Nederlands RadiogenootschapDEEL 22 No. 5 SEPTEMBER 1957

N e d e rla n d s Radiogenootschap

DEEL 22 No. 5 SEPTEMBER 1957

Calculation of true heights of electron density in the ionosphere

by N. Ganesan, M.Sc. *)

Summary.

F ollo w in g the w o rk o f W h a le and S ta n le y [1], S hin n an d W h a le [2], a n d Jackson [3], cu rv es have been o b tain ed show ing the v a ria tio n o f v ir­

tu a l heig h ts o f reflection w ith frequency] fo r a lin e a r lay e r. W ^ith the help of these cu rv es som e h \ f re co rd s m ade a t the D r. N e h e r L a b o ra to ry a t L eid sch en d am have been re d u ce d to those o f electron d e n sity as a fu n ctio n of tru e height. T he effect o f th e e a rth ’s m agnetic field h as b een ta k e n in to c o n sid eratio n in these calcu latio n s. T his p ra c tic a l m ethod seem s to be a c c u ra te as such cu rv es re d u ce d in this m a n n e r h av e been found to agree w ith th e a c tu a l d a ta of electron d ensities a t vario u s heights o b ­ tain e d d u rin g the sev eral ro c k et flights c a rrie d ou t ov er W r it e S an d s, N e w M exico. A ll c o m p u tatio n s are fo r v e rtica l p ro p a g atio n .

1. Introduction.

I f a plane polarized electrom agnetic w av e enters the iono­

sphere in a v ertical direction it p ro p a g a te s through a dispersive medium of g rad u ally decreasing dielectric co n stan t as a con­

sequence of increasing electron density. A s a result, the group velocity of the exploring w ave decreases an d becomes zero a t a certain value of electron den sity depending on the w ave fre ­

quency. A t this point the w ave is reflected b ack following the course in the rev erse order. The frequency which corresponds to the maximum value of electron density is kn o w n as the cri­

tical frequency of the p a rtic u la r layer. Thus the critical fre ­ quency of the u p p erm o st F a la y e r re p re se n ts the critical fre ­ quency fo r the ionosphere as a w hole an d a w ave w hose fre ­ quency is g re a te r th a n the critical frequency will n o t be r e ­

*) Io n o sp h e re D e p a rtm e n t, D r. N e h e r L a b o ra to ry , L eidschendam , H o llan d .

fleeted an d will get through the ionosphere. The plane polarized w a v e m ay be assum ed to be the re s u lta n t of tw o circularly polarized w av es ro ta tin g in opposite directions. In the N o rth e rn hem isphere the left h a n d e d w ave is called the o rd in ary com­

ponent and the o th e r the e x tra o rd in a ry component. D u e to the influence of the e a r th ’s magnetic field the p ro p ag atio n c h arac­

teristics of the tw o components are affected in different w a y s.

A norm al ionogram — the so called h ', f record — contains the virtual heights of reflection as a function of frequency [-4], since the d elay time b etw e e n transm ission and reception of a pulse of given frequency indicates the virtu al height fo r the p artic u la r frequency. The tru e heights are, how ever, less th a n the v irtu al heights.

In m ost of the older m ethods com putations of true heights from virtu al heights w ere m ade w ith o u t taking into account (1) the influence of the e a r th ’s m agnetic field and (2) the effect of collisions b e tw e e n electrons and gas molecules. Though the la tte r m ay not have much influence in the final resu lts especially a t high altitudes, the form er does p la y an im p o rta n t p a r t in the evaluation of group velocities. The influence increases a t higher latitudes and it has been found t h a t differences of as much as 50 °/0 occur in estim ates of la y e r thicknesses b e ­ tw e e n neglecting and taking into account the effect of the e a r th ’s magnetic field a t a latitu d e of a b o u t 60°. Also, in a n a ­ lysing some records inconsistent resu lts are o btained b y n e­

glecting the field, such as tw o distinct values of electron den­

sities a t one an d the same height. I t is only along the regions close to the magnetic e q u a to r th a t the field m ay be neglected for the o rd in ary component.

The ionosphere is assum ed to be horizontally stratified, the region b e ­ tw een any tw o layers having a con­

s ta n t electron density the value of which is n early equal to the maximum value of the lo w e r layer. This a s ­ sum ption seems to be a ccu rate as verified w ith the ac tu a l electron d en ­ sity distribution d a ta o btained from ro ck et flights [5]. W A h in a la y e r T y p ic al electron d e n sity dis- the electron density is approxim ately trib u tio n as a fu n ctio n of a linear function of height as show n

height. in Figure 1.

2. T he gyrofrequency.

T he gyrofrequency is the n a tu ra l frequency of ro ta tio n of ions aro u n d the lines of m agnetic field of the earth, the ions being no t subject to an electro-m agnetic w ave. D u e to its small mass, the electron has a g y rofrequency com parable w ith the frequency of radio w aves. If an electron comes u n d er the in­

fluence of an electro-m agnetic w av e the frequency of which is g re a te r th a n the gyrofrequency, the m otion of the electron is elliptic, the ratio of the m ajor an d the minor axes of the el­

lipse v a ry in g d irectly w ith the stre n g th of the e a r th ’s magnetic field and inversely w ith the frequency of the electro-m agnetic w ave.

The value of the gyrofrequency has been o b tain ed from the general expression,

2 nmc w h ere,

H = stre n g th of the e a r th ’s magnetic field in oersteds.

e = charge of the electron ( = 4,77 X I0' ,0e.s.u.).

m = m ass of the electron ( = 9,01 X IO-28 gm.).

c = velocity of electro-m agnetic w av es in free space ( = 3 X i o10 cm/s).

(

)

H w a s o b tain ed fo r a given height b y ex trap o latio n of the experim ental ground value b y the inverse cube law ,

H h = H 0 (rfr + h)i

( 2 )

w here,

Hh = stre n g th of the e a r th ’s m agnetic field in oersteds, a t height h.

H a = the field stre n g th a t ground level (= 0,473 o ersted for Leidschendam ).

r — radius of the e a rth ( = 6370 km).

h = height un d er consideration (taken as 1 50 km).

The gyrofrequencies and values of H calculated for various heights a re show n in T able 1.

