lunar lunar lunar lunar antenna antenna lunar

L U N A R P O I N T - T O - P O I N T C O M M U N I C A T I O N L . Eo V o g l e r¹

N a t i o n a l B u r e a u of S t a n d a r d s , B o u l d e r , C o l o⁰ A B S T R A C T

A p r e l i m i n a r y study of p o i n t - t o - p o i n t c o m m u n i c a t i o n s y s t e m s on the s u r f a c e of the m o o n is p r e s e n t e d in which ground w a v e p r o p a g a t i o n is a s s u m e d o v e r a lunar m o d e l c o n - sisting of a s m o o t h s p h e r e of h o m o g e n e o u s m a t e r i a l with no surrounding a t m o s p h e r e . The c o m m u n i c a t i o n s y s t e m is d e s c r i b e d in t e r m s of the p o w e r r e q u i r e d at the input t e r m - inals of the t r a n s m i t t i n g antenna in o r d e r to obtain a g i v e n s i g n a l - t o - n o i s e r a t i o at the r e c e i v e r , , Antenna c o n s i d e r a t i o n s and n o i s e e f f e c t s a r e d i s c u s s e d , and an e x a m p l e is g i v e n of a s y s t e m c o m p o s e d of a B e v e r a g e w a v e antenna t r a n s m i t t i n g t o w a r d s a v e r t i c a l e l e c t r i c dipole«,

I N T R O D U C T I O N

The p r o b l e m of d e t e r m i n i n g the r e q u i r e m e n t s n e c e s s a r y for adequate p o i n t - t o - p o i n t c o m m u n i c a t i o n s y s t e m s on the s u r f a c e of the m o o n i s , at the p r e s e n t t i m e , c o m p l i c a t e d by a l a c k of i n f o r m a t i o n c o n c e r n i n g lunar c o m p o s i t i o n and e n v i - ronment,, T h e p r e s e n c e or a b s e n c e of an i o n o s p h e r e , the v a l u e s to a s s u m e f o r c o n d u c t i v i t y , p e r m e a b i l i t y , and p e r m i t - t i v i t y of the lunar s u r f a c e m a t e r i a l , and the p o s s i b i l i t y of l a y e r i n g b e l o w the s u r f a c e a r e f a c t o r s affecting any c o n s i d e r - ation of c o m m u n i c a t i o n r e q u i r e m e n t s „ The e f f e c t of e x t r a - lunar n o i s e s o u r c e s on s i g n a l r e c e p t i o n can only be e s t i m a t e d using i n f o r m a t i o n g a i n e d f r o m E a r t h - b a s e d m e a s u r e m e n t s , Until such t i m e as actual e x p e r i m e n t s on the m o o n can be undertaken to p r o v i d e the n e e d e d i n f o r m a t i o n , lunar c o m m u -

Manuscript r e c e i v e d September 1 7 , 1962. The research reported in t h i s study has been sponsored by the Jet Propulsion Laboratory.

^ M a t h e m a t i c i a n , E l e c t r o m a g n e t i c R e s e a r c h G r o u p , R a d i o P r o p a g a t i o n E n g i n e e r i n g D i v i s i o n , C e n t r a l R a d i o P r o p a g a t i o n L a b o r a t o r y .

n i c a t i o n studies can g i v e only a g e n e r a l i n d i c a t i o n of what m a y be e x p e c t e d in the w a y of p o w e r r e q u i r e m e n t s and a n t e n - na t y p e sο

The lunar m o d e l a s s u m e d f o r the p u r p o s e s of the p r e s e n t paper is a s m o o t h s p h e r e of radius r^Q( = 1738 k m ) c o n s i s t - ing of a h o m o g e n e o u s m a t e r i a l c h a r a c t e r i z e d by a r e l a t i v e d i e l e c t r i c constant e^r, c o n d u c t i v i t y cr i n m h o s / m , and m a g n e t i c p e r m e a b i l i t y equal to that of f r e e s p a c e . The effects of any a t m o s p h e r e or i o n o s p h e r e surrounding the s p h e r e a r e n e g l e c t e d , which is p r o b a b l y j u s t i f i a b l e during the lunar night, but not n e c e s s a r i l y the d a y t i m e . The p r i - m a r y m e c h a n i s m of p r o p a g a t i o n is c o n s i d e r e d t o be the ground w a v e , the solution of which is w e l l known and m a y be e x p r e s s e d b y the Van der P o l - B r e m m e r r e s i d u e s e r i e s f o r d i f f r a c t e d w a v e s around a s m o o t h h o m o g e n e o u s s p h e r e ( 3 ) . ^ B e c a u s e of the d i f f i c u l t i e s inherent in the c o n s t r u c t i o n of any c o m p l e x antenna s t r u c t u r e s on the m o o n , l o w antenna heights a r e a s s u m e d , and, c o n s e q u e n t l y , height gain e f f e c t s a r e c o n s i d e r e d n e g l i g i b l e .

S Y S T E M LOSS

The concept of s y s t e m l o s s ( 1 6 , 17, 25) w i l l be used to d e s c r i b e the e f f e c t s of the v a r i o u s s y s t e m p a r a m e t e r s . S y s t e m l o s s L^s i s defined as the r a t i o , e x p r e s s e d in d e c i - b e l s , of the p o w e r p^t d e l i v e r e d to the input t e r m i n a l s of the t r a n s m i t t i n g antenna to the a v a i l a b l e p o w e r p^v at the r e c e i v - m g antenna t e r m i n a l s :^J

The s y s t e m l o s s m a y be d i v i d e d further into a f r e e space or i n v e r s e distance component that would be the l o s s e x p e c t e d b e t w e e n t w o i s o t r o p i c antennas situated in f r e e s p a c e , an attenuation A^t r e l a t i v e to f r e e space w h i c h accounts for the effects on p r o p a g a t i o n of the i n t e r v e n i n g t e r r a i n , and two t r a n s m i t t i n g and r e c e i v i n g antenna c o m p o n e n t s , L^. - Gj- and

N u m b e r s in p a r e n t h e s e s indicate R e f e r e n c e s at end of p a p e r .

