e d t h e o r e t i c a l curves f o r w e t r i c h s o i l and average s o i l agreement i s reasonably good, t h e experimental values than t h e t h e o r e t i c a l v a l u e s .

Derived v a l u e s i n Figure 16(c) w i t h (wet). Although t h e a r e somewhat g r e a t e r

F i n a l l y , t h e a t t e n u a t i o n of t h e current-wave on element #lw a s derived from t h e closed c i r c u i t impedance measurements given i n Figure 1 5 ( c ) and Equation (6). The i n p u t impedance of a transmission l i n e is given by (Ramo e t a l , 1967)

c

zi

=

z,

l + p e 1 - p e

where

-2yR -2ya

Z, = c h a r a c t e r i s t i c impedance Zi = i n p u t impedance

where

ZL = load impedance y =

where

Q

B

a

+ jB

(propagation c o n s t a n t )

= a t t e n u a t i o n constant (nepers/m) = phase constant

(3)

17

If the line is sh rt circuited, p e-2Yf

-

zo

- zi

zi

+

=

-1 and it follows from ( 3 )

=A+jB

zo "1-

T

(4)

3

r d9 If the characteristic impedance of the e ement is assumed to be r a 1 then,

e

and where

i!

R. and X. are the real and imagin ry parts respectively of the 1 1 input impedance,

J-

then

' -\?,

-(fi;+hgi,s

' C

and B =

Now, if

where

-2 RoXi (Ro + Ri12 + xi2

Xi = 0

= attenuation constant in dB/m

, 'r?

I\c

J

qW\

G

J

r

C

C

VG.

d

I &C/

a

I4 c r f

-'

I

The attenuation of the krrent-wave on the Beverage antenna can be (.,ib;i: obtained from ( 6 ) and a measurement of Zi at the antenna's resonant frequencles where Xi = 0 . This technique was tested on a Beverage element at CRC whose length and height above ground was 110 m and 1 m, respectively. The results are given in Figure 17 where a comparison is made between the attenuation determined from the current amplitude measurements along the wire and the

E

ar *('

18 v a l u e s determined from measurement of Zi. The r e s u l t s derived from t h e impedance measurements show a g r e a t e r degree of s c a t t e r because of i n t e r f e r i n g s i g n a l s on t h e w i r e a t t h e t i m e of t h e measurements. T h e o r e t i c a l curves are a l s o shown i n F i g u r e 1 7 , from which i t can b e concluded t h a t t h e ground a t CRC can b e c l a s s i f i e d as b e i n g between average s o i l (dry) and average s o i l (wet). The c u r v e g i v i n g a1 v e r s u s frequency f o r Beverage element 81 a t Debert i s shown i n F i g u r e 16(d) w i t h some superimposed t h e o r e t i c a l curves. The J h e o r e t i c a l curve f o r average s o i l (wet) shows t h e b e s t agreement w i t h t h e measurements, s u g g e s t i n g t h i s t o b e t h e s o i l t y p e a t Debert. This c o n c l u s i o n i s n o t i n disagreement w i t h t h e v i s u a l appearance and t e x t u r e of t h e ground a t Debert

.

From t h e measurement of t h e open and c l o s e d c i r c u i t impedances of Beverage element 81 a t Debert, one now knows t h e c h a r a c t e r i s t i c impedance of t h e antenna and t h e s o i l type a t Debert. This i n f o r m a t i o n then p e r m i t s c o r r e c t t e r m i n a t i o n of t h e antenna and i n a d d i t i o n a d e r i v a t i o n of a l l t h e antenna’s e l e c t r i c a l p r o p e r t i e s , i n p a r t i c u l a r , i t s g a i n and two dimensional radiation pattern.

3. 3.1

BEVERAGE ANTENNA PARAMETERS

DESIGN PARAMETERS

This s e c t i o n g i v e s t h e o r e t i c a l l y d e r i v e d d e s i g n parameters f o r Beverage antennas. It i s intended t h a t t h e material w i l l b e of s u f f i c i e n t scope t o allow t h e antenna engineer t o design antenna system u s i n g Beverage elements, which w i l l m e e t h i s requirements w i t h i n c o n s t r a i n t s s e t by a v a i l a b l e r e a l e s t a t e . I n o t h e r words, i f t h e antennas are t o b e i n s t a l l e d on ground whose e l e c t r i c a l parameters can be d e f i n e d by t h e range between poor s o i l (dry) t o wet r i c h p o i l , and t o have s p e c i f i e d v a l u e s of g a i n and take- off a n g l e s , t h e d a t a i n t h i s s e c t i o n w i l l allow f o r s e l e c t i o n of t h e optimum antenna l e n g t h and h e i g h t . The f o l l o w i n g parameters are given i n some d e t a i l :

-

g a i n of t h e antenna a t t h e nose of i t s r a d i a t i o n p a t t e r n (G ) r e l a t i v e N t o an i s o t r o p i c antenna;

-

3 d B ’ v e r t i c a 1 beamwidth (BWv);

-

3 dB azimuthal beamdwidth (BWA);

-

take- off a n g l e of t h e nose pf t h e r a d i a t i o n p a t t e r n (9 ).

N

These parameters are d e f i n e d i n d e t a i l i n F i g u r e 1 8 where t h e o r e t i c a l v e r t i c a l and azimuthal r a d i a t i o n p a t t e r n s are given f o r a t y p i c a l Beverage element. I n t h i s example t h e antenna i s s i t u a t e d over average s o i l (dry) and i t s length and h e i g h t a r e r e s p e c t i v e l y 110 m and 1 m.

19

*

F i g u r e s 11-1 t o 11-48 g i v e t h e o r e t i c a l v a l u e s of GN, BWv, BWA and JIN f o r Beverage a n t e n n a s w i t h l e n g t h s of 100, 200, 300 and 400 meters, h e i g h t s of 0.3, 1 . 0 , 2.0 and 3.0 meters, s i t u a t e d o v e r poor s o i l ( d r y ) , average s o i l ( d r y ) , and w e t r i c h s o i l ( s e e Table I ) . G e n e r a l l y , i t i s s e e n t h a t t h e g a i n GN i n each case t e n d s t o i n c r e a s e w i t h i n c r e a s i n g frequency, whereas t h e v e r t i c a l beamwidth B h , azimuthal beamwidth BWA and take- off a n g l e $N tend t o d e c r e a s e w i t h i n c r e a s i n g frequency. A s an example c o n s i d e r t h e Beverage antenna d e f i n e d i n F i g u r e 1 8 and c i t e d p r e v i o u s l y a s b e i n g t y p i c a l . Its parameters are g i v e n i n F i g u r e 11-21. The magnitude of t h e i r v a r i a t i o n s i n t h e frequency range 3 t o 25 MHz is as f o l l o w s : GN, -8.5 t o -0.5 dBi BWA, 65 t o 28" BWV, 46 t o 16" $ J ~ ,

24 t o 14"

The d i s c o n t i n u i t i e s t h a t appear i n t h e graphs are caused by t h e amplitude of t h e secondary l o b e i n c r e a s i n g monotonically as t h e frequency i s i n c r e a s e d and s u r p a s s i n g t h e magnitude of t h e main l o b e a t t h e s e d i s c o n t i n u i t i e s . The s i d e l o b e then assumes t h e r o l e of t h e main beam and t h e c u r v e s f o r B h , BWA and GN undergo d i s c r e t e changes i n l e v e l . It should b e n o t i c e d t h a t t h e s e d i s c o n t i n u i t i e s becorne more c l o s e l y crowded towards t h e low frequency end of t h e spectrum as t h e l e n g t h of t h e antenna i s i n c r e a s e d . Also, t h e graphs have been s c b - h e & s o t h a t t h e d i s c o n t i n u i t i e s do n o t appear t o be as a b r u p t as they a c t u a l l y are. An example of t h i s e f f e c t can be s e e n i n Figure 1 9 , which g i v e s p o r t i o n s of some v e r t i c a l r a d i a t i o n p a t t e r n s f o r a Beverage antenna w i t h t h e parameters l i s t e d f o r F i g u r e 11-36. These p a t t e r n s a r e given f o r t h e f r e q u e n c i e s 4 , 4.5, 5 and 5.5 MHz which encompass t h e frequency i n F i g u r e 11-36 (approximately 4.15 MHz) a t which d i s c o n t i n u i t i e s occur i n BWA, BWv and QN. A t a frequency of 4$0 MHz t h e v e r t i c a l p a t t e r n h a s a main beam a t 8.5" and a s i d e l o b e a t 29". A s t h e frequency i s r a i s e d t h e s i d e l o b e grows i n magnitude w i t h r e s p e c t t o t h e main beam. Its magnitude is g r e a t e r than t h a t of t h e main beam a t 4.5 MHz and t h u s i t assumes t h e r o l e of t h e main beam a t a frequency between 4.0 and 4.5 MHz. The switching of t h e r o l e s of t h e s e beams a t roughly 4 . 2 5 MHz a c c o u n t s i n F i g u r e 11-36 f o r t h e d i s c o n t i n u o u s jump from 9 t o 25" i n t h e curve f o r $N. S i n c e t h e d i s c o n t i n u i t i e s i n t h e curves f o r BWA and BWv occur a t t h e same frequency as t h a t f o r JIN, i t f o l l o w s t h a t t h e s e d i s c o n t i n u i t i e s can be a g t r i b u t e d t o t h e same mechanism. A b r i e f summary of t h e 1 0 MHz i n f o r m a t i o n contained i n t h e t h e o r e t i c a l c u r v e s f o r $N, GN, BWA and BWv i n F i g u r e s 11-1 t o 11-48 i s given i n F i g u r e s 20 t o 22. These are intended o n l y t o show t h e g e n e r a l t r e n d s i n t h e e l e c t r i c a l parameters of Beverage antennas as a f u n c t i o n of t h e i r l e n g t h and of t h e ground c o n s t a n t s of t h e e a r t h over which they a r e s i t u a t e d . A l l curves are s t r i c t l y a p p l i c a b l e t o only one RF frequency, namely, 1 0 MHz. This frequency w a s chosen because i t i s l o c a t e d a t t h e approximate middle of t h e a c t i v e HF band.

20

F i g u r e 20(a) g i v e s t h e g a i n of a Beverage element as a -.~nction of i t s l e n g t h f o r average s o i l ' ( d r y ) . It varies from -16 dBi f o r a n element h e i g h t of 0.3 m t o -2 dBi f o r an element h e i g h t of 3.0 m. There i s l i t t l e o r no v a r i a t i o n i n g a i n as t h e l e n g t h of t h e element i s v a r i e d from 100 t o 400 m. Curves g i v i n g t h e v a r i a t i o n of azimuthal beamwidth BWA of a Beverage antenna w i t h l e n g t h are shown i n F i g u r e 20(b). Roughly speaking f o r h e i g h t s between 1 and 3 m, BWA d e c r e a s e s from a v a l u e of 40" f o r an element l e n g t h of 100 m t o about 30" f o r an element l e n g t h of 400 m. On t h e o t h e r hand, t h i s g a r a m e t e r shows l i t t l e o r no v a r i a t i o n w i t h l e n g t h f o r an element whose h e i g h t I n t h i s l a t t e r example BWA has a c o n s t a n t v a l u e of above ground is 0.3 m. about 60". F i g u r e 2O(c) g i v e s v e r t i c a l beamwidths v e r s u s element l e n g t h s , f o r elements h e i g h t s between 0.3 t o 3 m. For an element l e n g t h of 100 m i t i s about 25" and d e c r e a s e s t o a v a l u e of about 17" a t an element l e n g t h of 400 m. Once a g a i n , f o r an element h e i g h t of 0 . 3 m, t h e r e i s l i t t l e o r no v a r i a t i o n of t h i s parameter w i t h l e n g t h . The v e r t i c a l beamwidth remains v i r t u a l l y c o n s t a n t w i t h a magnitude of 34". The take- off a n g l e of t h e beam of a Beverage element i s given a s a f u n c t i o n of l e n g t h and h e i g h t i n F i g u r e 20(d). It i s about 26" f o r an element h e i g h t of 0 . 3 and v a r i e s l i t t l e as t h e l e n g t h of t h e antenna i s changed. For element h e i g h t s between 1 and 3 m i t i s roughly 20" f o r element l e n g t h s of 100 m and d e c r e a s e s t o approximately 15" f o r element l e n g t h s of 400 m. The g a i n of Beverage elements f o r h e i g h t s above ground between 0.3 t o 3 m, l e n g t h s between 100 t o 300 m and s o i l types between poor s o i l (dry) and w e t r i c h s o i l i s given i n F i g u r e 2 1 ( a ) . Usually, t h e g a i n of t h e antenna i n c r e a s e s as t h e s o i l type i s v a r i e d from poor t o good b u t t h e magnitude of t h i s i n c r e a s e i s a t most 6 dB. For most antenna geometries t h i s v a r i a t i o n i n gain i s l e s s t h a n 2 o r 3 dB. The azimuthal beamwidth BWA of a Beverage antenna as a f u n c t i o n of h e i g h t , b n g t h and s o i l type i s given i n F i g u r e 21(b). Most of t h e v a l u e s shown i n t h i s f i g u r e f o r t h i s parameter l i e between 25 and 45". The v e r t i c a l beamwidth B Q i s given i n F i g u r e 2 2 ( a ) , and i t s v a l u e s are contained i n t h e i n t e r v a l from 15 t o 30" w i t h a median v a l u e of about 22". F i g u r e 22(b) g i v e s t h e take- off a n g l e QN of t h e beam of t h e Beverage antenna as a f u n c t i o n of ground t y p e , h e i g h t and l e n g t h . For most of t h e c o n f i g u r a t i o n s shown t h e magnitude of $N i s w i t h i n t h e i n t e r v a l 1 4 t o 25". The take- offbangle i s seen t o be r a t h e r i n s e n s i t i v e t o t h e type of ground beneath t h e antenna except f o r t h e case of an element whose l e n g t h and h e i g h t a r e r e s p e c t i v e l y 200 and 0.3 m. I n t h i s i n s t a n c e t h e take- off a n g l e v a r i e s from about 20 t o 10" as t h e s o i l type i s v a r i e d from poor t o good. Figure 23 g i v e s some comparisons of t h e o r e t i c a l and measured v a l u e s of gain and azimuthal beamwidths as a f u n c t i o n of h e i g h t of t h e element above t h e ground and frequency of t h e r a d i o energy received by t h e antenna. The measurements were made a t S h i r l e y Bay u s i n g a t r a n s m i t t e r towed by an a i r c r a f t There i s reasonably good agreement between t h e experi(XELEDOP, see p. 7 ) . mental and t h e o r e t i c a l curves i n F i g u r e s 23(a) t o 23(c) which g i v e t h e g a i n of a Beverage element, both as a f u n c t i o n of h e i g h t of t h e element above

, I "

21

ground and a l s o frequency of t h e r a d i o wave impinging on t h e antenna. F i g u r e s 23(e) and 2 3 ( f ) shoF; r e a s o n a b l e agreement between t h e experimental " and t h e o r e t i c a l c u r v e s f o r azimuthal beamwidth a s a f u n c t i o n of frequency of Poor agreement, on elements w i t h h e i g h t s above ground of 1 . 0 m and 1 . 7 m. t h e o t h e r hand, e x i s t s between t h e t h e o r e t i c a l and experimental c u r v e s i n F i g u r e s 23(d) of BW v e r s u s frequency f o r a n element whose h e i g h t i s 0 . 3 m. k

*

3.2

EFFICIENCY OF BEVERAGE ANTENNAS

Most of t h e measurements nade by CRC have been on Beverage elements which t y p i c a l l y a r e 110 meters long and have a h e i g h t above ground of 1 meter. They have been, f o r t h e most p a r t , e r e c t e d over s o i l which according t o Table I would b e c l a s s i f i e d as averag s o i l ( d r y ) . It w a s shown i n S e c t i o n 3.1 t h a t t h e g a i n of a Beverage antenna w i t h t h e s e parameters i s i n s e n s i t i v e t o t h e s o i l t y p e on which i t i s placed. F u r t h e r , t h e dimensions of t h i s Beverage element a r e compatible w i t h t h o s e of c l a s s i c a l HF a n t e n n a s . It f o l l o w s t h a t i t s parameters a r e probably a i r l y r e p r e s e n t a t i v e of t h o s e which are l i k e l y t o be used f o r Beverage ante-.na systems. T y p i c a l l y , i t has been found t h a t t h e s e Beverage elements have t h e f o l l o w i n g parameters:

-

power g a i n , 0 dBi;

-

d i r e c t i v i t y g a i n , 18 dB;

- azimuthal -

beamwidth,

'tC";

,

v e r t i c a l beamwidth, 2

s i d e l o b e s down 15-25 ..,

5 t h r e s p e c t t o main beam;

take- off a n g l e = 15".

The d i s c r e p a n c y shown above bet,, g a i n i s caused by i t s low e f f i z i As h a s been pointed o u t i n t h e 1 o f entenna is i t s low e f f i c i e c c y

t h e a n t e n n a ' s d i r e c t i v i t y g a i n and power

v which i s u s u a l l y less than 2 p e r c e n t . r a t u r e t h e major disadvantage of t h i s t y p e

It w i l l be demonstratec 1 t h a t t h e i n e f f i c i e n c y of t h e Beverage antenna does n o t l i m i t i t s usff1-!7~t?ssas a r e c e i v i n g antenna i n t h e HF band because of t h e i n h e r e n t l y n o i -ctromagnetic environment p r e s e n t w i t h i n t h i s band. It w i l l a l s o be c lbrn i n S e c t i o n 4 . 4 t h a t an " o v e r f i l l e d " l i n e a r C i h a t t h e h i g h e s t frequency) of Beverage phased a r r a y (spacing l e s s ti. a n t e n n a s h a s g r e a t e r e f f i c i e r - : . t an t h a t of a s i n g l e antenna because of decreased ground l o s s e s . F k a l l y i t w i l l be demonstrated t h a t a communicat i o n s antenna can be c o n s t r u z t e d \ i t h Beverage elements having a g a i n a t 1 0 MHz of 23 dB as a r e c e i v i i g an Znna and a g a i n of up t o 1 5 dB a s a t r a n s m i t t i n g antenna. The r e a l e ; t a t e requirements would b e s i m i l a r t o t h o s e of t h e l a r g e r c l a s s i c a l H F a n t e i n a s , roughly a s i t e whose dimensions w e r e 150 by 150 m. .?

Minimum and m a x i m u m e x e c t e v a l u e s of atmospheric and g a l a c t i c n o i s e f o r a Beverage antenna s i t u a ed i.. t h e n o r t h e r n hemisphere are given i n F i g u r e 24. These c u r v e s w e r : o b t . i n e d from t h o s e given i n C C I R Report 322 f o r a s h o r t v e r t i c a l antenna a s s . m i n g t h e d i s t r i b u t i o n of n o i s e t o be isotropic. I f t h e Beverage a n t * n n a rere 100 p e r c e n t e f f i c i e n t , i t would r e c e i v e

22

t h e same n o i s e power as t h e d i p o l e . The curves i n F i g u r e 24 are d i s p l a c e d downwards from t h o s e i n CCIR Report 322 t o account f o r t h e low e f f i c i e n c y of t h e antenna. A t 10 MHz, f o r example, t h e displacement i s 18 dB because t h i s i s t h e d i f f e r e n c e between t h e d i r e c t i v i t y and power g a i n s of t h e antenna. I f t h e antenna i s followed by a p r e a m p l i f i e r w i t h a n o i s e f i g u r e of s a y , 4.0 dB t h e antenna i s l i m i t e d by e x t e r n a l n o i s e , j u s t as a more e f f i c i e n t antenna would b e , between 2 . 3 and 18 MHz. Therefore, i t appears t h a t i n many cases t h e performance of t h e Beverage antenna as a r e c e i v i n g antenna w i l l n o t be s e r i o u s l y degraded as a r e s u l t of i t s low e f f i c i e n c y . I n S e c t i o n 4.4 i t w i l l &e shown t h a t t h i s i s p a r t i c u l a r l y t r u e f o r o v e r f i l l e d l i n e a r phased a r r a y s of Beverage antennas because of t h e i n c r e a s e i n e f f i c i e n c y t h a t i s expected t o be r e a l i z e d . Atmospheric and g a l a c t i c n o i s e are n o t t h e only types of n o i s e encounte r e d i n t h e HF band. Man-made o r s i t e n o i s e can i n many cases b e t h e predominant s o u r c e of n o i s e n e a r i n d u s t r i a l i z e d areas. The numerous coherent man-made s i g n a l s p r e s e n t i n t h e HF band can a l s o b e a s o u r c e of n o i s e . They can cause r e l a t i v e l y h i g h levels of intermodulation (IM) products t o be generated i n HF r e c e i v e r s because of n o n - l i n e a r i t i e s i n t h e i r v a r i o u s s t a g e s of a m p l i f i c a t i o n . S i n c e t h e HF band i s congested, t h i s s o u r c e of n o i s e can only be reduced by u s i n g receivers which are very l i n e a r and t h e r e f o r e expensive and by u s i n g h i g h l y d i r e c t i o n a l antennas. The SNR of a s i g n a l r e c e i v e d w i t h a Beverage antenna may i n many c a s e s b e g r e a t e r t h a n t h a t r e c e i v e d w i t h a more e f f i c i e n t antenna simply because i t h a s g r e a t e r d i r e c t i v i t y than many conventional antennas and t h e r e f o r e g r e a t e r a b i l i t y t o a t t e n u a t e s i g n a l s not a r r i v i n g from t h e d i r e c t i o n of t h e wanted t r a n s m i t t e r , thereby reducing t h e l e v e l of I M products i n a s s o c i a t e d r e c e i v i n g equipment.

3.3

RADIATION PATTERNS

3.3.1

I n d i v i d u a l Beverage Element

An e x t e n s i v e computer program h a s been developed a t CRC which i s capable of c a l c u L a t i n g a l l of t h e important e l e c t r i c a l parameters f o r Beverage antennas. The i n p u t s t o t h e program c o n s i s t of ground parameters (conduct i v i t y and d i e l e c t r i c c o n s t a n t ) , h e i g h t and l e n g t h of t h e antenna. It can be used t o c a l c u l a t e antenna g a i n , a t t e n u a t i o n , phase v e l o c i t y of t h e c u r r e n t wave on t h e w i r e and two dimensional antenna r a d i a t i o n p a t t e r n s . Some measured Beverage element r a d i a t i o n p a t t e r n s f o r 1 2 and 18 MHz are given i n Figure 25 f o r antenna h e i g h t s between 0 . 3 and 1 . 7 m. The measurements were performed a t S h i r l e y Bay on a Beverage antenna whose l e n g t h w a s 110 m. A t r a n s m i t t i n g d i p o l e (XELEDOP) w a s ued t o make t h e measurements ( s e e p. 7 ) . The s i d e and back l o b e l e v e l s f o r t h e p a t t e r n s shown i n F i g u r e 25 decrease q u i t e d r a s t i c a l l y w i t h r e s p e c t t o t h e main beam when t h e h e i g h t of t h e antenna i s lowered from 1 . 7 m t o 0.3 m. Dramatic evidence of t h i s i s seen from t h e p a t t e r n s i n F i g u r e 25(a) t o Figure 25(c). I n i t i a l l y t h e maximum f r o n t t o s i d e l o b e r a t i o i s -7.5 dB. This v a l u e d e c r e a s e s t o -15 dB a s t h e h e i g h t of t h e antenna i s lowered from 1 . 7 t o 0.3 m . On t h e o t h e r hand t h e g a i n of t h e antenna i n c r e a s e s almost l i n e a r l y w i t h h e i g h t , t h e g a i n being roughly 10 dB g r e a t e r a t 1.7 m t h a n a t 0.3 m. The antenna has good s i d e and

23 back l o b e r e j e c t i o n when H = 0 . 3 m , f = 1 2 MHz, and goo1 back l o b e r e j e c i o n when H = 1 . 7 rr,, f = 18 MHz. A comparison i s made i n F i g u r e s 26 and 27 of t h e o r e t i c a l r a d i a t i o n p a t t e r n s and t h e experimental p a t t e r n s shown i n p o l a r form i n Figure 25. I n most i n s t a n c e s t h e agreement between t h e two c u r v e s i s reasonably good f o r azimuths w i t h i n 260" of t h e b o r e s i g h t . The e x c e p t i o n t o t h i s occurs i n t h e two examples shown f o r a Beverage antenna whose h e i g h t i s 0.3 m. In these i n s t a n c e s t h e r e i s some disagreement between t h e Beverage a n t e n n a ' s t h e o r e t i c a l and experimental main beam p a t t e r n s . I n g e n e r a l t h e r e i s a l s o a discrepancy between t h e t h e o r e t i c a l and e x p e r i m e n t a l s i d e l o b e l e v e l s . I n many of t h e s e , though, t h e r e i s f a i r l y good agreement between t h e f i n e s t r u c t u r e of t h e t h e o r e t i c a l and experimental s i d e l o b e s .

~

Measured v e r t i c a l p a t t e r n s f o r a Beverage antenna l o c a t e d a t S h i r l e y Bay w i t h dimensions H = 1 . 7 m and L = 110 m are given i n F i g u r e 28. The measurements were a g a i n made w i t h an a i r c r a f t towing a t r a n s m i t t i n g d i p o l e (XELEDOP). While i t flew along a s t r a i g h t l i n e a t a c o n s t a n t a l t i t u d e of 300 m over t h e Beverage antenna t h e amplitude o f t h e s i g n a l a t t h e t e r m i n a l s of t h e Beverage was recorded. The recorded s i g n a l l e v e l w a s c o r r e c t e d f o r v a r i a t i o n s caused by t h e char;ging range and r a d i a t i o n p a t t e r n of t h e towed d i p o l e , a s t h e a i r c r a f t fleL- over t h e Beverage antenna. A s a check on t h e accuracy of t h e t e c h n i q u e t h e p a t t e r n of a monopole was measured and compared w i t h a t h e o r e t i c a l curve f o r a monopole antenna s i t u a t e d on average ground. Good agreement i s s e e n t o e x i s t between t h e two Beyond t h i s p o i n t t h e Xeledop d a t a a p p e a r s up t o an e l e v a t i o n a n g l e of 50'. t o become u n r e l i a b l e .