3. C alculation of the group index //.

The well know n expression for the (phase) refractive index fx, neglecting collisions, is

T A B L E 1.

H e ig h t (km ) H (o ersted ) f H (M e ) G ro u n d level 0,473 1,33

50 0,465 1,31

100 0,455 1,28

150 0,445 1,25

200 0,431 1,21

300 0,412 1,16

400 0,396 1,11

2. x (\ - x )

ft? — i --- --- — 2 (i — x ) — y* sin 0 ± f y4 sin4 0 4- 4y2 cos2 0 (1 — -r)2

w h ere, ^

4tiTV/

;r = ---2— mp*

N = n um ber of electrons p e r cm3.

p = an g u la r frequency of th e exploring w a v e (= 2n f).

f = freq u en cy of the w ave.

y = ratio of gyrofrequency to exploring w av e frequency ( = ƒ * / / ) •

0 = angle contained b e tw e e n the direction of w av e p ro p a ­ gation an d the direction of the e a r th ’s m agnetic field.

The u p p er ( + ) sign refers to the o rd in a ry com ponent and the lo w er ( —) sign to the e x tra o rd in a ry one. A lthough no d e ­ cision has been arriv e d a t as to the inclusion or omission of the L orentz polarisation term in expression (3), the tendency is to w a rd s the la tte r. I t seems it can be safely neglected above 4,27 M c /s of the exploring w ave frequency.

A ny com putation for the contribution to the v irtu a l height of a region of the ionosphere needs a n exact know ledge of the group velocity of the w av e of given frequency a t t h a t p a rtic u ­ la r region. The group velocity is expressed in term s of a c e r­

ta in q u an tity //, called the "group refractiv e index” , th e re la ­ tionship being given by,

G ro u p velocity = ---- (d)

P

w h ere c is the velocity of electrom agnetic w av es in free space.

N o w the group index is defined as,

/i' = f i + f i)[x

V

(5)

w h ere f is the exploring w ave frequency.

A t values of x approaching 1, /x tends to zero an d hence it is n o t convenient to compute fx from (5). A s is commonly done, one calculates the p ro d u ct fx^x! first. From (5) w e get,

a , f U + fXj ----

5 / d/x

(

6

S u bstituting the values of fx and —— ta k e n from (3) in (6) gives,

, T 2X* x { l - x ) rri, w = 1--- —— I---^ — J-U

D D2 ⁽⁷⁾

H ere,

D = 2 (l — x ) — y sin 0 + / y 4 sin* 0 + 4y* cos1 © (1 - x)2 (7a)

f D ' — 4 x + 2jj7j-z«2 0 + 2 {— y4 j*»40 + 2y*cos* 0(2, x — l ) ( l — •*■)}

Vy4 .re»4 0 + 4y2 coj2 0 (1 — ur)2

(7b) A lthough the p ro d u c t fxfx' can be calculated b y sh o rte r m e­

thods b y introducing a few approxim ations, expression (7) w as used in o rd e r to get more accurate values.

In the limiting case w h en x = I fo r the o rd in ary com ponent and x = I — y for the e x tra o rd in a ry component, fxfx' is given by the following,

fx/x = 1/sin

2 0

,

H/t

= ---

(9) (if—

+

0)

4. T he ordinary com ponent.

F o r the o rd in ary com ponent the values of fx are obtained from relation (3). Figure 2 show s fxfx as a function of x. Thus from kn o w n values of fx and fxfx', the q u a n tity /a' is obtained.

A s sta te d earlier w ith re g a rd to the shape of the lay er, it

iu-fi p ro d u c t fo r the o rd in a ry com ponent, L eid sch en d am , H o llan d .

is assum ed th a t the variation of electron density w ith height is approxim ately linear. If z be the height m easured verti­

cally to the tru e reflection point, D the re a l thickness of the p a r t of the lay er ex­

tending from the bottom of the lay er to the true reflection point, D ' the a p p a re n t thick­

ness corresponding to D for the p a rtic u la r frequency, w e have the w ell kn o w n relation,

D

II (10)

O

to the above as- sum ption this becomes,

D ' = (10a)

w h ere x z an d x a a re the values of x corresponding to N z and N a resp ectiv ely fo r the p a rtic u la r frequency, x T being in this case equal to I. In o rd e r to evaluate the integral in (10a) w e define a function Q as,

Q {/> x ) (11⁾

Therefore,

D ' = D

x x - {Q (ƒ, x z ) ~ Q (ƒ, x a)j w h ere x z = I.

(1 1a)

H o w ev er, in regions w h ere the electron density is constant, as is assum ed to be the case w h ere discontinuities occur in h ' , f records, this m ethod can n o t be used. In this case D ' is given by,

D '= n 'D ( lib )

A s (i tends to infinity w h en x tends to I, the integral in (11) cannot be evaluated as it is. The following tran sfo rm atio n is m ade use of,

t = I — x . T herefore,

J

Figure 3 show s [i "j \ — x as a function of |'' I — The in­

te g ra l is then equal to tw ice the a re a u n d er a curve for a given value of x. The curves in Figure 3 can be used directly to com pute jx , D or D ' w h en ev er form ula ( l i b ) is used. Typical curves for the v ariation of the in teg ral w ith ;t and for various frequencies are show n in F igures 4 and 5. To avoid crowding, Figure 4 show s curves fo r tw o frequencies only, 1,5 M c/s and 13 M c/s, and the values for o th er frequencies are o btained b y taking the differences in value for these frequencies from

0110950

j/ \ — x fo r the o rd in a ry com ponent, L eidschendam , H o llan d .

000 9 5 0

In te rp o la tio n values fo r Q curves, o rd in a ry com ponent, L eidschendam , H o llan d .

Figure 5 and adding them to the corresponding ones fo r 1,5 M c/s found from Figure 4.

5. T he extraordinary com ponent.

F o r the e x tra o rd in a ry com ponent reflection norm ally occurs for values of x given b y .r = I — y , if y is less th a n I, i.e. for frequencies g re a te r th a n the gyrofrequency. As only those values of y less th a n I are of in te re st w ith re g a rd to h , f records these alone will be considered here.