^In this paper capital l e t t e r s a r e used to d e s i g n a t e the d e c i b e l e q u i v a l e n t of the c o r r e s p o n d i n g l o w e r c a s e l e t t e r s ,

L^s = 10 l o g ( p^t/ p^r) = P^t - P^r [ 1 ]

e . g. , Ρ

t ⁵1 0 * t

L^r- G^r> w h i c h d e s c r i b e the e f f e c t s of the p a r t i c u l a r antennas used. T h u s , E q . 1 m a y be w r i t t e n as

P^t = L^s + P^r = 1 0 1 o g ( 4¹r d^o/ \ )² + A^t + ( L^t - + ( L^r - G^r> + P^r [ 2 ] w h e r e d^Q is the a r c distance s e p a r a t i n g the t w o antennas ( i n the f r e e s p a c e t e r m i t is a s s u m e d that a r c distance a p p r o x i - m a t e s the c h o r d d i s t a n c e ) , and λ is the f r e e space w a v e - length e x p r e s s e d in the s a m e units as d^Q. ^r is the

t r a n s m i t t i n g or r e c e i v i n g antenna gain r e l a t i v e to an i s o t r o p i c antenna, and ^r i s an antenna l o s s a r i s i n g f r o m its p r o x - i m i t y to the ground: L^{t j r} = 10 l o g r / r f , w h e r e r denotes the t e r m i n a l r e s i s t a n c e and r£ the r a d i a t i o n r e s i s t a n c e in f r e e s p a c e . N o t i c e that, in o r d e r to c a l c u l a t e the a v a i l a b l e p o w e r f r o m the output t e r m i n a l of the t r a n s m i t t e r , any t r a n s m i t t e r t r a n s m i s s i o n l i n e and i m p e d a n c e matching l o s s should be added to the r i g h t side of E q . 2. H o w e v e r , with c a r e f u l d e s i g n the e f f e c t of these l o s s e s m a y be m a d e n e g l i g i b l e .

Eq. 2 p r o v i d e s a f o r m u l a to find the t r a n s m i t t e r p o w e r n e c e s s a r y to obtain a g i v e n a v a i l a b l e p o w e r at the r e c e i v i n g antenna t e r m i n a l s . H o w e v e r , the p o w e r r e c e i v e d c o n s i s t s not only of the d e s i r e d s i g n a l but a l s o of r a d i o n o i s e s a r i s i n g f r o m both within and without the r e c e i v i n g s y s t e m . If r denotes the d e s i r e d m i n i m u m s i g n a l - t o - n o i s e p o w e r r a t i o that w i l l p r o v i d e a g i v e n g r a d e of r e c e p t i o n as m e a s u r e d at the r e c e i v e r p r e d e t e c t i o n output, and an e f f e c t i v e n o i s e f i g u r e f is defined as the r a t i o of the s i g n a l t o a r e f e r e n c e Johnson- n o i s e p o w e r r a t i o that is a v a i l a b l e f r o m a l o s s - f r e e r e c e i v i n g antenna to the r e c e i v e r p r e d e t e c t i o n output s i g n a l - t o - n o i s e r a t i o , then the r e c e i v e d p o w e r m a y be e x p r e s s e d ( 1 7 ) as

ρ = r f k t b / i [ 3 ]

*r Β ο c

w h e r e k g t^Qb is the r e f e r e n c e Johnson-noise p o w e r , k g is B o l t z m a n n ' s constant (= 1.38044 Χ I O "^{2 3}) , t^Q is a r e f e r e n c e t e m p e r a t u r e in d e g r e e s K e l v i n , b is the e f f e c t i v e n o i s e bandwidth in c y c l e s p e r s e c o n d , and i^Q = r / r^r, with r^r d e - noting the r a d i a t i o n r e s i s t a n c e of an e q u i v a l e n t l o s s l e s s antenna. The d e f i n i t i o n of f in t e r m s of n o i s e f i g u r e s of the component p a r t s of the r e c e i v i n g n e t w o r k can be shown t o be ( 1 )

f = f - 1 + f [ 4 ] e ctr

where f^e is the "noise f i g u r e " of the external noise and f^{c t r} is the noise figure of the antenna c i r c u i t , t r a n s m i s s i o n line and impedance matching c i r c u i t , and the r e c e i v e r .

Using the foregoing definitions and assuming a poorly- conducting ground such that r^r ~ r^, the t r a n s m i t t e r power may now be e x p r e s s e d as

Ρ = 20 1οβ(4πά / λ ) + A - (G^ + G ) + L t ο t t r t

+ R + F + B + 1 0 log(k_ t ) [ 5 ] Β ο

The following sections w i l l discuss the v a r i o u s components of E q^c 5o

N O R T O N S U R F A C E W A V E A T T E N U A T I O N A

N u m e r i c a l p r o c e d u r e s for the calculation of e l e c t r o m a g - netic fields diffracted around a smooth sphere have been developed by various authors ( 6 , 15, 3 )⁰ The ground wave may be e x p r e s s e d as a s e r i e s of residues that, if the func- tions of antenna height are equal to unity, depend on the radius of the sphere r^Q, the a r c distance d^Q separating the antennas, the f r e e space wavelength λ, the r e l a t i v e d i e l e c - t r i c constant e^r and conductivity <r of the ground, and the p o l a r i z a t i o n of the w a v e , T o e m p h a s i z e the fact that no height gain effects a r e included in the analysis presented in this paper, the t e r m " N o r t o n surface w a v e " (15) is used to denote the ground wave with antenna heights set equal to z e r o , In p a r a m e t r i c f o r m the Norton surface wave attenuation r e l a t i v e to an i n v e r s e distance field A ^ is conveniently plotted as a function of three p a r a m e t e r s : K , b^e , and x ^⁰

For horizontal p o l a r i z a t i o n ( K = K ^ ) and v e r t i c a l p o l a r i - zation ( K = Κ )

ι

Κ = ( 2 u r / λ )³

|τ I

h

L

| Τ

| 1

[ 6 ]

where [ Τ ^ | and JT^vj a r e plotted as functions of e^r and s = 60 λ σ ( m h o s / m ) in F i g s , 1 and 2« Values of € ^r > 10 a r e not shown because present information indicates that the r e l a t i v e d i e l e c t r i c constant of the moon is considerably l e s s than 10o H o w e v e r , JTjJ and J T^V| a r e e a s i l y obtained for other € ' s , since

r

] T^h|

2 2"

(e - 1 ) + s

r M

2 2 / 2 2 ' (€ - 1 ) + S / ( e + S )

r r 7 ] L i m i t i n g f o r m s of t h e s e functions f o r s m a l l s b e y o n d the r a n g e of the graphs a r e

| T I ^ N/ T ~ - X | T U ΝΓ Γ ~ Τ /⁶ , s - Ο [ 7 a ]

1 h¹ r ¹ ν ' r r

and f o r l a r g e s

[ TJ - N/ T , | τ ] ~ 1/\ΓΤ, s — oo [ 7 b ]