Figure 28(a) g i v e s t h e v e r t i c a l p a t t e r n of a Beverage element measured with a h o r i z o n t a l l y p o l a r i z e d Xeledop package. Figure 28(b) g i v e s a compariSOR between t h e p a t t e r n given i n Figure 28(a) and t h a t measured w i t h a v e r t i c a l l y p o l a r i z e d Xeledop package (dashed l i n e s ) . There i s reasonably good agreement between t h e two p a t t e r n s up t o an e l e v a t i o n a n g l e of 30'. B e y v d t h i s a n g l e agreement e x i s t s o n l y between t h e l e v e l s of t h e two sets of s i d e l o b e s . There i s disagreement i n t h e i r l o c a t i o n s . F i g u r e 28(c) g i v e s a comparison between t h e measured p a t t e r n of F i g u r e 28(a) and a t h e o r e t i c a l p a t t e r n . There i s reasonably good agreement between t h e two p a t t e r n s . Two e x c e p t i o n s t o t h i s , are t h e l o c a t i o n , once a g a i n , of t h e n u l l s and t h e l e v e l of t h e back l o b e s of t h e antenna. Agreement between t h e o r e t i c a l and e x p e r i m e n t a l Beverage antenna r a d i a t i o n p a t t e r n s have proved i n g e n e r a l t o be good except t h a t t h e l e v e l of t h e s i d e and back l o b e s i s u s u a l l y g r e a t e r f o r t h e measured p a t t e r n s than f o r t h e t h e o r e t i c a l ones. T y p i c a l l y t h e s i d e l o b e s of t h e o r e t i c a l p a t t e r n s are 25 dB lower than t h e main beam whereas measured v a l u e s a r e normally only about 15 dB below t h e level of t h e main beam. I t i s b e l i e v e d t h a t t h e discrepancy between t h e levels of t h e o r e t i c a l and experimental s i d e l o b e s f o r Beverage a n t e n n a s i s l a r g e l y due t o t h e component of h o r i z o n t a l p o l a r i z a t i o n possessed by t h e r a d i o waves used i n making t h e measurements. Although c o n s i d e r a b l e e f f o r t w a s extended towards e n s u r i n g t h a t t h e Xeledop antenna was v e r t i c a l when i t w a s b e i n g towed by t h e a i r c r a f t , i t i s l i k e l y t h a t t h e antenna possessed s u f f i c i e n t t i l t t o i n t r o d u c e

--

,

.

24 26 a s i g n i f i c a n t h o r i z o n t a l p o l a r i z a t i o n t o t h r a d i o waves i t e m t h e o r e t i c a l p a t t e r n s have been derived only f o r v e r t i c a l l y pol4 waves. For example, t h e maximum d e v i a t i o n between t h e experimc t h e o r e t i c a l p a t t e r n s i n F i g u r e s 26 and 27 occurs f o r azimuths o A t t h e s e azimuths t h e s e n s i t i v i t y of t h e antenna t o t h e horizon of p o l a r i z a t i o n of t h e r a d i o waves impinging on i t i s a m a x i m u m , hand t h e c l o s e s t agreement between t h e experimental and t h e o r e t i occurs f o r azimuths n e a r t h e b o r e s i t e and a n t i - b o r e s i t e d i r e c t i o antenna i s least s e n s i t i v e t o t h e h o r i z o n t a l component of t h e rat i t is being illuminated. Since skywaves, b e i n g e l l i p t i c a l : *.which i n h e r e n t l y have a component of h o r i z o n t a l p o l a r i z a t i o n t h e respor. antenna t o t h e h o r i z o n t a l component of p o l a r i z a t i o n of r a d i o wave t h a t should b e i n v e s t i g a t e d i n t h e f u t u r e .

3.3.2

It follows

fl

extends to a range ments made w i t h t h p a i r they a r e , a t

Beverage P a i r Antenna

The r o s e t t e a r r a y c o n s i s t e d of 24 Beverage elements separate1 azimuth. A segment of t h e a r r a y i s shown i n F i g u r e 2 9 . Each elemc m long w i t h a h e i g h t above ground of approximately 1 m. The elemen phased t o g e t h e r i n p a i r s w i t h power adders t o form 12 f i x e d beams s i n azimuth by 30'. A p l a n view of t h e o v e r a l l a r r a y i s shown i n Fil where each element p a i r o r Beverage p a i r i n F i g u r e 29 i s shown as or This diagram shows t h e azimuths of t h e f i x e d beams and g i v e s a n i n d i t h e area occupied by t h e a r r a y .

3.4 The d i s t a n c e between t h e two elements i n each Beverage p a i r was t o g i v e t h e a p p a r e n t phase c e n t r e s of t h e elements a s e p a r a t i o n of an mately x/2 a t 1 0 MHz. On s o l e l y i n t u i t i v e grounds, t h e apparent phas\ of Beverage antennas w a s taken t o b e t h e p o i n t on t h e antenna where tl amplitude of a current- wave, e x c i t e d by a t r a n s m i t t e r a t t h e feed poig t h e antenna, w a s 3 dB less t h a n i t s amplitude a t t h e f e e d p o i n t (See 4 3.5). This c o n f i g u r a t i o n w a s chosen t o i n c r e a s e t h e d i s c r i m i n a t i o n g< t h e element p a i r s by causing c a n c e l l a t i o n of t h e radio-wave energy arri from t h e s i d e s because of t h e X/2 s p a t i a l s e p a r a t i o n . Each element p a l connected, t o a s w i t c h box a t t h e c e n t r e of t h e a r r a y v i a an RF cable. i switch w a s operated remotely t o connect a r e c e i v e r l o c a t e d i n a b u i l d i 3 from t h e r o s e t t e a r r a y t o any one of t h e a r r a y ' s twelve element- pairs.

ISOLATIC One Be-

measured. . v o l t a g e in& applied t o antennas W a

3.5

5

The azimuthal p a t t e r n of one of t h e Beverage p a i r antennas i s g i v ?e Figure 3 1 ( a ) . This w a s measured a t 9 . 7 5 MHz u s i n g t h e towed t r a n s m i t t e r j technique (XELEDOP). I t i s t h e same p a t t e r n as t h a t shown i n Figure 5, except t h a t h e r e i t h a s been transformed i n t o p o l a r form. Figure 31(b) s t h e p a t t e r n given i n F i g u r e 31(a) w i t h some super-imposed skywave measuri ments. ThesC were measured w i t h t h e r o s e t t e a r r a y on signals- of- opportun P a r t of t h e d a t a w a s o b t a i n e d by monitoring t h e s i g n a l on each Beverage p41 antenna f o r a d u r a t i o n of 6 seconds, determining an average value of i t s I amplitude and t h e n p l o t t i n g t h i s v a l u e i n Figure 31(b). The azimuth of ea p o i n t corresponds t o t h e azimuth of t h e s i g n a l w i t h r e s p e c t t o t h e boresigl of t h e Beverage p a i r antenna on which i t w a s r e c e i v e d . The remainder were obtained from quasi- instantaneous measurements of t h e s i g n a l a t each antenn and p l o t t e d i n t h e same way. For t h e l a t t e r , a d i o d e switch a t t h e c e n t r e t h e a r r a y w a s p r o g r a m e d t o connect t h e r e c e i v e r t o t h e i n d i v i d u a l a r r a y members i n r a p i d s u c c e s s i o n . The dwell t i m e on each antenna p o s i t i o n w a s approximately 1.4 m s c . P i c t u r e s of o s c i l l o s c o p e d i s p l a y s of t h e s i g n a l

!

t

PHASE

25

amp1i ude were ob 3ined as the swi ch stepped sequentially through the various antenna positions. This technique allowed for measurement of the relative amplitudes of the voltages, induced by skywave signals at the antenna terminals, in a recording time that was short compared to the normal fading rate for HF signals.

*

There is reasonably good agreement between the two sets of measurements The azimuthal beamwidths and side lobe levels are essentialin Figure 31(b). ly the same in both cases suggesting that the measurements made with the towed transmitter and vertically polarized antenna gave a good approximation to the radiation pattern of the Beverage antenna appropriate for skywaves. In Figure 31(c) a comparison is given between the XELEDOP pattern of Figure 31(a) and a measurement made with a balloon. The latter was performed at 9 MHz with a transmitter and a vertically polarized half-wave dipole suspended from a balloon, of the type normally used to collect meteorological data. There is good agreement between the main beams of the two patterns but a fairly large discrepancy in the side and back lobe levels. These levels are considerably lower on the balloon measurements. This may result from the balloon-suspended-dipole being more closely vertically polarized than was the case f o r the Xeledop antenna towed by the aircraft. Some measurements of the vertical pattern of a Beverage pair are given in Figure 3 2 . The solid curve was deduced from the theoretical curve for a single element with ground parameters appropriate to average soil (dry). The theoretical results were augmented by 3 dB because there are two Beverage elements in each Beverage pair. Balloon and aircraft measurements are superimposed. The measurements show good agreement with one another and with the theoretical curve. The balloon measurements do depart, however, from the theoretical curve at low elevation angles, below, say 4' and in addition above about 2 4 " . The former discrepancy is due, as will be discussed in Section 3.6, to contamination by a ground wave component. This was radiated by the balloon suspended transmitter at these low elevation angles because its close proximity to the ground. Since the balloon measurements were made at a radius of p l y 0.488 km the balloon suspended dipole came to within A / 4 of the ground at the lower elevation angles indicated in Figure 3 2 . The low elevation angle aircraft measurements on the other hand were made with the test antenna at a much greater height and range and therefore were not affected by a surface wave component. Furthermore, the balloon measurements will also be somewhat in error because they were not made in the far field of the Beverage pair antenna. The near field of an antenna following Kraus (1950) is given by the following relation,

where

R

=

2L2/h

R

=

range from antenna to its near field

L

=

largest physical dimension of the antenna

h

=

wavelength

-

far field boundary

.

26

I t f o l l o w s from t h i s e x p r e s s i o n t h a t t h e Beverage p a i r n e a r f i e l d e x t e n d s t o a r a n g e of 0.81 km a t 10 MHz. S i n c e t h e r a d i a t i o n p a t t e r n measurements made w i t h t h e b a l l o o n were made w i t h i n t h e n e a r f i e l d of t h e Beverage p a i r they are, a t b e s t , a n approximation t o i t s f a r f i e l d p a t t e r n . A complete v e r t i c a l p a t t e r n f o r t h e Beverage p a i r i s g i v e n i n F i g u r e 33. T h i s w a s measured w i t h a n a i r c r a f t towing a s h o r t d i p o l e a n t e n n a and receiver (RELEDOP) and f l y i n g d i r e c t l y o v e r t h e Beverage p a i r a n t e n n a a t a c o n s t a n t h e i g h t of 3 . 1 lan. F o r t h i s measurement t h e Beverage p a i r w a s e x c i t e d a t 9.75 %Hz and t h e s i g n a l r e c e i v e d by t h e towed d i p o l e w a s r e c o r d e d . Balloon measurements made p r e v i o u s l y a t 9 . 0 MHz are superimposed f o r purposes of comparison (Litva and S t e v e n s , 1973). Although t h e r e i s d i s a g r e e m e n t i n t h e d e t a i l of t h e main l o b e and back l o b e t h e r e i s agreement i n t h e r e l a t i v e l e v e l s of t h e two. There i s a l s o some disagreement i n t h e l o c a t i o n and t h e beamwidths of It i s e x p e c t e d t h a t t h e a i r c r a f t measurements are t h e more t h e main beam. a c c u r a t e of t h e two b e c a u s e t h e former were made i n t h e f a r f i e l d of t h e Beverage p a i r , whereas t h e l a t t e r were made i n t h e n e a r f i e l d of t h e a n t e n n a . On t h e o t h e r hand i t must b e remembered t h a t t h e b a l l o o n measurements are l i k e l y t o b e less contaminated by a h o r i z o n t a l component of p o l a r i z a t i o n of t h e r a d i o waves e i t h e r t r a n s m i t t e d o r r e c e i v e d by t h e d i p o l e a n t e n n a s a l o f t d u r i n g each t y p e of measurement.

3.4

ISOLATION BETWEEN BEVERAGE ELEPIENTS

One Beverage p a i r of t h e Cambridge Bay r o s e t t e a r r a y w a s e x c i t e d w i t h a n RF g e n e r a t o r a t a number of f r e q u e n c i e s between 5.8 and 23.7 MHz and t h e v o l t a g e induced a t t h e t e r m i n a l s of e a c h of t h e remaining e l e v e n a n t e n n a s w a s measured. The r e s u l t s of t h e s e measurements a r e g i v e n i n F i g u r e 34. The v o l t a g e induced i n t h e two a d j a c e n t a n t e n n a s w a s a t l e a s t 30 dB below t h a t a p p l i e d t o t h e a n t e n n a b e i n g e x c i t e d . The v o l t a g e induced i n t h e non- adjacent a n t e n n a s w a s a t l e a s t 50 dB below t h e e x c i t a t i o n l e v e l .

3.5

PHASE CENTRE OF BEVERAGE ELEMENTS

S i n c e no c o n c r e t e e v i d e n c e e x i s t s a s t o t h e l o c a t i o n of t h e phase c e n t r e of t h e Beverage e l e m e n t , a n e s t i m a t e d phase c e n t r e w a s chosen, on i n t u i t i v e grounds a l o n e , t o b e t h e p o i n t a t which t h e a m p l i t u d e of a current- wave f e d i n t o t h e a n t e n n a by a t r a n s m i t t e r w a s a t t e n u a t e d by 3 dB from i t s v a l u e a t t h e a n t e n n a ' s i n p u t t e r m i n a l . Contours f o r 3- , lo-, and 20-dB r e d u c t i o n s i n t h e c u r r e n t were d e r i v e d from F i g u r e l l ( b ) and a r e shown i n F i g u r e 35 p l o t t e d on a graph whose c o o r d i n a t e s are f r e q u e n c y and d i s t a n c e . The 3-dB p o i n t moves away from t h e f e e d p o i n t as t h e frequency i s d e c r e a s e d . T h i s s u g g e s t s t h a t i f t h e e s t i m a t e d phase c e n t r e s of t h e two e l e m e n t s of an element p a i r a r e s e p a r a t e d by X/2 a t a p a r t i c u l a r frequency (10 MHz f o r t h e Cambridge Bay Beverage p a i r s ) , t h i s s e p a r a t i o n of x / 2 c a n b e m a i n t a i n e d o v e r a r a n g e of f r e q u e n c i e s i f t h e a n t e n n a s a r e on r a d i a l s s u c h as shown i n F i g u r e s 29 and 30. A s t h e f r e q u e n c y , f o r example, i s i n c r e a s e d and t h e wavelength d e c r e a s e d , t h e e s t i m a t e d p h a s e c e n t r e s of an element moves toward t h e f e e d p o i n t , where t h e s p a t i a l s e p a r a t i o n of elements i s a l s o l e s s . I n t h e case of d e c r e a s i n g frequency and i n c r e a s i n g wavelength t h e e s t i m a t e d p h a s e c e n t r e moves away from t h e f e e d p o i n t to a r e g i o n where s e p a r a t i o n of t h e e l e m e n t s i s g r e a t e r . By p l a c i n g t h e two element i n each p a i r on a p p r o p r i a t e r a d i a l s , t h i s X/2 s e p a r a t i o n o f , t h e e s t i m a t e d p h a s e c e n t r e s may b e m a i n t a i n e d o v e r a f a i r l y broad r a n g e of frequencies.

.

I 3.6

27

LOW FREQUENCY BEVERAGE ANTENNA

The original development work on the Beverage antenna was directed ..I toward developing an antenna for reception of trans-Atlantic low frequency radio waves. Although tests have not been carried out in this frequency band at CRC, it is felt that the antenna could, in some cases, replace the large vertical monopole antennas used currently for both transmitting and receiving skywaves at these frequencies. This applies to point-to-point application where a considerable saving might be realized in the cost of antennas.

*

Figure 36 gives the theoretical radiation patterns at 125 kHz for a Beverage antenna situated over poor ground with the following dimensions, H = 7.62 m, L = 7.4 km. It is to be noted that the gain at the nose of the patterns is -15 dBi which compares very favourably with antenna gains achieved presently with large towers. The cost of this type of Beverage antenna would be only about 1/10 that of a large LF tower which is a predominant antenna type at these frequencies. It should be emphasized that the antenna gain at these frequencies has not yet been validated by measurements. It is presented here as an area that deserves further investigation.

3.7

SURFACE WAVE G A I N OF BEVERAGE ANTENNAS 3.7.1

Theoretical Expression

An expression for the gain of a Beverage antenna for surface or ground waves can be obtained from Equation 33 in Travers et a1 (1964). It follows from this equation that the magnitude of the voltage at the terminals of a Beverage antenna illuminated with a surface wave is given by

1 - ejBoL cos 6 - YL Y - j B 0 cos 6 and

sin

'

, y=a+jf3

where

VT = l7MS amplitude of the terminal voltage

IEI

= FWS amplitude of surface wave field inte sity

X

=

free space wavelength

L

=

length of antenna

6

=

tilt angle of surface wave

a

= current-wave attenuation on antenna (nepers/metre)

8 n

=

Bo/n

=

antenna current-wave propagation factor

28

The wave tilt angle is given as Equation 41 in Travers et a1 (1964).

w = 21Tf

where

0

€0

= permittivity of free space

%= relative dielectric constant of the earth u = conductivity of the earth g With the substitution

r

= y

- jg,

cos 6

the expression for the terminal voltages becomes

T'

=

-rR

DL sin 6 2

1 - e

r

The power Pr that the antenna extracts from a passing surface wave is given by

]El2 gh2 Pr = P d x A = rl

41T

* where

Pd = power density

g = gain of antenna w.r.t. isotropic 17 = characteristic impedance of free space

(377 ohm)

. effective aperture of antenna

A =

The power delivered t o the terminals of the antenna is also given by

29

Solving the above three equations for gain g it follows that

3.7.2

*

Measured Surface Wave Gain

The surface wave gain of an antenna can be measured in at least two independent ways. First, the antenna is illuminated with a source and a measurement is made of both the field intensity at the antenna and the antenna's terminal voltage. Second, two antennas are excited with a transmitter, one whose gain is known and the other whose gain is unknown and the field intensity generated by each at some convenient distance, possibly 1 mile is measured and compared. An example of the first technique was performed with a Beverage pair antenna at Cambridge Bay. As discussed previously in Section 2.3.2(d) its gain was measured as a receiving antenna with a transmitter raised aloft by means of a weather halloon. Measurements were taken with the transmitter located on the boresight of Beverage pair #12, at a distance of 0.488 km from the centre of the array. While the height of the transmitter was varied the field intensity of the signal from the transmitter was measured at the centre of the array and is given in Figure 38. Concurrent measurements were made of the voltages at the terminals of Beverage pair antenna /I12 and also Beverage pair antenna 1 6 . As shown in Figure 30 these antennas were diametrically opposite to one another and therefore permitted simultaneous front and back lobe measurements. Values for the gain of the Beverage pair antennas were derived measurements of field-intensity and terminal voltages induced in the First, by calculating the effective aperture of the antenna and then the following well known relationship between effective aperture and

from the antennas. using gain.

* where

g = gain w.r.t. isotropic

A

=

effective aperture

.

=

wavelength

A

The gain of a Beverage pair antenna versus elevation angle is shown in Figure 39 and consists of four curves, two for spacewave or skywave signals and two for ground or surface wave signals. The curves on the left are for main-beam entry of signals, and on the right for backlobe entry. A field intensity of 6 7 . 3 dB above 1 pV/m was used in the calculation of the skywave curve. This is the resulting value of the field intensity of the direct and indirect rays from the balloon transmitter when at an elevation angle of 15O. However, it is essentially the magnitude of the direct ray; the indirect ray being negligible at this angle because it is near the pseudo-Brewster angle.

__

The portion of the curve for elevation angles less than about 4" in Figure 39 is thought to give the gain of the Beverage-element pair for surface b

30

o r groundwaves. Th f i e l d i n t n s i t i e s i n F i g u r e 38 f o r v e r t i c a l a n g l e s less , than about 4 " appear t o be g r e a t e r than might b e e x p e c t e d , s i n c e t h e c o e f f i c i e n t of r e f l e c t i o n f o r t h e i n d i r e c t r a y approaches -1, and a l a r g e n u l l should occur a t t h e s e low e l e v a t i o n a n g l e s . For ground c o e f f i c i e n t s of u = mho/m € = 1 0 , f o r example, t h e r e f l e c t i o n c o e f f i c i e n t s a t 4 " , 2", and 0.5" are r e s p e c t i v e l y 0.631-178", 0.81-179' and 0.951- 179.50", ( s e e Figure 7 ) . Accordingly, t h e f i e l d i n t e n s i t y s h o w n T i T i g u r e 38 a t t h e s e a n g l e s should b e reduced by 9 , 1 4 , and 25 dB, r e s p e c t i v e l y , from i t s peak v a l u e a t 15". S i n c e no deep n u l l i s a p p a r e n t , i t a p p e a r s t h a t a s u r f a c e wave h a s been generated t h e balloon- suspended t r a n s m i t t e r and i t s d i p o l e a n t e n n a , and t h a t t h e *by f i e l d i n t e n s i t y measured, e s p e c i a l l y a t very low v e r t i c a l a n g l e s , is due e s s e n t i a l l y t o t h i s wave. It might b e argued t h a t t h e r e a s o n t h e n u l l d i d n o t appear i n t h e v e r t i c a l r a d i a t i o n p a t t e r n of t h e Beverage p a i r a n t e n n a , a t low e l e v a t i o n a n g l e s , w a s because t h e s o u r c e w a s w i t h i n t h e a n t e n n a ' s n e a r f i e l d o r F e s n e l r e g i o n . T h i s argument i s r e a d i l y d i s p e l l e d by t h e r e a l i z a t i o n t h a t a t low e l e v a t i o n a n g l e s t h e d i r e c t and i n d i r e c t s p a c e waves from t h e b a l l o o n t r a n s m i t t e r c a n c e l because t h e ground r e f l e c t i o n c o e f f i c i e n t i s n e a r -1. T h e r e f o r e t h e wave t h a t propagated from t h e s o u r c e t o t h e Beverage p a i r antenna a t t h e s e low e l e v a t i o n a n g l e s can only have been a s u r f a c e wave.

The Beverage antenna i s s e n s i t i v e t o s u r f a c e waves because they t r a v e l w i t h a forward t i l t and t h e r e f o r e have a h o r i z o n t a l component of p o l a r i z a t i o n which i s a b l e t o induce a c u r r e n t i n t h e h o r i z o n t a l Beverage antennas. For a n g l e s less than 4" t h e a c t u a l v a l u e s 0 5 f i e l d i n t e n s i t y a t each a n g l e , r a t h e r than i t s v a l u e a t a v e r t i c a l a n g l e of 15" were used t o c a l c u l a t e t h e c r o s s s e c t i o n and g a i n of t h e element p a i r . A v a l u e of about 0 dBi w a s d e r i v e d from t h e s e measurements f o r t h e g a i n of a Beverage p a i r a n t e n n a . R e c a l l i n g t h a t t h e gain of a Beverage element i s 3 dB less t h a n a Beverage p a i r i t foliows t h e n t h a t g a i n of a Beverage element i s -3 dBi which i s i n reasonably good agreement w i t h t h e t h e o r e t i c a l r e s u l t s i n F i g u r e 37. The second of t h e two t y p e s of measurements mentioned a t t h e s t a r t of t h i s s e c t i o n was performed a t Area 9 ( n e a r Richmond, O n t a r i o ) . The ground, c a s can be s e e n from F i g u r e 32, i s much b e t t e r t h a n t h a t found a t Cambridge Bay. A comparison was made of t h e s u r f a c e wave f i e l d i n t e n s i t i e s generated by a r e f e r e n c e monopole antenna and a Beverage a n t e n n a a t a d i s t a n c e of about 1mile. I t w a s found t h a t t h e g a i n of t h e Beverage antenna w a s about 2 dB r e l a t i v e t o t h e monopole antenna. Since t h e t h e o r e t i c a l g a i n of a monopole antenna i s 5.16 d B i (Smith, 1946) i t appears t o f o l l o w t h a t t h e g a i n of a Beverage i s 7.16 dB. This r e s u l t s i n a discrepancy of about 1 4 dB w i t h t h e t h e o r e t i c a l c*urve i n Figure 32. C a r e f u l measurements w e r e made of t h e monopole a n t e n n a ' s g a i n by i l l u m i n a t i n g i t w i t h a s u r f a c e wave and measuring b o t h f i e l d i n t e n s i t y and t h e a n t e n n a ' s t e r m i n a l v o l t a g e . I t w a s found t h a t t h e monopole's average g a i n was -3 d B i , from which i t f o l l o w s t h a t t h e gain of t h e Beverage i s approximately -1 dBi. A f u r t h e r measurement w a s made a t Area 9 w i t h a Beverage antenna i n t e r c e p t i n g a s u r f a c e wave generated by a t r a n s m i t t e r a t a d i s t a n c e of 7 m i l e s . The frequency of t h e s i g n a l was 8.172 MHz. Both t h e f i e l d i n t e n s i t y n e a r t h e Beverage antenna and t h e t e r m i n a l v o l t a g e of t h e antenna were

31 measured. From t h i s measurement i t w a s deduced t h a t t h e s u r f a c e wave g a i n of t h e Beverage antenna w a s -9.5 dBi which i s i n c l o s e agreement w i t h t h e t h e o r e t i c a l r e s u l t s i n Figure 37. I t i s concluded from t h e l i m i t e d s u r f a c e wave d a t a p r e s e n t e d h e r e t h a t t h e r e i s agreement, w i t h i n experimental e r r o r , between theory and measurements. F u r t h e r measurenents need t o b e made t o confirm t h e dependence of t h e g a i n of t h e antenna on frequency.

*

3.8

THEORETICALLY DERIVED VALUES OF SURFACE WAVE G A I N

T h e o r e t i c a l c u r v e s g i v i n g t h e s u r f a c e wave g a i n of Beverage a n t e n n a s a r e shown i n F i g u r e 111-1 and 111-2. The a n t e n n a s are s i t e d on poor s o i l (dry) and r i c h s o i l (wet). T h e i r h e i g h t s and l e n g t h s are v a r i e d r e s p e c t i v e l y between 0.3 t o 3 m and 100 t o 300 m. It should b e noted t h a t t h e g a i n of t h e Beverage antenna t e n d s t o be h i g h e r when s i t e d on poor s o i l (dry) t h a n when i t i s s i t e d on r i c h s o i l (wet). For t h e most p a r t t h i s e f f e c t is due t o t h e t i l t of t h e s u r f a c e wave being greater and t h e r e f o r e i t s e l e c t r i c a l v e c t o r having a l a r g e r h o r i z o n t a l component p a r a l l e l t o t h e Beverage antenna, when p r o p a g a t i n g over poor s o i l than when p r o p a g a t i n g over good s o i l . I n m o s t i n s t a n c e s t h e g a i n of t h e antenna i s independent of i t s h e i g h t above ground f o r f r e q u e n c i e s below about 5 MHz. F u r t h e r , f o r f r e q u e n c i e s above 5 MHz t h e g a i n of t h e antenna a p p e a r s t o change l i t t l e a s i t s l e n g t h i s i n c r e a s e d from 100 t o 300 m. Below 5 MHz, on t h e o t h e r hand, t h e g a i n does tend t o i n c r e a s e monotonically a s t h e l e n g t h of t h e Beverage element i s i n c r e a s e d from 100 t o 300 m.