Unlike the m ethod of calculation used for the o rd in ary com­

ponent, it is found convenient to plot fx2 and fxfx' as functions of (x/l — y ) for the e x tra o rd in a ry component. In a similar w a y as indicated in the description for the o rd in ary component, the following tran sfo rm atio n is used for evaluating the integral

ij! d x,

X

t = i i - W i - y ) (13) Therefore,

X t

fi d x = — 2 (i — y) 1 t d t

o

(14)

B y plotting [a } I — (x/l — y) versus / J — {x /l — y ) the values of the integral in (14) are obtained in the same m anner as for the o rd in a ry component. Figure 6 contains the Q curves for the e x tra o rd in a ry com ponent as a function of x / l — y . In o rd er to reduce a p artic u la r value to th a t corresponding to x , it m ust be divided tb y (i — y ) for the frequency u n d e r consideration.

F ig. 6.

Q curves fo r the e x tra o rd in a ry com ponent, L eid sch en d am , H o llan d .

6. A nalyses of h ', f records.

In the following m ethod of analyses of h ' , f reco rd s m ade a t L eidschendam , the o rd in ary com ponent has been considered in p articu lar. The curves fo r the e x tra o rd in a ry com ponent m ay be u sed for checking the results.

T he main difficulty in computing electron densities a t various heights is in fixing a sta rtin g point, i.e. a height of know n electron density. H ence some assum ption has to be m ade in o rd e r to locate the lo w er limit of a certain layer. In view of the reg u larity show n b y the E layer, the E tra c e on the I i, f reco rd is m ost suited for any such com putation.

S tra ig h t line ap p roxim ation of the lo w e r lim it o f the

ionosphere.

Fig. 8.

C u rv e d eriv e d from s tra ig h t line ap p ro x im atio n o f fig. 7 a n d used fo r lo ca tin g h0 a t L eid sch en -

dam , H o llan d .

The electron density is assum ed to increase lin early w ith height from ha (tV ^ o) a t a ra te of IO4 electrons/cm3 p e r km. This is re p re se n te d b y the stra ig h t line L in Figure 7. The con­

tribution of this type of region to the v irtu al height for the o rd in ary com ponent is calculated w ith the help of expressions (11a) and (12). This is show n in Figure 8 w h ere a p p a re n t thickness D = (h ' — k 0) is p lo tte d versus frequency, w h ere h' is the v irtu a l height of reflection for the p a rtic u la r frequency.

Figure 8 is used in the following m anner for locating h0.

In the h ! , f record u n d er study tw o points w ell below the 2?lay er critical frequency are chosen w hose heights a re given b y h ' and h ' corresponding to the frequencies f x and respectively. L e t 77 be the g re a te r of the tw o an d h! —h = a . C or-_{2 I} responding quantities a a n d b are found for these frequencies from Figure 8. B y com pa­

ring Figure 8 w ith the actu al H , f reco rd u n d er study the bottom of the E region is ta k e n to be a stra ig h t line defined by,

hQ — h'^ — (a + b) a /a (15)

N o w it w ill be show n how a K , f reco rd can be transform ed into one giving the electron den sity as a function of tru e height.

F o r reasons of facility the h ' , f reco rd u n d er stu d y is first modified into one of v irtu al height as a function of electron density. A fte r locating ha b y the above m ethod on this profile,

T y p ic al cu rv es show ing v irtu a l heights a n d d eriv e d tru e heig h ts o f electron d en sity .

the region b etw een this point and the one corresponding to the electron den sity for the frequency f 2 is app ro x im ated by a stra ig h t line starting from ha and increas­

ing a t a ra te of (a'/a) X IO4 el/cm3/km. L e t the point P a co rre­

spond to the u p p er limit of the stra ig h t line. T hus the height of P 2(—h2) re p re se n ts the tru e reflection height of the virtual point P'2 w hose height is /«). This is illu stra te d in Figure 9.

The tru e height h 3 of a neighbouring point P 3 corresponding to the v irtu al point P'3 w ith critical frequency f 3 and electron density N 3 is o btained as follows.

W e m ake use of the relation,

— K + di d , (Q3 - Q,) (x3 - x 2)

obtain ed from (1 1a), for the o rd in ary component.

In (16).

k ' = height corresponding to the p o in t P '.

ho = height of the bo tto m of the E la y e r ( N f ^ o ) . d 1 = h 2 - h r .

d 2 = h 3 — h 2.

x = _8o ^

3 f \ 3

8o,6

■N..

(16)

o

N 3 a n d N 2 a re the electron densities a t P 3 an d P 2 respectively.

f 3 is the frequency corresponding to N 3 in Kc/s. T he Q's are to be found from Figures 4 an d 5.

In (16) all quantities except are kn o w n and so it can be easily computed. Thus the tru e height h3 of the point P 3 cor­

responding to the v irtu al height Ji3 of P j will be given by, h 3 = hQ + d T + d 2.

In this m anner the analysis is carried out till the point which corresponds to the maximum electron density of the E lay er w here a discontinuity norm ally occurs. The analysis a t this point m akes use of the assum ption t h a t the region im m ediately above this point rem ains densely ionised as s ta te d earlier. R e ­ ferring to Figure 11 let P m re p re se n t the tru e reflection point corresponding to the v irtu al point P'm on the h ' , f record. If P„ re p re se n ts the tru e reflection point corresponding to the maximum electron densitj^ of the E la y e r an d if P m and P n are linked, then the assum ed in te rla y e r d en sity w ould be too large.

This region is th erefo re approxim ated b y a stra ig h t line joining P,n a n d Pk w h e re Pk is a point on the tru e E tra c e a n d the value of its abscissa is given by 0,9 N , N being the maximum electron density of the E lay er. P ractice has show n this to be a suitable approxim ation, and m ay also be used a t o th er points w h ere discontinuities are observed. In such a region of tra n s i­

tion form ula ( l i b ) m ay be em ployed since f i is constant. In analysing night time records, the lo w er p a r t of the F la y e r is assum ed to be linear an d the analysis follows in the same lines as for the E layer.

7. R esults of measurements.

Figures 10 and 11 contain typical reco rd s tran sfo rm ed to show electron densities versus virtu al heights as w ell as true heights derived according to the described m ethod. In T able 2 are show n the tru e heights of electron density m axim a and the level of minimum ionisation (h„). The K , f records w ere m ade a t Leidschendam w ith a m odern ionosphere sounding equipm ent [6]. Also show n in T able 2 are the v irtu a l heights of points lying on the H , f records which co rresp o n d to 0,834 of the critical frequencies, such a height being sometimes ta k e n as the tru e height of the level of maximum ionisation (method of B ooker and Seaton).