S i m i l a r plots of b ° and b ° (the s u b s c r i p t s h and v a g a i n r e f e r r i n g to h o r i z o n t a l and v e r t i c a l p o l a r i z a t i o n , h v

r e s p e c t i v e l y ) as functions of €r and s a r e shown in F i g se 3 and 4. E x p r e s s i o n s f o r b ° and b ° a r e

h ν

b ° = 1 8 0 ° - t a n "_h ^X[ ( € - l ) / s ] , b ° = 2 t a n "_{r v r}¹ [ € / s j - t a n "¹^ - l ) / s ]

J L > r / j

[ 8 ] F i g s . 5 - 8 v s the distance p a r a m e t e r χ , w h e r e

x' = f3 d ( k m )

The N o r t o n s u r f a c e w a v e attenuation A^t i s g r a p h e d in

[ 9 ] o m c ο

with fm c denoting the f r e q u e n c y in m e g a c y c l e s p e r s e c o n d and d⁰( k m ) the distance m e a s u r e d in k i l o m e t e r s . It should be n o t i c e d that, in g e n e r a l , does not v a r y much with b , and l i n e a r i n t e r p o l a t i o n m a y be used f o r v a l u e s of b ° other than those shown. A l s o it can be s e e n that, f o r Κ > 10, A ^ a p p r o a c h e s a l i m i t i n g function that is p l o t t e d as the top c u r v e on e a c h g r a p h .

E q s . 2 and 5 a r e s t r i c t l y a p p l i c a b l e only f o r the c a s e of antennas s e p a r a t e d a sufficient d i s t a n c e a p a r t ( d^Q > > \ ) such that the magnitude of t h e i r mutual i m p e d a n c e is s m a l l c o m p a r e d to the s e l f r e s i s t a n c e s of the antennas ( 1 7 ) .

B e c a u s e of this r e s t r i c t i o n , A ^ is not shown in the f i g u r e s for v a l u e s of X Q < 1. A s d^Q ( o r X Q ) g o e s to z e r o , A^t a p p r o a c h e s 20 l o g = - 6 . 0 2 , w h i c h w o u l d c o r r e s p o n d to the s u r f a c e w a v e f i e l d intensity e x p e c t e d b e t w e e n s h o r t v e r t i - cal e l e c t r i c d i p o l e s situated n e a r e a c h other on a p e r f e c t l y conducting p l a n e .

A N T E N N A E F F E C T S A N D T H E W A V E A N T E N N A

The t e r m s L. and G^t _ (the subscript t, r r e f e r r i n g to either transmitting or r e c e i v i n g antenna) in E q . 2 d e s c r i b e the effects of the particular transmitting and r e c e i v i n g anten- nas used in the communication s y s t e m under considération»

Lj^ ^r is defined as the r a t i o e x p r e s s e d in decibels of the t e r m i n a l resistance of the antenna to its f r e e space radiation r e s i s t a n c e . Thus, as the height of the antenna above the surface is i n c r e a s e d , the r a t i o of the r e s i s t a n c e s approaches unity, and or L^r e f f e c t i v e l y b e c o m e z e r o . F o r heights near the surface, the r e s i s t a n c e is a function of the e l e c t r o - magnetic ground constants, €^r and r j -, and for p o o r l y con- ducting grounds ^r may b e c o m e v e r y l a r g e ( 2 1 ) , G^{t r} denotes the free space gain of an optimally oriented l o s s l e s s antenna above an i s o t r o p i c antenna; e. g„ , G^. = G^r = 101og(3/2)

= lo76 for e l e c t r i c current elements or e l e m e n t a r y d i p o l e s , and Gf = G = 2 . 1 5 for half-wave antennas.

L r

Although the separation of antenna effects into a free

space gain and a ground p r o x i m i t y loss is somewhat arbitrary, e s p e c i a l l y in the case of surface wave propagation, it is possible to reduce the effect of the ground and at least

approach a f r e e space condition for low antennas through the use of an appropriate ground s c r e e n . Discussions of antenna c h a r a c t e r i s t i c s and their modifications by ground s c r e e n s w i l l be found in R e f s . 18, 23, and 24. The r e s t of this s e c - tion w i l l be devoted to a discussion of the B e v e r a g e wave antenna ( 2 ) and d i p o l e - t y p e antennas.

The wave antenna in its s i m p l e s t f o r m consists of a long horizontal w i r e situated a short height above the ground and terminated at one end through its c h a r a c t e r i s t i c impedance.

It is a unidirectional antenna with the m a x i m u m gain in the direction of the antenna axis and toward the terminated end.

Wait (22) has shown that the v e r t i c a l e l e c t r i c field component of a wave antenna is proportional to a c o m p l e x factor T^v, t e r m e d the "wave t i l t " and defined by

Τ = ν ^{( e r}- l ) - is

1

2 / ( « ^r - i s ) [ 1 0 ]

and a function S¹* that depends on w a v e l e n g t h , e l e c t r o m a g - netic ground constants, antenna length and height, and an angle φ m e a s u r i n g the d i r e c t i o n in which the antenna is

pointing. S^!, obtained by integrating the contributions of all the elements along the antenna, is g i v e n by

1 - e x p[ - ( r- i ß cos φ) I ] ^r

( Γ - iß cos φ) a ^{1 J}

w h e r e β = 2 π/ λ , S. is the antenna l e n g t h , and Γ i s the p r o p - agation constant of the w i r e w h i c h f o r l a r g e antenna heights a p p r o a c h e s the p r o p a g a t i o n constant of plane w a v e s in f r e e s p a c e , iß. In t e r m s of the w a v e antenna p o w e r gain (13) r e f e r r e d to an i s o t r o p i c antenna (p / p . ) , this b e c o m e s

wa is ο

( ρ / p . ) = ( β 4 ο ο 3 ψ )2 J S ' L 2 IT Ι 2 ( 1 2 0 R / | Z I^Z) [ I Z ]

wa I S O r T ' ι ι ' ν ο ¹ o^{1 J}

w h e r e ZQ = R Q + i XQ is the c h a r a c t e r i s t i c i m p e d a n c e of the w a v e antenna. T h e t h e o r e t i c a l d e t e r m i n a t i o n of Lj. - G^t or

Lr - Gr f o r a w a v e antenna in t e r m s of its t e r m i n a l r e s i s t - ance is quite d i f f i c u l t . H o w e v e r , s i n c e these quantities a r e e s s e n t i a l l y e q u i v a l e n t to p o w e r r a t i o s m e a s u r i n g the e f f e c - t i v e n e s s of the antenna, an e s t i m a t e of t h e i r magnitude m a y be obtained b y setting

L - G„ ^ - 10 l o g ( p / p . ) [ 1 3 ]

t, r t, r w a i s o ^{L J}

The f a c t o r | TV| in E q . 12 is shown in F i g . 2 , and JS'| i s g r a p h e d in F i g . 9 as a function of the t w o p a r a m e t e r s (ai) and (β I) ( m - c o s φ ) , with the p r o p a g a t i o n constant Γ defined as