4. BEVERAGE ANTENNA SYSTEMS 4.1

INTRODUCTION b

Beverage antennas used a s elements o r b u i l d i n g b l o c k s f o r HF antenna systems w i t h l a r g e a p e r t u r e s a r e covered i n t h i s s e c t i o n . HF antenna systems a r e c u r r e n t l y b e i n g used f o r d i r e c t i o n f i n d i n g , over- the- horizon r a d a r s and point- to- point communications. I t w i l l be shown t h a t t h e e f f i c i e n c y of a l i n e a r a r r a y of Beverage antennas can be c o n s i d e r a b l y g r e a t e r than t h e e f f i c i e n c y of a s i n g l e Beverage antenna. I f a s u f f i c i e n t number of elements a r e phasfd t o g e t h e r , n o t only w i l l t h e r e s u l t i n g a r r a y be e f f e c t i v e a s a r e c e i v i n g a n t e n n a , b u t i t w i l l a l s o be e f f e c t i v e as a t r a n s m i t t i n g antenna.

Two t y p e s of a r r a y s w i l l be d i s c u s s e d i n d e t a i l ; f i r s t l y , t h e r o s e t t e a r r a y and s e c o n d l y , t h e l i n e a r a r r a y . Both of t h e s e have been e v a l u a t e d by CRC a t O t t a w a and a t Cambridge Bay, N.W.T., as communications, d i r e c t i o n f i n d i n g and r a d a r a n t e n n a s . The f i r s t i s recommended f o r use on point-top o i n t communication c i r c u i t s , and t h e l a t t e r f o r communications t e r m i n a l s r e q u i r i n g azimuthal d e x t e r i t y . The l a t t e r i s a l s o recommended as a r e l a t i v e l y inexpensive antenna system w i t h a p p l i c a t i o n s i n HF d i r e c t i o n f i n d i n g . A l l of t h e s e antenna systems have a r e l a t i v e l y low p h y s i c a l p r o f i l e because of t h e low p r o f i l e of t h e Beverage antenna which serves a s t h e b a s i c element f o r t h e s e systems. b

-

.

32

4.2

ROSETTE ARRAYS 4.2.1

Cambridge Bay Rosette Array

One of the first Beverage arrays developed at CRC was a rosette array installed at Cambridge Bay, N.W.T., which was described in some detail in Section 3.5. It might be reiterated that the elements were phased together in pairs with power adders to form 12 fixed beams separated in azimuth by 30". The azimuths of these 12 beams are given in Figure 30. Each Beverage pair was connected to a switch box at the centre of the array via an RF cable. The ewitch box consisted of twelve diode switcheF which facilitated selection of the output of any one of the Beverage pairs from the building housing the receiver. The rosette array of Beverage antennas and electrical switch constituted a receiving antenna with a 3 dB azimuthal beamwidth of 30" which was steerable in 360" of azimuth. No further results of the electrical parameters of the Beverage elements of the Cambridge Bay rosette array will be given since these were covered in some detail in Sections 2 and 3 . Rather, results of evaluations of the effectiveness of the Cambridge Bay rosette array as an HF direction finding and communications antenna will be given here. It should be stated in passing that this antenna was primarily used as an OTH radar receiving antenna at Cambridge Bay. Data showing its effectiveness in this capacity are not included here because of its classified nature (Jenkins and Hagg, 1975).

4.2.2

Rosette Array as a Communications Antenna

Figure 40 gives pictures of the CRT display of a Hewlett Packard spectrum analyzer connected alternately to a rosette Beverage pair and a monopole antenna resonant at 9.748 MHz. Both of these antennas were monitoring an HF signal whose frequency was 9.748 MHz and emanated from a transmitter at Alert. The pictures show signals in a 2 MHz portion of the HF spectrum centred on the frequency of the Alert signal. The SNR of the Alert signal with respect to interference levels in a 20.2 MHz band centred on the frequency of the Alert signal is indicated for

12 consecutive time intervals. The duration of time between measurements was a random variable but, on the average, it probably was 15 minutes. These values were obtained from the pictures of the spectrum analyzer display. This ratio indicates the effectiveness of an antenna in discriminating against interference. It was found to be considerably larger on the Beverage member than on the monopole antenna. The median SNR measured for the Beverage member was +20 dB and that for the monopole antenna was +5 dB. Therefore, the difference in SNR is +15 dB, which closely corresponds to the difference in directivity gains of the two antennas. For example, the directivity gain of the Beverage member is 18 dB and that of the monopole antenna 6 dB at 10 MHz which gives a difference of 12 dB in the gains of the two antennas. If the distribution of the interference were isotropic the difference in signalto-interference ratios measured on the two antennas would tend to approximate the difference in their directivity gains.

33

4.2.3

e

Rosette Array as a DF Antenna

The e l e c t r o n i c s w i t c h l o c a t e d a t t h e c e n t r e of t h e Cambridge Bay r o s e t t e a r r a y f a c i l i t a t e d r a p i d azimuthal s t e e r i n g o r s w i t c h i n g of t h e antenna beam. This p e r m i t t e d t h e t e r m i n a l v o l t a g e s of t h e 12 members of t h e r o s e t t e a r r a y t o be sampled i n a t i m e t h a t w a s s h o r t compared t o t h e normal f a d i n g p e r i o d of HF s i g n a l s . The amplitude of t h e s i g n a l s a t t h e t e r m i n a l s of t h e r o s e t t e a r r a y w a s found t o v a r y i n magnitude, a s w a s e x p e c t e d , w i t h t h e l a r g e s t s i g n a l appearing on t h e a r r a y member most c l o s e l y a l i g n e d w i t h t h e azimuthal d i r e c t i o n of a r r i v a l of t h e s i g n a l . I t w a s found t h a t t h e d i r e c t i o n of a r r i v a l of t h e s i g n a l could be i n t e r p o l a t e d between two a r r a y members from t h e r a t i o of amplitudes of t h e s i g n a l s on t h e s e two members. These i n i t i a l t e s t s suggested t h a t t h i s c o n f i g u r a t i o n of Beverage a n t e n n a s and e l e c t r o n i c s w i t c h could be t h e b a s i s f o r an i n e x p e n s i v e d i r e c t i o n f i n d i n g system w i t h a n accuracy of about 1 t o 2 degrees (J. L i t v a and E.E. Stevens, p a t e n t pending, 1973).

R e s u l t s of some i n i t i a l tests performed t o determine t h e f e a s i b i l i t y of d i r e c t i o n f i n d i n g w i t h t h e Cambridge Bay r o s e t t e a r r a y are given i n F i g u r e 41. These c o n s i s t of p i c t u r e s of t h e CRT d i s p l a y of a n o s c i l l i s c o p e monitori n g t h e a u d i o o u t p u t of a r e c e i v e r tuned t o a c c e p t WWV skywave s i g n a l s r e c e i v e d by t h e r o s e t t e a r r a y . Each t r a c e c o n s i s t s o f t h e t e r m i n a l v o l t a g e s of t h e 1 2 r o s e t t e antennas monitored c o n s e c u t i v e l y i n t i m e , each f o r a d u r a t i o n of 1 . 2 msec. Although a wide range of sampling t i m e s were p o s s i b l e only on: w a s a c t u a l l y used i n t h e s e p r e l i m i n a r y r e s u l t s . Each complete t r a c e consi,c i n g of samples of t h e 1 2 antenna t e r m i n a l v o l t a g e s provided by t h e r o s e t t e a r r a y r e q u i r e d 1 4 . 4 msec. F i g u r e 4 1 ( a ) , f o r example, shows q u i t e dramacically t h e manner i n which t h e antenna t e r m i n a l v o l t a g e s v a r y as t h e t e r m i n a l s of t h e 1 2 a n t e n n a s a r e sampled s e q u e n t i a l l y . The s t r o n g e s t s i g n a l appeared on antenna 6 whose azimuth w a s 143" ( s e e F i g u r e 3 0 ) . This s u g g e s t s t h a t t h e approximate azimuth of t h e s i g n a l w a s 143" 215". It w i l l b e shown t h a t t h e accuracy of t h i s b e a r i n g can b e improved by c o n s i d e r i n g t h e r a t i o of t h e amplitudes of t h e s i g n a l s on t h e two antennas a d j a c e n t t o antenna 6. D i r e c t i o n f i n d i n g traces o b t a i n e d w i t h a 15 MHz signal e m i t t e d by t h e WWV t r a n s m i t t e r l o c a t e d a t Boulder, Colorado are given i n F i g u r e s 41(b) t o 4 1 ( c f . Although t h e azimuth of t h i s t r a n s m i t t e r w i t h r e s p e c t t o Cambridge Bay i s 179.5", t h i s need n o t b e t h e azimuthal a n g l e of a r r i v a l of HF s i g n a l s emanating from t h i s t r a n s m i t t e r . Bearings of HF s i g n a l s are observed t o v a r y w i t h t i m e , p r i n c i p a l l y because of t i l t s i n t h e ionosphere. T h e r e f o r e t h e azimuthal a n g l e of a r r i v a l of HF s i g n a l s can d e v i a t e q u i t e markedly from i t s g r e a t c i r c l e bearing. I n F i g u r e 41(b) t h e s i g n a l of l a r g e s t amplitude appears on antenna 7 whose azimuth w a s 173". The s i g n a l amplitudes are almost e q u a l on t h e t y o antennas a d j a c e n t t o antenna 7 . This s u g g e s t s t h a t t h e azimuth of t h e s'ignal i s i n c l o s e agreement w i t h t h e azimuth of antenna 7 or 173". I n F i g u r e 4 1 ( c ) , on t h e o t h e r hand, t h e amplitude of t h e s i g n a l on antenna 8 i s almost e q u a l t o t h e amplitude of t h e s i g n a l on antenna 7 . I f t h e amplitude was t h e same on b o t h , t h e azimuth of t h e s i g n a l would b e 188", which i s h a l f way between t h e two a n t e n n a s . Since t h e amplitude i s somewhat less on antenna 8 than on 7 , i t f o l l o w s t h a t t h e azimuth o f t h e s i g n a l i s somewhat l e s s than 188" or approximately 185". On t h e o t h e r hand i n F i g u r e 41(d) t h e s i g n a l i s s t r o n g e s t on antenna 6 w i t h a s l i g h t b i a s towards antenna 5 , s i n c e t h e amplitude of t h e s i g n a l i s g r e a t e r on 5 than on 7 , T h i s s u g g e s t s t h a t t h e azimuth of t h e s i g n a l i n t h i s i n s t a n c e is about 135". T h i s simple example o u t l i n e s t h e mode of o p e r a t i o n f o r an inexpensive HFDF system u s i n g a r o s e t t e

34 a r r a y of 24-Beverage antennas. The t e c h n i q u e f o r determining a c o r r e c t i o n t o t h e i n i t i a l approximation of t h e signal's azimuth can be g r e a t l y r e f i n e d by t h e u s e of c a l i b r a t i o n curves. These c u r v e s g i v e t h e r a t i o of s i g n a l l e v e l on each a d j a c e n t antenna w i t h r e s p e c t t o t h e signal l e v e l on t h e c e n t r a l antenna f o r azimuths of k7.5' c e n t r e d on t h e azimuth of t h e c e n t r a l antenna. A small computer could then b e programmed t o s e l e c t t h e antenna w i t h t h e l a r g e s t s i g n a l , c a l c u l a t e a b e a r i n g c o r r e c t i o n and compute t h e c o r r e c t b e a r i n g by a p p l y i n g t h e b e a r i n g c o r r e c t i o n t o t h e azimuth of t h e antenna on which t h e l a r g e s t t e r m i n a l v o l t a g e w a s recorded.

*

F u r t h e r r e s u l t s o b t a i n e d w i t h t h e Cambridge Bay r o s e t t e a r r a y are given i n F i g u r e s 42 and 43. These were o b t a i n e d on skywave s i g n a l s from known t r a n s m i t t e r s and were o b t a i n e d from t h e p a t t e r n s i n F i g u r e s 42 and 43 by deducing t h e azimuth t h a t bi- sected t h e p a t t e r n s r a t h e r t h a n u s i n g t h e maxima of t h e p a t t e r n s . The g r e a t - c i r c l e azimuths of t h e t r a n s m i t t e r s are i n d i c a t e d . A s mentioned e a r l i e r t h e s e need n o t b e t h e t r u e b e a r i n g s of t h e s i g n a l s because t i l t s and i r r e g u l a r i t i e s i n t h e ionosphere can c a u s e t h e s i g n a l t o d e v i a t e from t h e g r e a t c i r c l e p a t h . Furthermore, s i g n a l s t h a t a r r i v e a t a r e c e i v i n g s t a t i o n v i a a s i d e s c a t t e r mode can b e d e v i a t e d by up t o 30-40' from t h e g r e a t c i r c l e p a t h . It i s s e e n , though, t h a t t h e s e c r u d e b e a r i n g s a g r e e t o w i t h i n about 8 ' of azimuth w i t h t h e g r e a t c i r c l e b e a r i n g s of t h e signals.

4.3

CAMBRIDGE BAY LINEAR ARRAY Description o f the Array

4.3.1

I n August 1973 a wide- aperture antenna w a s i n s t a l l e d a t Cambridge Bay, N.W.T. The antenna was a l i n e a r phased a r r a y of 32 Beverage elements. A l i s t of p e r t i n e n t parameters i s given i n Table 111. TABLE Ill Parameters of Cambridge Bay Wide Aperture Antenna

Aperture Inter-Element Spacing Boresight Direction Steer Capability Vertical Beamwidth Elevation Angle of Maximum Azimuthal Beamwidth

1.26 km (4,134 ft.) 40.65 m (1 33.4 ft.) 18.63" East of North (Alert direction) +6", in 10 steps 12', at 3 dB points (10 MHz) 15" (10 MHz) 1.2' (10 MHz)

*

A s c e m a t i c i l l u s t r a t i o n of t h e l i n e a r a r r a y and i t s phasing network i s given i n F i g u r e 44. The o u t p u t s were summed i n groups of 4 , i n 4 : l power combiners, t o g i v e 8 sub- array o u t p u t s which were then fed i n t o a s w i t c h box w i t h a p p r o p r i a t e l e n g t h s of phasing c a b l e s .

The c a l c u l a t e d beamwidth and d i r e c t i v i t y g a i n of t h e l i n e a r a r r a y are given i n F i g u r e s 45(a) and ( b ) . A t 1 0 MHz t h e s e are r e s p e c t i v e l y 1 . 2 ' and 34.6 dB. T h i s d i r e c t i v i t y g a i n i s n e a r t h e upper l i m i t achieved t o d a t e f o r HF a n t e n n a s . The s o l i d c u r v e s i n F i g u r e 45(c) g i v e t h e p o s i t i o n s of t h e primary g r a t i n g l o b e s w i t h r e s p e c t t o t h e main beam. These l o b e s r e s u l t from

35

acing bei r e a t e r t h a n 3/4A (Terman, 1 9 5 5 ) . Sin e each t h e i n t r - elemen t Beverage element h a s d i r e c t i v e p r o p e r t i e s , t h e g r a t i n g l o b e s are reduced i n g a i n from t h e main beam. Curve B i n F i g u r e 4 5 ( c ) g i v e s t h e a n g u l a r d i s p l a c e - ' ment beyond which t h e a m p l i t u d e of t h e s e l o b e s i s reduced by a t least 13 dB.

*

The dashed c u r v e s i n F i g u r e 4 5 ( c ) g i v e t h e l o c a t i o n of t h e secondary l o b e s which a r e p r e s e n t when t h e a r r a y i s s t e e r e d o f f b o r e s i g h t . These a p p e a r because t h e a r r a y i s s t e e r e d by a d j u s t i n g t h e p h a s e of groups of f o u r e l e m e n t s r a t h e r t h a n s i n g l e e l e m e n t s . T h e r e f o r e when t h e a r r a y i s s t e e r e d i t behaves l i k e a n a r r a y of 8 a n t e n n a s whose i n t e r - e l e m e n t s p a c i n g i s 4 t i m e s a s g r e a t as when t h e a n t e n n a beam i s on b o r e s i g h t . The a m p l i t u d e of t h e s e l o b e s i s determined by t h e p a t t e r n of f o u r Beverage a n t e n n a s phased t o g e t h e r , i n t h e same way t h a t t h e primary g r a t i n g l o b e a m p l i t u d e s are determined by t h e p a t t e r n s of t h e i n d i v i d u a l e l e m e n t s . F i g u r e 46 g i v e s some computed a r r a y p a t t e r n s a t 10 MHz f o r a z i m u t h s a d j a c e n t t o t h e main beam. I t can be s e e n t h a t t h e a m p l i t u d e of t h e s i d e l o b e s a d j a c e n t t o t h e main beam are 1 3 dB less t h a n t h e a m p l i t u d e of t h e main beam f o r t h e example showing a 1" steer. The a m p l i t u d e s of t h e s e c o n d a r y l o b e s on t h e o t h e r hand grow w i t h s t e e r a n g l e and become g r e a t e r t h a n t h a t of t h e main beam a t a steer a n g l e of 6". The measured p a t t e r n of t h e a r r a y w i t h a p e r t u r e w e i g h t i n g i s g i v e n i n F i g u r e L7(b). To i l l u s t r a t e t h e d e g r e e of a p e r t u r e w e i g h t i n g used h e r e , t h e r e s u l t s of measurement of t h e r e l a t i v e c u r r e n t a m p l i t u d e s a t t h e t e r m i n a t e d ends of t h e i n d i v i d u a l Beverage e l e m e n t s a r e g i v e n i n F i g u r e 4 7 ( a ) . Array w e i g h t i n g i s e v i d e n t , w i t h t h e c e n t r e e l e m e n t s g i v e n more weight t h a n t h e o u t e r e l e m e n t s . A t h e o r e t i c a l a r r a y p a t t e r n d e r i v e d from t h e measured c u r r e n t d i s t l i b u t i o n i s shown a s a dashed curve i n F i g u r e 4 7 ( b ) . Reasonably good agreement e x i s t s between t h e l o c a t i o n of t h e t h e o r e t i c a l and measured g r a t i n g l o b e s and some s i d e l o b e s . The l a c k of agreement between t h e g r a t i n g l o b e l e v e l s on t h e two p a t t e r n s r e s u l t s from t h e u s e of a s i n g l e - e l e m e n t t h e o r e t i c a l p a t t e r n whose s i d e l o b e l e v e l , w i t h r e s p e c t t o t h e main beam is lower t h a n are t h e measured s i d e l o b e l r Tels of s i n g l e Beverage e l e m e n t s . The measured 3 dB beamwidth of t h e a r r i y i s 2.3" . T h e o r e t i c a l l y , t h e beamwidth The a r r a y of an unweighted a r r a y w i t h an a p e r t u r e of 4000 f t . i s 1 . 2 8 " . w e i g h t i n g used s h o u l d c a u s e beam broadening by a f a c t o r of 1.5, which g i v e s a b e a d i d t h of 1.9", i n r e a s o n a b l e agreement w i t h t h e measured v a l u e .

4.4 LINEAR PHASED BEVERAGE ARRAYS FOR COMMUNICATIONS 4.4.1

Initial Considerations

I t h a s been demonstrated i n S e c t i o n 4 . 2 . 1 t h a t t h e SNR of t h e r a d i o energy r 6 c e i v e d by an a n t e n n a i n a p o i n t - t o - p o i n t communications c i r c u i t is roughly p r o p o r t i o n a l t o i t s d i r e c t i v i t y g a i n . C o n s i d e r a b l e improvement w a s shown t o b e r e a l i z e d from u s i n g a Beverage member w i t h a d i r e c t i v i t y g a i n of 18 dB r a t h e r t h a n a monopole w i t h a d i r e c t i v i t y g a i n of 6 dB.

The t h e o r e t i c a l d i r e c t i v i t y g a i n of t h e Cambridge Bay l i n e a r a r r a y is given, a s a f u n c t i o n of f r e q u e n c y , i n F i g u r e 45(b) and i s s e e n t o have been a p p r o x i m a t e l y 34 dB f o r f r e q u e n c i e s between 4 and 24 MHz. Although a n a n t e n n a of t h i s s i z e i s n o t p r a c t i c a l a s a communications- a n t e n n a , i t i s worthwhile t o c o n s i d e r t h e u s e of a n t e n n a s w i t h 8 o r 1 6 e l e m e n t s and a p e r t u r e s of 150 m f o r communications a p p l i c a t i o n s . They would have a z i m u t h a l beamwidths of lo",

I

36 e l e v a t i o n beamwidths of 20" and "take-off" a n g l e s of 15" a t 1 0 MHz. The d i r e c t i v i t y g a i n would b e 23 dB a t t h i s frequency. Such antennas l i k e l y t o be h i g h l y e f f e c t i v e on long range point- to- point c i r c u i t s because of t h e i r high d i r e c t i v i t y g a i n and l o w "take-off angles". The beamwidths are s t i l l s u f f i c i e n t l y broad t o p r e v e n t a t t e n u a t i o n of t h e HF s i g n a l due t o v a r i a t i o n s i n a z i m u t h a l a n g l e of a r r i v a l caused by i o n o s p h e r i c t i l t s and i r r e g u l a r i t i e s . The p a t t e r n of a n unweighted 8-element Beverage a r r a y w i t h an a p e r t u r e of 150 m i s given i n F i g u r e 48(a). The beamwidth a t 10 MHz i s 9" and t h e a d j a c e n t s i d e l o b e s are down from t h e main beam by 13 dB, as i s t o b e expected, s i n c e t h e i r level i s determined by t h e f u n c t i o n s i n x/x. The s i d e l o b e s can b e reduced by w e i g h t i n g of t h e a p e r t u r e of t h e a r r a y . Figure 48(b) shows t h e p a t t e r n t h a t r e s u l t s from applying cos2 weighting t o t h e a p e r t u r e of t h e a r r a y . The s i d e l o b e s are reduced by 20 dB from t h e unweighted case. The p r i c e t h a t i s p a i d i n u s i n g t h i s technique i s broadening of t h e main beam, i n t h i s c a s e by a f a c t o r of 1.6, and a r e d u c t i o n i n t h e g a i n of t h e antenna by approximately 6 dB. F i g u r e s 49 t o 5 1 show t h e e f f e c t of i n c r e a s i n g t h e number of elements from 2 t o 32 i n a n a r r a y w i t h an a p e r t u r e of 150 m. I t can be seen t h a t t h e g r a t i n g l o b e s can be made t o d i s a p p e a r by i n c r e a s i n g t h e number of elements i n t h e a r r a y and t h e r e b y r e d u c i n g t h e inter- element spacing. For example, i n c r e a s i n g t h e number t o 8 r e s u l t s i n a p a t t e r n w i t h no g r a t i n g l o b e s a t a frequency of 1 0 MHz. The p a t t e r n s are a l l c a l c u l a t e d f o r a frequency of 1 0 MHz. The d i r e c t i v i t y g a i n of t h e a r r a y ceases t o i n c r e a s e a p p r e c i a b l y once t h e r e a r e 4- elements i n t h e a r r a y a p e r t u r e . It c e a s e s t o i n c r e a s e e n t i r e l y when t h e a r r a y a p e r t u r e c o n t a i n s 8- elements. A t t h i s p o i n t t h e a r r a y i s f i l l e d i n ; i n o t h e r words, t h e inter- element spacing i s less than o r equal t o

3/4x. The t h e o r e t i c a l e f f i c i e n c y and power g a i n of a n a r r a y w i t h t h e followi n g parameters, assuming n o n - i n t e r a c t i n g Beverage elements, a r e given i n Figure 52;

-

a r r a y a p e r t u r e = 150 m; ?

- element l e n g t h = 110 m;

-

element h e i g h t = 2 m;

-

a r r a y azimuthal beamwidth = 10" ( a t 1 0 MHz);

-

number of elements = 1 t o 64.

The power gain i n F i g u r e 52 i n c r e a s e s monotonically w i t h t h e number of elements prov5ded t h e elements are independent (De S a n t i s e t a l , 1973). It i n c r e a s e s by 3 dB each t i m e t h e number of elements i s doubled, This one t o one r e l a t i o n s h i p between power g a i n and t h e number of elements i n t h e a p e r t u r e of t h e a r r a y s t a r t s t o b r e a k down when t h e elements are no l o n g e r independent because of high mutual c o u p l i n g r e s u l t i n g from t h e i r proximity. Although e f f i c i e n t antennas must b e s e p a r a t e d by a t l e a s t about X/2 t o p r e v e n t i n t e r a c t i o n by t h e i r i n d u c t i o n f i e l d s , i n e f f i c i e n t antennas can b e brought c l o s e r t o g e t h e r b e f o r e t h e r e i s a p p r e c i a b l e i n t e r a c t i o n . Travers e t a1 (1964) i n d i c a t e d t h a t t h e i n t e r a c t i o n between i n d i v i d u a l Beverage elements does n o t become a p p r e c i a b l e u n t i l t h e elements are spaced c l o s e r than t h e i r h e i g h t s above ground. For Beverage elements 2 meters i n h e i g h t , f o r example, t h i s

'

37 suggests t h a t an a r r a y a p e r t u r e can be f i l l e d , w i t h resultant increase i n power g a i n , u r : t i l t h e i n t e r - e l e m e n t s p a c i n g become of t h e o r d e r of 2 m. There' f o r e a n a r r a y whose a p e r t u r e w a s 1 5 0 m c o u l d accommodate a maximum of a b o u t 64 e l e m e n t s and a c c o r d i n g t o F i g u r e 5 2 t h e maximum power g a i n t h a t would b e a c h i e v e d i s 1 7 dBi. Although n o t i n d i c a t e d i n F i g u r e 52 i t i s expected t h a t t h e power g a i n of an a r r a y w i t h an a p e r t u r e of 150 m w i l l l e v e l o f f a t a b o u t 64- elements f o r a f r e q u e n c y of 1 0 MHz.

