RADIATION LABORATORY SERIES
Board of Editors
LOUISN . RIDENOUR, Editor-in-Chief
GEORGEB. COLLINS, Deputy Edi tor -in -Chief
BRITTON CHANCE , S. A. GOUDSMT, R. G. HEIIB, HUBERT M. JAMES, JULIAN K. KNIPP,
JAMES L. LAWSON , EON B. LINFORD, CAROL G. MONTGOMERY, C. NEWTON, ALBERT
M. STONE, Louxs A. TUENER, GEORGE E. VALLEY, J R., HERBERT H. WHEATON
1. RADAR SYSTEM ENGINEEi+lxG-Ridenour
2. RADAR AIDS TO ~AVIGATIOX—Hall
3. RADAR BEAcoNs—Roberts
5. PULSE Genera tors—6?asoe and Lebacqz
6. MICROWAVE MAGNETRONS—COllinS
7. KLYSTRONS A?JD MICROWAVE TmoDEs-Hamil ton, Knipp, and Kuper
8. PRINCIPLES OF MICROWAVE Cmmurrs-Montgomery, Dtck e, an d Pu rcell
9. MICROWAVE TRANSMISSION CIrwuITs—Ragan
10. WAVEGUIDE HANDBOOK—MarCUrIitZ
11. TECHNIQUE OF ?YIICROWAVEME,4sumnmsw-Montgomery
14. MICROWAVE ~u pLExE rm+-Smulzin a nd Montgomery
15. CRYSTAL RECTIFIERS— Torrey and Whitmer
16. MICIIOWAVE !vfIxERs-Pound
18. VACUUM TUBE AMPLIF IER —~’U@ and Wa !lm an
19. wAvE~oR~s—Chan ce, Hugh es, M ac.NT ich ol,.S a yre, and Williams
20. ELECTRONIC TIME Measurements—Chance, Hulsi zer , .Wac.Y ichol ,
and Williams
21. ELECTRONIC I Ns’rRuhiENm-Greenwood, Holdam , and MacRae
22. CATIIODE RAY TUBE DIspLAYs—So12er , Starr, a nd Va lley
23. .~lCRO WAVE REcE1 E Iw— Van Voorhis
24. THRESHOLD SIGNALs—Lawson and Uhlenbeck
25. THEORY OF SERvoiuEcIIANIsivs-J ames, N ich ols, an d Ph illips
26. RADAR SCANNERS AND RADOXES—CUdrJ , Karelitz, an d Turner
27. COMPUTING KIECHANISMSAND LINnGm-&oboda
28. I NDEx—Henney
UNIVERSITY OF PENNSYLVANIA
.
1947
J1cC,R,iW-HILL BOOK CoMP.iNY, INC.
A u lr!qhh rf?send
pert: ihrrrqf, ?na~j no! he reprod7wd
in 07(v Jm-TII wilhottl permission oj
the publishers.
 
Foreword
T
HE tremendous research and development effor t that wen t in to the
development of radar and rela ted techniques dur ing World War II
resulted not on ly in hundreds of radar sets for military (and some for
possible peacet ime) use but also in a grea t body of information and new
techniques in the elect ron ic and h igh-frequency fields. Because th is
basic mater ial may be of gr ea t value t o science and engineer ing, it seemed
most impor tant to publish it as soon as secur ity permit ted.
The Radia t ion Labora tory of MIT, which opera ted under the super-
vision of th e Nat ional Def n se Resear ch Committee, u nder took th e gr ea t
t ask of pr epa rin g t hese volumes.
Th e wor k descr ibed h er ein , h owever , is
the collect ive resu lt of work done at many labora tor ies, Army, Navy,
university, and industr ial, both in th is count ry and in England, Canada,
a nd ot h er Domin ion s.
The Radiat ion Labor t ry, once its pro osals were approved and
fin an ces pr ovided by t he Office of Scien tific Resea rch a nd Developmen t,
chose Louis N. Ridenour as Editor -in-Chief to lead and direct the ent ir e
project . An editor ia l staff was then selected of those best qualified for
th is type of task. Finally the au thors for the var ious volumes or chapters
or sect ions were chosen from among those exper ts who were in t imately
familiar with the var ious fields, ,and who were able and willing to wr ite
the summaries of them. This en t ire staff agreed to remain at work at
MIT for six months or more after the work of the Radiat ion Labora tory
was complete. These volumes stand as a monument to th is group.
These volumes serve as a memoria l to the unnamed hundreds and
thousands of oth er scient ists, engin eer s, and oth ers who actually car ried
on th e resear ch , developmen t, and engineer in g wor k th e results of which
are herein descr ibed. There were so many involved in th is work and they
wor ked so closely t oget her even t hou gh oft en in widely sepa rat ed labor a-
tor ies that it is impossible t o name or even to kn ow those wh o con tr ibu ted
t o a pa rt icu la r idea or developmen t .
On l cer ta in on es wh o wr ot e r epor ts
or ar t icles have even been ment ioned. But to all those who con tr ibu ted
in any way to th is grea t coopera t ive development en terpr ise, both in th is
count ry and in England, these volumes are dedica ted.
L. A. DUBRIDGE.
Preface
T
HE ear liest plans for t he Radia t ion La bora t ory Ser ies, made in t he fa ll
of 1944, envisaged only books concerned with the basic microwave
and elect ron ic theory and techniques that had been so thoroughly devel-
oped dur ing the war t ime work on radar .
These plans wer e la id aside for
a t ime when it became clear in this count ry that severa l months of fight ing
rem ine in the European war .
When work on the Ser ies was resumed in the ear ly summer of 1945, the
books planned, as before, dea lt with basic mat ter s and with techniques.
Every effor t was made to poin t ou t the genera l applicability of the work
repor t ed and to avoid specia l emphasis on its applicat ion to radar , since
radar it self was thought t o have only a limited impor tance.
The end of the Pacific war made it possible to put more effor t on the
job of prepar ing the Ser ies than had been available ear lier . The books
on theory and techniques having been planned as comprehensively as
appeared to be wor th while, t he work was ext ended by t e addit ion of
five books concern ed with radar and a llied systems.
Of those five books, th is is the only one that deals with radar it self.
One book takes up the use of radar in navigat ion, one concerns the design
of radar scanners and radomes, one t rea t s the design and const ruct ion of
beacon s, and one descr ibes hyperbolic naviga t iona l syst ems—in pa r ticu la r
Loran.
This book is in tended t o ser ve as a genera l t rea t ise and r efer en ce book
on the d sign of radar systems. No apology seems to be needed for the
fac that it dea ls pr imar ily-though by no means a ltogether -with micro-
wave pulse radar . Thousands of t imes as much work has gone in to pulse
radar as into any other kind, and the overwhehning major it y of this work
has been concerned with microwave pulse radar . The super ior ity of
microwaves for a lmost a ll radar purposes is now clear .
The fir st eigh t chapters of th is book are int ended to provide an in t ro-
duct ion to the field of radar and a genera l approach to the problems of
system design. Chapter s 9 through 14 take up the leading design con-
sidera t ions for the var io s impor tant component s tha t make up a radar
set . These chapters a re so thorough in their t rea tment tha t Chap. 15,
which gives two fa ir ly deta iled examples of actua l system design, can be
quite br ief. Chapters 16 and 17 take up two new and impor tant ancillary
ix
x PREFACE
techniques that a re not dea lt with fully elsewhere in the Ser ies: moving-
t a rget indicat ion and the t ransmission of radar displays to a remote
indicator by radio means.
For fuller informat ion than can be found in this book on any deta iled
point of design, t he reader is refer r ed to one of the other books of the
Ser ies. In a sense, th is book specia lizes to radar the techniques repot ied
mor e fully elsewh er e in t he Ser ies.
Radar is a ver y simple subject , and no specia l mathemat ical, physical,
or engineer ing background is needed to read and understand this book.
Because the book cover s the en t ire field of effor t of the Radia t ion
La bor at or y and t he ot her wa rt ime r adar establishments, it s cont ribut in g
authors a re more numerous than those listed for most other volumes of
this ser ies. I am especia lly grateful to L. J . Hawor th and to E. M.
Purcell, whose cont r ibu t ions have been more extensive than those of
other authors, and whose a vice on editor ia l problems has often been
ext remely helpful. In ad it ion to the authors a lready listed, whose
names appe r in the book in connect ion with the mater ia l t hey have
wr it t en , I wish to thank the following men for their work in provid-
ing essent ia l background mater ia l that did not even tually find it s wa
into t e book: R. M. Alexander , A. H. Brown, J . F . Car lson, M. A.
Chaffee, L. M. Hollingswor th , E. L. Hudspeth , R. C. Spencer , and I. G.
Swope. Changing plans for the book also reduced the acknowledged
cont r ibut ion of E. C. Polla rd far below the very considerable quant ity of
mat er ia l h e pr epa red.
I owe an apology to all t he authors for the liber ty I have often
taken in alter ing their or iginal t ext t o fit the final fr amework of the
book and my own ideas of style.
Beca use most a ut hors left t he Labora -
tory immedia tely on finishing their wr it ing, and much of the editor ia l
work had to be defer r ed unt il the book was substant ia lly complete, it has
not a lways been possible t o adjust with the authors the altera t ions in their
manuscr ipt s that have seemed desirable to me.
The genera l acknowledgments I owe as Editor-in-C ief of the Ser ies
a re set for th in the Ser ies Index. In connect ion with the prepara t ion
of this book, however , it is a pleasure to thank Dr . B. ~. Bowden, of the
Br it ish Air C mmission, not on ly for his assistance as an author but a lso
for his genera comments on the book as a whole. I am grateful to
Lois Capen for her wor k in following the prepara t ion of illust ra t ions, and
t o P hyllis Br own for gen er al s cr et ar ia l a ssist an ce.
LOUIS N. RIDENOUR.
1
3
6
1.5 Radar Systems .,..., . . . . . . 12
13
1.7 War time Rada r Developmen t in the U .S..
15
THE RADAR EQUATION FOR FREE-SPACE PROPAGA ION 18
2.1 The Meaning of F ree-space Propagat ion 18
22 Antenna Gain and Receiving Cross Sect ion .
19
2.3 Sca t ter ing Cross Sect ion of the Target 21
2.4 The Radar Equat ion .
21
2.6 The Beacon Equation. 27
TRE MINIMUM DETECTABLE SIGNAL. 28
2.7 Noise . . . . . . . . . . . . . 28
2.11 Effect of Storage on Radar Per formance
41
MICROWAVE PROPAGATION 47
2.12 Propag tion over a Reflect ing Sur f a r c 47
2.13 The Round Ear th. 53
2.14 Super refr act ion 55
2.15 At tenuat ion of Microwaves in the Atmosphere 58
CHAP. 3. PROPERTIES OF RADAR TARGETS .,. 63
SIMPLE TARGETS .,.,.... ..63
3.1
32
33
3.4
3.5
3.6
3.7
Cross Sect ion Expressed in Terms of the Field Quantit ies 63
Rayleigh Sca t ter ing from a Small Sphere. . 63
Sca t ter ng of a Plane Wave by a Sphere
64
65
67
Useof Absorbent Mater ia ls. . 69
xi
39 Actual Gomplex Targets. 75
3.10 Compound Targets Extended through Space 81
311 Extended Surface Targets 85
GFtOWNDPAINTING BY AIRBORNE RADAR 88
3.12 Specular and Diffuse Reflect ion 89
3.13 Sea Return and Ground Return . 92
3.14 Mounta in Relief.
CHAP. 4. LIMITATIONS OF PULSE RADAR 116
4 1 Range, Pulse-repet it ion Frequency, and Speed of Scan 116
4.2 Bandwidth , Power, and Informat ion-ra te. 121
4.3 Puke Radar a nd -w Radar .123
4.4 Clut ter . . . . . . . . . . . 124
127
127
5.3 Effect of Target .
131
132
57 Range-measur ing Doppler System. 139
5.8 F-m Range-measuring System.
5.10 Alternat ive F-m Ranging System
149
160
TYPES OF RADABIN~ICATOW. 161
6.2 Definit ions . . . . . . . . 161
163
164
167
171
175
69 Ear ly Aircra ft Warning Radar 175
6.10 PPI Radar for Search, Cont rol, and Pilotage 182
6.11 Height%nding Involving Ground Reflect ion. 184
6.12 Height -6nding with a Free-spa e Beam. 187
6.13 Homing . . . . . . . . . . .196
CHAP. 7. THE Elf PLO~31ENT OF RADAR DAT.k
213
EXTERNAL A1nSTORADAE ~-SE. 214
214
218
EXAMPLES OF RADAR ORGANIZATIONS
7.7 Close Cont rol with SCR-584 238
7.8 Teheran . . . . . . . . . . 240
8.2 Systems Pla ning
8.3 Genera l Ident ifica t ion System—IFF.
8.4 Radar Inter roga t ion vs. Specia l Inter roga tor s
8,5 Independence of In ter roga t ion and Reply.
8.6 Frequency Considera t ions
243
246
246
250
251
252
254
260
263
STATISTICAL CONSInERATION-S.
268
271
9,2 Round and Cut Paraboloid Antennas 272
93F anBeams . . . . . . . . .274
279
9.9 The Weight of MechanicalSc nners. 283
910 R-fTransmiesion Lines. 283
ELECTRICAL SCANNERS.
9.14 Schwa rzsch ifd An ten na .
295
9.15 SCI Height Finder .. .298
9.16 Other Types of E lect r ica l Scanners. : 302
THE STABILIZATION PROBLEM.
305
311
9.21 Radomes . . . . . . . . . 314
9.23 Elect r ical Transmission . 316
9.24 St ructura l Design of Radomes 316
9.25 Examples of Radomes
THEMAGNETRON. . . . . . . . 320
10.3 Elect ron Orbits and the Space Charge 330
10.4 Per formanceChar ts and Rieke Diagrams 336
10.5 Magnetron CharacteristicsAffecting Over-allSystemsDesign
TEE Puller . . . . . . . . . . .. 355
10.8 Load Requirements,. . ..362
109 The Hard-tube Pulser
11.1 The R-f Transmission Problem 391
11.2 Coaxial Lines . . . . . . .393
407
11.8 The Mixer . . . . . . . . 416
MOUNTING THE R-F PARTS.... . . . . .
11.11 Design Consider t ions for the R-f Head 421
11.12 Illust ra t ive Examples of R-f Heads 425
CWP, 1 . THE RECEIVING SYSTEM—RADAR RECEIVERS 433
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . ..433
12.2 A Typical R ceiving System 435
THE RECEIVER . . . . . . . . . . . . . . . . . . . . . . . . . .441
12,41 -f Amplifier D sign... . . . . . . . . . .. 442
12.5 Second Detector . . . . . . . . . . . . . . .. 449
12.7 Automat ic Frequency Control. 453
12.8 Protect ion against Extraneous Radia t ion. 457
TYPIC.AL RECEIVERS . . . . . . . . . . .. 460
470
THECATirOnE-RAYUBE . . . . . 475
13.2 Cathode-rayTube Screens 479
COormlNAmON WITH THE SCANNER
486
.,.
496
13.9 Elect ronic Switches . . . . . .. 503
510
INDICES . . . . . . . . . . . . .
513
 