Γ = a + i ß m [ 14 ]

w h e r e a and m a r e r e a l . Thus, when the antenna height h is sufficiently l a r g e , a = 0 and m = 1. A t l o w e r heights an approximate e x p r e s s i o n for the values of a and m has been given by C a r s o n ( 7 ) :

a/ß ~ m - 1 ~ 2^{3 / Z}( ß h ) J ^{€ 2}+ s ² i n ( 4 h / d^A) J [ 1 5 ]

w h e r e d^o is the d i a m e t e r of the antenna w i r e . F o r an antenna actually lying on the ground, Γ m a y be e x p r e s s e d as ( 9 )

R = « + i ß m = ß j m²- j ( *^r+ l ) + ΐ | - J ( €^R + l )²+ s²+ (^{€ r} + l ) ^ [ 1 6 ]

It should be n o t i c e d f r o m E q . 16 that the p r o p a g a t i o n constant of a w a v e antenna l y i n g on the ground m a y approach its f r e e space value if the r e l a t i v e d i e l e c t r i c constant is v e r y near unity and the conductivity is e x t r e m e l y s m a l l . T h e s e c o n d i - tions appear to hold f o r lunar s u r f a c e m a t e r i a l .

The e f f e c t of finite ground conductivity is quite pronounced on d i p o l e - t y p e antennas of s m a l l heights at the l o w e r f r e - q u e n c i e s . S o m m e r f e l d and R e n n e r ( 2 0 ) have i n v e s t i g a t e d ground p r o x i m i t y e f f e c t s f o r the c a s e of h o r i z o n t a l and v e r t i - cal e l e c t r i c d i p o l e s , and, using t h e i r e x p r e s s i o n f o r the antenna t e r m i n a l r e s i s t a n c e r , the quantity L^. ^r= 10 l o g ( r/ r ^ ) has b e e n c a l c u l a t e d and plotted v s s in F i g s . 1 1 - 1 4 for a v e r t i c a l e l e c t r i c d i p o l e . The c u r v e s show L^{f v} f o r v a r i o u s values of €^r and the height p a r a m e t e r a = 4ττη/λ, w h e r e h is the height in m e t e r s of the dipole above the ground; r , e x p r e s s e d in i n t e g r a l f o r m in the S o m m e r f e l d and R e n n e r p a p e r , was n u m e r i c a l l y e v a l u a t e d using an e l e c t r o n i c c o m - p u t e r .

E F F E C T I V E N O I S E F I G U R E

The e f f e c t i v e n o i s e f i g u r e f ( 1 ) d e s c r i b e s the n o i s e of the total r e c e i v i n g s y s t e m in t e r m s of the n o i s e f i g u r e s of its component p a r t s :

w h e r e ( 12)

and

f - 1 + f [ 1 7 ]

e ctr ^{L J}

ctr c c t c t r

£^c= l + ( !^c- l) ( t^c/ t^o) . £^t= 1 + ( i^t- D( t^t/ t^o) [ 1 8 b ]

4

i^c and i^t a r e the l o s s f a c t o r s ( i . e . , the r a t i o of the a v a i l - able input to output p o w e r s of the c o m p o n e n t ) of the antenna c i r c u i t and the t r a n s m i s s i o n line plus i m p e d a n c e matching c i r c u i t , r e s p e c t i v e l y , with t^Q and t^. being t h e i r c o r r e - sponding absolute t e m p e r a t u r e s ; f^r d e s i g n a t e s the r e c e i v e r n o i s e f i g u r e , and t is a r e f e r e n c e t e m p e r a t u r e . G e n e r a l l y

4

N o t i c e that the s y m b o l used in this s e c t i o n is not the s a m e as the t r a n s m i t t i n g antenna l o s s JL^ d i s c u s s e d in the s e c t i o n on t r a n s m i s s i o n l o s s .

speaking, the f a c t o r s f^e and f^c w i l l p r e d o m i n a t e in c a l c u - lating v a l u e s of f, e s p e c i a l l y at the l o w e r f r e q u e n c i e s ( 1 0 ) ; at high f r e q u e n c i e s f depends m o r e on f^t and f^r, w h i c h a r e b e s t obtained by d i r e c t m e a s u r e m e n t . With c a r e in the i m p e d a n c e matching c i r c u i t , one m a y w r i t e E q . 17 as

f = f + ( i - l ) ( f - 1 + t It ) + (f - 1 ) , 1 = 1 [ 19 ]

e c r c o r t

The e f f e c t i v e n o i s e f i g u r e now depends on the l o s s a s s o c i a t e d with the antenna c i r c u i t i^c, the absolute t e m p e r a t u r e of the antenna t^c, the r e c e i v e r n o i s e f i g u r e f^r, and the m e a s u r e of the e x t e r n a l n o i s e f .

e

A t the p r e s e n t t i m e , of c o u r s e , and until actual m e a s u r e - ments can be undertaken, the amount of e x t e r n a l n o i s e r e c e i v e d b y an antenna l o c a t e d on the m o o n can be only r o u g h l y e s t i m a t e d . It is l i k e l y that the p r e d o m i n a n t s o u r c e w i l l be g a l a c t i c ; h o w e v e r , c o n s i d e r a t i o n a l s o should be g i v e n to s o l a r n o i s e and n o i s e a r i s i n g f r o m the n e a r b y E a r t h . A n e s t i m a t e of g a l a c t i c n o i s e can be obtained f r o m r a d i o n o i s e maps p r e p a r e d by M e n z e l of the H a r v a r d C o l l e g e O b s e r v a t o r y ( 1 4 ) . T h e s e maps a l s o g i v e n o i s e i n t e n s i t i e s of d i s c r e t e g a l a c t i c s o u r c e s f o r v a r i o u s f r e q u e n c i e s . Using the f r e - quency v a r i a t i o n i n d i c a t e d in the text a c c o m p a n y i n g these m a p s , F^e = 10 l o g f^e ( c o n s i d e r i n g g a l a c t i c n o i s e o n l y ) i s plotted v s f r e q u e n c y in F i g . 10 f o r a r e f e r e n c e t e m p e r a t u r e t^Q = 288.39° K . Until data f r o m n o i s e m e a s u r e m e n t s taken a b o v e E a r t h ' s i o n o s p h e r e a r e a v a i l a b l e , it can be a s s u m e d only that the f r e q u e n c y v a r i a t i o n is as i n d i c a t e d in the f i g u r e for f r e q u e n c i e s l e s s than the p l a s m a f r e q u e n c y of about 20 M c / s e c ; h o w e v e r , it is p h y s i c a l l y apparent that the e x t e r - nal n o i s e f i g u r e c u r v e w i l l at l e a s t l e v e l off at s o m e l o w e r f r e q u e n c y . T h e e m p i r i c a l e x p r e s s i o n used to plot the g a l a c - tic n o i s e c u r v e is