*

The d i r e c t i v i t y g a i n i n F i g u r e 5 2 i n c r e a s e s m o n t o n i c a l l y w i t h t h e number of e l e m e n t s i n t h e array u n t i l i t c o n t a i n s 8- elements. A t t h i s p o i n t t h e a r r a y i s f i l l e d w i t h no f u r t h e r i n c r e a s e i n d i r e c t i v i t y g a i n t a k i n g p l a c e a s t h e number of e l e m e n t s i s i n c r e a s e d . A c t u a l l y l i t t l e i n c r e a s e i n d i r e c t i v i t y g a i n i s a c h i e v e d a t 1 0 MHz once t h e r e a r e 4- elements i n t h e a r r a y . I f t h e a r r a y were t o be used s o l e l y as a r e c e i v i n g a n t e n n a t h e r e would be l i t t l e a d v a n t a g e , e x c e p t f o r i n c r e a s e d e f f i c i e n c y , i n a d d i n g more t h a n 8e l e m e n t s p r o v i d e d t h a t t h e upper frequency w a s l i m i t e d t o 10 MHz. The number of e l e m e n t s , i n a c t u a l f a c t , s h o u l d b e doubled t o 1 6 i n o r d e r t h a t t h e a r r a y b e f r e e of g r a t i n g l o b e s up t o 20 MHz. I n i t i a l l y t h e e f f i c i e n c y of t h e a r r a y i n F i g u r e 52 i s about 1.0 p e r c e n t which i s s i m p l y t h e e f f i c i e n c y of a s i n g l e e l e m e n t . It i n c r e a s e s slowly w i t h t h e number of e l e m e n t s u n t i l t h e a r r a y i s f i l l e d . Beyond t h i s p o i n t t h e r e is a f a i r l y r a p i d i n c r e a s e and i t i s expected t h a t a maximum e f f i c i e n c y of a p p r o x i m a t e l y 32 p e r c e n t would o c c u r when t h e a r r a y c o n t a i n e d 64- elements. Although not shown i n F i g u r e 52, i t is e x p e c t e d t h a t t h i s c u r v e w i l l a l s o l e v e l o f f when t h e a r r a y c o n t a i n s 64- elements j u s t as t h e d i r e c t i v i t y g a i n l e v e l e d o f f when t h e a r r a y c o n t a i n e d 428 e l e m e n t s .

4.4.2

Beverage Array as a Point-to-Point Communications Antenna

Some i n i t i a l measurements which are c o r r o b o r a t e d by more e x t e n s i v e measurements a t D e b e r t , N.S. have been conducted a t O t t a w a t o e v a l u a t e t h e performance of a l i n e a r a r r a y as a p o i n t - t o - p o i n t communications a n t e n n a . An &element a r r a y w i t h an a p e r t u r e of 149.3 m h a s been e r e c t e d and p o i n t e d towards A l e r t . The performance of t h e a r r a y h a s been compared t o t h a t of a r e s o g a n t A/4-monopole a n t e n n a . h skywave s i g n a l emanating from a t r a n s m i t t e r l o c a t e d a t A l e r t w a s monitored s i m u l t a n e o u s l y on b o t h a n t e n n a s . Each a n t e n n a w a s a t t a c h e d t o a H e w l e t t Packard spectrum a n a l y z e r and t h e spectrum a n a l y z e r s were s e t t o perform r e p i t i t i o u s s c a n s o v e r a 50 kHz f r e q u e n c y band t h a t w a s c e n t r e d on t h e frequency b e i n g monitored. The v i d e o o u t p u t of t h e spectrum a n a l y z e r w a s r e c o r d e d on a c h a r t r e c o r d e r . F i g u r e 53 g i v e s a n example of t h e r e c o r d s o b t a i n e d u s i n g t h i s t e c h n i q u e . Two t r a c e s a r e shown, one i s t h e v i d e o ou>put of t h e spectrum a n a l y z e r a t t a c h e d t o t h e Beverage antenna a r r a y and t h e . o t h e r i s t h e v i d e o o u t p u t of t h e spectrum a n a l y z e r a t t a c h e d t o t h e monopole a n t e n n a . The I F bandwidth of t h e spectrum a n a l y z e r w a s 100 Hz and t h e t o t a l s c a n t i m e w a s 100 sec. I n each case t h e predominant v e r t i c a l traces as i n d i c a t e d i n F i g u r e 53 r e p r e s e n t t h e A l e r t s i g n a l . Although t h e h o r i z o n t a l a x i s i s c a l i b r a t e d i n u n i t s of t i m e i t c o u l d a l s o b e c a l i b r a t e d i n u n i t s of frequency. I t i s t o b e noted i n t h i s example t h a t t h e s i g n a l - t o - i n t e r f e r e n c e r a t i o achieved w i t h t h e monopole a n t e n n a i s a b o u t 23 dB whereas t h a t achieved w i t h t h e Beverage a r r a y i s a b o u t 11 dB g r e a t e r or 34 dB. S i m i l a r l y t h e s i g n a l - t o background n o i s e l e v e l (SNR) of t h e monopole a n t e n n a i s a b o u t 45 dB whereas

38 t h a t of t h e Beverage a r r a y i s about 60 dB. The d i s t i n c t i o n between i n t e r f e r e n c e and n o i s e used h e r e i s t h e following; i n t e r f e r e n c e i s coherent and t h e r e f o r e emanates from o t h e r HF t r a n s m i t t e r s , whereas n o i s e i s broadband and emanates from e l e c t r i c a l power l i n e s , e l e c t r i c a l machines, atmospherics and e x t r a - s t e l l a r s o u r c e s . Since t h e d i r e c t i v i t y g a i n of a monopole antenna i s about 4 dB and t h a t of t h e Beverage a r r a y i s 23 dB i t is s e e n t h a t t h e improvement i n S N R r e a l i z e d on t h e Beverage a r r a y over t h a t of t h e monopole antenna i s roughly e q u a l t o t h e d i f f e r e n c e i n t h e d i r e c t i v i t y g a i n s . F u r t h e r r e s u l t s obtained from a comparison of t h e l i n e a r a r r a y and a a e f e r e n c e A/4 monopole antenna are given f o r a 3-hour p e r i o d on 7 October 1974 i n Figure 54. This f i g u r e shows t h e d i f f e r e n c e i n SNRs achieved on t h e two antennas. The median d i f f e r e n c e v a l u e is 1 5 dB, which is somewhat s h o r t of t h e expected v a l u e of 1 9 dB given by t h e d i f f e r e n c e i n d i r e c t i v i t y g a i n s of t h e s e two a n t e n n a s . I t i s t o be expected t h a t a l o n g e r sampling of d a t a would have r e s u l t e d i n a median v a l u e which would have been i n c l o s e r agreement w i t h t h e expected v a l u e .

4.4.3

E f f i c i e n c y o f a L i n e a r Beverage A r r a y

I n an a t t e m p t t o v e r i f y t h e b a s i c assumption of independent elements used t o d e r i v e F i g u r e 52, r e c o r d s such as t h o s e shown i n F i g u r e 53, w e r e s c a l e d t o determine t h e g a i n of t h e Beverage a r r a y w i t h r e s p e c t t o t h a t of a monopole antenna. Using t h e t h e o r e t i c a l g a i n of a monopole antenna w i t h r e s p e c t t o an i s o t r o p i c antenna f o r skywaves t h e g a i n of t h e Beverage a r r a y w i t h r e s p e c t t o an i s o t r o p i c antenna i s t h e n r e a d i l y determined. R e s u l t s showing t h e g a i n of t h e Beverage a r r a y w i t h r e s p e c t t o t h a t of a monopole are given f o r a 3 hour i n t e r v a l i n Figure 55. The median v a l u e of g a i n of t h e Beverage a r r a y w i t h r e s p e c t t o a monopole antenna w a s found t o be 1 0 dB. Since t h e g a i n of a monopole antenna a t an e l e v a t i o n a n g l e of 13", which i s t h e predominant a n g l e of a r r i v a l of t h e skywave s i g n a l s from A l e r t , i s -1.5 d B i and t h e t o t a l Beverage a r r a y l o s s e s due t o a t t e n u a t i o n i n l i n k i n g c a b l e s and power d i v i d e r s were about 2.0 dB i t follows t h a t t h e g a i n of t h e Beverage a r r a y i s 10.5 dBi. The,power g a i n G of an antenna (Kraus, 1950) i s given by

where

C

= t h e e f f i c i e n c y of t h e antenna ( f r a c t i o n of t h e power f e d i n t o

t h e antenna t h a t i s a c t u a l l y t r a n s m i t t e d )

.

D = d i r e c t i v i t y gain

The d i r e c t i v i t y g a i n of an antenna i s determined p r i m a r i l y by t h e two dimens i o n a l g e o m e t r i c a l shape of t h e a n t e n n a ' s r a d i a t i o n p a t t e r n and i s given t o good approximation f o r small beamwidths by 41,253

D = BW x BUV A

where, t h e numerator i s t h e number of square degrees i n a sphere.

I

39

S i n c e t h e d i r e c t i v i t y g a i n of t h e Beverage a r r a y i s 2 3 d B a t t h e f r e q u e n c y of t h e A l e r t s i g n a l and i t s power g a i n , as j u s t d e t e r m i n e d , i s 10.5 dBi i t f o l l o w s t h a t i t s e f f i c i e n c y i s - 12.5 dB o r 5 . 6 p e r c e n t . The e f f i c i e n c y on t h e o t h e r hand of a s i n g l e Beverage element of t h e type used i n t h e a r r a y i s a b o u t 1 p e r c e n t . T h e r e f o r e t h i s a r r a y of 8- elements h a s a n e f f i c i e n c y which i s a b o u t 4 . 6 p e r c e n t g r e a t e r t h a n t h a t o f a s i n g l e Beverage e l e m e n t . T h i s f i n d i n g i s i n c l o s e agreement w i t h i n c r e a s e i n e f f i c i e n c y p r e d i c t e d by F i g u r e 52 w i t h 3- elements i n t h e a r r a y a p e r t u r e r a t h e r t h a n a s i n g l e e l e m e n t .

*

An e x p l a n a t i o n f o r t h e i n c r e a s e d e f f i c i e n c y t h a t can b e r e a l i z e d by t h e a r r a y i n g of i n e f f i c i e n t a n t e n n a s i s most e a s i l y a r r i v e d a t by c o n s i d e r i n g t h e a n t e n n a as a r e c e i v i n g a n t e n n a . I f t h e power r e c e i v e d by one a n t e n n a monitori n g a s i g n a l i s P , t h e power r e c e i v e d by 2 a n t e n n a s , provided t h e r e is s u f f i c i e n t s e p a r a t i o n between them so t h a t t h e y are i n d e p e n d e n t , i s 2 P. If t h e s e two a n t e n n a s a r e phased t o g e t h e r t h e g a i n of t h e r e s u l t i n g a n t e n n a i s , a s a r e c e i v i n g a n t e n n a , 3 dB g r e a t e r t h a n a s i n g l e a n t e n n a . It f o l l o w s from t h e r e c i p r o c i t y theorem f o r a n t e n n a s t h a t t h e g a i n of t h i s a n t e n n a as a t r a n s m i t t i n g a n t e n n a h a s a l s o i n c r e a s e d by t h e same amount o v e r t h a t of a s i n g l e a n t e n n a . For a n a r r a y of n i n d e p e n d e n t a n t e n n a s t h e power r e c e i v e d i s n times as g r e a t a s t h a t r e c e i v e d w i t h a s i n g l e a n t e n n a and t h e r e f o r e t h e power g a i n of t h e a r r a y of a n t e n n a s i s g r e a t e r t h a n t h a t of a s i n g l e a n t e n n a by t h e f a c t o r AG = 1 0 l o g n

where

A G , i s t h e i n c r e a s e i n g a i n of a n a r r a y o v e r t h a t of a s i n g l e a n t e n n a .

When a n t e n n a s w i t h a n e f f i c i e n c y of 1 . 0 a r e a r r a y e d t o g e t h e r t h e power g a i n r e a l i z e d w i t h t h e a r r a y r e l a t i v e t o a s i n g l e element c a n o n l y b e due t o t h e i n c r e a s e d d i r e c t i v i t y g a i n of t h e a r r a y . On t h e o t h e r hand when i n e f f i c i e n t a n t e n n a s a r e a r r a y e d t o g e t h e r t h e r e s u l t i n g i n c r e a s e i n t h e power g a i n can s t e m from a n i n c r e a s e b o t h i n t h e d i r e c t i v i t y g a i n and e f f i c i e n c y of t h e a r r a y w i t h r e s p e c t t o a s i n g l e element. The i n c r e a s e i n e f f i c i e n c y of a n a r r a y o v e r a s i n g l e element arises from a r e d u c t i o n i n ground l o s s e s b r o u g h t a b o u t by t h e a r r a y ' s lower e l e c t r i c a l e n e r g y d e n s i t y which i s l e s s , s i m p l y because t h e t o t a l e l e c t r i c a l energy i s s p r e a d o v e r a l a r g e r area ( D e S a n t i s , 1973). As a n example of h i g h l y i n e f f i c i e n t a n t e n n a s l e t u s c o n s i d e r Beverage a n t e n n a s , which a r e p o s t u l a t e d ( T r a v e r s e t a l , 1964) t o m a i n t a i n a f a i r l y h i g h d e g r e e of i s o l a t i o n u n t i l t h e i r s p a c i n g i s less t h a n t h e i r h e i g h t above ground. An approximate r e l a t i o n s h i p between t h e a z i m u t h a l beamwidth of a n a n t e n n a , i n p a r t i c u l a r , of an a r r a y of a n t e n n a s , and i t s a p e r t u r e i s g i v e n by

51.7

BwA =

where

Nh

NX = t h e a p e r t u r e of t h e a n t e n n a i n wavelengths.

S i n c e t h e a z i m u t h a l beamwidth of a Beverage a n t e n n a ( f = 10 MHz, H = 2 m, L - 110 m , a v e r a g e s o i l - d r y ) i s 40" i t s e f f e c t i v e a p e r t u r e i s 1.3X. This s u g g e s t s t h a t a t 10 MHz t h e d i r e c t i v i t y g a i n of a n a r r a y of t h e s e Beverage a n t e n n a s i s e s s e n t i a l l y e q u a l t o t h e d i r e c t i v i t y g a i n of a s i n g l e Beverage

.- b

.

.

40 antenna u n t i l t h e a r r a y a p e r t u r e i s g r e a t e r t h a n 39 m. From what h a s been s a i d above, up t o approximately 20 n o n - i n t e r a c t i n g Beverage elements could be phase t o g e t h e r i n an a p e r t u r e of 39 m. A t 10 MHz t h e i n c r e a s e i n power gain t h a t would b e r e a l i z e d i s 13.0 dB. The m a j o r i t y of t h i s increase must be a t t r i b u t e d t o t h e i n c r e a s e d e f f i c i e n c y of t h e a r r a y r e l a t i v e t o a s i n g l e element s i n c e t h e d i r e c t i v i t y g a i n of t h e a r r a y i s e s s e n t i a l l y t h a t of a s i n g l e Beverage element o r 18 dB. It follows t h a t t h e g a i n of t h i s a r r a y would be 12.0 dBi i f t h e g a i n of a s i n g l e element i s assumed t o be -1 dBi. The e f f i c i e n c y then of t h i s a r r a y would b e -6.0 dB o r about 25 p e r c e n t whereas t h e e f f i c i e n c y of a s i n g l e element is only about 1 p e r c e n t . 0

There i s a n o t h e r p o i n t of view t h a t can b e brought t o b e a r i n e x p l a i n i n g t h e i n c r e a s e i n e f f i c i e n c y t h a t i s achieved w i t h a r r a y e d antennas. It can be a l s o used t o determine t h e maximum power g a i n t h a t can b e achieved w i t h an a r r a y whose p h y s i c a l dimensions are f i x e d . It is a r e l a t i v e l y w e l l known f a c t i n antenna t h e o r y t h a t t h e minimum e f f e c t i v e proximity of t h e elements i n an a r r a y i s determined by t h e s i z e of t h e elements' e f f e c t i v e a p e r t u r e s . I n o t h e r words, f o r a one o r two dimensional a r r a y of f i x e d p h y s i c a l a p e r t u r e t h e maximum g a i n t h a t can be achieved i s r e a l i z e d when a s u f f i c i e n t number of elements i s placed i n t h e a p e r t u r e s o t h a t t h e p e r i m e t e r s of t h e e f f e c t i v e a p e r t u r e s of a d j a c e n t antennas a r e e s s e n t i a l l y touching one a n o t h e r . A s m a l l degree of o v e r l a p p i n g i s p o s s i b l e s i n c e t h e r e g i o n n e a r t h e c e n t r e of t h e e f f e c t i v e a p e r t u r e s of each element h a s g r e a t e r weight than t h e r e g i o n n e a r t h e p e r i m e t e r s .

The g a i n of an a r r a y w i t h N elements arrayed such t h a t t h e e f f e c t i v e a p e r t u r e s are n o t overlapping, i s given by N x A where A i s t h e e f f e c t i v e a p e r t u r e of one of t h e a r r a y elements. The g a i n of t h e a r r a y i s then given by

where

%=

g a i n of t h e a r r a y

A = e f f e c t i v e a p e r t u r e of one element (= gX2/4r)

N = number of elements

I f i n a f i r s t approximation one approximates t h e e f f e c t i v e a p e r t u r e A of an element w i t h a s q u a r e t h e l e n g t h of one s i d e i n wavelengths i s given by

where

g = g a i n of an element

LA = l i n e a r dimension of e f f e c t i v e a p e r t u r e of a r r a y element Table IV g i v e s t h e g a i n and e f f i c i e n c i e s of a Beverage antenna a r r a y with a p h y s i c a l a p e r t u r e of 150 m f o r 1 6 , 22 and 32 Beverage elements. It i s assumed t h a t t h e a r r a y i s on average s o i l ( d r y ) , element l e n g t h s are 150 m

41 and element h e i g h t s are 2 m. The g a i n of a s i n g l e element varies between - 4.5 dBi and 2.3 dBi i n t h e frequency range 5 MHz t o 20 MHz. I n t h e same frequency i n t e r v a l t h e e f f e r t i v e a p e r t u r e of a s i n g l e Beverage antenna varies from 101.7 m2 t o 30.4 m2 and correspondingly t h e width of i t s e f f e c t i v e a p e r t u r e v a r i e s between 1 0 , i m and 5.52 m. It follows t h a t if t h e r e i s t o be no overlapping of e f f e c t i v e a p e r t u r e s i n t h i s frequency range t h e minimum inter- element spacing must :e 10.1 m. The remainder of t h e t a b l e g i v e s t h e g a i n s and e f f i c i e n c i e s of t 5 e a r r a y antenna f o r 1 6 , 22 and 32 elements when overlapping of e f f e c t i v e a p e r t u r e s t a k e s p l a c e t h e t o t a l e f f e c t i v e a p e r t u r e N x A i s a d j u s t e d t o e n s u r e t h a t t h e common areas are only counted once and t h e r e s u l t a n t i s given as N x A ' . TABLE / V Gain and Efficiency of a Bc wage Antenna Array Determined From Effective Areas Aperture = 150 m Average Soil (Dry)

Frequency

5 PIHz

1 5 MHz

2 0 MHz

1 - 1.0 d R i .251

1 - -_1.0 d R i .317

1 2.3 d B i

7.53 m ; 6 . 9 m2 .o % 6 '1 m ' 1 0 . 4 m2

6.34 m 40.11 m2 2.2 % 16 10 m

5.52 m 30.4 m 2 2.3 % 16 10 m 486.4 m 2 14.34 dRi

10 MHz L

N

1 - 4 . 5 dR .I68

G

5 L

A N S

N x A GN

I

I

10.1 m I 1 0 1 . 7 m' 1.8 % 16 10 m 1627.2 m2 7.53 dRi :

5.66 % 22 ~7 m 2 2 3 7 . 4 m' 1565.8 m: 7.37 d B i ~

N S

N x A N x A' GN

4.84

G = gain w.r.t. dBi LA= width of effective area in wavelength L = width of effective area in metres A = effective area

I

__ 3 1 %

1

.84 m

.3hP

14.4 dRi

6--.-8-2 % 22 7 m 668.8 m2 668.2 m 2 15.7 dRi

4.84 m

9.33 % 32 4.84 m

2. , m

1 .1 d R i

_--_-

A ' = effective area aausted to account for overlapping S = separation of elements (metres] N = number of elements

42

The results in Table IV for 16 elements are equivalent to those of Figure 52. The efficiency at 10 MHz, for example, has increased from 2 per cent for a single element to 6.31 per cent for the array of 16 elements. The results of Table IV and Figure 5 2 diverge for N equal to 22 and 32 because correction for overlapping of effective areas was not taken into account in the derivation of Figure 52.

*

5.

5.1

SITING

CONCLUSIONS AND RECOMMENDATIONS

OF HF ANTENNA

A . A n effective means of measuring the homogeneity of a potential antenna site is to erect a monopole antenna and measure its radiated field with an airborne receiver and,shortdipole antenna (RELEDOP). B. The electrical constants of the ground are probably most easily determined with a temporary Beverage antenna. The attenuation of the currentwave on the antenna is measured at a number of frequencies in the HF band and the soil constants (soil type) are determined by reference to Appendix I.

5.2 BEVERAGE ANTENNA PARAMETERS A . Extensive measurements were made of Beverage antenna parameters and compared with theoretical results. The complement of measured parameters include the following;

-

input impedance

- characteristic impedance

-

current-wave attenuation

*

- current-wave phase velocity - isolation between elements

-

space-wave power gain surface-wave power gain

- azimuthal radiation patterns (space wave)

-

eleva'tion radiation patterns (space wave)

The agreement between the experimental and theoretical results was, except for a few instances, reasonably good. It follows that the theoretically derived parameters can be used with confidence in the design.of communications circuits using Beverage antennas and in the design of Beverage antenna systems. B . Theoretical design parameters are given in Appendices I, I1 and 111. Appendix I gives the current-wave attenuation and characteristic impedance of Beverage antennas. These can be used to determine the power rating requirements and magnitudes of terminating resistors. The remaining design parameters are given in Appendix 11. These consist of azimuthal beamwidth, vertical

*

.

,"

43

beamwidth, take- off a n g l e and power g a i n . of Beverage antennas f o r s u r f a c e waves.

Appendix I11 g i v e s t h e power g a i n

C. I t w a s shown t h a t t h e Beverage antenna i s a h i g h l y e f f e c t i v e HF r e c e i v i n g antenna. T h i s s t e m s from i t s h i g h d i r e c t i v i t y g a i n ( - 1 7 dB), broad band c h a r a c t e r i s t i c s (3-30 MHz) and low take- off a n g l e ( - 15.0"). Its o t h e r a t t r i b u t e s c o n s i s t of low r e a l e s t a t e requirements and low procurement, i n s t a l l a t i o n and maintenance c o s t s . A s a r e c e i v i n g antenna i t h a s been found t o be more t h a n , o r a t l e a s t as e f f e c t i v e a s , c l a s s i c a l HF a n t e n n a s i n maximizing t h e SNR of r e c e i v e d s i g n a l s .

*

5.3

BEVERAGE ANTENNA SYSTEMS

A . A r o s e t t e a r r a y of Beverage a n t e n n a s w a s shown t o b e an e f f e c t i v e HF r e c e i v i n g antenna w i t h a mean d i r e c t i v i t y g a i n of about 1 7 dB and an e f f e c t i v e azimuthal steer c a p a b i l i t y of 360". It w a s a l s o shown t o have p o t e n t i a l a s an HF d i r e c t i o n f i n d i n g antenna system. B. L i n e a r phased a r r a y s of Beverage antennas were shown t o be e f f e c t i v e 0°F and HF point- to- point communications antennas. HF r e c e i v i n g a r r a y s having mean d i r e c t i v i t y g a i n s of 23 dB have been t e s t e d and found t o b e e f f e c t i v e i n a c h i e v i n g h i g h SNRs on communications c i r c u i t s . Maximum d i r e c t i v i t y g a i n s achieved by c l a s s i c a l HF antennas are u s u a l l y about 16-18 dB. C. It w a s shown t h a t a n a r r a y of Beverage antennas can have g r e a t e r e f f i c i e n c y than a s i n g l e Beverage antenna. E f f i c i e n c i e s of up t o 1 0 p e r c e n t can be achieved u s i n g Beverage elements whose e f f i c i e n c i e s i n d i v i d u a l l y a r e about 2 p e r c e n t . I t w a s shown t h a t c o n s t r u c t i o n of antenna a r r a y s w i t h power g a i n s which v a r i e d from 7 dBi t o 16 dBi i n t h e frequency i n t e r v a l 5 MHz t o 20 MHz a r e p o s s i b l e u s i n g Beverage antennas as a r r a y elements. The r e a l e s t a t e requirements a r e 150 m by 150 m. These g a i n s compare v e r y f a v o r a b l y w i t h t h e l a r g e r c l a s s i c a l HF antennas and t h e c o s t s are about 1 / 8 - 1/10 those of c l a s s i c a l antennas. e

5.4

THEORY

A f a i r l y complete d e s c r i p t i o n of t h e e q u a t i o n s used i n d e r i v i n g t h e t h e o r e t i c a l Beverage parameters used i n t h e body of t h i s r e p o r t i s given i n Appendix I V . Equations a r e a l s o given f o r c a l c u l a t i o n of t h e e l e c t r i c a l parameters of a r r a y s of Beverage antennas. A l i s t i n g and d i s c u s s i o n of t h e CRC Beverage antenna computer program i s a l s o given.

A . A p r o t o t y p e t r a n s m i t t i n g Beverage antenna should b e b u i l t , t e s t e d and demonstrated. P u r e l y economic c o n s i d e r a t i o n s serve a s t h e major j u s t i f i c a t i o n f o r t h i s recommenation. On t h e b a s i s of t h e r e s u l t s given i n t h i s r e p o r t , i t a p p e a r s h i g h l y probable t h a t t r a n s m i t t i n g Beverage antennas can be designed, b u i l t and maintained a t a f r a c t i o n of t h e c o s t of c l a s s i c a l antennas, such as rhombics and log p e r i o d i c s , w i t h a performance which e q u a l s o r exceeds t h a t of t h e s e c l a s s i c a l a n t e n n a s . D e t a i l e d measurements need t o be made t o v e r i f y t h a t t h e power g a i n s which have been p r e d i c t e d i n t h i s r e p o r t can be r e a l i z e d

--

c

.

44 in practice. If one considers the savings in capital expenditures that could be realized by agencies using Beverage antennas rather than classical antenna in long range circuit applications, and the relatively modest resources required to have these tests performed, one is forced to acknowledge with the validity of this recommendation.