4 P M (U niv. tim e), L eid sc h en d a m , H o llan d ). 1954, 12.30 P M (U n iv . T im e), L eid sch en - dam , H o llan d .

T A B L E 2.

D a te an d univ. tim e

C ritic al freq u en cy fc (M c /s)

M ax im u m electron d e n sity N o ./c m 3

K km

T ru e ht.

o f m ax.

el. dens- (km )

V irtu al height

(km )

4th June '54 (2 A M )

2,2 6 X 104 110 192 240

7 th June 54 (4 P M )

4,9 30 X 1 0 4 80 260 300

2 1 st D ec. '54 (1 2 .3 0 P M )

4.9 30 X 1 0 4 80 230 245

25 th D ec. '55 (3 A M )

3,4 14,5 X I 0 4 130 210 320

24 th F eb . '56 (2 .2 9 P M )

9,7 117 X 1 0 4 90 267 275

16th M a y 56 (10.59 A M )

4,8 29 X 1 0 4 85 185 350

16th M a y ’56 (3 .2 9 P M )

6,0 ■7T X ^O 95 280 525

The analyses so fa r carried out show th a t the F a lay er behaves more reg u larly in its height variations th a n can be expected b y inspection of the H , f records. This can be a p p re c ia te d w h en one com pares the d a y and night summer values w ith those during w inter. A lthough the F 2 ionisation is much g re a te r during the w inter, heights a re lo w er th a n those corresponding to the same values of electron d en­

sity in summer. So it is clear th a t abnorm al values of virtu al heights often observed in h‘, f records are due to group re ta rd a tio n in the lo w er regions of the ionosphere. A s s ta te d earlier tru e heights derived by the m ethod described have been found to agree w ith the actu al d a ta o b ­ tain ed from ro ck et flights a t W h ite Sands, N e w M exico, as can be seen from the results of one such m easurem ent r e p ro ­ duced in Figure 1‘2.

A cknow ledgem ents.

M a n y th an k s are due to D r. C. T. F. van d e r W y c k for his kind in terest and guidance in the w o rk and to Ir. P. L. M . van

B erk el for his m any valuable suggestions.

R eferences.

(1) H. A. W h a 1 e and J. P. S t a n l e y , J. Atmos. T err. Phys., 1, 82 (1950).

(2) D. H. S h i n n and H. A. W h a l e , J. Atmos. T err. Phys., 2, 85 (1952.

(3) ]. E. J a c k s o n , J. Geophys. Res., 61, 107 (1956).

(4) P. L. M. v a n B e r k e 1, Tijdschrift N .R.G ., X V III, 149 (1953).

(5) J. C. S e d d o n, J. Geophys. Res., 59, 463 (1954).

(6) P. L. M. v a n B e r k e l , Tijdschrift N .R.G ., 19, 305 (1954).

0 6 16 2 i

F ig . 12.

E le ctro n d ensities com puted from h', f re co rd an d c o m p a­

rison w ith ro c k et m ea su re ­ m ents, 10.00 H o u rs (M S T )

7 th M a y , 1954 [3],

Radio R elay System s

by H. Stanesby, M.I.E.E.

Lecture delivered to the Nederlands Radiogenootschap on 5th March 1957.

1. Introduction.

The subject of my lecture, ra d io -re la y system s, is of special in terest a t p resen t because international ag ree­

m ent on m any of th eir ch a r­

acteristics w a s recently ob­

tained in the C .C .I.R .*) a t W a r s a w , and a consider­

able num ber of system s are now being built in various countries.

Time will no t allow me to go into the h isto ry of ra d io ­ relay systems, although the e a r lie s t—v e ry ru d im en tary in c h a ra c te r —w e re incor­

p o ra te d in national te le ­ phone system s over 25 y e a rs ago. N o r will it allow me pj ^ to describe the m any diffe- P o s t office ra d io re la y links F e b ru a ry 1957. r e n t e.y P e s th a t are now in use. H ow ever, the m ap in Fig. 1, showing the extent to which rad io -relay system s have been installed in the U nited Kingdom, might be of interest.

Because time is short, I shall concentrate mainly on the general ch aracteristics of the larger-capacity system s used on both sides of the A tlantic to handle hundreds of telephone channels or tele­

vision .— the b ro a d b a n d systems •— so called because the input

r) C om ité C o n su lta tif In te rn a tio n a l des R adiocom m unications.

signal occupies a b a n d of frequencies p erh ap s several megacycles p e r second wide. T hen I shall re fe r briefly to the m ore-recently- developed tro p o sp h eric-scatter system s — system s which, al­

though th ey have much sm aller traffic-handling capacity, have some very interesting features.

2. U H F and SH F w ave-propagation.

The system s I am considering op erate on U H F an d S H F * ) frequencies ranging from a b o u t 500 to 10,000 M c/s — very much higher th a n are used for really long-distance communications or even for television b ro a d c a stin g ; and I shall begin b y con­

sidering rad io -w av e p ro p ag atio n a t these frequencies.

A t such frequencies th ere is no reflection from the ionosphere, so re a lly long-distance p ro p ag atio n in a single hop is out of the

question —• unless, as has been suggested, the sig­

nals are reflected b y the moon! B uth the tro p o ­ sphere, which extends up to 12,000m or so, does affect the pro p ag atio n of these w aves, an d to a g re a te r e x ten t as the dis­

tance from the tra n sm it­

te r to the receiver increas­

es. N o rm a lly the tropo- shere re fra c ts an d sc a t­

te rs the w aves som ew hat, and a t times w h en it is not well mixed — w hen it is stratified •—• it m ay reflect them as well. The clear atm osphere is v ir­

tually tra n s p a r e n t up to say 10,000 M c/s, b u t a t higher frequencies w a te r v ap o u r and oxygen cause some absorption, as is show n in Fig. 2. This figure also show s t h a t rain, and to a lesser ex ten t mist and cloud, affect trans-

*) U H F an d S H F re fe r to freq u e n c y ran g es o f 3 0 0-3000 a n d 3000- 30,000 M c /s resp ectiv ely .