f = 1.585 X 1 0⁵ f "²"³, f < 200 e m c m c

f = 6.467 X 1 0⁶ f "³ , f > 200 [ 2 0 ] e m c m c

In the c a s e of s o l a r n o i s e and n o i s e s f r o m t e r r e s t r i a l s o u r c e s , it is p r o b a b l e that n o t i c e a b l e e f f e c t s g e n e r a l l y w i l l occur only at the l o w e r f r e q u e n c i e s , e x c e p t during p e r i o d s of e x t r e m e s o l a r a c t i v i t y when c o n s i d e r a b l e n o i s e at a l l f r e q u e n c i e s m a y be e x p e c t e d ( 4 ) . A l s o , of c o u r s e , s o m e r a d i o n o i s e w i l l be

g e n e r a t e d by the s u r f a c e of the m o o n i t s e l f . N o attempt is made in the p r e s e n t paper to i n v e s t i g a t e these a s p e c t s of the p r o b l e m .

The antenna c i r c u i t n o i s e f i g u r e f^{c >} depending as it does on the antenna l o s s and absolute t e m p e r a t u r e of the antenna, w i l l v a r y a c c o r d i n g to the type of antenna used, the e l e m e n t s of the c i r c u i t , and whether the antenna is in d i r e c t sunlight or not. Antenna l o s s is b e s t obtained by d i r e c t m e a s u r e m e n t ; h o w e v e r , if m e a s u r e m e n t s a r e i m p r a c t i c a l , iQ m a y be

a p p r o x i m a t e d by the " g r o u n d - p r o x i m i t y " l o s s i^r d i s c u s s e d in the s e c t i o n on antenna e f f e c t s .

C A L C U L A T I O N O F R E Q U I R E D P O W E R

A t t e m p t s have b e e n m a d e r e c e n t l y to deduce the e l e c t r o - m a g n e t i c p r o p e r t i e s of the m o o n¹ s s u r f a c e m a t e r i a l through the use of r a d a r data (19)« Although d i f f e r e n c e s e x i s t c o n - c e r n i n g the e x a c t i n t e r p r e t a t i o n of the data (5, 11), t h e r e is g e n e r a l a g r e e m e n t that the r e l a t i v e p e r m i t t i v i t y is not far a b o v e unity and that the conductivity is quite l o w . In any c a s e the graphs d i s c u s s e d in the p r e c e d i n g s e c t i o n s a r e a p p l i c a b l e to a w i d e r a n g e of v a l u e s of € ^r and cr .

Senior and S i e g e l ( 1 9 ) e s t i m a t e the r e l a t i v e p e r m i t t i v i t y and c o n d u c t i v i t y of lunar s u r f a c e m a t e r i a l to be € = 1.1

—4 /

and ο- = 3,4 X 10" m h o s / m . M a t e r i a l s constituting E a r t h ' s c r u s t have l a r g e r v a l u e s , although s o m e substances such as e x t r e m e l y d r y , c o a r s e q u a r t z i t i c sand a r e s o m e w h a t this o r d e r of m a g n i t u d e . F o r the purpose of a r r i v i n g at s o m e e s t i m a t e of lunar p r o p a g a t i o n c o n d i t i o n s , it w i l l be a s s u m e d that €^r r a n g e s f r o m 1.1 to 2.0 and σ l i e s b e t w e e n 10"^

and 10 m h o s / m .

If one m e a s u r e s the a r c distance d in k i l o m e t e r s and ο

c h o o s e s a r e f e r e n c e t e m p e r a t u r e t^Q = 288.39° Κ (as in the s e c t i o n on e f f e c t i v e n o i s e f i g u r e ) , the r e q u i r e d t r a n s m i t t e r p o w e r g i v e n by E q . 5 m a y be r e w r i t t e n as

w h e r e L is c a l l e d the b a s i c t r a n s m i s s i o n l o s s and is g i v e n [ 2 1 ]

by

U = 32.45 + 20 l o g d ( k m ) + 20 l o g f + A

b ° ο m c ' ο ^x ' ⁶ m c t [ 2 2 ]

F i g . 15 shows c u r v e s of f o r v e r t i c a l l y p o l a r i z e d w a v e s as a function of f r e q u e n c y and f o r the d i s t a n c e s i n d i c a t e d . V a l u e s of A^. w e r e obtained f r o m F i g s . 5 - 8 b y l i n e a r i n t e r - polation in both the Κ^γ and b ° d i r e c t i o n s , K ^v b e i n g g i v e n by F i g . 2 and E q . 6, and b ^ being r e a d f r o m F i g . 4. N o t i c e that the b a s i c t r a n s m i s s i o n l o s s v a r i e s i n v e r s e l y with c o n - ductivity at the l o w e r f r e q u e n c i e s , w h e r e a s at high f r e q u e n - c i e s , the e f f e c t of v a r i a t i o n with <r b e c o m e s n e g l i g i b l e .

If one now a s s u m e s a c o m m u n i c a t i o n s y s t e m c o n s i s t i n g of, for e x a m p l e , a h o r i z o n t a l t r a v e l i n g w a v e antenna of length i = λ / 4 l y i n g on the m o o n ' s s u r f a c e and t r a n s m i t t i n g t o w a r d s a s h o r t v e r t i c a l e l e c t r i c d i p o l e at a height h = λ / 1 6 p l a c e d s o m e distance away and in an o p t i m u m d i r e c t i o n f r o m the t r a n s m i t t e r (φ ~ 0 ° ) , one m a y e s t i m a t e the p o w e r r e q u i r e - ments f r o m E q . 2 1 . A n e s t i m a t e of L^t - G^- as a function of f r e q u e n c y m a y be obtained f r o m E q s . 12 and 13 by a s s u m i n g the f r e e s p a c e value for the w a v e antenna c h a r a c t e r i s t i c i m p e d a n c e JZ^o|^ R^Q = 120 π and using E q . 16 and F i g s . 2 and 9.