,

B. Extensive measurements should be made of a Beverage antenna's power gain and radiation pattern using the RE'LEDOP techniques.

Effort and resources dedicated to obtaining detailed radiation pattern measurements are justified, even at this stage in the development of the Beverage antenna, to determine the degree to which their measured patterns depart from the theoretical model. The description of the Beverage antenna in terms of measurements is not yet as complete as is the theoretical model of the antenna. Future applications of this antenna as adaptive radar antennas and direction finding antennas are likely to require detailed knowledge of its radiation patterns. It will be particularly important to discover to what extent wide aperture linear arrays, for example, are degraded by inhomogeneous ground and also to determine the limitation imposed by a Beverage antenna's environment on the beam shaping of wide aperture arrays. C. A prototype HF direction finding Beverage array system should be built, tested and referred to industry for further development.

Once again economic consideration come to the fore as justification for further work in this area. Existing high frequency direction finding systems are extremely expensive due largely to their antennas and goniometers. As a consequence they are used only where large expenditures can be justified. An inexpensive HFDF system is likely to find fairly widespread application in areas where large initial capital expenditures are not justified, such as;

- tracking of radio buoys at sea to measure ocean currents,

- radio tracking of oil spills at sea, - regulatory location of transmitters, - mgasurement of variations in angle of

arrival of HF signals for

scientific purposes,

- portable HFDF system for gathering of intelligence,

-

systems requiring multiple, automated DF stations.

*

6. ACKNOWLEDGEMENTS

The authors wish to acknowledge M r . E.E. Stevens. His enthusiasm and appreciation of the potential of the Beverage antenna contributed greatly to this work. Useful discussions with M r . E.L. Hagg and Dr. R.W. Jenkins are also acknowledged.

45

7. 1.

Beverage, H.H.,

C.W.

REFERENCES

Rice and E.W.

R e l l o g g , The Wave Antenna, a New Type,. V O l . 42, February 1923.

of Highly Directive Antenna, Trans. A . I . E . E . , 2.

P.E. M a r t i n and W.M. S h e r r i l l , Use of the Beverage Antenna i n Wide Aperture High Frequency Direction Finding ( P a r t IV: Theory),

Travers, D.N,

I n t e r i m Report f o r C o n t r a c t NObsr-89345, 23 March 1964.

*

Southwest Research I n s t i t u t e ,

3.

T r a v e r s and R. Lorenz, CircuZar Arrays of Beverage Antennas f o r High Frequency Radio Direction Finding, Paper s u b m i t t e d f o r T e c h n i c a l Program Southwestern I E E E , A p r i l 1965.

4.

Terman, F.E., E l e c t r o n i c and Radio E n g i n e e r i n g , McGraw-Hill Book Company, I n c . , New York, 1955.

5.

Ramo, S., J . R . Whinnery and T. Van Duzer, Fields and Waves i n Communication Electronics, John Wiley & Sons, I n c . , New York, 1967.

6.

L i t v a , J. and E . E . S t e v e n s , Performance and EvaZuation of the Cambridge Bay Beverage A r r a y , Proceedings of t h e OHD T e c h n i c a l Review Meeting,

M a r t i n , P.E.,

D.N.

May 2-3, 1975, Colorado S p r i n g s , Colorado, 1973.

7.

J e n k i n s , R.W. and E.L. Hagg, Final Report on the Canadian Polar Cap 3 Experiment a t Cambridge Bay, N.W.T., CRC Report No. 1975.

8.

L i t v a , J . and E.E. S t e v e n s , Rapid Azimuthal Determination of Radio S i g n a l s , CRC 1340-144, P a t e n t Pending, 30 J a n u a r y 1975.

9.

DeSantis, C.M., D.V-. Campbell and F. Schwering, An Array Technique for Reducing Ground Losses i n t h i HF Range, IEEE Trans. on Ants. and Prop., V O l AP- 21, No. 6 , November 1973.

.

10. H e r l i t z , I v a n , Appendix B, AnaZysis of Action of Wave Antennas, An ?Appendix to t h e paper by Beverage, Rice, and K e l l o g , The Wave Antenna, a New Type o f Highly Directive Antenna), T r a n s a c t i o n s of t h e American I n s t i t u t e of E l e c t r i c a l E n g i n e e r s , Volume 42, 1923, pp. 260-266.

EZectric Transmission Lines, M c G r a w - H i l l Book Company,

11.

S k i l l i n g , H.H., I n c . , 1951.

12.

The Royal S i g n a l s Handbook of Line Communication, V O l . 1 , 1947, Seventh Impression 1964, p. 7 4 7 .

13.

R a m 0 Winnery Van Duzer, op. c i t . , p . 1 7 .

14.

Kraus, J . D . ,

15.

S t r a t t o n , J . A . , Electromapetic Theory, M c G r a w - H i l l , Secs. 9.4 and 9.9.

16.

Feldman, C . B . , The OpticaZ Behuviour of the Ground f o r Short Radio Waves, Proceedings of t h e I . R . E . , V O l . 21, N o . 6 , J u n e 1933, pp. 764-801.

Antennas, McGraw-Hill Book Company, I n c . , 1950, p. 53. New York, 1941,

46

17.

Carson , ) R . , Wave Propagation i n Overhead Wire with Grounc Return, B e l l Systems T e c h n i c a l J o u r n a l , V O l 5, 1926, pp. 539-554.

18.

Wise, W.H., Propagation o f High Frequency Currents i n Ground Return Circuits, P r o c e e d i n g s of t h e I n s t i t u t e of Radio E n g i n e e r s , V O l . 22,

.

A p r i l 1934, pp. 5221527. 19.

Kraus, op. c i t . , pp. 76-77.

20.

Kraus, i b i d , p . 66.

21.

O r r , W i l l i a m , H e r b e r t G. Johnson

22.

Gold, Bernard and C h a r l e s M. Rader, Digital Processing of Signals, McGraw H i l l Book Company, 1969, pp. 162-164.

23.

G i l c h r i s t , A.W.R., The Use and Properties of Window Functions in S p e c t m AnaZysis, CRC Report No. 1221, November 1971, O t t a w a .

24.

T a y l o r , T.T., Design of Line-Source Antennas f o r Narrat B e m i d t h and Low SideZobes, IRE T r a n s a c t i o n s on Antenna P r o p a g a t i o n , V O l ume AP-3 ,

e

VHF Handbook

1956

pp. 90-97.

Number 1, J a n u a r y 1955, pp. 16-28. 25.

ROSS, W., E.N. Bramley, and G.E. Ashwell, A Phase-Comparison Method of Measuring the Direction of ArrivaZ of Ionospheric Radio Waves, Proc. I.E.E., 1951, 98, P t . 111, p. 294.

.

,

0 @ @ @

@ INSULATOR

ANCHOR ROD ANCHOR

@POST

@ TRANSFORMER, MATCHING

CEDAR

@ ANTENNA WIRE, STRANDED AWG 14 STRAIN @ RESISTOR

TURN BUCKLE INSULATOR

WET TYPE

Figure

I,

@CABLE

RF

@ GROUND @GROUND

SCREENS ROD

.Components of an H F Beverage antenna. Typically the height above ground is 1 to 2 metres and the length is 100 to 150 metres.

400150

co U

49

8ol 70-

e

A 60m 0

- 2 6 JULY 1972

ARRAY ABSENT

5040

'

I

I

0

I

I

I

80

40

1

I

1

I

I

I

I

I

I

120 160 200 240 AZIMUTH (DEGREES)

I

280

I

I

I

320

360

Figure 4. Field Intensity at a Distance of 610 m vs. Azimuth from a Quartetwave Monopole at the Centre of the Array (U).

0-5

-

-10-

-15-

= -20c

m e

-z

25-

ALTITUDE = 10.000 FT ELEVATION = 11.6O

-30-35

\

\

2&

h&P&

I

2864

I

& 3;O"

b"

340" liOa(4dDi AZIMUTH(DEG)~ I I

$0"

\iOo

I

lobo I& \

I \

i40" I

\

:b"~ O O o

-

Figure 5. Relative Field Intensity Measured at a Range of 14.8 km from a Monopole Antenna and Beverage Pair Antenna both Excited by a 9.75 MHz Transmitter.

50

10

-

m

-180

-

im

no SEA

-mo -I40

$ -

-

-120 8

WATER

WET RICH SOIL

*

b -

- *g w

- 80

U

-60

0 2-

40

I

- 40

-

XI 20

- 20

-

10 0

l

5

I

l

I

I

I

I

I

25 35 45 55 ELEVbTlON 8NGLE I D E G I

I5

ELEVATION ANGLE IDEG)

-

c

I

I

I

I

65

-0

I

85

75

POOR SCnL

-180

-160

8

-

.

!I

-140

-

9""

-

b

-100

f

Y)

Y

2

-120 n

-* Y

1 3

04-

- 8o

Y

I

- 60 a

0 2-

0 5

15

25

35 45 55 65 ELEUTION ANGLE (OEGI

75

85

- 40

-20 -

1 5

1

1

15

,

1

25

1 1 1 1 I I l l 35 45 % 65 ELEVATICU ANGLE I D E G I

I

IS

1

l 85

I

Figure 6. Reflection Coefficients at 10 MHz for Sea Water, Wet Rich Soil, Average Soil (Wet) and Poor Soil.

51

t ‘-160

-140

-

In

-120

-

g

-2 0

-100

-

Y

0

3

-80

-

%

9

- 60 IL

- 40

-

-20

O

ELEVATION ANGLE

IDEG 1

~

O DRY GRANllE 160

140

f * 2 0

I0

r.50

I-

- 180 DRY

E_

SAND

c* 5 0 mmha/m

55

+}w=

ELE

I = IOMH2

80

WN ANGLE

65

75

85

IDEG I

a

60

-40

-

- 20 O

L

r

5

r

‘5,

r

35 45 55 65 ELEVATION ANGLE IDEG I

75

85

Figure 7. Reflection Coefficients at 10 MHz for Average Soil (Dry), Dry Sand and Dry Granite.

52

120

1\

0 DISTANCE (mila)

Figure 8. Measured field intensity from a A/4 monopole antenna excited with a 9.75 MHz transmitter. Transmitter power has been normalized to 1 kw. Theoretical results are included and show fall off of field intensity with distance for werage ground (wet) and poor ground.

1972

I WY SOlL 2 POOR s a L ( D R Y ) 3 POOR SOlL 4 MR&ESOlL(ORI) 5 AVERAGE SOIL (WET) 6 WET RlW SOIL 7 SEA WATER

Figure 9. Comparison of field intensity measured at a distance of 0.610 km from position o f the center of the rosette array with theoretical values for earth types varying from dry sand to sea water.

54

e

W

P -10W

> F a

( a ) RELATIVE AMPLITUDE OF RF CURRENT ALONG ANTENNA.

40 60 80 100 120 DISTANCE FROM FEED POINT (METERS)

0

20

0

4

0

I2 16 20 FREQUENCY ( M H t )

24

Figure 11. Relative Amplitude and Attenuation Constant vs. Frequency for a Beverage Antenna.

55

AVERAGE SOlL (DRY)

EXPERIMENTAL I!

WET RICH SOIL

Figure 7 2. Cornporison of experimental current-wove ottenuotion ot Cambridge Boy and theoreticol current-wove ottenuotions for overoge soil (dry), overoge soil (wet) and wet rich soil.

56

P

Lu

r

8

c 8

AVERAGE SOIL (WET)

16.0

v = 3x 10" mho/m WIRE RADIUS = 1 . 0 2 6 ~ K ) ~(N* ~ m12 COPPER WIRE)

.84.82

2

4

6

8

0

12 14 16 18 FREQUENCY ( M H t )

20

22

24

u = IO-*mho/m WRE RAWS=1.02611IO'~m "112 COPPER WIRE)

I ,

2

r , 6I

4

I

I

8

I 10

I

,,

I

12 14 I6 FREWEMCY ( Y W

I

I8

I

H-30m --H=lOm

H=o.~

.9E c

3.9

s

n80.3m

.9:

WET RICH SOIL

= 26.0 0

= ~ X I O - **o/m

WIRE

RADWS 1.026 x 163m(W12 COPPER WIFE)

.82

2 . 4

6

6

10 12 14 FREQUENCY (MHZ)

Figure 14. Comparison of theoretical and experimental values of the current-wave velocity factor as a function of frequency for uverage soil (dry), average soil (wet) and wet rich soil.

20

I

Z2

I

I (LI

1

58

700-

AVERAGE solL(DRY)

(b 1

EXPERIMENTAL CURVE

w

a 100-

3

0 0

(a) Composite input impedance of 8-elements.

1

1

4

1

1

1

1

1

1

8 12 16 FREQUENCY (MHz)

1

1

20

1

I

24

(b) Comparison of experimental and theoretical input impedance for element #l.

19007

1800-

1700-

v)

1500-

(d)

1300-

I 51100-

W

900-

W

y

700-

-g

300100

1

1

0 2 4

1

6

1 8

1 1 1 1 1 1 1 1 10 12 14 16 18 20 22 24

(c) Input impedance of element #l terminated in a short circuit.

0

(d) Input impedance of element #1 terminated in an open circuit.

Debert Input Impedance Measurements on Beverage Antennas Terminated in an Open Circuit, a Short Circuit and the Antenna 3 Characteristic lmDedunce.

I

59

l l l 1 1 1 l l i 0

(a) Characteristic input impedance of element #1 derived from open and short circuit input impedance measurements.

1

I.'-

0 0.8-

s 0.6I-

[*-=

1

6

8 10 12 14 16 18 20 22 24 FREQUENCY (MHz 1

(b) Open and short circuit resonance number frequency.

(C)

EXPERIMENTAL CURVE WET RICH SOIL

2 4

-E

4

V W ~ J ~

WERIMENTAL CURVE

\

m 0

Y

SOIL (WET)

z 0

>- 0.4-

8c 0.2-

I

w o >

k

k

e

1 0

1 4

1

1

1

1

1

1

1

1

1

8 I2 16 20 FREQUENCY ( MHr 1

(c) Comparison of experimental and theoretical current-wave phase velocity for element #1.

1

I

1 I I 1 1 1 1 ~

I

I I I1111~

24

(d) Comparison of experimental and theoretical attenuation for element #l.

Figure 7 6. Debert Element #I Measured Chorocteristic Impedonce, Current- wove Phase Velocity and Comparison of Meosured Current- Wove Attenuation with Some Theoretical Curves

60

c

I

3

I

I

ON

I

I

(D

I

cu -I

I

I Q)

0

( W 8 P ) NOllVnN3UV

I

I

8

1

I

0

61

2 70.

Figure 18. Typical theoretical elevation and azimuthal radiation patterns for a Beverage element situated over average soil (dry) and whose length and height are 110 m and 1 m, respectively. The 3-dB vertical beamwidth B W p take-off angle $N, gain GN and 3-dB azimuthal beamwidth BWA as defined in Section 3.1 are illustrated. t

-

62

7oo

90"

-30

-35

GAIN

-25 (dBi)

-15

-20

Figure 19. This diagram demonstrates the source o f the discontinuities in Figs. 11- 1 to 11-48. In particular, it shows that the discontinuities in Fig. 11-36 are caused by a secondary lobe growing in magnitude with increasing frequency and surpassing the main lobe.

H=XOm

f

M-2.0n 2,

W h

I

...

-'

I

I

I

I

& I

0 , 0

I 00

=

~=a3m

? I

.- . .

I=K)yII

200 300 LENGTH l m )

1

1 400

" 1 0

I

no

I

200 LENGTH

I

500

I

400

(n)

Figure 20. Gain, azimuthal beamwidth, vertical beamwidth and take-off angle of a Beverage antenna on average soil (dry) at 10 MHz for lengths between 100 and 400 m and heights between 0.3 and 3.0 m.

63

5-

3-

-

-I

P

-I-

2 a

0

-3-

-5-

.OOl

.oOol

CONDUCTIVITY

I

.01 mho/m

FREOUENCY = 10 MHz

a

--&--

--____

H = I Om

I

I

I

001

01

01

CONDUCTIVITY

Imhoh)

Figure 21. Gain, and azimuthal beamwidth of a Beverage antenna at 10 MHz as a function of soil conductivity, length and height.

64

70-

60-

- 40-

-B

L=Kx)m.H 2 . 0 m

,L=Kxlm,

H13.0m

\. 0.O

I

\ I 0.I

I

I

,001

.01 CONDUCTlVlTY

(mho/m

ro60-

-d -I

50-

FREOUENCY = 10 M*

n

9 40m W

I

c-

30-

~

L *loom. H=3m

W J (3

z

a 20-

i5 5 W

j

10-

0-

.&

.01

0.1

CONDUCTIVITY (mhdm)

Figure 22. Vertical Beamwidth and Take-off Angle of a Beverage Antenna at 70 MHz as a Function of Soil Conductivity, Length and Height.

5

-1

EXPEMMENTAL f = 18 MHz L = llOm $ =5 6 '

-8

z 4

-12

=

-16

0

AVERAG ( DRY

-

/

H=03m

/ EXPERIMENTAL AT ABOUT I I a

2 02

o

06

+

w

14 18 HEIGHT ABOVE GROVND (rn)

22

0

8

4

12 16 FREOUENCY ( MHz )

701

20

28

24

(el

H=lOrn =

THEORETICAL AVERAGE SOIL ( D R Y )

0-1

rn THEORETICAL \ AVERAGE SOIL (DRY) A , AT THE NOSE

- __- -

----

\

'.

..

-*

5

-8

- -- -A,

$--94"

0

EXPERIMENTAL AT ABOUT 9'

-16

(b)

-20+7------77 02

104

0 06

10 14 18 HEIGHT ABOVE GROUND ( m )

22

1

0

1

1

4

1

8

1

1

1

1

1

12

16 FREOUENCY ( MHz 1

1

1

20

,

,

]

28

24

H=17m

'"1 10

0

4

8

12 FREOUENCY

16 ( MHz)

v

20

24

2

6

10

14 18 FREOUENCY ( M H z )

22

26

Figure 23. Comparison of Theoretical and Measured Values of Gain GN and Azimuthal Beamwidth BMfA o f a Beverage Antenna. The Measurements were made at Shirley Bay with the Antenna on Average Soil (Dry).

120-

100-

t

80c

m

$ 60W B m a

m 400

Y

E

9 20-

0-

-200. I

I

I

0.2

0.3

I

I

I

I

I l l

0.5 0.7

1.0

I

I

2

3

I

I

I I I I I

7 10 FREQUENCY ( M H r ) 5

1

I

20

30

I

I 50

I l l ]

I

70

100

Fam = Median of the hourly values of Fa within a time block. Fa = Effective antenna noise factor which results from the external noise power available from a loss-free antenna. Figure 24. Variation of Radio Noise with Frequency for a Receiving Beverage Antenna. Noise Data was Obtained from CClR Report 322.

67

270°

(a) Azimuthal pattern for Beverage antenna, L=llOm, H=1.7m and f=18MHz.

(d) Azimuthal pattern for Beverage antenna, L=llOm, H=1.7m and f=12MHz.

180°

0

270”

(b) Azimuthal pattern for Beverage antenna L=llOm, H=0.9 and f=18MHz.

270”

( c ) Azimuthal pattern for Beverage antenna, L = l 1Om, H=0.3m and f= 18 MHz.

.

.

‘

2jo”

(e) Azimuthal pattern for Beverage antenna, L=llOm, H=9.9m and f=l2MHz.

270°

(f) Azimuthal pattern for Beverage antenna, L=11Om, H=0.3m and 6 1 2MHz.

Figure 25. Measured azimuthal radiation patterns o f Beverage antennas for 12 and 18 MHz. The length of the antenna was 1 1 0 m and height was varied between 0.3 and 1.7 rn.

68

-

THEORETICAL-AVERAGE SOlL (WET)

80-

100-

L = IlOm H = 0.3m

EXPERIMENTAL

-

__-----

. *

JI

80

n

AZIMUTH

L = IlOm H = 1.7m f = l8MHz

(DEG.)

FMure 26. Comparison of theoretical and experimental patterns at 7 8 MHz for a Beverage antenna. The experimental patterns are those shown in polar form in Fig. 25 (a, 6, c).

-180

440

-100

-60

-2b

26

$0

I60

lk~

AZIMUTH ( DEG. 1

Figure 27. Comparison of theoretical and experimental patterns at 12 MHz for a Beverage antenna. The experimental patterns are those shown in polar form in Fig. 25 (d, e, f).

69

'RN

(a) The solid curves give the measured vertical radiation patterns for Beverage and A/4 monopole antennas obtained with a horizontally polarized XELEDOP. The dashed curve gives the theoretical pattern for a

A/4 monopole antenna.

130°

I100

7oo

goo

50"

30"

(b) Comparison of measured vertical radiation patterns for a Beverage antenna obtained with horizontally and vertically polarized XELEDOPs.

130"

70°

I100

50°

t

30"

too -70

-80

-90

-100 -110

-120

-110

-100 -90

-80

-70

dB/m (c) Comparison of measured and theoretical vertical radiation patterns for a Beverage antenna.

figure 28. Comparison of theoretical and measured vertical radiation for a Beverage antenna at 78 MHz. The measurements were made at Shirley Bay on a Beverage antenna whose length was 110 m and height was 1.7 m.

70

ANTENNA WIF

E TO RECEIVER

Figure 29. A Portion of the Beverage Rosette Array.

i

W

SCALE

Figure 30. Modified Plan View of the Beverage Antenna Array Showing the Azimuths of the 72 Fixed Beams.

--

c

71

(a) Azimuthal pattern of Beverage pdir antenna. Measurement was made with a vertically polarized XELEDOP antenna. This pattern was shown in rectilinear form in Fig. 5.

(b) Comparison of azimuthal pattern obtained with the vertically polarized XELEDOP and skywave of opportunity.

Comparison of azimuthal patterns obtained with the vertically polarized XELEDOP and a vertical dipole and transmitter suspended from a Balloon.

Fiwre 31. Comparisons of measured azimuthal radiation patterns at 9.75 MHz for a Beverage pair antenna at Cambridge Bay.

72

34-

-

0

+

30-

-

-$

+

26-

Ib

-

0

22-

W - 1 -

+ +

BALLON MEASUREMENTS SEPT 1972 o AIRCRAFT MEASUREMENTS A N . 1974 ~. THEORETICAL CURVE + 3 dB FOR AVERAGE SolL (DRY) +

(3

z

18-

z 0

I-

-

9 w

14-

w

-

J

+

0

IO-

* o

6-

-

2I

+

+

+O0+

+ +O +

0

I

+

I -5

0

:

I

L

I -15

40

-

7

-20

GAIN (dB)

Figure 32. Vertical Radiation Pattern for the Beverage Pair Antenna Pointed T0ward.s Alert at a Frequency of about 9.5 MHz.

1300

I10'

!

30°

,

.lo'

.OO 0

-10

-20

-30' AMPLITUDE

AIRCRAFT (XELEDOP)

-30

- dB

------BALLON

-20

-10

--THEORETICAL AVERAGE SOIL (DRY)

Figure 33. Comparison of theoretical and measured radiation patterns for a Cambridge Bay Beverage pair antenna. The balloon measurements were made at 9.0 MHz and the XELEDOP measurements were made at 9.75 MHz. The theoretical curve was derived for a frequency of 9.5 MHz and average soil (dty). c

73

18.5MHz

\

-120

' , 0

1

1

80

40

i

120

~

i

1

i

~

i

160 200 240 280 AZIMUTH (DEGREES)

~

320

1

360

Figure 34. Mutual Coupling Between Antenna Elements of the Rosette Array.

-

280-

w 240Iw 2 200w

v

0

z

e V)

* 2 5

16020dB

I

0

I 4

I

I

8

I

1

I

I

I

I

12 16 20 FREQUENCY ( MH t )

1

I 24

Figure 35. Attenuation Contours for R F Currents on a Beverage Antenna.

1

1

~

'

~

74

140°

80°

I20°

60°

4oo

20°

1600,

e

- O0

180O-

200"-

-340O

2200

240°

260°

280°

3oO0

320°

(a) Theoretical vertical radiation pattern for a Beverage antenna at 125 kHz over poor soil (dry).

140°

120°

80°

600

40°

ISO0-

* WOO-

2000-

220°

240°

260°

280°

300°

320°

(b) Theoretical azimuthal radiation pattern for a Beverage antenna at 125 kHz over poor soil (dry).

Figure 36. Theoretical radiation patterns for Beverage antennas situated on poor soil. The length of the antenna is 2.4 km and its height is 7.62 m.

75

THEORETICAL CURVE - CAMBRIDGE BAY

‘01

CAMBRIDGE BAY

U W

/

-15

/

-20

’

-25

I

0

,

2

(NEAR RICHMOND) V = .03mho/m c=

I 4

I

24

I

I

6 810 FREQUENCY (MHz 1

I

20

I

I

30 40

Figure 37. Comparison of Experimental and Theoreticalhrface Wave Gains of Beverage Pair and Single Beverage Antennas for Average Soil (dry) and Wet Rich Soil, Height = I m and Length = I I0 m.

I 0 ASCENT , A DECENT

30°,

y-.

‘ . .

Figure 38. Field Intensity at the Center of the Array From a Balloon-Suspended Transmitter.

.+ .+.+. .+.DESCENT ASCENT /

FREQUENCY = 9 MHZ

+

/

dBi

dBi

Figure 39. Gain of Beverage Element vs. Elevation Angle.

76

BEVERAGE PAIR ANTENNA

MONOPOLE ANTENNA

Signal-to-interference taken almost simultaneously on a Beverage pair antenna and a quarter wave monopole antenna for 12 consecutive time intervals. I

Interval

1 2 3 4 5 6

+5 +14

10 11

+30 +19 +21 +15 +34 +23 +26 +37 +14

12

+5

7* 8* 9* *

Signal-To-Interference Ratio (dB) Beverage Pair Monopole

- 13 -3 +12 +8 +10 -2 +4 0 -16 +6 +16 +16

* Spectrum analyzer outputs shown above.

Figure 40. CR T displays of a spectrum analyzer connected alternately to a monopole antenna and a Beverage pair antenna. In each instance the Alert signal appears at the center of the display and the other signals are interferringsignals. The I F bandwidth of the spectrum analyzer was 3 kHz; the width of the spectrum window scanned was 2 MHz and the scan time was 0.1 secfdiv. Table show some measured signal-tointerference ratios on the two antennas.