A "— ■—

/

/>

1

^\

7 v

I i I i '

Vt m o (OXYGSPHERIC

:n ANDGASES WATER VAPOUR)

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A tten u a tio n due to atm o sp h eric gases, fog a n d rain .

mission som ew hat — more a t the higher frequencies. A p a r t from this absorption, the tro p o sp h ere has four main effects which can conveniently be described in term s of w h a t h appens w ith light w a v e s:

(a) The decrease of refractive index w ith height delays the a p p a re n t setting of the sun b y curving the ra y s. F o r light, refraction a t the horizon is n e a rly 35 minutes of arc, more th a n the angular diam eter of the sun. F o r radio w aves much the same happens, and as is illu strated in Fig 3, the ra y cu rv atu re for a well-mixed atm osphere has the same effect as increasing the e a r th ’s radius b y g.

F ig.

Illu stra tio n o f allo w an ce fo r m b y in creasin g effect

arm ai atm o sp h eric refractio n ive e a rth rad iu s.

(b) The variation of refractio n w ith time causes sta rs to twinkle.

I t also causes fading of radio w aves.

(c) A fte r sunset th ere is still plenty of light for some time. If th ere w ere no atm osphere to s c a tte r the light back it w ould im m ediately become pitch d ark. I t is the same w ith radio w aves — the scatterin g of the w av es b y the atm osphere greatly increases the stren g th of signals w ell beyond the horizon as can be seen in Fig. 4.

(d) Finally, on occasions mirages occur. Sim ilar conditions can cause the reflection of radio w av es w ith the possibility of anom alous propagation, w ave-interference an d serious fading.

W i t h this inform ation it can be und ersto o d w h y there are tw o w idely-different types of radio-relajr system . The first in which signals are tra n sm itte d over a sequence of line-of-sight p ath s w ith stations a t intervals of 50 km or so, and w here only low p o w e r is needed because the p a th loss is relatively small. T hen th ere are the so-called tro p o sp h eric-scatter system s

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in which ad jacen t stations m ay be several hundred kilom etres a p a r t and much higher tra n s m itte r po w ers are needed.

3. L ine-of-sight system s.

The p ath s used for the line-of-sight system s m ust no t only be clear, b u t application of the w av e-fro n t principle of the f a ­ mous D u tch scientist H u y g en s show s th a t to avoid unnecessary loss, m ajor obstructions should be sufficiently rem oved from the line-of-sight for the p a th via an obstruction to be a t le a st ^ w avelength longer th a n the d irect p ath . In practice, to allow for abnorm al refractio n conditions, w e seek w h en choosing s ta ­ tion sites to satisfy this condition for an effective e a rth radius of 0.7 times the tru e radius. F ree-sp ace p ro p ag atio n will then be ap p ro a c h e d for a large p roportion of the time, although for p erh ap s 0.1 p e r cent of the time fading m ight rise to as high as 10 db.

I shall now briefly outline the form t h a t a line-of-sight radio- re la y system might tak e before considering its com ponent p a rts and its ch aracteristics in m ore detail.

In larg e-cap acity rad io -relay systems the radio-frequency c a r­

riers are frequency-m odulated w ith a b a se b a n d spectrum , i.e.

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nels or of television. R eferring to Fig. 5, a num ber of such m odulated carriers are fed through combining filters to a common aerial w hence th ey are ra d ia te d in a n a rro w beam. F u rth e r along the route the ca rrie rs are received on a directional aerial, a fte r which they are sep erated , individually amplified and changed som ew hat in frequency, recom bined an d re -ra d ia te d over the next section of route. This process is re p e a te d a t stations spaced on the averag e say 50 kilom etres a p a rt. F inally a t the receiving term inal the carriers a re sep erated , amplified an d the original b ase b a n d signals are reco v ered by dem odulation.

E ach of the ca rrie rs provides a b ro a d b a n d channel of com­

munication, and a ra d io -re la y system generally provides one or m ore such channels for each direction of transm ission. W h e r e th ere is need for only one w o rk in g channel, providing a second channel m ay w ell be the m ost convenient w a y of guarding a- gainst equipm ent fa ilu r e ; and w h ere tw o or m ore w orking chan­

nels are needed, p erh ap s for m ulti-channel telephony an d te le ­ vision, if th e y have similar characteristics a common stan d b y channel should suffice. If telep h o n y is to be tra n sm itte d the individual telephone channels w ould norm ally be assem bled by frequency-division multiplex in the b aseband, in the w a y th a t has been recom m ended internationally fo r cable and radio sys­

tem s b y the C C I T T *) and the C C I R respectively. This w ould facilitate interconnection. Television, how ever, is much more easily han d led if the signals a re applied, unchanged, to ra d io ­ relay system s, w h e re a s for long-distance coaxial-cable tr a n s ­ mission they m ust be raised som ew hat in frequency — a com­

plicated process w hich w e are fo rtu n a te to escape.

Fig. 6 show s in more d etail the m ajor units t h a t go to make up a term inal tra n sm itte r, a re p e a te r and a term inal receiver, and the frequency-changing processes involved. The filters used for combining and sep aratin g different b ro a d b a n d channels are om itted to avoid complicating the diagram .

In a term inal tra n s m itte r the b a se b a n d signal, a fte r amplifi­

cation, m ight frequency-m odulate a c a rrie r either a t the final ra d ia te d frequency, f„ or a t an interm ediate frequency f w h i c h is a fte rw a rd s raised to the final frequency in a frequency-changer.

The m odulated c a rrie r is then amplified before being fed w ith o th e r carriers to the aerial.

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In a re p e a te r the received carrier, f„ a fte r being sep arated from the o th e r b ro ad b an d -ch an n el carriers, is reduced to in te r­

m ediate frequency in a frequency-changer, amplified, limited and raised in a second frequency-changer to a frequency f2 differing so m ew h at from the incoming frequency. Then it is fu rth e r am ­ plified before being combined w ith the o th er m odulated carriers for o n w ard transm ission over the next section of route. The frequency shift, f2 -— f, , which is small com pared w ith the fre ­ quencies f, and f2 themselves, is determ ined only b y the fre ­ quency of the shift oscillator which can be crystal-controlled.