F i g s . 11 and 12 with a - π/4 g i v e s an e s t i m a t e of ^^c( ^ H^r\ and, by c o m p a r i s o n with F i g . 10, it can be s e e n that in this e x a m p l e the e x t e r n a l n o i s e tends to "blanket out" the e f f e c t of the r e c e i v i n g antenna c i r c u i t l o s s . Thus, if one a s s u m e s the e f f e c t i v e n o i s e f i g u r e to be a function only of the e x t e r n a l n o i s e f^e and a r e c e i v e r n o i s e f i g u r e of, say, f^r = 4

F = 10 l o g ( f^e+ 3 ) , i^t = i^c = 1 [ 2 3 ] the r e q u i r e d t r a n s m i t t e r p o w e r f o r a g i v e n type of s e r v i c e

under the f o r e g o i n g r e s t r i c t i o n s can be c a l c u l a t e d f r o m E q . 21 by setting G^r = 1.76 and making use of F i g s . 10 and 15 and E q . 23. F i g . 16 shows v a l u e s of P^t - ( R + B ) as a function of f r e q u e n c y f o r antenna s e p a r a t i o n distances of 10,

100, and 500 k m . The w a v e antenna length of ί = λ / 4 and v e r t i c a l d i p o l e height of h = λ / 1 6 w e r e a r b i t r a r i l y c h o s e n , the m a i n c o n s i d e r a t i o n being the c o m p l e x i t y of the p h y s i c a l s t r u c t u r e s of the antennas. Of c o u r s e , at l o w f r e q u e n c i e s e v e n antennas of these d i m e n s i o n s m i g h t be v e r y difficult to construct under w o r k i n g conditions on the m o o n . N o t i c e that at v e r y s h o r t d i s t a n c e s p r o p a g a t i o n w i l l be by l i n e - o f - s i g h t r a t h e r than s u r f a c e w a v e due to the d i p o l e being at a height other than z e r o . The t r a n s m i s s i o n l o s s in this c a s e should

be c a l c u l a t e d b y the standard g e o m e t r i c a l optics m e t h o d . It should be e m p h a s i z e d that this p a r t i c u l a r c o m b i n a t i o n of antennas is meant m e r e l y to i l l u s t r a t e the use of E q . 21 in e s t i m a t i n g p o w e r r e q u i r e m e n t s . Other antenna c o m b i n a t i o n s must be i n v e s t i g a t e d b e f o r e a d e c i s i o n is made as to what w i l l constitute the m o s t e f f i c i e n t lunar c o m m u n i c a t i o n s y s t e m .

Now to e s t i m a t e the r e q u i r e d p o w e r supplied to the input t e r m i n a l s of the t r a n s m i t t e r , one needs only to d e s i g n a t e the type of c o m m u n i c a t i o n s e r v i c e d e s i r e d , thus s p e c i f y i n g R and B . F o r e x a m p l e with standard b r o a d c a s t s e r v i c e and a bandwidth of 10 k c , R is g i v e n the value 39 db ( 8 ) and Β = 40 db, so that 79 db should be added to the c u r v e s of F i g . 16 to obtain the r e q u i r e d p o w e r in d e c i b e l s a b o v e 1 w . Thus the p o w e r r e q u i r e d for this type of s e r v i c e at a r a n g e of 10 k m and f o r a f r e q u e n c y of 300 k c / s e c w o u l d be about 10 db or

10 w . F o r a l o w - g r a d e v o i c e c o m m u n i c a t i o n s e r v i c e and 6 kc bandwidth, R = 9 db ( 8 ) , Β = 38 db, and 47 db would b e added to the c u r v e s . The r e q u i r e d p o w e r in this c a s e at a distance of 100 km and f o r a f r e q u e n c y of 100 k c / s e c would be about

16 w . A t the f o r e g o i n g f r e q u e n c i e s , the s t r u c t u r a l d i m e n - sions of both antennas w o u l d , of c o u r s e , be quite l a r g e . F o r s m a l l e r antennas p o w e r r e q u i r e m e n t s m a y be e s t i m a t e d f r o m F i g . 16 b y r e a d i n g the c u r v e s at h i g h e r f r e q u e n c i e s .

In the p a r t i c u l a r i d e a l i z e d s y s t e m d e s c r i b e d by F i g . 16, a number of points should be noted: 1) the r e q u i r e d p o w e r does not v a r y a p p r e c i a b l y o v e r the r a n g e of €^ a s s u m e d , and, thus, f o r this m o d e l the r e l a t i v e p e r m i t t i v i t y of the lunar s u r - f a c e is not e s p e c i a l l y c r i t i c a l f o r p r o p a g a t i o n c o n s i d e r a t i o n s ;

2) p r o p a g a t i o n out to s o m e w h a t b e y o n d 100 k m is p r a c t i c a l for m o s t types of s e r v i c e , at l e a s t at M F or b e l o w ; 3) the c u r v e s indicate an o p t i m u m f r e q u e n c y e x i s t s , depending on the conductivity of the lunar s u r f a c e and the r a n g e of p r o p a - gation; f o r the c o n d u c t i v i t i e s and d i s t a n c e s shown, the o p t i - m u m f r e q u e n c y l i e s in the L F band. It should be kept in mind that the e f f e c t i v e n o i s e f i g u r e of the r e c e i v i n g s y s t e m w a s c o n s i d e r e d to be only a function of g a l a c t i c n o i s e ( w h i c h , of c o u r s e , is e x t r a p o l a t e d at the l o w e r f r e q u e n c i e s ) and a r a t h e r low r e c e i v e r n o i s e f i g u r e . If the r e c e i v i n g antenna l o s s J ?^C w e r e l a r g e enough, it is apparent f r o m E q . 19 that F w o u l d have h i g h e r v a l u e s than those a s s u m e d . A l s o , during the lunar day, the antenna t e m p e r a t u r e t w o u l d i n c r e a s e , thus

making the e f f e c t i v e n o i s e f i g u r e e v e n h i g h e r » A C K N O W L E D G M E N T S

The author g r a t e f u l l y a c k n o w l e d g e s the a s s i s t a n c e of the f o l l o w i n g p e r s o n n e l in the p r e p a r a t i o n of this r e p o r t :

J. E . H e r m a n , J. L⁰ N o b l e , P^e G, R a t c l i f f e , and R . E . W i l k e r s o n⁰ S p e c i a l thanks g o to J. L . N o b l e f o r his a s s i s t - ance in the c a l c u l a t i o n and plotting of the attenuation c u r v e s and to L . A . C h a r l e s f o r the typing of the m a n u s c r i p t . The author a l s o thanks K , A , N o r t o n and J. R . W a i t of the

N a t i o n a l B u r e a u of Standards B o u l d e r L a b o r a t o r i e s and P a u l S. Goodwin of Jet P r o p u l s i o n L a b o r a t o r y f o r t h e i r s u g g e s t i o n s and g u i d a n c e .