13.14 B-Scope Design . . . . . . . . . . . . . . . . . . . . ..528
13.16 The “ Resolved Time Base”
Method of PPI Synthesis . 534
13.17 Resolved-cu rrent PPI 538
13.18 The Method of Pre-t ime-base Resolu t ion . 544
13.19 The Range-height Indica tor . 545
SIGNAL DISCRIMINATION, RESOLUTION, AND CONTRAST. 54s
1320 Resolu t ion and Con trast 548
13.21 Special Receiving Techniques for Air -to-land Observa t ion . 550
CHAP. 14. PRIME POWER SUPPLIES FOR RADAR. 555
.41RCRAFT SYSTEMS
Wave Shape . . . . . . . . .
Dir ect -d r ven Gen er at or s.
Motor-a ltern ator Sets
Speed Regu lators . . . . . . .
Summary of Recommendat ions for Aircraft Radar Power
555
1410FixedLocations. . . 583
14 11 Large Systems Where No Commercial Power Is Available, 584
1412 Smaller Mobile Units
CHAP. 15. EXAMPLES OF RADAR SYSTEM DESIGN 588
1511 n t roduct ion . .,.,. . . 588
152 The Need for System Test ing. 590
DESIGN OF A HIGH-PERFOEXANCE RAnAR FOB Am SURVEILLANCE AND
CONTROL, . . . . . . . . . . . 592
153 Init ia l P lanning and Object ives 592
15.4 The Range Equat ion . ,595
155 Choice of Pulse Length .596
15.6 Pulse Recurrence Frequency 598
15.7 Azimuth Scan Rate... . . . . . . .. 599
15.8 Choice of Beam Shape. 600
159 Choice of Wavelength . ,604
15.10 Components Design 606
15.11 h fodifica tion s an d Addit ion s,
609
DESIGN OF A LIGHTWEIGHT AIRBORNE RADAR FOR NAVI~ATION 611
15.12 Design Object ives and Limitat ions. 611
15.13 General Design of the AN/APS-10. 614
15.14 Detailed Design of the AN/AP&10 616
CHAP. 16. MOVING-TARGET INDICATION 626
INTRODUCTION . . . . . . . . . . . . ...626
626
16.3 A Pract ica l MTI System. . . 632
16.4 Alter a t ive Methods for Obtaining Coherence.
635
16.5 Stability Requirements. 638
16.6 In ternal Clu t ter Fluctua t ions . 642
16.7 Fluctuat ions Due t o Scanning 644
16.8 Receiver Character ist ics : 646
16.9 Target V sibility . . . . . . . . .,...,..,.....649
16.10 Choice of System Constamts. 653
MOVING-TABGET INDICATION ON A MOVING SYSTEM . 655
16.11 Compensat ion for Velocit y of System . . 655
1612 The Nonc heren t Method. . 656
16.13 Beat ing Due to Fin ite Pul e Packet 657
COMPONENT DESIGN . . . . . . . . . . . . . . . . . . . . . . . . .658
16.15 The Stable Local Oscilla tor . 659
16.16 The Coheren t Oscilla tor 662
16.17 The Receiver . . . . . . . . . . . . ...665
16.19 Delay-line Signal Circu it s : . . . 672
16.20 Delay-line Tr igger Circu it s 675
16.21 Special Test Equipment 677
CHAP. 17. RADAR RELAY.... . . . . . . . . . .. 680
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . ...680
17.2 The Elements of Radar Relay. 681
MISTHODS OF SCANNER DATA TRANSMISSION
17.3 Genera l Methods of Scanner Data Transmission.
17.4 Methods of Combat ing In ter ference
17.5 The Method of Incrementa l Angle.
17.6 The Phase-shift Method
17.8 Pulse Method for Relaying Sine and Cosine.
17.9 Comparison of Synchroniza t ion Methods.
...
17.10 Antennas, Frequencies, and the Radiat ion Path. 713
17.11 Genera l Transmit ter and Receiver Considera t ions 717
17.12 A 300-Mc/sec Amplitude-modula ted Equ pment . 719
17.13 A 100-Mc/sec Frequency-modula ted Equipment . 721
17.14 Microwave System for Point -to-point Service. 723
RA~AR RELAY SYSTEMS . . . . . . . . . . . ...726
17.15 A Ground-to-ground Relay System
726
INDEX . . . . . . . . . . . . . . . . . . . . . .
737
BY LOUIS N. RIDENOUR
101. What Radar Does. —Radar is an addit ion to man’s sensory
equ ipmen t wh ich a ffor ds gen uinely n ew fa cilit ies.
It enables a cer ta in
class of objects t o be “seen”
—t ha t is, det ect ed a ndloca ted—a t dist an ces
far beyond those a t which they could be dist in uished by the unaided
eye. This ‘(seeing” is unimpaired by night , fog, cloud, smoke, and most
ot her obst acles t o or din ar y vision.
Radar fu r her permits the measure-
ment of the range of the obje t s it “sees” (this verb will herea ft er be used
without apologet ic quota t ion mark ) with a convenience and precision
ent irely unknown in the past .
It can also measure the instantaneous
speed of such an object toward or away from the observing sta t ion in a
simple and natura l way.
The super ior ity of rada r to ordinary vision lies, then , in the grea ter
dist ances a t which se ing is possible with radar , in the ability of radar to
work regardless of light condit ion and of obscura t ion of the object being
seen , and in the unpara lled ease with which ta rge range and its ra t e of
change can be measured. In ce ta in other respects radar is defin itely
infer ior to the eye. The deta iled defin it ion of the picture it offers is v ry
much poorer than tha t afforded by the eye.
Even the most advanced
rada r equipment can on]y show the gross out lines of a large object , such
as a ship; the eye can—if it can see the ship a t a ll—pick out fine deta ils
such as the rails on the deck and the number or cha racter of the flags a t
the masthead. Because of this grossness of radar vision, the object s
tha t can usefully be s en by radar a re not s numerous as the object s
tha t canabe dist inguished by t he eye.
Radar is a t it s best in ea ling with
isola ted ta rget s loca ted in a rela t ively fea tureless background, such as
a ircraft in the a ir , ships on the open sea , islands and coast lines, cit ies in
a plain, and the lik . Though modern high-defin it ion rada r does afford
a fa ir ly deta iled presenta t ion of such a complex ta rget as a city viewed
from the air (see, for example, Fig. 335), the rada r pic ure of such a
ta rget is incomparably poorer in deta il than a ver t ica l photograph taken
u nder fa vor able con dit ion s wou ld be.
One fu r ther proper ty of radar is wo th remarking: it s fr eedom from
difficult ies of perspect ive, By suitable design of the equipment , the
picture obta ined from a radar set can be presen ted as a t rue plan view,
1
HOW RADAR WORKS 3
the rada r picture would have been unaffected while photography or
ordinary vision wou ld h ave been useless.
1.2. How Radar Works.—The coined word roda r is der ived from the
descr ipt ive ph ra se
“radio detect ion and ranging. ” Radar works by
sending ou t radio waves from a t ransmit ter powerfu l enough so tha t
measurable amounts of radio energy will be reflected from the object s to
beseenby therada r toaradio receiver usua lly loca ted, for conven ience,
a t the same site as the transmit ter .
Th e pr oper ties of t he r eceived ech oes
a re used to form a pictu re or to determine cer ta in proper t ies of the object s
tha t cause the echoes. Therada r t ransmit ter may send ou t c-w signa ls,
or frequency-modula ted c-w signals, or signa ls modula ted in oth er ways.
Ma ny sch em es ba sed on tra nsm ission s of va riou s sor ts h ave been pr oposed
and some of hem have been used. Chapter 5 of this book t rea ts the
genera l radar problem, in which any scheme of t ransmit ter modula t ion
may be used, in a very fundamenta l and elegant way.
Despite the grea t number of ways in which a radar system can in
pr inciple be designed, one of these ways has been used to such an o er -
whelming degree tha t the whole of this book, with the except ion of Chap.
5, is devoted to it . When radar is men t ioned without qua lifica t ion in
this book, pulse rada r will be meant .
NTOapology for th is specia liza t ion
is eeded. Thousands of t imes as much effor t as tha t expended on all
other forms of radar pu t together has gone in to the remarkably swift
developmen t of pulse rada r since its or igin in the yea rs just before World
War II.
In pulse rad r , the t ransmit ter is modula ted in such a way tha t it
sends ou t very in tense, very br ief pulses of radio energy a t in terva ls tha t
a re spaced ra ther fa r apar t in terms of the dura t ion of each pulse. Dur ing
the wait ing t ime of the t ransmit ter between pulses, the receiver is act ive.
Echoes a re received from the nearest object s soon a fter the t ransmission
of the pulse, from object s fa r ther away at a sligh t ly la er t ime, and s on .
When sufficien t t ime has ela psed t o a llow for th e recept ion of ech oes from
the most distan t object s of in terest , the t ransmit ter is keyed aga in to
send another very shor t pulse, and the cycle repea ts.
Since the rad o
waves used in radar a re propaga ted w th the speed of ligh t , c, the delay
between the transmission of a pulse and the recept ion of the echo from
an object a t range R will be
(1)
the factor 2 en ter ing because the distance to the ta rget has to be t raversed
twice, once ou t and once back, F igure 1.2 shows schemat ica lly the
pr in ciple of pu lse r ada r.
 