77

1

1

1

1

1

1

1

1

1

1

1

I 2 3 4 5 6 7 8 9 D i l i ! 2 i 3

(a) Sequential sampling of the terminal voltages of the (c) Sequential sampling of the terminal voltages of the 12 Beverage pair antennas at Cambridge Bay monitoring 12 Beverage pair antennas at Cambridge Ba$, wwv on 15 MHz somewhat latter in time than (b). monitoring wwv on 10 MHz. The sampling time for each antenna was 1.2 psec and the I F bandwidth of the receiver was 10 kHz.

(b) Sequential sampling of the terminal voltages o f the 12 Beverage pair antennas at Cambridge Bay, monitoring wwv on 15 MHz.

(d) Sequential sampling of the terminal voltages of the 12 Beverage pair antennas at Cambridge Bay, monitoring wwv on 15 MHz, somewhat latter in time than (c).

Figure 41. Photographs o f the CRT display of an oscilloscope monitoring the video output of a receiver whose input is connected in rapid succession by a diode switch t o the 12 Beverage pair antennas at Cambridge Bay monitoring wwv.

78

." 1924 LT 2 OCT 1972 EEC LONDON 6.11 MHZ

003

223

343 323

283

303

243 263 283

303

1550 LT '

\ I

I43

123

.'

\

~

103 083 0 6 3, 0 4 3

.

2 OCT 1972 4 3 w w v 20MHZ

323

313 333 6

4

1415 LT 24 SEPT 1972 353 W W V 25MHz

Figure 42. Direction Finding Patterns Obtained With the Beverage Array from Known Transmitters. 323

343

003 023 043 063

083 22 SEPT. 1972 2300 LT RADIO JAPAN TOKYO 21 MHz

143

203

223

2

!63 283

303

323 9 OCT. 1972 43 1034 LT W W V l5MHz

'I43/ / / / / I 123

103 C

Figure 43. Further Examples of Direction- Finding Patterns on Signals from Known Transmitters.

*

.

79

BEVERAGE ANTENNA

i 7

TO OPERATIONS BUILDING

L

4134.55'-

TO ALERT

E

L-

o 0

3

4:l POWER COMBINER SWITCH BOX WITH PHASING CABLES 2:l POWER COMBINER

Figure 44. Schematic of the 32-Element Linear Phased Beverage Array Installed at Cambridge Bay, N. W. 7:

80

c.

v)

w

.

W

I

a

FREOUENCY (MHr)

W

m

* (d)

Azimuthal beamwidth of the Cambridge Bay linear array.

0

4

8

12 16 20 FREOUENCY ( MHt)

24

26

(b) Directivity gain of the Cambridge Bay linear array.

c

0 L

4

8

I2 20 FREOUENCY ( MHr 1

24

26

PRIMARY GRATING LOBE

---- SECONDARY GRATING LOBE B- PRIMARY LOBES DOWN AT LEAST 13 dB 5

(c) Azimuths of the primary and secondary grating lobes of the Cambridge Bay linear array.

Figure 45. Azimuthal Beamwidth, Directivity Gain and Location of Grating Lobes for the Cambridge Bay Array.

-40

c40

-*

-*

- -N

--(u

-0

-0

-Y

7

-7 -? -?

-cu

n Y

1

"Q -?

rK

W W

-z

-0 n

-Y -7

0

0 -'u

0

Y

I

I

I

Q

-W

-w

-W

-*

-*

--o

--N

- -N

--N

-0

-0

-0

--N

-? -? -?

-

-0

-cu

0

Y

I

I

0

9

rr) I1

a

W W

!7i

0

-7 -'Q -?

:

-*

a

"Q -?

-?

n

-G

0 Y

I

-Y

I

-7

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(a) Current amplitude measured across the aperture of the Cambridge Bay linear phased array at the terminated ends of the Beverage elements.

(b) Comparison of the theoretical and measured radiation patterns o for the Cambridge Bay linear array at 9.75 MHz.

Figure 47. Sampling of the Current Amplitude Across the Aperture of the Cambridge Bay Linear Phased Array and a Comparison of Theoretical and Experimental Radiation Patterns.

83

(b) Theoretical azimuthal pattern at 10 MHz of a weighted 8-element linear phased Beverage array with an aperture of 149m. Cos2 weighting was applied to the antenna aperture.

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(a) Theoretical azimuthal pattern at 10 MHz of an unweighted 8-element linear phased Beverage array with an aperture of 149m.

Figure 48. Theoretical Patterns at 10 MHz of an Unweighted and Weighted Linear Beverage Array With an Aperture of ISOm.

84

400

800

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140°

(a) Two-elements

320

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240°

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.

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(b) Four-elements figure 49. Theoretical 7 0 MHz azimuthal pattern for a Beverage antenna array with a 150m aperture. The elements are 17Om long and their he&ht above ground is 2m.

85

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(b) Sixteen-elements Figure 50. Theoretical 10 MHz azimuthal pattern for a Beverage antenna array with a 150m aperture. The elements are 11 Om long and their height above ground is 2rn.

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320'

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280'

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Figure 51. Theoretical 10 MHz azimuthal pattern for a Beverage antenna array with a 15Om aperture. The elements are 1IOm long and their height above ground is 2m.

- 70

ELEMENT LENGTH = llOm ELEMENT HEIGHT = 2 m AVERAGE GROUND (DRY 1 APERTURE = 150m

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Figure 52. Directivity gain, power gain and efficiency at 10 MHz of a Beverage array with an aperture of 150m as the number of elements in the array is increased from 1 to 64. The length of each element is 1 lorn, its height above ground is 2m and the elements are sited on average ground (dry).

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Figure 54. Difference in the SNR of the 10.6 MHz Alert signal received on the 8-element Beverage array with that received simultoneously on a XJ4 monopole antenna. This data was taken on 7 October 1974 between 1210 and 1530 LT. 50-

GAIN OVER MONOPOLE

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figure 55. Gain of an 8-element Beverage orray with rewect to o X/4 monopole. Both antennas were locoted ot Ottawa and were simultaneously monitoring o sky wave signal emanating from a transmitter ot Alert.

A P P E N D I X

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Theoretical Curves for Attenuation, Characteristic Impedance and Velocity Ratio

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Figure 11- I . Des&n Parameters for Poor Soil (Dry), H = 0.3m, L = I OOm.

-

L = 200 rn H * 0.3 rn =6 u = 0.3 x I0-3rnho/rn

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Figure 11-2. Design Parameters for Poor Soil (Dty), H = 0.3m, L = 2OOm.

1

24

1

99

90-

80-

-

L=300m H=O 3 m

€=a

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50-

r-I3

Figure 11-3. Design Parameters for Poor Soil (Dry), H = 0.3m, L = 300m.

r 3

90-

80-

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-

L= 400m

H=03m

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figure 11-4. Design Parameters for Poor Soil (Dry), H = 0.3m, L = 400m.

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100

i

L=IOOm H=lm

c.8

U = O . ~ X10-5mho/m

70

- -I

60

--3

-

-5 I

--5

-- -75*

Figure 11-5. Design Parameters for Poor Soil (Dty), H = lm, L = 1Oom.

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907

-

L.200 m H = lm .a8 u = 0.3x 10-

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mho/m

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I

Figure 11-6. Design Parameters for Poor Soil (Ow), H = lm, L = 2oOm.

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101

L.300 m

H=lm t.8

o =O . ~ X I O m - ~h o h

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Figure 11-7. Design Parameters for Poor Soil (Dty), H = lm, L = 30Om.

90

-

00-

L=400m H=lm c = 8 v = 0.3x10-3mho/m

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FREOUENCY (MHZ)

Figure 11-8. Design Parameters for Poor Soil (Dry), H = lm, L = 400rn.

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901

r4

L = lOOm H=2m r.8 -3 u = O 3x10 mho

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Figure 11-9. Design Parameters for Poor Soil (Dry)l H = 2rnlL = I OOm.

F'

L = 200m

H=2m

2

0

-

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0

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FREQUENCY (MHZ)

Figure 11- 10. Design Parameters for Poor Soil (Dry)l H = 2m, L = 20Om.

l

103

L=300m

Fiaure Il-11. Design Parameters for Poor Soil (Dry), H = 2m, L = 300m.

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L = 4 0 0m H.2 m f U

=e

= 0.3 x 10- mho/m

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l

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Figure 11-12, Design Parameters for Poor Soil (Dry), H = 2m, L = 4mm.

l

24

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104

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20

22

24

Figure 11- 13. Design Parameters for Poor Soil (Dry), H = 3m, L = 1OOm.

90-

eo-

- 6 L=200m H=3m c=8 Q - 0.3 x 10-3mho/m

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1

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1

1

12 14 16 FREOUENCY (MHZ)

1

1

18

1

1

20

1

1

22

Figure 11- 14. Design Parameters for Poor Soil (Dry), H = 3m, L = 200m.

-12 24

L=300m H=3m U = 0.3 x 10-

rnho/rn

. I

Ftjure 11- 15. Design Parameters fo: Poor Soil (Dry), H = 3m, L = 300m.

90

-

-- 6

L.400 rn

-

-

H=3m

80-

- 4

cr = 0 . 3 ~ 1 0 -mho/rn ~

-

70 -

- 2

-

-

-

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60 -

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W

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W

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a

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10-

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I

2

4

6

8

1

1

10

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r - r v 18

20

1

22

Figure 11-16. Design Parurneters for Poor Soil (Dry), H = 3m, L = 4OOni.

24

106

L

90-

80-

L = 100 m H.0.3 m €=I2

-2

u =0.003 rnho/m

-

-0

-

-

70

-

--2

-

60I

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-- 4

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p 50-

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w

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a

w

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m

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30-

-

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20-

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10-

-

1- 14

Figure 11-1 Z Design Parameters for Average Soil (Dry), H = 0.3m, L = 1OOm.

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10

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Figure II- 18. Design Parameters for Average Soil (Dry), H = 0.3m, L = 200m. -. c

.

m

0

105

L.300 m H=3m U = O . ~ X I O mho/m -~

2

4

6

8

10

12

14 16 FREOUENCY ( M H z )

18

20

22

24

t :::

F w r e 11- 15. Design Parameters fo. Poor Soil (Dry), H = 3m, L = 300rn.

90 -

80 -

-6 L.400 m H = 3 m C . 8

u = 0.3 x 10- mho/m

-4

70 -

-2

60 -

-0

50-

--2

-

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W

W J

0

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z

a

-- 4 w

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10-

-12

Figure 11- 16. Design Parurneters for Poor Soil (Dry), H = 3rn, L = 40Oni.

106

L- 100 m Hr0.3 m I?=

t

12

U =0.003

mho/m

-I\

70

t-4-

-

10-

0

- -14 I

2

I

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l

l

6

l

FREOUENCY (MHz)

Figure 11-1 7. Design Parameters for Average Soil ( D I ~ )H, = 0.3m, L = loom.

'01

:H; Y=0.3 O mm

80

u = 0.003mhdm

to

L.

-2

J

-I4

107

-

90-

t = 300 m

-

H.O.3 m f = 12

-2

-

u = 0 003 mholm

80-

-

-0

-

70-

-

--2

-

-- 4 .-

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14

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24

FREQUENCY ( M H r )

Figure 11-19. Design Parameters for Average Soil ( D I ~H) ~ = 0.3m, L = 300m.

90-

L . 4 0 0 rn H =0 . 3 m

-

2

6.12 cr= 0.003rnho/rn

80-

-

0

70-

-

c

-2

60-

- -

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v)

-zm

W

0

50W

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-

0

--6Z

-

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W

z

a .

-

30-

-

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20-

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-

10-

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W

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2

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4

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6

1

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8

I

10

I

I

,

I

I

I

12 14 16 FREQUENCY ( M H s )

I

1

18

1

1

20

1

1

22

1

1

24

Figure 11-20. Design Parameters for Average Soil (Dry)l H = 0.3m, L = 400m.

1

'

0

4

--8

10-

-f

m

108

90-

L.100 m

-

H=lm

€.I2 Q = 0.003 m b / m

80-

-

\

70-

60-

*

w

-

-w

-

W

: 50W 0

w 402

(3

z a

-

I:

30-

- 10

20-

10-

FREQUENCY ( M H t )

Figure 11-21. Design Parameters for Average Soil (Dty), H = lm, L = 1O h . 901

80-

L92OO m n=lm € = 12 Q9 0.003 m b / m

-

70-

-

-

66-

I n -

W W

a 50-

8 0 340-

W t

4

-

30-

-

20-

10-

-

1- 14

Rgure 11-22. Design Parameters for Average Soil (Dry), H = lm, L = 2OOm. c

-

109

L =300 rn H=lrn

80-

= 12 cr = 0.003 mho/m

E

70-

-

- 60U

Y

W

-

50-

CJ W

D

-

w 40J

0

z

-

a

30-

20 10-

-

Figure 11-23. Design Parameters for Average Soil (Dry), H = lm, L = 300m.

90-

80-

L =400 H=lm c =I2 Q=

0.003 m h o h

70-

*

U

F:

60Y

-

W

50W

-n W

W

J

W

z

a

40-

-

30-

20 10-

-

1

-I4

Figure 11-24. Design Parameters for Average Soil (Dry), H = lm, L = 400m.

1.10

90-

- 4

€=I2 0.003 mho/m

-

Q=

80-

*

-

L =I00 H = 2m

70-

-

60-

-

5 W

-2

-0

-

--2

500

w

-

-

0

--4

-

40(3

z

-

a

--6

-

30-

-

- -8

-

20-

-

--I0

-

10-

-

--I2

0

I

I

I

2

I

I

I

6

4

I

I

I

I

12

10

8

I

I

14

I

I

16

I

18

I

~

1 I 1 ~I

20

22

I

I

24

Figure 11-25. Design Parameters for Averuqc Soil (Dry), H = 2ni. L = I VOni.

L =zoo H.2 m

,

6 =I2 cr= 0.003mho/m

I

0-

2

4

A

6

8

r

I- I I - T T - 7 1 7 - T - T - l 12 14 16 18 20 22 FREOUENCY (MHz)

I T 10

F i y i m 11-26. Design Purarneters for Average Soil (Dry),

I

H = 2rn, L = 200rn.

I+ 24

f m

-

0

f a (3

111

L =300 H:2m f = 12 5 ; 0.003 mho/m

7

1

8 O i

I

1

I

707'

604

0

40 (3

z

a 301

20-1

I 1

2

4

6

8

10

12 14 16 FREOUENCY ( M H z )

18

20

22

24

Figure 11-27. Design Parameters for Average Soil (Dty), H = 2m, L = 300m.

-

gO1

L=400m H=2m c = 12 170.003 mho/m

""1

- 4

- 2

-

70

-0

-

60

m

w W

W

0

-

--2

50-

-

z a

.m

--4f

-

-

40W

-

0

-

--6

-

30-

--8

-

20-

--I0

-

10-

-

,--I2

2

4

6

8

10

12 14 16 FREOUENCY (MHz.)

18

20

22

Figure 11-28. Design Parameters for Average Soil (Dry), H = 2m, L = 400m.

24

a w

112

j 90

00

*

w

n"

'I L=ZOO m I4~3.m 812

u 0.003 m W m

'4

-.

113

90-1

~ = 3 0 rn 0 H=3m c = 12

u =0.003mho/m

80

70

i

60

0 W J

0

40

z

20

- 12 2

4

6

8

10

12 14 16 FREQUENCY ( M H z )

18

20

22

24

Figure 11-31. Design Parumeters for Average Soil (Dry), H = 3m, L = 300m.

L = 4 0 0 rn H=3m c.12

u =0.003 mholm

* 60

1: 6

--2

--4

--6

-- 8

- -10

-

Figure 11-32. Design Parameters for Average Soil (Dry), H = 3rn, L = 400rn.

-.f a

*

114

80-

70h

60c3

v

L = lOOm H = 0.3m Q = 26 6 0.03mho/m

--I0

h

iz

Y

t

W J

a

0

50-

Y

-45 z

zW

40-

30-

--20

20-

Figure 11-33. Design Parameters for Wet Rich Soil, H = 0.3m, L = 1OOm.

- -5

9080-

70-

--to

4

-Ei 60- 50-

H = 0.3m 6

P

W J

W

= 26 0.03mho/m

c

g

Q=

Y

--I5 Z

40-

a

z a 30-

(3

20-

--20

IO0-

I

5

10

15 20 FREQUENCY ( MHz

Figure 11-34. Design Parameters for Wet Rich Soil, H = 0.3m,

25 L = 200m.

115

i

i.-300 m H = 0.3 m

-6

t=26 U= 0.03 m h o h

-8

- 10

j

60

"'

5

--I4

a

-

0

--I6

--I8

- - 20

-

t

-22

Figure 11-35 Design Parameters for Wet Rich Soil, H = 0.3m, L = 3OOm.

-

90-

L=400m H =0.3m c =26 u = 0.03mho/m

80-

--6

-

-

--8

-

70-

--I0

-

-

60-

-I n -

--I2 -

50-

W

0

-

'fl 400

z

--I4

$

-

(3

-

3P-

-

--I8

-

20-

-

--20

-

10-

0

D

--I6

-

a

m

I

-

W

- - 22 I 2 -

I

I 4

I

I 6

I

I 8

I

I 10

I

I 12

'

Ih

I

~

16

I

18

r

I 20

l

22

I

FREOUENCY (MHZ)

Figure 11-36. Design Parameters for Wet Rich Soil, H = 0.3m, L = 400rn.

I

22

'

I

~

116

- 2

90i

901 -

L =100 m H=l m

8080-

u =0.03 mho/m

-J

-0

-

-- 2

70-

e

g -

-- 4

60-

m

-

w

--6

50-

W W n

-

-

y 405 W 2

5

a

--8 0

-

a

- -10

30-

--I2 20-

-

- -14

10-

0

I 2

~

-

~ 4

~

I

~

t

)

I

I

b

I

I

b I I I A 1I8 1 I I 20 I 6I

22 1

1

24 1

-I6

1

6

FREQUENCY (MHZ)

Figure 11-37. Design Parameters for Wet Rich Soil, H = Im, L = JOOm.

c

~=200m H=l m E =26

00 -

- 2

-

u =0.03mho/m

-

-0

-

70-

--2

1

--4

=m

- 0

--6

z

5 U W

-- 8

-

-

--I0

- -12

--I4

0 2I

I

4I

'

6

I

I,

'

~b

1 1 1 I :I 14 16 FREQUENCY (MHZ)

~ 18

1 20

1

' 22

Figure 11-38. Design Parameters for Wet Rich Soil, H = lm, L = 200m.

~ 24

1

~

~

1

~

117

-3

'

-I

- -I

- -3

- -5

.m

- za W

---7

--9

--I1

7-13

0

-

1

+

-

2

-

,

4

1

1

6

1

[

8

,

1 10

1

1 1 1 1 , 1 , 12 14 16 18 FREQUENCY (MHr)

1

I1 I

20

I

I

22

Figure 11-39. Design Parameters for Wet Rich Soil, H = lrn, L = 300m.

Figure 11-40. Design Parameters for Wet Rich Soil, H = lm, L = 400m.

I

-

24

118

90-

-

-

80

70-

60I

e

v ) -

W W

g 50-

w

-

0

40(3

z

-

a

30

-

20-

Figure 11-41. Design Parameters for Wet Rich Soil, H = 2m, L = loom.

8

90-

L=200m H.3 m c.26 U = 0.03mhdm

80-

-

6

70-

4

60-

2

I

v

)

w

50-

w

5 0

-

W 40J (3

z a

30-

20-

-

'"1 I 01

1

2

1

I

4

I

I

6

I

I

Ib

I

I

I I I 14 16 FREOUENCY (MHt)

12

I

I

1 18

1

I 20

I

I

22

Figure 11-42. Design Parameters for Wet Rich Soil, H = 2m, L = 200m.

I

I

22

I

'

-10

119

l01 I

0

1-

1

2

4

1

1

8

6

1

1

10

I

I

I

I

I

I

12 14 16 FREOUENCY ( M H r )

I

I

18

1

I

20

L

22

o

24

Figure 11-43. Design Parameters for Wet Rich Soil, H = 2m, L = 300m.

90-

L=400m

-

-

H=3m

26

E -

80-

-6

U - @.03mho/rn

-

70

-

- 4

-

?

- 2

60m W

50CJ

- 0

0

-

W

-

z a

5

4

- - 2cl

w J 40CJ

-

-

-

-

3’0-

- -4

-

-

20-

--6

-

10-

0

1

2

1

1

4

1

1

6

1

1

8

1

1

1

10

12 14 16 FREOUENCY (MHz)

1

1

1

1

I

I

I

18

1

1

20

1

I

I

22

Figure 11-44. Design Parameters f o r Wet Rich Soil, H = 2m, L = 400m.

,

24

!

- 10

120

I

I

I

I

Figure 11-45. Design Parameter for Wet Rich Soil, H = 3rn,

I

5

10

I

I

L = 1OOrn.

15 20 FREQUENCY ( MHz

25

Figure 11-46. Design Parameters for Wet Soil, H = 3m, L = 200rn.

-.

121

-5

,O-i

- 60

c

L = 300m H= 3 m

/ /

Y

-0

C =

26

Q=

0.03mho/m

5 c3

c3

z

- -5 20

IGN

--I0

I

I

I

I

I

Figure 11-47. Design Parameters for Wet Rich Soil, H = 3m, L = 300m.

9 0 -5

.-

c5

60

m 0

L = 400m H= 3 m 26 Q = 0.03mho/m

GN

50

Y

€ =

- 02

a

c3

- -5

I

I

1

5

10

I 15 FREQUENCY

I

I

20

25

( MHz

Figure 11-48. Design Parameters for Wet Rich Soil, H = 3m, L = 400m.

- -10

122

A P P E N D I X

I 1 1

Theoretical Curves for Surface Wave Gain

123

l01 54

H=3m H=2m

n

H= Im

a 2

-5

(3

-l01

e

f

POOR SOIL (DRY) L=100 m

POOR SOIL (DRY) L = 200 m

1 [ 51 -

0

5

0

10 15 20 25 30 FREQUENCY ( MHz)

5

10 15 20 25 30 FREQUENCY (MHz)

I

‘Ol

H=3m H=2m H=lm AVERAGE SOIL (DRY)

1

-15

I

5

0

AVERAGE SOIL (DRY)

1 I I I 1 10 15 20 25 30 FREQUENCY ( MHz

0

5

10 15 20 25 FREQUENCY (MHz

30

.-

-10

-%-z -5

2

I

L=100 m

-10

L= 200 m

-25- I

I

I

I

I

I

I

-20

0

5 10 15 20 25 FREQUENCY ( MHz)

30

Figure Ill-I. Theoretical Surface Wave Gain of Beverage Antennas with Lengths of 100 and 200rn1 Heights of I , 2, and 3m Over Poor Soil (Dry), Average Soil (Dry)l and Rich Soil (Wet). ,/

124

POOR SOIL (DRY) L = 300m

s 0-E:l!) z

H-3m

h Y

-5-

0-

(3

-10

I

I

I

I

AVERAGE SOIL L=300m

.-

I

(DRY)

5-

200 m

-I5

I

I

I

I

I

AVERAGE SOIL H = 0.3m

5 H=3mz

CI

(DRY)

i;;-- ; n

5-

e

POOR SOIL H = 0.3 m

5

I

1

(DRY)

0-

2

-5-

(3

-10I

-7I'

I

I

I

I

1

-10-

-15-

I

I

I

I

I

1

L = ~ V O ~

-I 5

0

5

10 15 2 0 25 30 FREQUENCY ( MHz 1

0

5

10 15 20 25 30 FREQUENCY ( MHz 1

Figure 111-2. Theoretical Surface Wove Gain of Beveroge Antennas with o Length of 300rn, Heights of I , 2, ond 3m over Poor Soil (Dry), Averoge Soil (Dry) ond Rich Soil (Wet). Curves ore also Given for o Height of 0.3rn, Lengths of 100, 200 ond 300rn and Poor Soil (Dry), Averoge Soil (Dry) ond Rich Soil (Wet).

125

A P P E N D I X

I V

An Analysis o f the Beverage Antenna and Its Applications t o Linear Phased Arrays In the analysis which follows consideration is given to the formulation The work follows the notation of Beverage and Herlitz(1,lO) and is extended in order to consider the effects of mismatching at the terminating end. Since the response of this antenna is greatly affected by the ground constants over which the antenna may be installed, an in-depth analysis is included in order to determine the antenna response for varying ground parameters that are likely to be encountered. The work also includes the application of the Beverage antenna to linear phased array systems. of the elevation radiation pattern for the Beverage antenna.

1 26

S E C T I O N

1

Analysis of t h e Beverage Antenna

*

Consider a p l a n e wave i n c i d e n t on t h e Beverage antenna a t some elevat i o n a n g l e 3, and p r o p a g a t i n g i n t h e d i r e c t i o n as shown i n Figure IV- 1. For an elemental l e n g t h dx from p o i n t P, where P is midway between A and B , a v o l t a g e Vgdx w i l l b e induced on t h e l i n c The magnitude of t h i s v o l t a g e w i l l be d e p E d e n t on t h e p a r a l l e l component E of t h e v e r t i c a l l y p o l a r i z e d e l e c t r i c P f i e l d Ev such t h a t

- -

E = Ev s i n I) cos 8 P

(1:l)

where 8 i s t h e azimuthal a n g l e of t h e p l a n e wave w i t h r e s p e c t t o t h e antenna. However, i f w e assume f o r t h e moment t h a t 8 i s z e r o t h e n

- -

E = Ev s i n I) P

Since

k-

P

(1:2)

l i e s parallel t o the l i n e a p o t e n t i a l gradient r e s u l t s giving -dv =

dx

E

( 1 :3)

P

?

Therefore t h e v o l t a g e induced i n t h e l i n e i s ( 1 :4) Equation (1:4) may be thought of a s a v o l t a g e g e n e r a t o r on t h e l i n e i n s e r i e s w i t h two impedances ZIN(A) and ZIN(B), where ZIN(A) i s t h e impedance looking i n a t P towards A and ZIN(B) i s t h e impedance l o o k i n g i n a t P towards B , g i v i n g r i s e t o an elemental c u r r e n t i where S

127

P L A N E WAVE /

DIRECTION OF / PROPOGATION

B

Figure I V - I . Model o f the Beverage Antenna

ZIN(A) and ZIN(B) may b e e x p r e s s e d t h r o u g h t h e u s u a l t r a n s m i s s i o n l i n e e q u a t i o n s (See f o r example s k i l l i n g ( l 1 ) ) as

ZL ZIN(A)

+

= Zo

20

+

j Z 0 tanh

jZ,

tanh

y y

($ -

x)

]

(1:5)

(1:6)

y i n e q u a t i o n s (1:5)

y=a+jf3

L

where

and (1:6) i s t h e complex l i n e c o n s t a n t d e f i n e d as

a

(1:7)

is t h e a t t e n u a t i o n c o n s t a n t i n n e p e r s p e r u n i t l e n g t h

f3 i s t h e p h a s e c o n s t a n t i n r a d i a n s p e r u n i t l e n g t h ZB i n e q u a t i o n (1:6) r e p r e s e n t s t h e t e r m i n a t i n g impedance a t B. w e assume a p e r f e c t l y matched s y s t e m , t h e n Z

--

b

.