R eferring to the figure, an e rro r in the higher-frequency “ R .F . oscillator” does not therefore affect the value of f2, it cancels out, although it affects the centering of the signal in the I.F . band.

If the shift oscillator is accurate no frequency e rro r will be introduced in the R .F. signal by the frequency-changing p ro ­ cesses, and erro rs will not accum ulate along the route.

The limiter ensures th a t the input signal to the R .F . amplifier is held constant a t its optimum value reg ard less of fading in the previous section of route.

The term inal receiver calls for little comment. In it the c a r­

rie r is reduced to interm ediate frequency, limited, and applied to a discrim inator w here the b aseb an d signal is recovered.

The interm ediate-frequency band used a t all points should be the same reg ard less of the b ro a d b a n d channel involved. The C C I R has recom m ended a m id-band frequency of 70 M c/s for all radio-relay system s operating above 1000 M c/s, which makes

it easy to interconnect b ro a d b a n d channels a t interm ediate frequency.

3.1 Techniques used in L ine-of-sight System s.

3.1.1 Generation and Am plification o f Oscillations.

The generation and amplification of oscillations a t frequencies of the o rd e r of thousands of megacycles p e r second presen ts m ajor problem s, an d special valves a re need ed : G rounded-grid triodes can be used, b u t th ey m ust be specially designed w ith microscopic electrode-clearances to reduce electro n -tran sit times, and w ith electrodes so sh ap ed t h a t they can form p a r ts of r e ­ sonant cavities. M o re o v e r the gain p e r stage is relatively low, and hitherto, the alignm ent of amplifier chains has been difficult due to interaction b etw een stages. I believe th a t considerable progress has, how ever, recently been m ade in the N e th e rla n d s in solving the alignm ent difficulties b y using ferrite isolators.

The altern ativ e is to employ the principle of velocity-m odu­

lation, in w hich electro n -tran sit time is an essential and not an undesirable factor. A t a point in an electron-beam a longitudi­

nally-applied radio-frequency electric field is m ade to v a ry the electron-velocity w ith time. F u rth e r along the beam these elec- tro n -velocity variations build up electro n -density variations, i.e.

electron-bunches, which give up some of th eir energy to suitably- placed electrodes leading to an o u tp u t circuit. V a ria tio n s of this them e are used in a num ber of different ty p es of valve suitable for generating and amplifying U H F o r S H F oscilla­

tions. T w o ty p es, the reflex-klystron and the travelling-w ave valve, are show n d iagram m atically in Fig. 7.

In the reflex-klystron, w idely used as an oscillator, the elec­

tron-beam is reflected back along itself by a reflector electrode, and the input and o u tp u t electrodes are common. V elocity v a ­ riations introduced in the outgoing beam give rise to density v ariations in the reflected beam , energy from which is used to sustain oscillations in a cavity connected to the electrodes.

The most direct w a y of frequency-m odulating a carrier is to apply the b a se b a n d signal to the reflector-electrode of a reflex- klystron oscillator. The input signal p o w e r required is negligible, an d linear frequency-deviations of several megacycles p e r second are read ily obtainable. A lternatively, several different m eans are available for producing a m odulated c a rrie r a t interm edia­

te-frequencies an d tran slatin g it to the desired rad io frequency.

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F ig. 7.

V elo city-m odulation valves.

F o r amplification travelling-w ave valves m ay be use d; they o p erate b y a process of interaction b etw een a w ave pro p ag ated along a cylindrical helix and an electron-beam passing axially through it. The input signal is applied to the first p a rt ol the helix and velocity-m odulates the beam. F u rth e r along the beam electron-bunches a p p e a r and re tu rn more p o w e r to the helix th a n w as ab so rb ed from it initially, hence there is amplification.

A s much as 30 db gain p e r stage can be obtained over very wide bandw idths, the tuning adjustm ents are uncritical, and ou t­

p u t pow ers of 5-15 w a tts are possible, depending on frequency.

In the U nited Kingdom, travelling-w ave valves are generally used in large-capacity systems. H ith erto , because suitable low- noise valves could not be obtained, very-low -level U H F and S H F signals have no t been amplified directly. They have been tra n sla te d to an interm ediate frequency, for which low-noise

valves are readily available, and amplified and limited a t th a t frequency. Then, if a re p e a te r station is involved, the signal is raised again in frequency, and amplified in a travelling-w ave valve amplifier to a level of 0.5 — 15 w a tts. But if it is desired to recover the b aseb an d signal a t a term inal station the signal is dem odulated. F o rtu n ately , low-noise travelling-w ave valves have recently become available, and, for rep eaters, the double­

frequency-changing process is not now essential. Thus re p e a te rs can be made w ith say lo u r travelling-w ave valves providing all the amplification, the small change in frequency needed before signals are passed to the next repeater-section being introduced

Fig. 8.

T w o a ll-trav e llin g -w a v e-v a lv e re p e a te rs.

in one of the travelling-w ave-valve stages or in a se p a ra te c ry sta l mixer. T w o re p e a te rs of this type are show n in Fig. 8.

3.1.2. Frequency changing.

The tra n sla tio n of a low-level received signal to an in te r­

m ediate frequency is carried out in a low-noise silicon-crystal frequency-changer. The noise-factor is a b o u t 12 d b ; in other w ords, the random -noise o utput is some 12 db higher th an th a t due to th erm al noise in the circuit connected to the input term inals. F o r tran slatin g an I F signal back to U H F or S H F , how ever, a germ anium -crystal frequency-changer is generally used, because much higher signal levels are involved.

As has a lre a d y been m entioned, a travelling-w ave valve can be used to introduce m oderate changes in the frequency of a U H F or S H F signal, in, for example, an all-travelling-w ave- valve rep eater. If oscillations of a frequency equal to the d e­

sired change are applied to the electron-gun of a travelling- w ave valve, they v ary the beam -velocity and phase m odulate an3r signal amplified by the valve. In this w a y high-level side­

bands can be g en erated spaced on either side of the original signal b3^ the desired frequency-change, and one can be selected w ith a filter. Such a frequency-changer has a g a m of 10—20 db, w hereas a c ry s ta l lrequency-changer has a loss of 10 db or more.