Target
JL~~=~
(c) ,%
Radar
_L...__
(a) Pulsehas jus t beenemit tedfrom radar
aat . (b)P ulaereachesta rget. (.) Scat ter edenergy,etu rn sfromt ar get;tr an sZnittedpu l`e
carrieOn, (d) Echo pulsereachesra dar .
 
5
theclue totheease t ithwt ich range can remeasured by radar . Range
me surement is r educed t o a measurement of t ime, and t ime can be
measured perhaps more accura tely than any other basic physica l quan-
t ity. Because the velocit y of light is high, t he in terva ls of t ime tha t
must be measured in radar ar e shor t .
Numer ically, t he range cor r e-
sponding to a given delay t ime is 164 yd for each microsecond elapsing
between the t ransmission of the pulse and the recept ion of the echo. If
it is desired to measure range to a precision of 5 yd, which is necessa ry in
some applicat ions of radar , t ime interva ls must be measured with a
precision bet t er than & psec. Modern elect ronic t iming and display
techniques have been developed to such a poin t that this can readily be
done.
One of the simplest ways in which radar echo signals can be displayed
is shown in Fig. 1.3. The beam of a ca thode-ray tube is caused to begin
a sweep from left t o r igh t across the face of the tube at the instant a pulse
is sent fr om t he t ran smit ter .
The beam is swep to the r ight a t a un iform
r at e by m eans of a sawt oot h a veform applied t o t he h or izon ta l deflect ion
pla tes of the CRT. The outpu t signals of the radar r eceiver a re applied
to the ver t ica l deflect ion pla tes.
To ensure tha t the weakest signals
tha t a re a t a ll det ectable a e not missed, t he over -a ll gain of the receiver
is high enough so that thermal noise or igina t ing in the recei er (Sec. 2.7)
is percept ible on the display. The two signals that r ise significant ly
 
6
INTRODUCTION
[SEC.1.3
pulse leaking in to the receiver , and on the r igh t , the echo signal from a
radar t arget . The ta rget in the par t icu lar case of F ig. 1“3 is the ear th ’s
moon.
The measurement of range by means of radar is thus a st ra igh t forward
pr oblem of t ime mea su remen t.
It is a l o desirable to be able to measure
the direct ion in whi h a ta rget lies as viewed from a radar sta t ion . In
pr inciple, th is can be done on the basis of tr iangula t ion , using range
in form ation on t he same ta rget fr om two or m or e separ ate ra da r locat ion s.
Although this method permits of grea t accuracy and has occasionally
been used for special purposes, it is far more desirable from the stand-
poin t of simplicity and flexibility to measure direct ion , as well as range,
from a single rad r sta t ion . Measurement of t a rget bear ing was made
possible by the development of radio techniques on wavelengths shor t
enough to permit the use of h ighly direct ional antennas, so tha t a more
or less shar beam of radi t ion cou ld be produced by an antenna of
r ea sonable physica l size.
When the pulses ar e sen t ou t in such a beam, echoes will be received
on ly from ta rgets tha t lie in the direct ion the beam is poin t ing.
If the
antenna , and hence the radar beam, is swept or scanned around the
hor izon , the st rongest echo will be received from each target when
the beam is poin t ing direct ly toward the ta rget , weaker echoes when the
beam is poin ted a lit t le to one side or the other of the ta rget , and no echo
at all when it is poin t ing in other direct ions.
Thus, the bear ing of a
ta rget can be determined by not ing the bear ing of the radar antenna
when that ta rget gives the st rongest echo signal.
This can be done in a
var iety of way , and more precise and conven ien t means for determin ing
ta rget bear ing by means of radar have been developed (Chap. 6), but the
met hod descr ibed h er e illu st ra tes t he basic pr in ciple.
It is conven ien t to ar range the radar display so that , i tead of show-
ing ta rget range on ly, as in Fig. 1.3, it shows the range and angular
disposit ion o all ta rget s at all azimuths. The plan-posit ion indica tor ,
or PPI, is the most common and conven ien t display of th is type. F igure
1.1 is a photograph of a PPI-scope.
The direct ion of each echo signal
from the cen ter of the PP shows its direct ion from the radar ; its distance
from the cen ter is propor t iona l to target range. Many other forms of
indicat ion a re conven ien t for specia l purposes; th e var ious types of indi-
ca tor a re ca ta loged in Chap. 6.
1.3. Componen t s of a Radar System.—A radar set can be considered
as sepa rable, for t he pu rposes of design a nd descr ipt ion , in to sever al m ajor
compon en ts con cer ned wit h differ en t fu nct ion s.
F igure 1.4 is a block
diagra of a simple radar set broken up in to the componen t s ordinar ily
dist in gu ish ed fr om on e a not her .
 