IN

(A) = Z

IN

(B) = Zo

However, if

(1:8)

128

then, V dx

(1:9)

3 L

2ZO A t p o i n t x t h e phase a n g l e of t h e c u r r e n t is w i t h r e s p e c t t o P w i l l b e determined through t h e propagation l e n g t h x-cos JI t o b e

*

i

S

(1:10)

=

c i s t h e v e l o c i t y of l i g h t

where

w i s t h e r a d i a n frequency

The induced c u r r e n t i s w i l l c a u s e a c u r r e n t wave t o traverse t h e w i r e i n t h e d i r e c t i o n of propagation, t h a t i s , towards B. This c u r r e n t wave may be expressed as (12)

\ = i e -Y 8

(+- .>

(1:11)

and t h e r e f o r e (1:12) Combining t h e exponents i n x and f a c t o r i n g o u t t h e c o n s t a n t term r e s u l t s i n (1:13) c

Since y =

a

+jB

then,

ib

V =gdxe 2ZO

-(a

+ 36)

R

2 e

(=

+ jB

C

(1:14)

The phase c o n s t a n t of t h e l i n e B , may b e expressed as

.

B = -w 1.1

(1:15)

where p i s t h e v e l o c i t y of propagation of t h e w i r e , t h e r e f o r e (1:16)

--

c

-.

129

where N

1!

= C

The t o t a l c u r r e n t a t B a s a f u n c t i o n of t h e e l e v a t i o n a n g l e $ w i l l b e t h e sum of t h e e l e m e n t a l c u r r e n t s o v e r t h e t o t a l l e n g t h of t h e l i n e , o r i n o t h e r W O Y d S , t h e i n t e g r a l of e q u a t i o n (1:16). S i n c e P h a s been chosen as t h e r e f e r e n c e p o i n t , w e may i n t e g r a t e them to R thus, 2 2

(1:17)

- -R

2

which r e s u l t s i n

[y]

Rsinh

(1:18)

YlR 2

where y1 =

a

+

jB ( 1

-

(1:19)

N c o s $)

Thus e q u a t i o n (1:18) may b e used t o c a l c u l a t e t h e e l e v a t i o n r a d i a t i o n p a t t e r n of a p e r f e c t l y matched Beverage a n t e n n a t h a t i s , when ZL = Z O . However, a c h i e v i n g a p e r f e c t l y matched system i s e x t r e m e l y d i f f i c u l t , e s p e c i a l l y when o p e r a t i n g o v e r a wide f r e q u e n c y r a n g e , and t h e r e f o r e one must c o n s i d e r t h e e f f e c t s of a mismatched system. I n o r d e r t o u n d e r s t a n d t h e e f f e c t s of mismatching, c o n s i d e r a s i g n a l impinging on t h e a n t e n n a w i r e from t h e r e v e r s e d i r e c t i o n ( i . e . >go"). A c u r r e n t wave ia w i l l r e s u l t and w i l l p r o p a g a t e towards A where

+

c

V i

a

= Ad x e j 2Zo

wx c o s c

q.J

e

-Y

(+ -

x) ( 1 :20)

Combining t h e exponents i n x and f a c t o r i n g o u t t h e c o n s t a n t term i n t h e same manner as f o r i ( e q u a t i o n ( l : 1 6 ) ) r e s u l t s i n b i a

Vdx

= L e

- -Y2R

e

220

[a

+

jB ( 1

+M

cos $ ) ] x

(1:21)

The t o t a l c u r r e n t I a t A as a f u n c t i o n of $ t h e e l e v a t i o n a n g l e i s s i m p l y t h e i n t e g r a l of e q u a t i o n (1:21) t h u s ,

V I,($)

= A 2zo e

R -

- -Y R 2

I. _ -R

r

2

[a

+ jb

(1 + N cos @ ) ] x dx

(1:22)

130

which r e s u l t s i n ( 1 :23)

where

y2 =

a

+jB

(1 + N cos

Q)

(1:24)

A t p o i n t A, t h e t e r m i n a t i o n end, a r e f l e c t i n g c u r r e n t i b

5

w i l l result i f Thus

# Z O and w i l l proceed t o propagate towards t h e r e c e i v f n g end B.

v ib

2

[y]

y1111sinh

z A e - 2 2ZO

-

Y2R

pL

(1:25)

2

i s t h e r e f l e c t i o n c o e f f i c i e n t given by (11)

Where P

L

pL

Thus t h e r e f l e c t e d c u r r e n t

$

-

ZL

- zo

ZL

+ zo

(1:26)

a t B w i l l be (1:27)

The t o t a l c u r r e n t a t B, t h e r e c e i v i n g end, w i l l then b e

?

or

The above anablysis assumes t h a t no r e f l e c t i n g c u r r e n t s occur a t B ( i . e . t h e l i n e i s c o r r e c t l y terminated a t t h e r e c e i v i n g end). I n o r d e r t o complete t h e f u l l two dimensional r a d i a t i o n p a t t e r n , t h e term cos Q must b e m u l t i p l i e d by cos 0 i n y1 and y2 ( e q u a t i o n s (1:19) and (1:24)) thus

+jB

y1

= a

y2

= = + f3

-N (1 + N (1

cos Q cos 0 ) cos

Q

cos 0 )

( 1 :30) ( 1 :31)

The r e s u l t a n t e q u a t i o n f o r the. rwo dimexsional r a d i a t i o n p a t t e r n ther, becomes,

v

[y]

sinh

YK.

--ylll

+ P e -Y 2 L

2

[y]

sinh

ynR 2

L

Pow?. Dewlopti!



A 2

I f t h e i n t e r - e l e m e n t spacing D i s g r e a t e r than h a l f a wavelength then s i n %ax < 1, and t h e angular d i s t r i b u t i o n w i l l r e p e a t beyond la m a x From a sampled d a t a theory p o i n t of view, sampling t a k e s p l a c e a t less t h a n t h e Nyquist r a t e and t h e r e f o r e a l l i a s i n g o c c u r s .

I

I

1.

Ba,sed upon t h e above procedure, a program w a s w r i t t e n i n t h e F o r t r a n IV language f o r u s e on t h e Sigma 9 computer a t C.R.C. i n o r d e r t o determine t h e performance of l i n e a r a r r a y systems. The program e s s e n t i a l l y computes t h e r a d i a t i o n p a t t e r n f o r an a r r a y of i s o t r o p i c s o u r c e s , u t i l i z i n g t h e D i s c r e t e F o u r i e r Transform (DFT), and then by t h e method of beam p a t t e r n m u l t i p l i c a t i o n w i t h n o n - i s o t r o p i c element, namel y t h e Beverage antenna, c a l c u l a t e s t h e r e s u l t a n t beam p a t t e r n f o r a n a r r a y of n o n - i s o t r o p i c elements o r Beverage a n t e n n a s . The beam p a t t e r n r e s u l t s are i n t h e form of a l i n e a r p l o t of azimuth a n g l e a g a i n s t g a i n i n d e c i b e l s normalised t o t h e maximum v a l u e . A t y p i c a l o u t p u t r e s u l t appears i n F i g u r e IV-4).

148

---

-

D i S ? L A V I N L I N E A R F-?%F THE NUMBER Of

ELEHENTS USED

-

R A D I & T I O N PATTERN

-

INTER- ELEMENT S P A C I Y G I M E T E R S ) FREQUENCY

I \ HHZ

I

VELOCITY

nf

PRWYGATION

-

RATIO

ATTENUAlIClN C@YSTANT I D B / W E T C R )

PHASE CUNSTACT

~

HEIOMT Yf

lRADIANS/ttETERl

I

lMttO/METEPI

I

.C540C2

20

rERYIhATING IrDEDANCE ELEVATI-t,

I

499.36

A'dGLE OF S I G N A L

POWER G , b I h 3F A N T .

I

-

.110989

-

1.00 12.0

.t03033

W I R E R A L I U S I h HLTERS ICOPPER a I R f )

IWPED.

130.3'2

.911 0

AWTEYNA ABOVE OROUND I H f T l R S )

COMPLLX C U I R A C T .

L I N E A R ARRAY OF B E V ER AGE Af.TENNAS

7.00

R E L A T I v L C I A L E C T R I C CONSTANT OF B R O c h C

GROUNLl C O V D U C T I V I T V

A

5.00

M I R E LENGTH I H E T E R S I

BEVERAGL- ANTENNA

f&

16

*

.013260

*98*631

-26.971

CHMS

Oung

IDEGREESI

=

82-00

-

ARRAV- R E k T U IS* 7 R O P I C R A D I A T C R 6.1*5DR NGR*A..ISED I \ T E N S I T V P A ' T f R

1.G3fl PER D I v -5C.O

0.0

-25.q

-*-t-*-*-*-*-*-*-*-*-*~~-*-~-*-*-*-*-+-.~*~*-*-*-*-*

176.16* l72.30* 161.41+ 16*.*b* 160. '56.314 :s 2 * 2 5 * lc7.61*. ;s2.9** 137.96. .56+ 1Ph.53+

A

I I H

+

***

U 1 w A N G L E

.

.. .

.- -

t

Ill.*@.

'17.37.

D E G R E

C?.69* h>.52+

f

37.'6r

53-07. *7..**

*?.re+

S

+

3?.39*. 27.95.

23-69, A

z I

M U

T U

A N G L E D

E G I?

f E

s

A

.

2

I r

.

*

19.56* 15.5** 11.59. 7.70, 3.8.. .30.

0

3.8**

.

.* .* .* .*

..

7.71.

.t

11.59* lS.50* 19.56*

23.69* 27.95+ 32.19*r 37.06. 42.-0* r7.0.. 53.17* 6'*52* hY.63* iin.37. 7 1 9 . bS* 7?h.53* 132.56* (37.96, 1oa.90* 1*7.61*.

ISI.05*

+

. . +

+

+

z z

t

:SL.31*

u

i .Deb*+

T

&6*.*6*

H

16m-O

A

I 7a.3sr* 176.1~* 8".'C*

h

I*

-*-.-*-*~,~~~*-*-*~*~t-'-.-.-.-.-.-*-.-~~.~*.*~.~.~*~.

.

..

Figure IV-4. Typical Computer Output Result b

-

8.

-*

-

149

S E C T I O N

5

'Primary' Grating Lobes Beyond t h e c e n t r a l r e g i o n s t h e r a d i a t i o n p a t t e r n f u n c t i o n r e v e r t s t o ,

sin

('7

sin

(F s i n

E =

s i n 0) (5:l)

0)

A Note t h t t some v a l u e of 0 such t h a t s i n 8 = 1, r s i n 8 = 5, then f o r Equation ( 5 : l ) may be any v a l u e of N > 1, e q u a t i o n ( 5 : l ) i s & d e t e r m i n a t e . e v a l u a t e d , however, by t h e u s e of L ' H o s p i t a l ' s r u l e t o g i v e , (5:2)

Thus a ;eccndary l o b e of amplitude N , which may be defined as t h e 'primary' g r a t i n & l o b e , w i l l appear a t some a z i m u t h a l a n g l e 8 given by

8

= arc sin

(' +)

(5:3)

The word, 'primary', i s used h e r e t o d i s t i n g u i s h t h i s t y p e of g r a t i n g l o b e from'that of a n o t h e r type t o b e d i s c u s s e d i n a l a t e r s e c t i o n . The 5 s i g n i n e q u a t i o n (5:3) i n d i c a t e s t h a t two g r a t i n g l o b e s e x i s t and are p o s i t i o n e d s y m e t r i c a l l y a t +0 from b o r e s i g h t . For example, i f t h e inter- element s p a c i n g D i s e q u a l t o one wavelength (D = A ) , then two primary g r a t i n g l o b e s w i l l appear a t 2 from b o r e s i g h t . I f , however, t h e inter- element s p a c i n g D i s much g r e a t e r thag one wavelength (D >> A ) , then f o r every wavelength A contained i n t h e inter- element spacing D such t h a t

,

nX < 1 D multiple grating lobes w i l l e x i s t . given as

8n = a r c s i n

n = 1, 2 , 3 ,

---

(5:4)

T h e i r p o s i t i o n s i n azimuth w i l l then be

(i g)

(5:5)

150 Since t h e v a l u e of s i n 8 f o r any given v a l u e of n , takes on f o u r p o s s i b l e values i n complete azimu,.l, i t can b e concluded t h a t t h e p o s i t i o n s of t h e g r a t i n g lobes i n t h e second h a l f of t h e r a d i a t i o n p a t t e r n i s t h e m i r r o r image of t h e f i r s t h a l f . As an example, l e t h = 30 meters and D = 40.65 meters, then f o r n = 1, t h e f i r s t g r a t i n g l o b e s w i l l appear a t ,

e

= arc s i n

e

= 180.0'

(i E)

40.65

=

+47.55O

(5:6)

For t h e m i r r o r image, 5 47.550

(5:7) (5 : 8 )

= 132.45O and 227.55'

nh f o r n = 2, then D > 1 and t h e second g r a t i n g l o b e extends beyond t h e ' v i s i b l e ' region (using antenna theory p a r l a n c e ) , and t h e r e f o r e , is n o t v a l i d . The p o s i t i o n of t h e primary g r a t i n g lobes, which have been determined i n t h e foregoing example, are exemplified i n t h e p o l a r p l o t of Figure IV- 5.

\

300'

60'

-\

\

c

.

2100

/ /30

11

i

90"

I

.\

240°

120"

I

210'

180"

1500

Figure IV-5. Polar Plot Illustrating the Position of the Grating Lobes for the Example Given on Page 150.

151

S E C T I O N

6

Beam Steering F o r s p e c i a l r e q u i r e m e n t s i t may b e n e c e s s a r y t o s t e e r t h e beam from b o r e s i g h t i n t o t h e d i r e c t i o n of t h e s i g n a l s o u r c e . To meet t h i s r e q u i r e m e n t , d e l a y l i n e s may b e i n s e r t e d i n t o t h e a r r a y system i n o r d e r t o s t e e r t h e beam. For example, i f t h e r e a r e 32 e l e m e n t s i n a g i v e n a r r a y system, 3 1 d e l a y l i n e s would b e r e q u i r e d ( e x c l u d i n g t h e r e f e r e n c e e l e m e n t ) , i n o r d e r t o steer t h e beam t o a g i v e n a n g u l a r p o s i t i o n . Furthermore, i f t h e beam were t o b e s t e e r e d 210.0 d e g r e e s a t i n t e r v a l s of 1.0 d e g r e e , i t would r e q u i r e t h e u s e of 620 v a r y i n g l e n g t h s o f d e l a y l i n e i n o r d e r t o a c h i e v e t h i s . However, t h e maximum amount o f beam- steering t h a t may b e achieved w i l l b e dependent on t h e beamwidth o f any one element.

The 'Segmented' Array: I n o r d e r t o r e d u c e t h e number of d e l a y l i n e s used f o r beam s t e e r i n g , t h e a r r a y may b e a r r a n g e d i n groups o r segments, w i t h M segments of n e l e m e n t s p e r segment. T h i s method r e s u l t s i n a secondary a r r a y system where e a c h segment may b e r e f e r r e d t o as one element f o r M e l e m e n t s . The s p a c i n g between t h e segments, o r e l e m e n t s of t h e secondary a r r a y , w i l l b e n t i m e s t h e o r i g i n a l i n t e r - e l e m e n t s p a c i n g D of t h e primary array. For t h e c a l c u l a t i o n of t h e d e l a y l i n e s r e f e r t o F i g u r e IV-6. The f i r s t segment (segment 1 ) i s c o n s i d e r e d t o b e t h e r e f e r e n c e segment. The l e n g t h L i s c a l c u l a t e d f o r t h e f i r s t element (element 5 ) i n segment 2 f o r a given a z i m u t h a l steer a n g l e . The method as d e s c r i b e d i s t h e n r e p e a t e d f o r t h e remaining segments i n o r d e r t o c a l c u l a t e t h e remaining d e l a y l i n e s . Using t h e p r e v i o u s example, t h e number of d e l a y l i n e s r e q u i r e d t o steer t h e beam 210.0 d e g r e e s from b o r e s i g h t w i l l n o t b e 140. The method r e s u l t s i n a cons i d e r a b l e r e d u c t i o n i n t h e number of d e l a y l i n e s r e q u i r e d and i n a d d i t i o n r e d u c e s t h e complexity of t h e a s s o c i a t e d s w i t c h i n g system. However, t h e method r e q u i r e s t h e payment o f a p e n a l t y ; as p r e v i o u s l y mentioned, t h e amount of beam- steering a v a i l a b l e i s determined by t h e beamwidth of any one element and s i m i l a r l y , f o r t h i s method, t h e amount of beam- steering a v a i l a b l e w i l l b e d e t e r m i n e s by t h e beamwidth of any one segment. P L A N E WbVE

Figure I V-6. Illustration of the Segmentation of the Lineor Array.

152

Consider one segment of 4 elements. The summation of t h e a r b i t r a r y phase $I i s d e p i c t e d i n F i g u r e I V - 7 . L e t A(x) be t h e x co- ordinate of A , and l e t A(y) be t h e y co- ordinate of A t h e n , A2 = a 2 ( 4

+6

cos $I

The maximum v a l u e of A2 o c c u r s when

4

+

4 cos 24

= 0.

+

2 cos 34)

(6:l)

Thus,

* A2

max

(6 :2 )

= 16a2

For t h e h a l f power p o i n t s , A2

max = 8 a 2 2

(6:3)

and t h e r e f o r e ,

2 = 3 cos

4 +

2 c o s 2$

+

cos 34

(6:4)

Equation ( 6 : 4 ) i s s a t i s f i e d when $I = 41.0 d e g r e e s , and t h e r e f o r e 0 t h e azimuthal a n g l e a t which t h e h a l f power p o i n t s occur may b e determined from equation (5 :3) t o g i v e

0 = +arc s i n For an example l e t ?

X

36i1D

)

degrees

(6:5)

= 30.0 meters and D = 40.65 meters t h e n ,

0 =+arc s i n (0.084) = +4.82

length

(

degrees

Thus, t h e beam- steering l i m i t s a r e H.82" from b o r e s i g h t f o r a waveX = 30.0 meters.

F i g u r e IV18 shows p l o t s of t h e r a d i a t i o n p a t t e r n i n t h e c e n t r a l r e g i o n f o r steer a n g l e s from b o r e s i g h t t o 5.0 d e g r e e s i n increments of 1.0 degree. The l i n e a r a r r a y w a s i n t h e 'segmented' c o n f i g u r a t i o n , w i t h 4 elements p e r segment, w i t h an inter- element s p a c i n g D and wavelength A of 40.65 meters

153

*

Figure I V- 7. Phasor Diagram of One Segment of 4 Elements.

-

U

BEAMSTEER =O.O"

BEAMSTEER = l.OOo

BEAMSTEER = 3.00°

BEAMSTEER = 4.00"

BEAMSTEER. 2.00"

IEAMSTEER = 5.00"

-10

-20

m T)

- 30

-40

- 50

-5

-3

-I

0 I

3

5

-5

-3

AZIMUTH

-I 0 I ANGLE

3 (DEG)

5

-5

-3

-I 0 I

Figure IV-8. Radiation Patterns in the Central Region For the Beamsteers as Shown.

3

5

154

'S~~GIZ~ Grating L - ~ J 'Lobes: I f t h e l i n e a r a r r a y system is i n t h e segmented c o n f i g u r a t i o n , t h e system may b e thought of as a secondary a r r a y system, where each segment r e p r e s e n t s one element i n t h e a r r a y . The i n t e r segment s p a c i n g , denoted by Ds, i s t h e n g i v e n by

D idn Sre

S

=

ND,

(6:6)

N i s t h e number of e l e m e n t s used i n t h e segment. D i s t h e o r i g i n a l inter- element spacing.

I f t h e inter-segment s p a c i n g Ds is much g r e a t e r t h a n a wavelength (Ds >> A ) , ' s e c o n d a r y ' g r a t i n g l o b e s w i l l r e s u l t . The word, ' s e c o n d a r y ' , d i s t i n g u i s h e s t h e t y p e of g r a t i n g l o b e s which i s now under c o n s i d e r a t i o n from t h e t y p e p r e v i o u s l y mentioned. To d e t e r n i n e t h e p o s i t i o n i n azimuth of t h e s e c m d a r y g r a t i n g l o b e s e q u a t i o n ( 5 : 5 ) , p r e v i o u s l y used f o r d e t e r m i n i n g t h e p o s i t i o n s i n azimuth of t h e primary g r a t i n g l o b e s , may be u s e d , e x c e p t t h a t D must be r e p l a c e d by D t h u s , S

8

n

f o r n = 1,2,3,---

,

= arc s i n

(6:7)

nX such t h a t jj-5 1. S

F i g u r e s IV-9 t o IV-13 i l l u s t r a t e t h e p r e s e n c e of t h e s e c o n d a r y g r a t i n g l o b e s r e s u l t i n g from t h e a r r a y system b e i n g i n t h e segmented c o n f i g u r a t i o n . Four elements were used p e r segment w i t h a n i n t e r - e l e m e n t s p a c i n g of 40.65 meters. The t o t a l number of e l e m e n t s used i n t h e a r r a y w a s 3 2 . These r e s u l t s were o b t a i n e d a t a f r e q u e n c y of 1 0 MHz (A = 30.0 meters) and may be compared t o t h e r e s u l t o b t a i n e d i n F i g u r e IV- 5 where t h e a r r a y w a s n o t i n t h e segmented configuratidn.

.

.

.. c

-

155

330"

0"

30"

60"

300".

/

270"-

-90"

2 4 p

'120"

210"

180"

Figure /V-9. Polar Plot for Beamsteer = 1.0"

150"

156

330"

O0

30"

0

300°,

,60°

270"

-90"

\

240°/

/

/

210"

I

180"

Figure I V- 10. Polar Plot for Beamsteer = 2.0"

\ 150°

120"

157

330"

0"

30"

300:

,60°

270"-

-90"

24W'

'120"

0 fi*

/ 210'

I 180'

Figure lV-11. Polar Plot for Bearnsteer = 3.0"

?, \ 150'

158

330"

O0

30"

e

60"

300°\

/

270O-

-900

240°'

'120°

Fkyre I V- 12. Polar Plot for Beamsteer = 4.0"

159

300'

/

60'

270'-

- goo

240:'

'120'

210°

180'

Figure I V- 13. Polar Plot for Beamsteer = 5.0"

150'

160

S E C T I O N

7

Amp1 itude Weighting

*

Amplitude ~ e i g h t i n g " ~ )may b e a p p l i e d t o t h e l i n e a r a r r a y i n t h e form of

A(R) = 0 . 5 4

+

0 . 4 6 cos

2lTR

(7:l)

Consider a continuous a p e r t u r e of l e n g t h L w i t h a p l a n e wave i n c i d e n t on t h e a p e r t u r e a t some a n g l e 8. The wave f i e l d i s given by,

2~ R s i n 8

,j

E(R)

= e

(7 :2)

I f amplitude w e i g h t i n g i s a p p l i e d i n t h e form as shown i n e q u a t i o n ( 7 : l ) t h e n ,

E(R) = ( 0 . 5 4

+

j?

0 . 4 6 cos

R) e

R sin e (7 :3)

The f a r f i e l d d i s t r i b u t i o n i s t h e F o u r i e r Transform of e q u a t i o n (7:3) t h u s ,

2lT where L i s t h g s p a c e frequency of p e r i o d L. (7 :4) r e s u l t s i n

E =

m

where

-

I

" c

x = x

-

(

sin 0

(7 :5)

X

-

The e v a l u a t i o n of e q u a t i o n

*) L

(7 :6)

161

I f x = 0.0 ( i . e .

Av ), t h e n E w i l l a t t a i n i t s maximum v a l u e of sin 6 = L (7 : 7 )

E = 0.54 L max

Emax,

A t t h e h a l f power p o i n t , E i s 3 dB below o r E = 0.38 L a d t h i s gives from r i s e t o a v a l u e of x = 2 . 0 4 7 r a d i a n s . S i n c e x = IT L ( s i n 6

e q u a t i o n ( 7 : 6 ) , t h e n a t t h e h a l f power p o i n t s ,

2.047 =

x

71 1 L

t>

-%

(7 : 8 )

Thus, sin 8

Let sin 6

-L

a

2.047h 7TL

(7 : 9 )

= s i n a, t h e n

sin

Again i f

Ap -= L

a

=

2.047A

(7 : l o )

71L

is small then, a=----

7TL

x 57.29578 =

37.332X degrees L

(7 :1 1 )

The qeamwidth which i s d e f i n e d as 2 4 i s t h e n g i v e n by

Beamwidth =

74.665A

degrees

(7 :12)

Thus by t h e a p p l i c a t i o n of t h e w e i g h t i n g f u n c t i o n as shown i n e q u a t i o n ( 7 : l ) t h e beamwidth w i l l i n c r e a s e by 3 2 . 2 % t o t h a t w i t h no w e i g h t i n g . However, of t h e main l o b e . t h e a d j a c e n t s i d e l o b e s w i l l b e reduced t o l e s s t h a n 1% Successi\ie s i d e l o b e s , however, w i l l tend t o i n c r e a s e i n a m p l i t u d e and exceed 1%. It w i l l a l s o b e n o t e d t h a t t h e main l o b e w i l l r e d u c e i n a m p l i t u d e t o 0 . 5 4 compared t o t h a t w i t h no w e i g h t i n g . The v a l u e of 0 . 5 4 , which may b e d e f i n e d as t h e n o r m a l i s i n g f a c t o r , i s used t o n o r m a l i s e t h e r a d i a t i o n p a t t e r n when w e i g h t i n g , of t h e form d e s c r i b e d above, i s a p p l i e d . The e f f e c t s of t h e beam p a t t e r n when t h i s form of w e i g h t i n g i s a p p l i e d a r e e x e m p l i f i e d i n t h e l i n e a r p l o t of F i g u r e ( I V - 1 4 ) .

162

c

1333 I164 996 828 662 496 331

165

AZIMUTH

165 3.31

00

ANGLE

496 662 828

996 1164 1333

(DEG )

Figure IV-14. Illustration in Linear Form of the Radiation Pattern With the Application of Amplitude Weighting.