3.1.3. Combination and Separation of Broadband Channels A typical frequency p a tte rn for a six -b ro ad b an d radio-relay system is show n in Fig. 9. In any given repeater-section six go

■ and six re tu rn channels are grouped in tw o adjacent bands, and

CARRIER FREQUENCES OSCILLATOR FREQUENCIES

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Fig. 9.

R ad io freq u en cy a rra n g e m e n t fo r six R .F . channels.

a t a rep eater-statio n corresponding go and re tu rn channels are interchanged in frequency. The filters needed for combining and isolating these channels are m ade up of sections of waveguide, some forming re so n a n t cavities and others forming connecting links and junctions. The filtering is more easily described in term s of reception ra th e r th an tra n sm issio n : The combined signals

from the receiving aerial are passed through a series ol branching filters w here most of the signal p o w e r of each channel is di­

verted into a sep a ra te branch. O n e such filter is show n in Fig. 10.

In each b ranch fu rth er selectivity is introduced by a filter con­

sisting of a num ber of reso n an t cavities connected in tandem

Fig. fO.

B ran ch in g filter fo r 4.000 M c /s ra d io -re la y system .

through sections of w aveguide. A four-cavity filter of this type is illu strated in Fig. 11 w ith a curve showing the insertion- loss/frequency characteristic.

In a tra n sm itte r a similar a rran g em en t of w aveguide filters is used for combining b ro a d b a n d channels, b u t the direction of transm ission is, of course, reversed.

3.1.4 A eria l System s and Feeders.

A t the high frequencies used for rad io -relay system s it is possible to obtain v e ry high directivity w ith aerials of m ode­

r a te size, directivity being expressed as the ra tio of the p o w e r ra d ia te d in, or received from, the desired direction, to th a t for a n isotropic aerial used u n d er the same conditions. A t a given frequency' the p o w e r gain of a properly-designed aerial, w h e th e r used for transm ission or reception, is directly p ro p o rtio n al to its area, and, for a given absolute area, the gain increases by 6 db if the frequency is doubled. The relationship b etw een gain and frequency' for a 10-ft diam eter p araboloidal-reflector a erial is

Fig. 11.

C o n stru ctio n an d in se rtio n -lo ss/freq u en cy c h a ra c te ristic of 4000 M e s fo u r-ca v ity w a v eg u id e filter

show n in Fig. 12, w ith a radiation diagram taken a t 4000 M c/s.

High directivity is desirable, not only because it reduces the overal loss b etw een tran sm itter and receiver, b u t because it reduces interlerence and m ulti-path propagation.

A t3<-pical aerial installation for a 4000 M c/s r e p e a te r station is show n in Fig. 13. T here are tw o 10-ft d iam eter aerials lacing in each direction, one for transm ission and one lo r reception, and each aerial is connected to the internal equipm ent b3r a feeder of rectangular-section waveguide.

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P e rfo rm an ce of 10 -fo o t-d iam eter p a rab o lo id a l-reflec to r aerial.

Fig. 15.

In term ed ia te re p e a te r sta tio n , 4000 M c /s radio re la y system . All the aerials are similar, but it is convenient to consider their action in term s of transm ission: A t the focus of the p a r a ­ boloid the w aveguide-feeder term inates in a small directional feed which d istributes radiation over the surface ol the reflector w hence it is reflected in a n a rro w beam. The feed is designed to irrad iate the reflecting surface w ith o u t allow ing appreciable energy to fall outside the perip h ery because this w ould give

rise to b a c k w a rd and sidewaj-s radiation. In practice such an aerial can be m ade to have an effective gain equal to th a t of an ideal unilorm ly-irradiated paraboloid having 60-70°/o °f the area, combined with sid ew ay s and b a c k w a rd radiation which is a t least 40 db below th a t along the main beam.

3 .2 D is to rtio n a n d N o ise .

I will tu rn for a moment to the distortion and noise th a t can arise in b ro a d b a n d rad io -relay systems, considering first the transm ission of a num ber of telephone channels a rra n g e d side b y side in the frequency spectrum . W h e n , in a communication S3Tstem, currents oi different frequencies are subject to non-linear distortion, spurious com ponents arise, nam ely harm onic and in ter­

m odulation products, and if they fall n e a r the original frequen­

cies they might cause interference. Similarly, if a band of fre ­ quencies is subject to non-linear distortion, the harm onic and interm odulation products will fall in o th e r bands which m ay overlap the first and give rise to interference. This is illustrated in Fig. 14. In terference and noise due to interm odulation con­

stitute one ot the m ajor problem s in designing radio-relay sys­

tem s for m ulti-channel telephony.

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Illu stra tio n of the w a y in w hich in term odulation p ro d u c ts can cause in terferen ce in m u lti-ch an n el telephone system s.

The main ad v an tag es of using frequency-m odulation instead of am plitude-m odulation on b ro a d b a n d radio-relay system s are the signal/noise improvement, the fact th a t am plitude distortion need not be avoided in amplifying the m odulated carrier, and

the relative ease w ith which linear frequency-m odulation c h arac­

teristics can be obtained and the overall gain of a system can be held constant. F o r telephony, interm odulation, and hence non­

linearity, m ust be k ep t a t very low levels. Because, in frequenc3r- m odulation, the baseb an d signal is transform ed into variations of the carrier frequency, the w aveform of these variations must be faithfully preserved, otherw ise non-linear distortion will re ­ sult. F req u en cy is proportional to the rate o f change o f phase w ith time, a n d if a frequency-m odulated w ave is passed through circuits introducing phase-shift which varies w ith frequency, its in stantaneous frequency will be changed slight^'. If the phase- shift/frequency characteristic is non-linear it modifies the w a v e ' form of the frequency-excursions and d isto rts the b aseb an d sig­

nal a t the receiving end. T herefore, w hen multi-channel tele­

phony is handled by frequency-m odulation, the need for linear phase-shift/frequency ch aracteristics is just as pressing as the need for amplltude-WneeLr'ity in system s using am plitude-m odulation, and in both cases d e p a rtu re s from linearity cause interm odulation.

O n the other hand, the transm ission of television is relatively e a s y : T here is no difficulty in keeping the b aseb an d am plitude- frequency characteristic flat if w ide band-w idths are used, and this also ensures th a t there is little overall phase distortion.