7
fir ing of the modula tor . This sends a high-power , h igh-voltage pulse to
th e magnet ron , which is the type of transmit t ing tube almost universally
used in modern radar . For the br ief dura t ion of the modulator pulse,
which may typically be 1 ~sec, the magnet ron oscilla tes at the radio
fr equ en cy for wh ich it is design ed, usually some th ou sands of m egacycles
per second. The r -f pulse thus produced t ravels down the r -f t ransmis-
sion line shown by double lines in Fig. 1.4, and p sses through t e two
switches designated as TR and ATR. These are gas-discharge devices
of a very special sor t . The gas discharge is sta r ted by the high-power
Rotatingantenna
—1
4!
FIG.1.4.—Blockdiagramof a simpleradar.
r -f pulse from the t ransmit ter , and main ained for the urat ion of that
pulse; dur ing this t ime the TR (for t r ansmit- eceive) switch connects
the t ransmit ter r -f line to the antenna, and disconnects the mixer and the
rest of the radar receiver shown below the TR switch . The ATR (for
ant i-TR) switch , when fired, simply permits the r -f pulse from the trans-
mit ter to pass through it with negligible loss. Between pulses, when
these gas-discharge switches are in an unfir ed state, the TR switch
connects the rnher to the antenna, and the ATR disconnects the magne-
t ron to preven t loss of any par t of the feeble received signal.
After passing through these two switches, the t ransmit ter pulse
 
INTRODUCTION [SEC.1.4
an tenna is designed in such a way tha t the beam shape it produces is
suitable for the requirements the radar set must meet . It is mounted on
a scanner which is a rranged to sweep the beam through space in the
ma ner desired; simple azimuth rota t ion is indica ted in Fig. 1“4.
After the t ransmission of the pulse, the discharges in the TR and
ATRst itches cease andthesystem isready to receive echoes. Echoes
are picked up by the antenna and sen t down the r-f line to the mixer .
The mixer is a nonlinear device which , in addit ion to receiving the signals
from the antenna , is supplied c-w power from a loca l oscilla tor opera t ing
at a frequency only a few tens of megacycles per second away from the
magnet ron frequ ency. The difference frequency that resu lt s from mixing
these two signals conta ins the same in telligence as did the or igina l r -f
echoes, but it is a t a sufficien t ly low frequency (typica lly, 30 Me/see) to
be amplilied by mor e or less con ven tion al t ech niqu es in t he in termedia te-
frequency amplifier shown. Output signals rom the i-f amplifier a re
demodu la ted by a detector , and the resu lt ing unipolar signals a re fur ther
amplified by a video-frequen y amplifier simila r to those familiar in
te levis ion technique.
The outpu t signals of the video amplifier a re passed to the indica tor ,
which displays t em, let u say for definiteness, in plan-posit ion form.
In order to do this, it must receive a t iming pulse from the modula tor , t o
indica te the instan t a t which each of the uniform range sweeps out from
the cen ter of the PPI tube should begin. It must a lso receive from the
scanner informat ion on the direct ion in which the an tenna is poin t ing,
in order tha t the range sweep be executed in the proper direct ion from the
cen ter of the tube. Connect ions for accomplish ing this a re indica ted in
the Fig. 1.4.
In Chaps. 9 to 14, inclusive, the deta iled design of each of the com-
ponen ts shown in Fig. 1.4 is t rea ted.
In a ddit ion , con sider at ion is given
to the problem of supplying r imary power in a form suitable for use with
a r ada r set ; th is is e pecia lly difficu lt an d importa nt in t he ca se of a irborn e
radar .
1.4. The Per formance of Radar .-In discussing the per formance of
radar , one usua lly refers to its range pwfor rnunce-tha t is, t e maximum
distance at which some ta rget of in terest will retu rn a sufficien t ly st rong
signal to be detected. The factors tha t determine range per formance ar
numer us and they in teract in a ra ther complica ted way. Chapter 2 is
devoted to a discussion of them, and Chap. 3 dea ls with the importan t
mat ter of the proper t ies of radar ta rget s.
Th e usu al in verse-squ are law wh ich gover ns t he in ten sit y of ra dia tion
from a poin t source acts to determine th e ra nge depen dence of the fract ion
of the tota l t ransmit ted energy tha t fa lls on a ta rget . So far as the echo
 
9
t ion , so tha t the inverse-square law must be applied again to determine
t he ran ge depen dence of t he amount of ech o en er gy reaching t he r eceiver .
In consequence, the echo ene gy received from a target var ies with the
inverse four th power of the range from the rada r set to the ta rget , other
fa ct or s being con st a nt .
To be detectable, a signal must have a cer ta in minimum power ; let
us ca ll the minimum de ectable signal t lt i~.
Then the maximum range
of a rada r set on a ta rget of a given type will be determined by Smi.,
a ccor din g t o t he expr ession
S.n = g,
where K is a constant and Pt is the power in the t ransmit ted pulse, t o
()
m.
Equat ion (2) displays t he difficu lty f increa sing t he ra nge per form ance
of a radar set by ra ising it s pulse power .
A 16-fold increase i power is
required t o double the range.
10,CQO
10?m
Date
100
80
Date
However formidable this requirement appears, one of the most
remarkable facts of the war t ime years of development of radar is tha t
pract icable pulse owers in the microwave frequency range (about 1000
Me/see and above) have increased by a factor of hundreds in a r ela t ively
shor t t ime. This stupendous advance result ed from the invent ion and
rapid improvement of the mult icavity magnet ron , which is descr ibed in
Chap. 10. Figure .5 shows the history of magnet ron development , with
respect to pulse power and efficiency, a t the t hree most important micro
wave bands exploit ed dur ing the war .
The cur ves ar e ra ther arbit ra r ily
 
[SEC.14
step in output power was due to an improvement in the magnet ron it self.
The increase at 10-cm wavelength in the ear ly par t of 1941 as brought
a out by the development of modula tors of higher power .
It is impor tant to rea lize that the cu ves of Fig. 1.5 lie above one
a other in the order of increasing wavelength no because development
was begun ear lier a t 10 cm than at 3 cm, and ear lier a t 3 cm than at 1 cm,
but because magnet rons of the type used in radar are subject to inherent
limita t ions on maximum power which are more severe the shor ter the
wavelength . The same is t rue of the r-f t ransmission lines used a t
microwave frequencies. The horizonta l dashed lines shown in Fig. 15a
show the maximum power that can be handled in the standard sizes of
‘‘ waveguide”
used for r -f t ransmission at the three bands.
A similar ly spectacula r decrease in the minimum detectable signal,
due to the improvement of microwave radar receiver s, has marked the
wa r yea r s.
In the wavelength bands above about 10 m, natural “sta t ic”
and man-made in ter ference set a ra ther high noise level above which
signals must be detect ed, so that there is lit t le necessity for pursuing the
best possible r eceiver per formance.
This is not t rue at microwave fre-
quencies.
Natural and man-made in ter ference can be neglected a t these
frequeficies in compar ison with the unavoidable inherent noise of the
receiver . This has put a premium on the development of the most
sensit ive receiver s possible; a t the end of 1945 microwave receiver s wer e
within a fa tor of 10 of theoret ica lly per fect per formance. Improvement
by this factor of 10 would increase the range of a radar set only by the
factor 1.8; and fur ther receiver impro ement ca today be won only by
the most painstaking and difficult a t tent ion to details of design.
Why Microwave s?-The reader will have observed tha t when radar is
discussed in what has gone before, microwave radar is assumed. his is
t rue of the balance of this book as well. So far as the authors of this
book are concerned, the word m.dar implies not only pulse radar , as has
a lready been remarked, but microwave pulse radar .
Though it is t rue
that the effor t s of the Radia t ion Labora tory were devoted exclusively to
microwave pulse radar , this at t itude is not ent irely parochia lism. The
fact is tha t for near ly every purpose served by radar , microwave radar
is preferable. Th re are a few ap lica t ions in which longer -wave radar
is equally good, and a ver y few wh er e long wa ves a re defin it ely pr efer able,
but for the overwhelming major ity of radar applicat ions microwave radar
is demonstrably far more desirable than radar opera t ing a t longer
wavelengths.
The super ior ity of microwave radar ar ises largely because of the
desirability of focusing radar energy into sharp beams, so tha t the direc-
t ion as well as the range of ta rgets can be determined. In conformity
 