R E F E R E N C E S

1 B a r s i s , A . P . , N o r t o n , K . A . , R i c e , P . L . , and E l d e r , P . Η . , " P e r f o r m a n c e p r e d i c t i o n s f o r s i n g l e t r o p o s p h e r i c c o m m u n i c a t i o n links and f o r s e v e r a l links in t a n d e m , ¹¹ N a t l . B u r . Standards T N 102 ( A u g u s t 1961), s e e A p p e n d i x I I L

2 B e v e r a g e , H . H^c , R i c e , C . W . , and K e l l o g g , E . W , ,

" T h e w a v e antenna, ^M T r a n s . A m . Inst. E l e c . E n g r s . 42, 215 ( 1 9 2 3 ) .

3 B r e m m e r , Η . , T e r r e s t r i a l R a d i o W a v e s ( E l s e v i e r P u b l i s h i n g C o . , A m s t e r d a m , 1949).

4 B r o w n , R . H . and L o v e l l , A . C . Β . , T h e E x p l o r a t i o n of Space by R a d i o ( C h a p m a n and Hall L t d . , L o n d o n , 19 57).

5 B r o w n , W . Ε . , " A lunar and p l a n e t a r y e c h o t h e o r y , ¹¹ J. G e o p h y s . R e s e a r c h 6_5, 3087 ( 1 9 6 0 ) .

6 B u r r o w s , C R . and G r a y , M . C . , " T h e e f f e c t of the e a r t h ' s c u r v a t u r e on g r o u n d - w a v e p r o p a g a t i o n , " P r o c . Inst.

R a d i o E n g r s . 29_, 16 ( 1 9 4 1 ) .

7 C a r s o n , J. R . , " W a v e p r o p a g a t i o n in o v e r h e a d w i r e s with ground r e t u r n , " B e l l S y s t e m T e c h . J. 5, 539 ( 1 9 2 6 ) .

8 C o m i t é Consultatif International des R a d i o c o m m u n i c a - tions, "Bandwidths and s i g n a l - t o - n o i s e ratios in c o m p l e t e s y s t e m s , " V I P l e n a r y A s s e m b l y , Internatl. R a d i o Consulta- tive C o m m i t t e e ( G e n e v a ) 1, 30 (1951).

9 C o l e m a n , B . L . , " P r o p a g a t i o n of e l e c t r o m a g n e t i c d i s - turbances along a thin w i r e in a h o r i z o n t a l l y stratified

m e d i u m , " P h i l . M a g . 41_, 276 ( 1 9 5 0 ) .

10 C r i c h l o w , W . Q . , Smith, D . F . , M o r t o n , R . Ν . , and C o r l i s s , W . R . , " W o r l d w i d e r a d i o n o i s e l e v e l s e x p e c t e d in the f r e q u e n c y band 10 kc to 100 M c , " N a t l . B u r . Standards C i r c u l a r 557 ( A u g u s t 1955).

11 D a n i e l s , F . Β . , " A t h e o r y of r a d a r r e f l e c t i o n f r o m the m o o n and p l a n e t s , " J⁰ G e o p h y s . R e s e a r c h 66, 1781 ( 1 9 6 1 ) .

12 F r i i s , Η . Τ . , " N o i s e f i g u r e s of r a d i o r e c e i v e r s , "

P r o c . Inst. R a d i o E n g r s^e 32^, 419 ( 1 9 4 4 ) .

13 M a r t i n , C . A . and W i c k i z e r , G. S. , "Study of B e v e r a g e w a v e antenna f o r use with l o w - f r e q u e n c y L o r a n , " R C A , F i n a l E n g . R e p . on C o n t r a c t W - 2 8 - 0 9 9 - a c - 3 1 5 ( 1949).

14 M e n z e l , D, Η . , " C o s m i c n o i s e s u r v e y , " H a r v a r d C o l l e g e O b s e r v a t o r y , C a m b r i d g e , M a s s .

15 N o r t o n , Κ . A . , " G r o u n d - w a v e f i e l d i n t e n s i t y , " P r o c . Inst. R a d i o E n g r s . 29, 623 ( 1 9 4 1 ) .

16 N o r t o n , Κ . A . , " T r a n s m i s s i o n l o s s in r a d i o p r o p a g a - t i o n , " P r o c . Inst. R a d i o E n g r s . 146 ( 1 9 5 3 ) .

17 N o r t o n , Κ . A . , " S y s t e m l o s s in r a d i o w a v e p r o p a g a - tion, " J. R e s e a r c h N a t l . B u r . Standards 63D, 53 (July - A u g u s t 1959)o

18 Schelkunoff, S . A . and F r i i s , Η . Τ . , A n t e n n a s : T h e o r y and P r a c t i c e (John W i l e y and Sons I n c . , N e w Y o r k , 1952).

19 S e n i o r , T . B . A . and S i e g e l , K . M . , " A t h e o r y of r a d a r s c a t t e r i n g by the m o o n , " J. R e s e a r c h N a t l . B u r . Standards 64D, 217 ( M a y - June I 9 6 0 ) .

20 S o m m e r f e l d , A . and R e n n e r , F . , " S t r a h l u n g s e n e r g i e und e r d - a b s o r p t i o n b e i dipolantennen, " A n n . P h y s . 4 1 , 1 ( 1 9 4 2 ) .

21 W a i t , J. R . , " R a d i a t i o n r e s i s t a n c e of a s m a l l c i r c u l a r l o o p in the p r e s e n c e of a conducting ground, " J. A p p l . P h y s . 24, 646 ( 1 9 5 3 ) .

22 W a i t , J. R . , " R a d i a t i o n f r o m a ground antenna, " Can.

J. T e c h n o l . 32, 1 (19 54).

23 W a i t , J. R . and S u r t e e s , W . J. , " I m p e d a n c e of a t o p - l o a d e d antenna of a r b i t r a r y length o v e r a c i r c u l a r grounded

s c r e e n , " J. A p p l . P h y s . 25, 553 (1954).

24 Wait, J. R . , "Effect of the ground s c r e e n on the field radiated f r o m a m o n o p o l e , " Inst. R a d i o E n g r s . T r a n s , on Antennas and P r o p a g a t i o n A P - 4 , 179 (1956).

25 Wait, J. R . , " T r a n s m i s s i o n of power in r a d i o p r o p a - gation, " E l e c . R a d i o E n g r . 36, 146 (1959).

0.1,

I t

10 7

1 5 y s

1 3 F u k L A K b t b : | l y s

2.5' 2

I7j _1/2

" |T1 " n | L vV t r >i ^h|s[V(e -l)* + S° T^{2 1/2}

-

Ï2

" Kh- [ VC II ι ο / /ν/ J. = 3.02 χ I0~2 / | Th| ' f m c I.I . ro : MOON'S RADIUS = 1738 km. î"

. ro :

|Γ

FOR SMALL

!