Reduction in Gain w i t h PmpZitude Weighting: Since t h e a p p l i c a t i o n of amplitude w e i g h t i n g reduces t h e amplitude of the r a d i a t i o n p a t t e r n , then t h e r e d u c t i o n i n g a i n i n d e c i b e l s may be given as

(7 :13) where x i s d e f i n e d i n e q u a t i o n (7:6).

+ Taylor Weighting: Taylor (24) w e i g h t i n g i s p a r t i c u l a r l y u s e f u l i n w i d e a p e r t u r e , narrow beamwidth, l i n e a r a r r a y systems, where t h e main-lobe t o s i d e l o b e v o l t a g e r a t i o h a s been s p e c i f i e d . T h i s form of weighting a l s o i n s u r e s t h a t t h e s u c c e s s i v e s i d e l o b e s remain a t t h e s p e c i f i e d v o l t a g e r a t i o o u t t o some i n t e g e r number d e s i g n a t e d

z.

L e t t h e r 3 d i a t i o n p a t t e r n resemble t h e following f u n c t i o n i n t h e c e n t r a l

region F (M) = cos

IT

-4

where CI i s a number somewhat g r e a t e r than u n i t y and-5s becomes z e r o a t a corresponding i n t e g e r d e s i g n a t e d n. U

i s d e f i n e d by:

(7 :14) chosen such t h a t F(M)

163

n

rJ=

(7 :15)

dA2+ (z- $)

2

A h a s t h e p r o p e r t i e s such t h a t cosh -ITA i s t h e main- lobe t o s i d e - l o b e v o l t a g e To d e t e r m i n e t h e F o u r i e r r a t i o . M i s an i n t e g e r r a n g i n g from 0 < M 5

n.

c o e f f i c i e n t s o r F(M), one must e v a l u a t e t h e p r o d u c t s

-IT-1 F(M) = C

\I

IT

m

(7 :1 6 )

11 n=n

n = l

where C i s a n a r b i t r a r y c o n s t a n t and may b e t a k e n t o b e cosh 7TA. I n o r d e r t o d e t e r m i n e t h e w e i g h t i n g f a c t o r s t h e i n v e r s e F o u r i e r Transform must b e performed on e q u a t i o n ( 7 : 1 6 ) , and t h i s i s g i v e n g e n e r a l l y a s ,

W(P) =

1

ZIT

F(0)

+

2

S(M)

I (7:17)

cos MP

M = l where

P2 = < II

-

> -

S i n c e F(M) is z e r o f o r M = n , t h e n t h e summation t e r m i n a t e s a t M = n , t h u s s i m p l i f y i n g t h e e v a l u a t i o n of e q u a t i o n (7:17). T a y l o r h a s produced a t a b l e of v a l u e s (Table IV- 1) i n c l u d i n g t h e t h r e e * p a r a m e t e r s n e c e s s a r y i n o r d e r t o c a l c u l a t e t h e c o r r e s p o n d i n g w e i g h t s namely, A 2 , 0 , and n. Another u s e f u l p a r a m e t e r , d e s i g n a t e d B,, and found i n column

3 of t h e t a b l e , may be used t o d e t e r m i n e t h e a c t u a l beamwidth o f a l i n e a r a r r a y s y s t e m when t h i s form of w e i g h t i n g i s a p p l i e d . The a c t u a l beamwidth i s g i v e n by,

.

B A c t u a l beamwidth =

"

= a . X degrees ND

(7 :18)

For example, i f a designed main- lobe t o s i d e - l o b e v o l t a g e r a t i o i s t o b e 100.00 (40dB), and ii i s chosen t o b e 6 , t h e n from t h e t a b l e , 0 =1.04298 and 6, = 68.76". u s e d , t h e n t h e a c t u a l beamwidth w i l l b e ,

I f a wave number o f 42.21 i s

A c t u a l beamwidth = 68.76 x 1.04298 d e g r e e s . = 1.70 42.21

.

..

b

'

(7 :19)

164

TABLE JV-1

Design s i d e - lobe r a t i o

cm

A2

rl

(Side- lobe voltage ratio)

dB)

TI

Values of t h e parameter

-

n = 2

( i n den.)

-

-

n = 3

-

n = 4

n = 5

I

, 28.65

0

1.00000

5

1.77828

34.49

3.16228

40.33

5.62341

45.93 51.17

10 15

10.0000

20

0.00000

1.08838

1.07514 1.07268

1.11631

1.09528

I. 08043 1,06949

1.10273

1.08701

1.07490

1.06554

1.08698

1.07728

1.06834

1.06083 11.0546)

1.06934

1.06619

1.06079

1.05538

1.05386

1.05231

1.18672

1.13635

1.16908

1.12754

0.58950

1.18689

1.14712

0.90777

1.12549

1.12133 1.09241

- --

56.04

1.29177

---

1.74229

---

35

56.2341

64.78

2.25976

40

100.0000

68.76

2 .a4420

I

I

!

1.06534 1.06350

, 1.06112

i

1.05052

Beamwidth Spread (Percent): The p e r c e n t a g e s p r e a d i n beamwidth when 40 dB T a y l o r w e i g h t i n g i s a p p l i e d may b e determined, by f i r s t , d e t e r m i n i n g t h e beamwidth of t h e s i n x/x r a d i a t i o n p a t t e r n u s i n g t h e same wave number. For example, i f t h e wave number of 42.21 i s used t h e s i n x/x beamwidth w i l l b e

-

c

(7 : 2 0 )

The Beamwidth s p r e a d i n p e r c e n t w i l l b e Beamwidth s p r e a d =

-

1.7

1.7

1.2

I

i 1.05816 1i

1.04298

Beamwidth = 50.65 = 1 - 2 0 42.21

I

I .06667

1.08492

1.29351 1.24393

60.55

i 1.11111

, n = 1-----j

1.10203

0.14067 0.33504

17.7828

n = 7 I

1.10727

1.14286

31.6228

-

n = b

1.07692

1.20000

25

.

1.09091

1.33333

30

-

(7 :21)

= 292

Thus, w i t h t h e a p p l i c a t i o n of T a y l o r w e i g h t i n g , t h e beamwidth w i l l i n c r e a s e by 29%.

I t h a s been determined n u m e r i c a l l y t h a t w i t h t h e a p p l i c a t i o n of t h i s form of w e i g h t i n g t h e main l o b e w i l l r e d u c e i n a m p l i t u d e t o 0.551 compared t o t h a t w i t h no w e i g h t i n g . Thus, t h e beam p a t t e r n o b t a i n e d w i t h 40 dB T a y l o r w e i g h t i n g a p p l i e d h a s been n o r m a l i s e d t o t h i s v a l u e . The e f f e c t s of 40 dB T a y l o r w e i g h t i n g on t h e beam p a t t e r n i s e x e m p l i f i e d i n t h e l i n e a r p l o t of F i g u r e IV- 15.

'

I

I

165

1333

1164

996

828

662

496

3.31

:65

00

AZIMCIT~I ANGLE

165 331 (DEG )

496

662

828

996

1164 1333

Figure I V- 15. Illustration in Linear Form of the Radiation Pattern with Application of Taylor Weighting.

Reduction i n Gain With Taylor Weighting: Since the a p p l i c a t i o n of Taylor weighting reduces the amplitude of the r a d i a t i o n pattern, then the reduction i n gain i n d e c i b e l s may b e given a s (7 :21) where F(M) i s defined i n equation (7 : 1 6 ) .

?

" c

.

166

S E C T I O N

.

*

8

Azimuthal Bearing Errors Caused by Linear Array on Sloping Ground

Azimuthal bearing errors w i l l r e s u l t i f the linear antenna array system i s i n s t a l l e d on sloping ground. The magnitude of t h i s error w i l l be dependant upon the true azimuthal bearing of the signal and i t s elevation angle. To i l l u s t r a t e t h i s , consider the diagram of Figure IV-16.

Z

5

>

I Y

X Figure I V- 16. Illustration of the linear Array on Sloping Ground

167

I n t h i s diagram, t h e u n i t v e c t o r A , i n t h e d i r e c t i o n of t h e l i n e a r a r r a y , h a s a n e l e v a t i o n a n g l e B w i t h r e s p e c t t o t h e x, y plane. The u n i t v e c t o r S r e p r e s e n t s a s i g n a l v e c t o r having a n e l e v a t i o n a n g l e Q and an azimuthal a n g l e 8 . The p r o j e c t i o n of t h e S v e c t o r on t h e x, y , z , c o o r d i n a t e s w i l l g i v e

* where B1 i s t h e a n g l e between t h e S v e c t o r and t h e y c o o r d i n a t e , a1 i s t h e a n g l e between t h e S v e c t o r and t h e x c o o r d i n a t e , and 5?, 9 , z are u n i t v e c t o r s in the x, y, z directions respectively. Similarly for the A vector A

A =

x^ cos B

+2

sin

8

(8:2)

Since w e are i n t e r e s t e d i n t h e a n g l e y between t h e v e c t o r s S and A , then t h e r e s u l t a n t c o s i n e of t h e a n g l e y i s simply t h e d o t product of S and A. Thus, cos (y) = S . A t h e r e f o r e ,

cos(y) = cos

a1

cos B

+

sin

From a knowledge of r i g h t s p h e r i c a l t r i a n g l e s cos given by,

a1

Q

sin

8

(8:3)

may be deduced and i s

Therefore c

C O S ( ~=) cos J, cos 6 cos B

+

s i n J, s i n

8

(8 :5)

To s i m p l i f y m a t t e r s , assume t h a t t h e f r o n t o r main l o b e i s b r o a d s i d e t o t h e l i n e a r a r r a y system ( i . e . 8 = 9 0 . 0 " ) , then

cos(y)

=

s i n J, s i n

B

(8 : 6 )

Thus f o r an a r r a y having an e l e v a t i o n a n g l e of 8 , t h e v a l u e of y t u r n s out t o be a f u n c t i o n of t h e e l e v a t i o n a n g l e J , of t h e s i g n a l . For example, i f B = 2.0" and J , = 20.0" then

y

= a r c cos ( s i n ( 2 0 ) s i n ( 2 ) ) =

89.3"

(8 :7)

.

168 The b e a r i n g e r r o r Ay which r e s u l t s from t h e a r r a y b e i n g on s l o p i n g ground i s

Ay

= 90.0

-

arc cos (sin

JI

sin 6)

(8 : 8 )

From t h e foregoing example, A0 t u r n s o u t t o b e 0 . 7 O . This b e a r i n g e r r o r is p a r t i c u l a r l y important i n wide a p e r t u r e , narrow beamwidth, l i n e a r a r r a y systems. The r e s u l t is t h a t as t h e e l e v a t i o n a n g l e of t h e s i g n a l i n c r e a s e s , t h e a r r a y beam t e n d s t o steer away i n azimuth from t h e d i r e c t i o n of t h e s i g n a l soblce. Eventually, a t some e l e v a t i o n a n g l e , t h e beam w i l l steer s u f f i c i e n t l y away so t h a t t h e d i r e c t i o n of t h e signal is o u t s i d e t h e beamwidth of t h e a r r a y . These v a r i a t i o n s i n t h e e l e v a t i o n a n g l e are a r t i c u l a r l y n o t i c e a b l e f o r r a d i o waves t h a t propagate v i a t h e ionosphere( 25P

.

169

S E C T I O N

9

Radiation Pattern Format on as a Function of the Rad a1 Distance R For a performance e v a l u a t i o n of a l i n e a r a r r a y system, t h e t e s t t r a n s m i t t e r s h o u l d b e p l a c e d a t some r a d i a l d i s t a n c e R from t h e system i n o r d e r t o minimize i n t e r f e r e n c e caused by t h e F r e s n e l e f f e c t . Consider a l i n e a r a r r a y system of a p e r t u r e l e n g t h L , and a l s o c o n s i d e r a p o i n t s o u r c e a t some r a d i a l d i s t a n c e R from t h e l i n e a r a r r a y as shown i n F i g u r e IV-17. Radio waves emanating from t h e p o i n t s o u r c e w i l l produce a curved w a v e f r o n t w i t h r e s p e c t t o t h e l i n e a r a r r a y . For some g i v e n l e n g t h 2, t h e p r o p a g a t i o n l e n g t h S may b e g i v e n as

S = (Ri

+

(Z

-R

+

(9:l)

b u t Ro = R s i n 0 and 2 = R c o s 8 and t h e r e f o r e S may be g i v e n i n terms of 0 , R and R t o be

s = For a g i v e n R and 8 , S(R> may b e e v a l u a t e d by u s e of t h e Maclaurin series t o t h e second o r d e r term t o b e

S(R) =

II c o s 0

-

t 2(1 - cos 28) 2R

Thus t h e phase a n g l e @ may b e g i v e n as a f u n c t i o n of

@(A)

=

2n x

(9 :3)

R t o be

R cos 0 - 'lt2 ( 1 - cos 2e) RX

(9 : 4 )

The second term i n Equation (9:4) r e p r e s e n t s t h e i n t e r f e r i n g - p h a s e e f f e c t , o r I f w e now assume o r t h o g o n a l F r e s n e l e f f e c t f o r a g i v e n r a d i a l d i s t a n c e R. c o n d i t i o n s (I.E. 8 = go"), t h e n

@(I,)

=

2nR2

RX

(9:5)

(excluding t h e minus s i g n ) IT

Using t h e c r i t e r i a t h a t t h e i n t e r f e r r i n g phase s h a l l n o t exceed - r a d i a n s a t 8 L , t h e n R may be g i v e n as

2 .

..

b

'

170

R = -2L2 A

(9 :6 )

With t h e c r i t e r i a above, Equation (9:6) r e p r e s e n t s t h e boundary c o n d i t i o n between t h e n e a r f i e l d o r F r e s n e l zone, and t h e f a r f i e l d o r Fraunhofer region. The r e s u l t obtained i n Equation ( 9 : 6 ) a l s o a p p e a r s i n Kraus(26). From Equation ( : : 6 ) i t w i l l b e noted t h a t f o r a given a p e r t u r e l e n g t h L, t h e boundary c o n d i t i o n i s i n v e r s e l y p r o p o r t i o n a l t o t h e wavelength A .

4

L

*

Figure I V-17. Illustration of a curved wave front emanating from the point P and which is arriving at some angle 0 w.r.t. the linear array of length L. L

171

*

0042: C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C

C C C C C C C C C

?

ROOK# 2 7 6 9 0 0 s 07/16/75 11:19 P ~ ~ G R ATp1 M C B M P U T t AND D I S P L A Y THE R A D I A T I B 9 PATTER'.l F V R A L I N F A K A R R A Y 9F BEVERAGE ANTENNAS. THE NUMBflH OF E L EMENTS ( N R X ) , USED T h THE A R R A Y MUST BE A \ I N T E G E R P3NER OF TW9 E L E M t N T S AND N 9 T T B EXCEED 6 4 T.rE A R R A Y M A Y BE: ' S E G M E N T F D ' P R B V I U I N G THE T P T A L NUMBER B F E L E M E k T S t!SFD I h THE S Y S T E M ARE E X A C T L Y DIVJSABLE BY THE kUMBFR BF E L E M E N T S CHOSEN FBR THE SEGMEblT. R A D I A T I B N P A T T t r R N S ARE ALSO CRMPUTED FOR THE A RRAY SYSTEM ON L I N F A R S L B P I N ~GROU'*D C S S I N E W E I G H T I N G O R 4 0 0 8 TAYLOR W E I G H T I N G M A Y BE- A P P L I E D T 3 THE A R R A Y SYSTEM. IF THE A R R A Y 1s SEGMENTED# THE WEIGHTS ARE APPLIED T O THE SEGMENTS B'QLYo THE I N P U T P A R A M E T E R S R E Q U I R E D F B R THE PRBGRAM AKE AS FRLLflWS: D**.*.*THE I N T E R - E L E M E N T S P A C I N G D I N PETERS NRX. ONIJMBER 8 F E L E M E b T S FAV......THE FREQUENCY B F B P E Y A T I B Y I N MHZ THETA.oo.*BEAMSTEFR ANGLE ( D E G R E E S ) N P T * * e * * * T H E NUMBFR OF ELEMENTS PER SEGMENTS ( I F N P T = l r THE A R R A Y IS N O T SEGMENTED) ALPHA*..***THE E L E V A T I B N ANGLE B F THE S I G N A L I N DEGQEES ( I F A L P H A = 0.01 GRBUND d A V E C O N D I T I e N S ARE ASSUMED) ~ E T A I I ~ . * G R B U N D E L E V A T I O N ANGLE(DEGREES1 ISKIP.*r*.PARAMETER F9R S E L E C T I E N B F A P P R B P R I A T E k E I G H T I N G FtltdCTIBN ISKIP = O...NB WE I G H T I N G I S K I P r: l * * r C B S I N E N E I G H T I N G I S K I P 6 2**0TAYLBR kEIGHTING XLENGTH..***ANTENNA LENGTH ( M E T E R S ) EG**.e..***.RELATIVE DIALECTRIC CONSTANT SIGMAo*e..**GRBUND C B N 3 U C T I V I T Y (MHB/HETER) H * * . * * * * * . * * A N T E N N A HEIGHT (MFTERS) R A D I U S * r r . * * W I R E RADIUS (METERS) THE A B s P ~ L U T E VALUE OF THE CBMPLEX C H A R A C T E R I S T I C IMPEDANCE ZB IS TAKEN AS THE T E R M I N A T I N G I M P E D A h C E ZL. EXAMPLE PIF PARAMETERS:7 I 160 5. D 0. D 1 ~ 2 2 D. 0 . 0 0 , 1 0 0 . ~ 12 D *003#1 D 1 0 0 2 6 E - 4 DATA P A R A M E T E R S START I N CBL. 1 8F DATA CARD

B.J.

Q 0 B K MARCH 3 0 1 9 7 5

C DIMENSIeN B R G ( 9 9 9 ) , W ( ~ 5 6 ) r I T I T L E ( 5 0 0 ) r ( 0 : 2 C ) O ' , I D L I N E ( 100 ) D R B U F(2009I D A 6 U F ( 2 5 6 )

*I.T

*rFT(2000)rXLL(128)rWF(328)#XGAM(2) CeMPLEX CWBUF ( 5 1 2 ) I CMBUF ( 512 1 CRUF ( 6 41 0 C B U F ? ( 6 4 1 X G A M M A DZBr Z I N E Q U I V A L E N C E ( X G A M M A D X G A M ( ~ 1) DATA I T I T L E I ' A Z I M U T H A N G L E DFGREES ' / 1 C / ? 9 9 * 9 9 8 / +D ILIM/128/ READ I N DATA PARAMETERS ISKIPDXLENGTHD I N P U T D,NRXDFAV, THETA,hrPT, ALPHA,BETA, +EGDSISMA,HD R A D I U S T+i€TA = T H E T A / 5 7 * 2 9 5 7 8

+D

C

172

A L P Y A ~= ALPHA/57*29578 BETA = B E T A / 5 7 * 2 9 5 7 8 XLAMBDA = C / F A V DY 4 0 I = 1 J I L I M / 2 XLL(1) = o * o WF(I) = ?*O 40 CHUF(1) = C M P L X ( l * r O * ) CALL N I S E ( E G I S I G M A J H , R A D I U S J X L E N G T ~ J X G A M J Z ~ ~ F A V # +XCiAMMAr XFJJ D B ) 0 ZLL = C A B S ( Z B ) C A L L DELAYCeNST I NPT) D, THETA, XLAMBDAJ CBUFI N R X j XL L J N H 1 I F ( I S K 1 P * E Q * O ) G B TO 4 3 I F ( I S K J P * E O * 2 ) G B 1 0 200 CALL NEIGHT(NRX~CRUFJNPT,WF) Gt! T O 4 3 200 CALL T A Y l ~ R ( N R X J C B U F , D ~ W F J N P T ) 43 D13 30 I = 1 J I L I M 30 C M B U F ( 1 ) = C M P L X ( @ * O B O * O ) MCNTR = 1 + (ILIM/2) LCNTR = M C W T R (YRX/Z) D 0 2 N = 1 D NRX CYBUF(LCNTR-~+N) = CBUF(N) 2 CONTINUE M = ALBG(FLBAT(ILIM))/ALUG(2*~) + 0.5 C A L L F A S T 4 ( M J CriBUF J rl J - 1 ) DB 3 4 5 N 1 0 ILIM 345 A R U F ( N ) = C A B S ( C M B U F ( N ) ) / F L B A T ( N R X ) AMPMX = A B U F I I ) Cf3NST = X L A M R D A / ( U r F L B ~ T ( I L I M I1

-

1;) = 0 DO 7 7 2 I * 2 J I L I M IF(AMPMX *GE* A R U F ( 1 ) ) G B T 0 772 AMPYX = A B U F ( I ) XI) 1-1 7 7 2 CtlN'TINUE 773 WRITE(lORrl2 W H 1 T E ( 1 0 8 ~ 1 3 NRX W R I T E ( I O S J I ~0 W R I T E ( 1 O 8 r 2 3 FAV W R I T E ( 1 0 8 r 2 9 XLENGTH w R I T E ( 1 0 8 ~ 2 8XN

173

175

22 23 29 28 39

FORMAT ( 8 x 1 1 2 8 2 7 x 1 F 6 * 2 , 2 5 X r F 5 * 3 1 F O R M A T ( / ' F R E Q U E N C Y I N MHZ = ' r F 5 m 2 ) F B R M A T ( / ' B E V E R A G E ANTEkNA WIRE LENGTH ( M E T E R S ) = ' r F 6 r 2 ) F B R M A T ( / t V E L B C I T Y BF P R B P B G A T I B N R A T I B = ' r F 5 . 3 ) F @ R M A T ( / f C B M P L E X CHARACT. I M P E D * ZB = ( t r F 7 * 2 r ' ~ t r * F 7 * 2 r ' ) VHMSt) 3 1 F U R M A T ( / ! T E R M I N A T I N G IMPEDANCE. = ' r F 7 m 2 r t 8Ht'lST) 3 2 F S R M A T ( / ' E L E V A T I O N ANGLE OF S I G N A L ( D E G R E E S ) = ' r F 5 . 2 ) 3 3 F B R M A T ( / t H E I G H T O F ANTENNA ABBVE GROUND ( M E T E R S ) s t F 5 . 2 ) 3 4 F O R M A T ( / ' R E L A T I V E D I A L E C T R I C C 0 N S l A N T B F GROUND = t r F 4 . 1 ) 35 F B R M A T ( / t G R B U N D C S N D U C T I V I T Y ( M H B / M E T E R ) * ' r F R . 6 ) 3 6 F @ R M A T ( / ' N I R E R A D I U S I N METERS (CBPPER W I R E ) = ' j F 8 . 7 ) 37 F O R M A T ( / t P H A S E CBNSTANT ( R A D I A N S / M E T E R ) = ' I F 8 . 6 ) 3 8 F B R M A T ( / t A T T E N U A T I B N CONSTANT ( D B / M E T E R ) = ' r F 8 m 6 ) 5 9 F R R M A T ( / t P B W E R G A I N OF A N T * A R R A Y R E L o T O I S B T R f l P I C ' r + ' RAOIATBR ~ ' r F 8 . 3 , ' D B ' )

*

END

C C C

StJRROUTINE D E L T A ( * J E G , E B I S I G M A J A D E L T A ) SclBRBUTINE T O CALCULATE THE GRnUND WAVE T I L T A NG L E R e J * R O g K MARCH 3 0 1 9 7 5 S 1 = EG 1.

-

s12 = SlrSl S2 = SIGMA/(EO+W) s22 = S 2 r S 2 s3 s12 + s 2 2 54 = E G r E G s5 = s 4 + s22 s55 = s 5 r s 5 DELTA = S 3 I S 5 5 DELTA = D E L T A * * * 2 5 ADELTA = A T A N t D E L T A ) RETURN END f

C C C C

S U B R B U T I N E RHOV ( X I 1 8 W , E B J E G I S I G M A I R H B ) S U B R B U T I N E TO CALCULATE THE V E R T I C A L GRBUND R E F L E C T I B N C O E F F I C I E N T FBR A GIVEN ELEVATIBN A N G L E ( x I l ) * 8 . J m R e e K MARCH 30 1 9 7 5 CfjMPLEX RHBDc 2 r z r A 8 c Y = Om=SIGYA/(W+EU) Z = CMPLX(EGJY)

B = ces(x1i) 6 = BrB A = z+SIN(xIl) C = Z- B c2 = cSQRT(C) RkiB = ( A C2)/(A RETUR N END

-

+ C2)

176

e

177

*

C C C

178

t

179

R88K,276900S 07/16/75 12:40 SUBRBUTINE G R N D T ~ L T ( N R X J D , C B U F ~ T H E T A , A L P H A J ~ E T A , X L A ~ B D A ) SUBROUTINE 18 CVMPUTE THE PHASE E R R 0 R S ACR0SS THE ARRAY A S S O C I A T E D W I T H A GHBUND TI LT ( B E T A ) B * J * R e O K MARCH 3 0 1975 COMPLEX C B U F ( 1 ) 3 DATA PI/3*14159265/ I F ( A L P H A * E Q * * O * L N D o BETA * t Q * e 0 ) R E T U R N SA = S I N ( A L P H A ) * S I N ( B E T A ) EP = ( P I / ? . ) ACBS(SA) CUNST = 2 r r P I + S I N ( E P ) r D / X L A M B D A D 0 10 N = 1 I NRX P d I = CONST+FLOAT(N-11 X = CBS(PH1) Y = SIN(PH1) C ! ~ U F ( N )= CBUF(N)+CMPLX(XJY) 10 CtlNT INU€ RET U R N END

0008:

-

8

C C C C

S U B R B U T I N E OELAYCBNST ( h P T , D 0 THETA, XLAYBDA8COUF, NRXI XLLI N R ) SUBRBUTJNE T 8 D E T E R M I N E THE DELAY CSNSTANCE PER SEGMENT 8F THE L I N E A R A R R A Y FBR A G I V E N STEFR A ~ G L E ;THETA* B * J * R B O K MARCH 3 0 1 9 7 5 DIMENSION X L L ( 1 ) COMPLEX C B U F ( 1 ) D AT A P I / 6 * 2 8 3 1 8 5 3 1 / NR (NRX/NPT) I F ( T H E T A * E Q * O*O)RETURN Dl = F L B A T ( N P T ) ~ D * S I N ( T H E T P ) / X L A M B D A 02 = P I v D l D 9 10 I = 1 0 N R - 1 PHI = FLRAT(Il*D2

-

180

181

182

183