THE PERFORMANCE OF RADAR 11
the beam passing th rough an aper tu re of given size depends on the ra t io
of the diameter of the aper tu re to the wavelength of the radia t ion in the
beam, the sharpness of the beam produced by a radar an tenna (which
can be thought of as a sor t of aper tu re for the radio energy) depends on
the ra t io of the antenna dimensions to the wavelength used. For an
antenna of given size, the breadth of the beam produced is propor t ional
t o the wavelength . These sta tements a re made precise in Sec. 9.1.
Par t icular ly in the case of a irborne radar , where a large antenna
cannot be tolera t ed for aerodynamic reasons, it is impor tant t o produce
sharp radar beams with an anten a st ructu re of modest size.
This
demands the use of microwaves. Roughly speaking, microwaves are
radio waves whose wavelength is less than 30 cm.
Radar defin it ion , it s ability to discr iminate between target s close
together in space, improves as the beamwidth is nar rowed. Target s a t
the same range can be dist inguished by radar as being separa te if they
are separa ted in azimuth by an angle larger than one beamwidth; thus
the quality of the pictu re afforded by radar improves as the beamwidth
is reduced. For an an tenna of given size, the beamwidth can be decreased
on ly by lower in g t he wa velen gt h.
The fin ite velocity of light sets a limit to the desirable beamwidth if
a region of fin it e size is to be scanned at a given speed by a radar set .
Chapter 4 considers th is and other limitat ions of pulse radar in s me
detail.
The Propagation of Micr owaves. —Fur th er lim it at ion s on t h e per form-
ance of radar ar ise from he propagat ion proper t ies of radio waves in the
m icr owave r egion of t he elect roma gn et ic spect r um.
Like light , micro-
wa ves a re pr opa ga ted in st ra igh t lin es.
Unlik e r adio waves a t fr equencies
lower than about 30 Me/see, microwaves are not reflected from the
ionosphere. This means that the maximum range of a radar set whose
per formance is not otherwise limited will be set by the opt ica l hor izon
which occurs because the ear th is round. This is in fact the limitat ion
on the per formance of the best radar Set s de eloped dur ing the war .
Under cer ta in condit ions, bending of the microwave beam around the
ear th is produced by meteorologica l condit ions (Sec. 2.14). This can
increase the range of a radar set beyond the opt ica l hor izon , bu t such
ph en omen a a re r ela tively r ar e an d essen tia lly u npr edict able.
A lower limit on the wavelengths which can be used for pract ica l
radar systems is fixed by the onset of a tmospher ic absorpt ion of micro-
wave energy.
Below a wavelength of about 1.9 cm, ser ious absorpt ion
occurs in moist a tmosphere, because of a molecu lar t ransit ion in water
vapor which can be excit ed by the radiat ion (Sec. 2.15). For th is reason ,
2 cm is about the shor test wavelength at which ra ar systems of good
 
12
INTRODUCTION
[SEC.1.5
where high absorpt ion can be tolera ted or is even welcome, shor ter wave-
lengths can be used, but 2 cm is a good pract ica l limit . The war t ime
dev lopment of radar components and systems at 1.25 cm antedated the
discovery of the st rong water -vapor absorpt ion at this wavelength . A
wavelength of 1.25 cm is, for tu itously, very near ly the most unf or t t inate
choice that could have been made in the development of a new shor t -
wavelengt h band.
105. Radar Systems.—The uses made of radar were so var ious under
war t ime condit ions that many different systems were developed to fill
different needs. These systems usually diff red more in regard to beam
shape, scanning means, and mode of indicat ion than in regard to any
other proper t ies. Chapter 6 gives a br ief conspectus of the pr inc pal
var iet ies of radar , wit especia l emphasis on those types that promise to
have an impor tan t peacet ime use.
Two examples of th e detailed design
of radar systems are given in Chap. 15, after the componen ts of radar
syst em s h ave been discu ssed.
Considerable use has been made of radar beacons. These ,are devices
which , on receiving a pulse or a ser ies of proper ly coded pulses from a
radar set , will send back in reply a pulse or a ser ies of coded pulses. A
great increase in the flexibility and conven ience of the use of radar under
cer ta in condit ions can be obtained by the use of such beacons.
A br ief
account f their proper t ies and uses, though not of their design , will be
found in Chap. 8.
Toward the end of the war , two major’ developments occur red which
pr om ised t o ext en d gr ea tly t he applicability of pu lse r adar u nder u nfavor -
a bl con dit ion s. Means wer e developed for r epr odu cin g r ada r in dica tion s
at a point distant from the set tha t gathered the or iginal data; the in telli-
gence necessary was t ransmit ted from the radar to the distant indica tor
by radio means. This radar relay, as it has come to be called, is descr ibed
in some deta l in Chap. 17.
Chapter 16 deals with another impor tant development—namely, the
modifica t ion of pulse-radar equipmen t so that it will display onl tar gets
that are in mot ion rela t ive to the radar . Such moving-target indica t ion
is potent ially of grea t impor tance in freeing radar from the limita t ions of
site. At the present , a radar site must be chosen with carefu l a t tent ion
to the surrounding ter ra in ; hills or buildings with in the line of sight can
retu rn st rong “permanent echoes” which mask target signals over a large
par t of the desirable coverage of the set . In mount inous temati, this
problem is very ser ious. An arrangement that gives signals only from
targets tha t are moving ap ears to be the best solu t ion to the permanen t-
echo problem.
 
13
informat ion afforded by radar is usually a t least as impor tant as is the
radar it self. A ood organiza t ion can make excellen t use even of in fer ior
radar in formation , as was proved by the success of the Br it ish Home
Chain of r adar sta t ions, t he first la rge-sca le r adar installat ion t o be made.
An inadequate organiza t ional set -up can do a poor job, even though
provided with splendid radar from the techn ica l standpoint . The many
problems that en ter in to the crea t ion of an ade uate organiza t ion for the
use of radar data have not received he study that they should. Despite
th is fact , Chap. 7 a t tempts to provide an in t roduct ion to th is sor t of
planning, and to ra ise some of the impor tan t problems, even though they
may n ot yet be sa t isfactor ily solved.
106. The Ear ly History of Radar .—Though the complete h istory of
the or igins and the growth of modern radar is a long and complica ted one, 1
it will be of some in terest to sketch here its main lines, with especia l
r efer ence to Allied developmen t s.
Successfu l pu lse radar systems were developed independent ly in
Amer ica , England, France, and Germany dur ing the la t ter 1930 s. Back
of their development lay half a cen tu ry of radio development for commu-
nica t ion purposes, and a handful of ear ly suggest ions tha t , since radio
waves a re known to be reflected by objects whose size is of he order of a
wavelength , they migh t be used to detect objects in fog or darkness.
The fact tha t radio waves have opt ica l prope t ies ident ica l with those
associa ted with ordinary visible light was established by Heinr ich Her tz
in 1886, in the famous ser ies of exper i en ts in which he fir st discovered
radio waves. Her tz showed, among other th ings, tha t radio waves were
reflected from solid objects. In 1904 a German engineer , Hu smeyer ,
was gran ted a pa ten t in severa l coun t r ies on a proposed way of using
th is proper ty in an obstacle detector and navigat ional aid for ships. In
J une 1922, Marcon i st rongly u rged the use of shor t waves for radio
detection.
The pr inciple of pu lse ranging which character izes modern radar was
fir st u sed in 1925 by Br eit a nd Tu ve, of t he Ca rn egie In st it ut ion of Wa sh in g-
ton , for measur ing the heigh t of the ionosphere. 2 After the successfu l
e per im en ts of Br eit and Tu ve, th e r adio-pu lse ech o tech nique becam e th e
established m eth od for ion osph er ic invest iga t ion in all cou ntr ies.
The
step from this techn ique to the not ion of using it for the detect ion of a ir -
craft and ships is, in ret rospect , no such a grea t one; and var ious indi-
viduals took it independen t ly and almost simultaneously in America ,
1For the fulles t t rea tmentof radar his tory available, the reader is refer redto the
officia lh istory of Div 14, NDRC,
“Rada r” by H . E . Gu er la c, t o be publish ed by
Lit t le, Brown, & Co., Boston .
2M. A. Tuve and G, Breit , “Terr estrialMagnetismand AtmosphericElectricity,”
Vol. 30, March-December1925, PP. 15-16. AlsoPhys ev, 28,
 