S

! 1

! 1

0.01 0.05 0.1 0.5 1.0 5 10 50 100

S = 6 0\ c r( m h o s / m ) = 1.8 χ IO⁴ a( m h o s / m) / f^mc

F i g . 1 P a r a m e t e r | T j J f o r h o r i z o n t a l p o l a r i z a t i o n

ι.οι—ι ι ι 11 im—ι ι ι ι um—ι ι ι 11 mm—ι ι ι 11 ni

Q g _ ( ( s

K^ = [{2irr⁰/\y^/5\Tjy^l = ^02%\0-^z/\T^w\-i^mc^/3

r0 MOON'S RADIUS = 1738 km 0 7 4—4 μ -

Ι ILΓι 1

M v lu o — γ τ ~ : : ^ ^ p r a g^ ^ y ^ ^

ι

FOR S M A L L S | TV| ^ ' "

FOR LARGE S= | TV| ~ I A / S

0

I I i 11 ilill 1 I M Hill 1 ι 11 nui ι ι 11 Mil

0.01 0.05 0.1 0.5 1.0 5 10 50 100 S = 6 0 X c r( m h o s / m ) = l. 8 x Ι Ο4 ó ( m h o s / m ) / fm c

F i g o 2 P a r a m e t e r | Τ^γ[ f o r v e r t i c a l p o l a r i z a t i o n

I80( 1 ι ι ι IM 1 ι ι ι ι.πι 1 ι ι min 1 ι Ι Ι llliL^Jgü^M^JJ^PB^I Ι Ι I 111II

™ 1111 1 lllH^SffHr ~ F

i l # ^

180— ~J~" J Τ

1 ji^^v j b°

9 0 j ==::;;=3ΔeSl =P^^^! |

-20 r 1 1 ι ι ι ι ι Μ 1 1 Ι | | | 1 I I 1 1 Ι Ι Ι Ι Ι I Ι 1 1 — Γ ~

80 1 ^ ^ ^ ^ - - - - ^ ^ ^ ^ ^

ιοο — ^ - Ξ = - ^ ^ " ^ ^ Λ ν Γ - \ " Λ \ :

1.0 2 3 4 5 7 10 20 30 40 50 70 100 200 300 500 1000 2000 5000 Χο= f i u f d o ( k m )

F i g . 5 N o r t o n s u r f a c e w a v e attenuation A ^ , b = 0 °

- " 1

ι ι ι

ι ι ^{m u h — I} ι

M I H I — Γ Τ Π

^ = _^K^IO

10 2 3 4 5 7 10 20 30 4050 70 100 200 300 500 1000 2000 5000

*o,= Wc/5d0 ( k m )

F i g o 6 N o r t o n s u r f a c e w a v e attenuation A ^ , b = 4 5 °

K £ l O

10 2 3 4 5 7 10 20 30 40 50 70 100 200 300 500 1000 2000 5000

xo = W ^ o ( k m )

F i g . 7 N o r t o n s u r f a c e w a v e attenuation A , b = 9 0 °

Ë ^{ι ι ι h i h i — ι} ι Μ Ι Ι Η Ι — ι ι ^ι n u n — π ~ Π

0 — " — ^ ^ ^ ^ ^ ^

^ ^ ^ ^ ^

2 8 0

: ^{ΐ ΐ ^ β}

*ο = ÚìΓ Cl⁰ ( k m )

F i g o 8 N o r t o n s u r f a c e w a v e attenuation A^_, b = 180°

1.0

0.5

0.1

0.05 I S ' I

0.005

( / 3/ ) ( m - c o s

FOR S M A L L i a / ) : l S l " | 2^ G 4^ r^F* L' ^ H h h F O R L A R G E ( a / ) : i S ' l - l / i a f )

0.001 0.005 0.01 0.05 0.1 0.5 1.0

ai

5 10 50 100

Figo 9 P a t t e r n factor ] S ' | for a horizontal t r a v e l i n g wave antenna of length ϋ

110 100 90 80 70 60 . <»>

- 50 en

2 40

- 3 0 - L

0.020.03 0.05 01 0.2 0.3 0.5 0.7 I 2 3 5 7 10 20 30 50 70 100 200300 500 1000

F i g . 10 External noise figure F

j ^{^ α π 4 ι}

ο.οοι 0.01 0.1 I 10 100 1000 10000

S = 6 o \ a ( m h o s / m ) = 1 . 8 χ ΙΟ4 σ(mhos/m)/fkt

Me

F i g , 11 Ground p r o x i m i t y effect ^ for v e r t i c a l e l e c t r i c d i p o l e , € = L O I '

r

j —j

0.001 0 . 0 1 0 . 1 I 10 100 1 0 0 0 1 0 0 0 0

S = 60 ë cr ( m ho s / m ) = 1.8 χ I O4 a ( m h o s / m ) / f Mc

F i g , 12 Ground p r o x i m i t y e f f e c t ^ for v e r t i c a l e l e c t r i c d i p o l e , € = 2 '

F i g . 13 Ground p r o x i m i t y e f f e c t ^ for v e r t i c a l e l e c t r i c d i p o l e , € = 5 '

r

IOo.ooi ooi οι ι '* ιο loo ⁼ 1000 10000

s = 6 0 X a ( m h o s / m ) = ι 8 χ ι ο4 c r ( m h o s / m ) / fM

F i g . 14 Ground p r o x i m i t y e f f e c t ^ for v e r t i c a l e l e c t r i c d i p o l e , € = 10 '

οι ι ι ι ΜΙΝΙ—ι ι ι Μ Ι Ν Ι — Γ τ π π π ι — ι ι | | i | | | | —ι ι ι m u

2 0 — 1 - L — — ' ' ' ' ' 1 1 ' ' — I 1

^5;. VERTICAL POLARIZATION

loo

1 2 0

— V \ " ' t \ ^ " t w ^ —

l

V p t t r w " T ^ W

V t ï f t t i — - f r ^ J 11 l l l l -

180

> vP ^"~H 1 " m i "

200 \ — r V i H — f \ — I — ~ i ^:

220 U 4 M - i — - ^ x — I !—U--

240 H i f t H i r — » — f

Vb>d⁰=500km \ V

260

4 . Hill ^ i f

280

1 j l -

sopi

11iiiiiii 11 iiiiiii w min 1 1 i i i i m ^ ι m i n i

0.01 002 003 005 00701 0.2 0 3 05 0.7 I 2 3 5 7 10 20 30 50 70 100 200 300 5007001000

F i g , 15 B a s i c t r a n s m i s s i o n l o s s f o r v e r t i c a l l y p o l a r i z e d N o r t o n s u r f a c e w a v e s

F i g . 16 Ρ - ( R + B ) for w a v e antenna and v e r t i c a l dipole