N e ith e r is there difficulty in preserving sufficient linearity; small d e p a rtu re s from perfection only a lte r the tone gradations of the picture slightly. Interm odulation as such is of no significance.

In planning rad io -relay system s it is im p o rtan t th a t random noise and, w here multi-channel telephony is involved, interm o­

dulation noise should not exceed tolerable limits. U n d e r non­

fading conditions random noise is reduced relative to the signal b y increasing the frequency deviation, bu t interm odulation is then increased because a larg er frequency excursion is more likely to extend into regions w here the R F and I F phase ch a­

racteristics are non-linear. If o th e r system p aram eters, e.g. tr a n s ­ m itter-pow er, aerial-gain, etc., have been fixed, th ere is an o p ­ timum value for the deviation.

3.3 Frequency Pattern of Broadband Channels.

As th eir name suggests, b ro a d b a n d radio-relay s3rstems occupy considerable frequency space. A t the input and o u tp u t term inals 600 telephone cha nnels w ould occupy a b aseb an d extending up to 2.5-1 M.c/s and 625-line television signals w ould extend up to a t least 5 M c/s. Even for low -deviation ratio s each Ire-

quency-m odulated c a rrie r w ould therefore sp re a d over 6 M c/s or more. If six b ro a d b a n d channels are provided on the same system and different frequencies are used for the tw o directions of transm ission, hundreds of megacycles p e r second of b a n d ­ w id th are needed.

Fig. 9 show s the arran g em en t of b ro a d b a n d channels a d o p ted b y the C C I R a t W a r s a w last y e a r jointly w ith an interm ediate frequency ot 70 M c/s. O v e r any section of route the low er six channels w ould be used for one direction of transm ission and the upper six for the o th er direction; and adjacent chan­

nels would use different polarizations to reduce the iiltering needed for separation. A t a re p e a te r station the go and retu rn channels w ould be interchanged in frequency in passing from one section of route to the next. The high-level signals being tran sm itted from the re p e a te r statio n in either direction are then in different b an d s from the low-level signals being received, which reduces the likelihood of interaction.

T here w ere m any factors th a t influenced the choice a t W a r ­ saw , and here it is possible to mention only a few : (a) the images of receive channels should not fall in tran sm it channels, (b) the images of tran sm it channels should not fall in receive channels, and (c) referring to Fig. 6, harm onics of 213 M c/s, the frequency used in shifting the location of b ro a d b a n d channels a t a re p e a te r station, should not fall n e a r the frequency of oscillations derived from a mixer into which the 213 M c/s is injected. This la st requirem ent leads to preferred values for the centre frequency, fD, of the frequency p a tte rn , because for cer­

tain values of fol sa3r -1003.5 or 2004.5 M c/s, harm onics of the shift frequency, i.e. harmonics of 213 M c/s, do not fall near any of the receive-beating-oscillator frequencies. If common- transm it-and-receive an ten n ae are used, some of the sources of interference become poten tially more dangerous, and the re ­ com mended a rra n g e m en t for a system of th ree b ro a d b a n d ch an ­ nels on com m on-transm it-and-receive aerials is to use C hannels

1. 3 and 5; or C hannels 2, 4 and 6.

T here is little do u b t th a t the agreem ent reached a t W a r s a w will do much to facilitate the planning of international b r o a d ­ b an d ra d io -re la y system s.

4. T ropospheric-scatter system s.

As has been indicated earlier, in the U H F and S H F bands the signal stren g th fa r b ey o n d the horizon is fa r g re a te r than

it w ould be if th ere w ere no atm osphere, because, it is said, small-scale variations in the refractive index of the atm osphere to some ex ten t sc a tte r the w aves aro u n d the cu rv atu re of the earth . H o w ev er, there are others w ho claim th a t the signals tra v e l fa r beyond the horizon because th ey are p a rtia lly r e ­ flected b y stratification of the troposphere, including the tropo- pause, the level a t which the te m p e ra tu re ceases to fall w ith height — again a b o u t 12,000 m. Fig. 15 illustrates the me­

chanism : If tw o directional aerials are o rien tated so th a t

the m ajor lobes of their polar diagram s overlap, some energy ra d ia te d by one will be received by the o th er by scattering in the volume of the atm o sp h ere w here th ey overlap. The received energy varies inversely as a high p o w e r of the angle, 0 , a t

Fig. ] 6.

V ariatio n o f b ey o n d -th e-h crizo n p ro p a g atio n losses w ith d istan ce (L incoln L ab o ra to ry )

F i j r . 1 7 .

10 M e tre aerial used for tro p o sp h e ric -sc a tte r com m unication.

which the tw o beam s intersect, hence for minimum atten u atio n they should be directed to w a rd s the local horizon.

Because the aggregate signal is the summation of signal com ponents from various p a rts of the scatterin g region the signal fades rap id ly ; m oreover there is some variation of the median value from hour to hour, d ay to d ay and month to month. Fig. 16 illustrates the variation of field stren g th w ith distance on 400 M c /s during the w inter. I t is interesting to note th a t field stren g th falls off more and more slow ly as the distance increases.

I t is found th a t there is little short-term correlation b etw een the strength of signals received a t points say 100 or more w avelengths a p a r t a t right-angles to the direction of p ro p a g a ­ tion. H ence for these signals the p o w er gain of aerials does not continue to increase in pro p o rtio n to th eir a re a as the a re a is increased indefinitely. N evertheless, it is profitable to use aerials up to say 50 w avelengths in diam eter — app ro x i­

m ately 20 m etres d iam eter for a frequency of 800 M c/s. This lack of correlation does, how ever, make it possible to use di­

v ersity reception and transm ission w ith aerials th a t are quite close together. By using v ery high tra n sm itte r pow ers, v e ry large aerials, p erh ap s 10 or 20 m etres in diam eter, and di­

versity, it is possible to tran sm it multi-channel telephony and television over 300 km o r more w ith o u t any interm ediate s ta ­ tion. A ph o to g rap h of a 10-metre aerial used on such a system is show n in Fig. 17. The main elements of a tro p o sp h eric-scatter term inal using double-diversity reception are show n in Fig. 18.

Such a station might w o rk on frequencies u p w a rd s of 400 M c/s.

BASEBAND SIGNAL

12 - 60kc/s