14
INTRODUCTION
[SEC.1.6
England, France, and Germany, about t en years after the or igina l work
of Breit and Tuve.
The research agencies of the Amer ican Army and Navy have a long and
complicated history of ear ly exper iment , tota l fa ilure, and quali ied suc-
cess in the field of radio detect ion . The in terested reader will find this
dea lt with at length in Dr . Guer lac’s h istory. 1 Her it will be sufficien t
t o repor t the ear liest full successes.
In ear ly 1939, a radar set designed
and built a t the Naval Research Labora tory was given exhaust ive
test a t sea during bat t le maneuvers, insta lled on the U.S.S. New York.
The fir st cont ract - for the commercia l manufacture of radar equipment
was let as a r esu lt of t hese t est s, for t he con st ru ct ion of six sets, designa ted
as CXAM (Sec. 6.9), duplica t ing tha t used in the tr ia ls. In November
1938, a radar posit ion-finding equipment in tended for the cont rol of
ant ia ircraft guns and searchlights, designed and built by the Signal Corps
La bor at or ies of t he Army, wa s given ext en sive t est s by t he Coast Art iller y
Board, represen ing the using arm.
This set a lso went in to quant ity
manufacture, as the SC R-268 (Sec. 6 14). An Army long- ange a ircra ft -
detect ion set whose development had been requested ear lie by the Air
Corps was demonst ra ted to the Secreta ry of J t ’a r by the Signa l Corps
Labora tor ies in November 1939. A cont ract for the product ion of thk
equipment , the SCR-270 (and SCR-271; see Sec. 6.9) was let in August
1940.
Brit ish radar was developed a t about the same t ime but its applica t ion
proceeded at a somewhat faster pace under the immedia te threa t to
England and with considerably grea ter realism during the ear ly years of
the war . Dur ing the winter of 1934-1935, the Air Minist ry setup a Com-
mit tee for the Scient ific Survey of Air Defense.
Among t he suggest ion s
it r eceived was a carefully worked out plan for the detect ion of a ircraft
by a puls method, submit ted by a Scot t ish physicist , now Sir Rober t
Watson-Watt , then at the head of the Radio Depar tment of the Nat ional
Phys ica l Labora tory.
The first exper imenta l radar system of t he type suggest ed by Watson-
Watt was set up in the la te spr ing of 1935 on a small island off the east
coast of England. Development work during the summer led to the
blocking-out of the main fea tures of the Brit ish Home Chain of ear ly-
warning sta t ions (Sec. 6“9) by fall.
Work began in 1936 toward set t ing
up five sta t ions, about 25 miles apar t , to protect the Thames estuary.
By March 1938, all these sta t ions—the nucleus of the final Chain-were
complet e and in opera t ion under the charge of RAF personnel.
Br it ish radar development effor t was then brought t o bear on a irborne
radar equipment . Two types were envisaged: a set for the detect ion of
sur face vessels by pat rol a ircra ft (called ASV, for air to sur face vessel),
1op. ant.
15
and an equipment for enabling night fighters to home on enemy aircraft
(ca lled AI, for a ircraft in tercept ion). Work was concent ra t ed on ASV
fir st , and an exper imenta l equ ipm nt was successfully demonst ra ted
dur ing fleet maneuvers in Sept ember 1938. Exper imenta l AI equipment
was working by J une, 1939, and it was demonst ra ted to the chief of RAF
Fighter Command in August of that year . The Air Minist ry asked that
30 such systems be insta lled in a ircraft in the next 30 days. Before the
end of September a l these systems had been insta lled, four having been
ready on the day war broke out .
Emphasis on a irborne radar under lined the poin t tha t , if sharp radar
beams were ever to be produced by antennas small enough to car ry in an
~Plane, wavelengths shor ter than the 1+ m used in ear ly Brit ish air -
borne equipment would have to be employed. This led to the effor t
that the Brit ish put in to developing a genera tor of microwaves which
could give pulse power adequ te for radar use.
By ear ly 1940, a Br it ish
version of the mult icavity magnet ron had been developed to the point
where it was an ent irely pract icable source of pulsed microwave energy,
and the history of modern radar had begun.
1.7. Wart ime Radar Development in the United States. —Before the
end of 1940, the work on radar of Amer ican a d Br it ish laborator ies had
been combined as a re ult of an a gr eem ent between t he two gover nmen ts for
exch ange of t echnica l in forma tion of a m ilit ar y n at ur e. A Br it ish Technica l
Mission a rr ived i Washingt on in Sept ember 1940 and mutual disclosur es
were made of Brit ish and Amer ican accomplishments in radar up to that
t ime. Members of the Brit ish mission visit ed the N’aval Research
Labora tory, t he Army Signal Corps Labora tor ies at For t Monmouth ,
and the Aircra ft Radio Labora tory at Wrig t Field, as well as manufac-
tu r ing establishments engaged in radar work. They demonst ra ted their
version of the cavity magnet ron and furnished design informat ion that
enabled U S. manufacturers t o duplica te it prompt ly.
In discussions with the Microwave Commit tee of the Nat ional
Defense Research Commit t ee, which had been set up a few months before,
members of the Brit ish Mission proposed two specific project s which
they suggested that t he United Sta tes under take: a microwave aircra ft -
in ter cept ion equipment , and a m icr owa ve posit ion fin der for a nt ia ir cr aft
lire cont rol.
To implement their decision to follow these suggest ions, the Micro-
wave Commit tee of the NDRC decided to set up a development labora-
tory staffed pr imarily by physicist s from a number of un iversit ies.
They were encouraged in this st ep by the success that the Brit ish had
already exper ienced with civilian war t ime radar development agencies
staffed with physicist s having no specia l radio exper ience but good
 
[SEC.1°7
Microwave Commit tee persuaded the Massachuset t s Inst itu te of Tech -
nology to accept th e responsibility of administer ing the new laboratory,
The Radia t ion Laboratory, as it was named, opened its doors ear ly in
November 1940. The director of the laboratory th roughout it s 62
months of life was Dr . L. A. DuBr idge.
The Army and Navy development laborator ies were glad to depend
on the new Radiat ion Laboratory for an invest igat ion of the usefu lness
for radar of the new microwave region of the radio spect rum. They were
fu lly occupied with the u rgen t engineer ing, t ra in ing, and installat ion
problems involved in get t ing radar equ ipment that had already been
developed out in to actual military and naval service. At the end of
1940, t he u se of m icr owa ves f or r ada r pu rposes seemed h igh ly specu la tive,
an d t he Ser vice labora tor ies qu ite pr oper ly felt it t heir du ty t o con cen tr at e
on radar techn iques that had already been worked ou t successfu lly.
Dur ing 1941, while the Navy was installing long-wave search radar
and medium-wavelength fire-con t rol radar on ships of the fleet , and the
Army was sending ou t Signal Aircra ft Warning Bat ta ions equ ipped with
the SCR-270 and ant iaircraft ba t t er ies with the SCR-268, not a single
item of radar equ ipment based on the new microwave techn iques was
delivered for opera t ional use. However , development work at t he
Radiat ion Labor at ory h ad br oa den ed far beyon d t he t wo specific pr oject s
sug ested by the Br it ish Technical Mission , and microwave equipment
was showing grea t promise for many wart ime uses.
A few impor tan t dates will indicate the way in which this develop-
ment was proceeding. On J an. 4, 1941, the Radiat ion Laboratory’s first
microwave radar echoes were obta ined. A successfu l fligh t test of a
working “breadboard” model of an a irborne radar in tended for AI use
was made on March 10, in a B-18A furn ished by the Army Air Corps.
In this figh t it was found that the equ ipment was ext remely effect ive in
search ing for sh ips and su faced submarines at sea .
In the la te spr ing of 1941, an exper imenta l microwave sea-search
U.S.S.
Semmes. On J une 30, the Navy let the fir st product ion cont ract for
microwa e radar equ ipment based on the work of the Radia t ion Labora-
tory. This was for a product ion version of the set that had been demon-
st r ated on the Semmes.
At the end of May, a prototype of the microwave an t ia ircraft posit ion
finder developed at the Radia t ion Labora t ry was in opera t ion . It
accomplished the then-astonish ing fea t f t racking a ta rget plane in
a zimut h a nd eleva tion wholly a ut omat ica lly.
These and oth er ea r ly successes led t o an increasing Service in terest in
microwave radar , which had seemed so specu la t ive a ven tu re in 1940.
 
17
by the fact tha t the personnel of the Radiat ion Labora tory, which had
been about 40 at the beginning of 1941, rose to near ly 4000 by mid-1945.
Similar ly, t he Radar Sect ion of the Naval Research Labora tory inc eased
its personnel to 600. The Radio Posit ion Finding sect ion of the Signal
Corps Labora tor ies grew into the Evans Signa l Labora tory, with a peak
personnel of more than 3000. A similar growth took place a t the Air -
craft Radio Labora tory a t Wright Field.
A t remendous amount of work was car r ied out dur ing the war by the
research and engineer ing sta ffs of many industr ia l concerns, both la rge
and small. In some cases, these firms, working either independent y
or on development or product ion cont ract s with the armed forces or with
NDRC, engineered cer ta in types of radar set s all the way through from
th e basic idea t o the finished product .
To a la rger exten t , the cont r ibu-
t ion of industry was to take the prototype equipment produced in
government laborator ies and make the design suitable for quant ity
manuf a ct ure and for service use t inder combat condit ions.
The ar t
advanced so rapidly in the ear ly years that manufacturers were oft en
called upon to make major changes dur ing the course of prod ct ion in
order to take account of new lessons from both the labora tor ies and the
battlefields.
The growth of the radar indust r , which scarcely e isted before 1940,
is in icated by the fact that by the end of J une 1945, approximately
$2,700,000,000 wor t h of radar equipment had been delivered t o t he Army
and the Navy. At the end of the war , radar equipment was being
produced at a ra te of more than $100,000,000 wor th per month .
The enormous war t ime investment of money, skill, and product ive
facilit ies in radar paid the Allies handsome dividends with the fleet , in the
air , and on the bat t lefield. 1 The uses of radar in a peacefu l wor ld were
jusb beginning to be worked out in 19 6. Some of these are dealt with
in Vol. 2 of this ser ies. But the technica l ach ievement represen ted by
the war t ime development of radar seems very near ly unpara lleled. In
terms of the t ime in tervening between ‘the recept ion of the fir st radar
signals and the la rge-sca le use of radar in the war , it is as if, seven years
aft er the first fa lter ing fligh t of the Wright brother s at Kit ty Hawk, the
a irplane had been developed in to a powerfu l weapon of which thousands
were in constant use.
1The s tory of radar ’sopera t iona luse in the war is told , in a way tha t is somewhat
blu r red abou t the edges by the censor sh ipobtz in ing just before the end of the war
with Japan , in a pamph let en t it led “Radar : A Repor t ,on Sciencea t War ,” released
by t he J oin t Boa rd on Scient ificInformat ion Policy on Aug. 15, 1945. I t is obtain-
able from the Super in t enden tof Documen t s, U .S. Governmen t Pr in t ing Office,
\ Vashington,D.C.
BY E. M. PURCELL
The opera t ion of a radar set depends on the det ect ion of a weak
signal r etu rned from a distant reflect ing object .
The factors which
con tr ol t he st ren gt h of t he sign al so r eceived a re clea rly of fir st impor ta nce
in determining the maximum range of det ect ion of a given ta rget by a
specified r ada r set .
In Sees. 2.1 to 26 we shall formula te and examine
the basic rela t ion between these quant it ies, which is commonly known
as the “radar equa t ion. ”
Specifica lly, we wan t t o der ive an expr ession
for the peak radio-frequency signal power S, available at t he terminals
of the radar an tenna, which will involve measurable proper t ies of the
t ransmit t ing and receiving antenna system, the t ransmission path
Now this rela t ion will not suffice
to fix the maximum range of det ect ion unless the minimum power
requ ired for detect ion , Sk, is known.
This impor tant quant ity S~t i we
pr efer t o discuss separately, beginning in Sec. 2.7 below. It will be found
to depend on many other factors, not all readily accessible to measure-
ment , ranging from thermal noise in a resistor t o the in tegra t ing proper t y
of the eye of the radar observer .
Thus we choose to divide the problem
into two par t s, by a fict it ious boundary, as it were, between the radar
antenna and the rest of the set .
The rela t ions which we shall develop
in Sees. 2.1 t o 2.6 are wholly geometrical ones in the sense that t he factors
upon which the received power S depen s are all lengths, apar t from
t ra nsm it ted power P, t o which, of cou rse, S is a lways pr opor tion al.
THE RADAR EQUATION FOR FREE-SPACE PROPAGATION
2.1. The Meaning of Free-space Propaga t ion.-For tuna tely,
the
the
quasi-opt ica l na tu re of m icr owa ve pr opa ga tion perm it s us t o con cen tr at e
our a t ten ion at the outset on a very simple case, which we shall ca ll
“free-space propagat ion.”
Th e cir cumst an ces implied wou ld be r ea lized
exact ly if radar set and ta rget were isola ted in unbounded empty space.
They are rea lized well enough for pract ica l purposes if the following
condit ions are fu lfilled :
1, No large obstacles in te vene between antenna and ta rget , a long
an opt ical line of sight .
18
19
2. No a lternate t ransmission path , via a reflect ing sur face, can be
followed by a substant ia l fract ion of the radia ted ener y.
3. The in terven ing atmosphere is homogeneous with r espect t o index
of refract ion , a t th e frequency used.
4. The in terven ing atmosphere is t ransparen t , i.e., does not absorb
energy from the wave, a t the frequency used.
Condit ion 1 rest r ict s our a t ten t ion to ta rget s within the hor zon .
Condit ion 2 bars, for the presen t , considera t ion of radar search at low
angles over water , a lthough la ter we shall include this case by a su itable
modifica tion of t he r ada r equ at ion .
Microwave radar over land appears
t o be r ela tively fr ee, even at low an gles, fr om t he reflect ion effect s wh ich
are so pronounced at longer wavelengths. In any case, if the direct ivity
of the antenna pa t tern is such that very lit t le energy st r ikes th e reflect ing
sur face, Condit ion 2 is fulfilled. Any implica t ions of Condit ions 3 and 4
which are not self-eviden t will be clar ified in the last par t of th is chapter ,
wh er e ot her t ypes of pr opa ga tion will be discu ssed.
If, n ow, t hese con di-
t ions of free-space propaga t ion apply, the resu lt is very simple: The
t ransmit t ed wave, a t any considerable distance from the an tenna, 1 has
spher ica l wavefron t s—limit d in exten t ,. of cou rse, by the radiat ion
pa t tern of the an tenna—which spread so that the in tensity of the dis-
tu rbance falls off with t he inverse square of th e distance.
2.2. Antenna Gain and Receiving Cross Sect ion . -If the t ransmit t ing
an tenna were to radia te energy isot ropica lly-that is, uniformly in all
direct ions—the power flow through unit area at a distance R from the
an tenna could be f und by dividing P, the tota l radia ted power , by
4TRZ. A directive antenna, however , will concen t ra te the energy in
cer ta in direct ions. The power flow observed at some distan t poin t will
differ by some factor G from that which would be produced by an antenna
r adia tin g isot ropica lly t he same t ot al power .
This factor G is called the
“gain” of the an tenna in the direct ion in quest ion .
By ou r defin it ion ,
the gain of the hypothet ica l isot ropic radia tor is 1 in ever y direct ion . For
any other an tenna G will be great er than 1 in some direct ions and less
than 1 in others. It is clea r that G could not be grea ter than 1 in every
direct ion , and in fact the average of G taken over the whole sphere must
be just 1.
Usually we are in terested in an tennas for which G has a very pro-
nounced maximum in one direct ion , that is to say, antennas which
1The limitat ion implied is to distancesgreaterthan all/X,where d is t he wid th of
the an t ennaaper tu r eand x the wavelength . At dist ancesR less than this (less than
366 ft , for example,for x = 3 cm, d = 6 ft ), t h e in t en sit y does not fa ll off a s 1/RJ .
Althoughthisr egion has been unti l now of no interestfor radar appli at ions,one can
ant icipateth e development of short -ran ge,very-high-resolutionradar for which thc
nearzone,so defined,will be.of primar y import an ce.
 
[SEC.22
radia t e a well-defined beam. This maximum value of G we shall denote
by GO. The nar row, concent r a ted beams which are character ist ic of
microwave radar requ ire, for their format ion, antennas la rge compar ed
to a wavelength . In near ly every case the radia t ing system amounts to
an a per tu re of la rge a rea over which a substant ia lly plane wa ve is excit ed.
For such a system, a fundamenta l rela t ion connect s the maximum gain
G,, the a rea of the aper tur e A, and the wavelength :
(1)
The dimensionless factor .f is equal to 1 if the excita t ion is uniform in
phase and ntensity over the whole aper tu re; in actual antennas f is often
as la rge as 0.6 or 0 7 and is ra rely less than 0.5. An antenna formed by a
paraboloidal mir ror 100 cm in diameter , for a wavelength of 10 cm,
would have a gain of 986 according to Eq. (1) with ~ = 1, and in pract ice
might be designed to at ta in GO = 640.
The connect ion between gain and beamwidth is easily seen. Using
an a per tu re of dimensi ns d in both irect ions a beam may be formed
whose angular width , 1 deter mined b diffract ion , is about X/d radians.
The radia ted power is then mainly concen tr a ted in a solid angle of X2/dZ.
An isot ropic radia tor would spread the same power over a solid angle
of 4T.
Th er efor e, we expect t he ga in t o be a ppr oxim at ely 4rd2/X’, which
is consistent with Eq. (1), since the a rea of the aper tur e is about d’. For
a more r igorous discussion of these quest ions the r eader is r efer r ed to
Vol. 12, hap. 5.
A complementa ry proper ty of an antenna which is of impor tance
equal to that of the gain is the e.fective receiving cross section. This
quant ity has the dimensions of an area , and when mult iplied by the power
density (power per unit a rea) of an incident plane wave yields the tota l
signal power available a t the terminals of the antenna.
The effect ive
receiving cross sect ion A, is rela ted to the gain as follows:
A . G@2.
4rr
(2)
Note that G, not Go, has been wr it ten in Eq. (2), the applicability of
which is not rest r icted to the direct ion of maximum gain or to beams of
any specia l shape. Once the gain of the antenna in a par t icular direct ion
is specified, it s effect ive r eceivin g cr oss sect ion for pla ne wa ves in ciden t
jrom tha t direct ion is fixed. Equat ion (2) can be based r igorously on the
Reciprocity Theorem (see Vol. 12, Chap. 1). Compar ing Eqs. (2) and
(1) we observe that , if the factor j is unity, the effect ive r eceiving cross
1Wher ever a pr ecise defin it ion of beamwidt h is in t ended, we shall mean t h e
angularintervalbetweentwo directionsfor which G = G,/2.
 
21
sect ion of an an tenna in the pr incipa l direct ion is precisely the area of
the aper tu r e; in other words, a ll the energy inciden t on the aper tu re is
absorbed. Quit e gener ally A, will depend on the area of the antenna
aper tu re and not on~, whereas GOwill depend on A/h2.
2.3. Sca t ter ing Cross Sect ion o the Target .—We have to consider
how the t a rget it self en t er s the radar problem. Eviden t ly we need some
measure of the amount of power reflect ed by the ta rget . For this
purpose we define the sca t ter ing cross sect ion of the t a rget u as follows:
u (dimensions of an area) is t o be 4T t imes the ra t io of the power per un it
sol d angle sca t t ered back toward the t ransmit ter , t o the power density
(power per unit area ) in th wave inciden t on the t a rget . In other
words, if a t the t a rget t he power inciden t on an area u placed normal
t o the beam were t o be sca t tered uniformly in all direct ions, the in tensity
of the signal r eceived back a t the radar set would be just what it is in the
case of the actual t a rget . In some respect s “radar cross sect ion” is a
more appropr ia te name for u in so far as it indica tes tha t we are concerned
only with the power sca t tered dir ect ly back toward the t ransmit ter .
It is essent ia l t o rea lize tha t the cross sect ion of a given t a rget will
depend not on ly upon the wavelength but upon the angle from which the
t a rget is viewed by the radar . The fluctua t ion of u with “t a rget aspect ,”
as it is ca lled, is due to the in t er fer ence of r eflect ed waves from var ious
par t s of the ta rget (see Chap. 3 .
only for cer ta in specia l cases can u be
ca lcu la ted r igorously; for most t a rget s u has to be infer r ed from the radar
da t a t h emselves.
Usually this cannot be done in any uniform way
because of the fluctua t ion refer r ed to, and it may be well t o asser t a t th is
point tha t in telligen t use of the formulas which we shall der ive, in all of
which u appea rs, r equ ir es an a ppr ecia tion of t hese limita tions.
2s4. The Radar Equat ion. -With the per t inen t quant it ies defined it is
now a simple mat ter to formula te the radar equa t ion .
If S is the signal
power received, P t he t ransmit ted power , G the gain of the antenna , A the
wavelength , a the radar cross sect ion of the t a rget , and R t h e dist an ce
to the ta rget or range, th is rela t ion must hold:
‘ ‘(s)(&)(z)
(3a)
The quant ity in the fir st parent esis is the power density in the incident
wave a t the ta rget . The first two terms in paren theses together give the
power density in the retu rn ing wave a t the radar antenna , and the last
factor will be recognized as the receiving cross sect ion of the radar
antenna, from Eq. (2). Rear ranging terms, for compactness,
S= P=.
THE RADAR EQUATION [SEC.25
Again we call a t tent ion to the fact that Eq. (3 b), like Eq. (2), con ta ins G
rather than Go, and is not rest r ict ed to any par t icu lar direct ion or to
beams of any specia l shape. The sole rest r ict ion which has not yet been
made explicit is tha t G shou ld not vary significant ly over th e angle which
the ta rget subtends at the radar antenna .
Usually we shall be in tere ted in the signal tha t is retu rned when the
ta rget lies somewhere a long t e maxi um of the radar beam, and we
shou ld then replace G by G,. It is inst ruct ive to proceed then to elimi-
nate GOby means of Eq. (l), obtain ing
S = P(TA ‘j2
(4a)
Note tha t AZnow appears in the denominator , while the numerator con-
ta ins the square of the area of the antenna aper tu re. A fur ther manipu-
la t ion of Eq (4a) is of in terest .
Suppose the minimum power requ ired
for sa t is fa ctory det ect ion , Smin, is known; we may solve Eq. (4a) for the
maximum r an ge of det ect ion , R~..:
4 PuA ‘jz
(4b)
At this poin t it may be well to get an idea of the order of magn itude
of the quantit ies involved by inser t ing numbers not unusual in war t ime
pulse-radar pract ice. If we choose X = 0.10 ft ( = 3.0 cm), P = 10’
wat ts, A = 10 ft 2, j = 0.6, u = 100 ftz (typica l for small a ir craft ),
& = 5 X 10–12 wat ts, we btain R~.. = 155,000 ft or 29 sta tu te miles.
We observe that a 16-fold increase in t ransmit ted power is requ ired to
double the maximum range; on the other hand, it would appea that R~..
could be doubled by doubling the linear dimensions of the antenna. But
the la t ter step would at the same t ime reduce the beamwidth by a factor
of 2 and as we shall see in Sec. 2“11 that th is indirect ly affects St i.. A
ch an ge in wavelen gth is even mor e difficu lt t o discuss as it enta ils chan ges
in S~i., P, and possibly u as well.
2.5. Beams of Special Shapes.—In severa l applica t ions of radar , use
is made of an antenna designed to spread the radia ted energy ou t over a
considerable range in ang e in one plane.
The object us ally is to
increase the angular region cover e at one t ime. An example of such a
radia t ion pat tern is the simple
“fan beam” sketched in Fig. 2.1. It is
easy to produce such a beam by means of an an tenna whose effect ive
aper tu re is wide in the direct ion in which the beam is to be nar row and
nar row in the direct ion in which the beam is to be broad. The con-
nect ion given by Eq. (1) between aper tu re and gain st ill holds, implying
that by reducing the ver t ica l dimension of the antenna aper tu re (in
 
23
for the radia ted energy has been spread out over a la rge solid angle.
Consider the problem of design ing a radar set with the requiremen t
imposed tha t the ver t ica l beamwidth be B. Let us recast Eq. (4) in a
form appropr ia te for th is case, in t roducing explicit ly the ver t ica l and
hor izonta l dimensions of the antenna aper ture, which we denote by b
and a respect ively. To a good enough approxima t ion we can set b = k/B.
Then A’ = azbz = a2A2/~2, and inser t ing th is in Eq. (4b) we have
J
R—
m.. =
4iTSmirJ32”
(5)
The range no longer depends explicitly on t he wavelen gt h.
From what has been sa id it should be clea r tha t an ex ess of antenna
_——-—
FIG.2.1.—Aradiat ionpat ter nof th isshapeis calleda “ fan beam.”
detect in g ta rgets in tha t direct ion is wastefu l It wou ld be most desirable
to adj us~ the- direct iona l pa t tern of the antenna so tha t just the desired
angular coverage, and no more, would be obta ined.
A prescr i t ion for
such an antenna pa t tern can be obta ined from the basic radar equa t ion,
Eq. (3b), in any given case. A par t icu la r y import n t and inst ruct ive
example is tha t of a irborne ground-mapping radar , which we shall now
examine i det a il.
The object here is to obta in a rada r picture, from above, of a circu la r
a rea on the ground stretch ing o t in all dire t ions from the a ircra ft t o
 
[SEC.2.5
t ime, a na r row radia l st r ip ext ending outward from, for example, t he
point direct ly be eath th aircra f and rota t ing or “scanning” this st r ip
about a ver t ica l axis (see Fig. 2.2).
Evident ly some sor t of fan beam, as
nar row as possible in the hor izonta l direct ion but spread out ver t ica lly, is
demanded. To find the shape which the beam should have, in a ver t ica l
plane, t he proper t ies of the t a rget must be taken into account . Unlike
the t a rget s previously discussed, which were assumed to be small tom.
pared to the cross sect ion of the beam and to be charact er ized by a fixed
radar cross sect ion u, the ground is an extended, or compound
target.It
consist s of a mult itude of small sca t ter ing or reflect ing object s, many of
F-, -
‘T
FIG.2.2.—Theproblemof th e ground-mappingntenna .
which cont r ibut e to the echo received at any instant .
It is easy to see
tha t t he area of the patch on the ground, such as C in Fig. 2.2, from which
echoes can be received at one instant is propor t iona l to the width of the
radar beam at the range in quest ion and t o the pulse durat ion. Also, the
effect iveness of such a pa tch undoubtedly depends on the angle from
which it is viewed. A deta iled discussion of his mat ter must be reserved
for Chap. 3, but the f regoing remarks should make plausible the follow-
ing hypothesis :
(6a)
in which a is the beamwidth in azimuth and L is a factor having the
dimensions of a length tha t con ta ins the pulse length and otherwise
 
25
expr esses well enou gh for ou r pu rposes th e effect of viewing th e ech oin g
area obliquely, at least when 0 is small.
(In Fig. 22 the ver t ica l angles
h ave been exagger a ted, for cla rit y.)
Subst itu t ion of this expression for a in the adar equat ion , and the
replacement , of R by h/sin 0, h being the height of the aircraft , leads to
s = P = = p~2&;&4 ‘.
(4r)’R4
(6b)
If S is to be independen t of 0 between O = 00 and 8 = 7r /2, we must
requ ir that G(o) vary aa CSC20 through this angular in terval. The ideal
antenna pat tern then would be descr ibed by
G = Go=&
G = O, at all other angles.
}
(7)
The requirement of Eq. (7) impos s a rest r ict ion on the maximum
gain GOwhich can be ach ieved and hence on he maximum range. To see
th is, let us compute the average of the gain of the antenna over all
d ir ect ions , or l/47rJ J G d~ ext en ded over t he wh ole sph er e, wh er e d~ is th e
element of solid angle. By the defin it ion of gain th is in tegra l must be
equal to 1. But first someth ing must be said about the shape of the
antenna pat tern in the ther plane--tha t is, in a plane normal to the fan
beam. Suppose th t the hor izonta l width of the antenna aper tu re has
been fixed by other design considera t ions a t the value a. The ma imum
gain possible will be obta ined if t he illuminat ion of th e antenna aper tu re
is un iform hor izontally, and in th is case it can be shown that in any
plane such as ACEF, Fig. 2“2, the gain as a funct ion of the angle @
will bel
x
()
G= GosO
and we have to requ ire L
G cos @d@ dtl = 1. Sin ce G is ver y
47r o _;
1This expressionwill,be recognized as the diffract ion pat tern of a rectangular
aper ture . See Vol. 12, Sec. 49.
 
[SEC.2.5
small except for small values of O, and since G vanishes for values of o
outsi e the in terval 00 to ~/2, it is permissible to write and evaluate the
in tegra l as follows ;
()
7ra4 2
GO = ~sec OOCSC00,
Return ing nowto Eq. (6b), if Gisreplaced byther igh t-hand side of
Eq. (n ), andareplaced byk/a , weobta in ,forS,
S = PLah tanz 0,
When O,issmall, asisusually thecase, it ispermissible toreplace h/tan 00
by Rti, the maximum range, wh c leads tothefinalr ela t ion
(13)
The appearance of Xin this formula, which isto be cont rasted with
theresult obta ined for thesimple fan beam and poin t target , Eq. (5), can
be t raced to the influence of the hor izon ta l beamwidth upon the effect ive
cross sect ion of the extended target .
ot her system paramet ers, P, L!&,
and a, a le specified, the quant ity
hR2 is fixed. That is to say, the maximum range obtainable is inversely
propor t ional t o the square root of the height of the aircraft , keeping
everyth ing about the radar set constan t but the ver t ica l radiat ion
pat tern of the antenna, which we assume to be adjusted to opt imum
sh ape for each heigh t.
A problem rela ted to the preceding one is met in the design of ground-
based air -search radar , which may be requ ired t o provide uniform cover -
age at all ranges for point t arget s (a ircraft ) flying a some limit ing
alt itude h. Here, however , u is g nera lly assumed to be constant : the
reader will easily ver ify that th is assumpt ion leads again to the requ ire-
ment that the gain vary as CSC20, but with a diflerent final resu lt for the
depen den ce of S u pon h, R, and a.
It turns ou t in fact that for th poin t
t arget with u independen t of angle, the quant ity hR~,. is con st an t, r at her
 
27
In pract ice it is not feasible to produce a pa t tern which exa t ly meets
the specifica t ion of Eq. (7) but a reasonable approximat ion has been
achieved in severa l instances.
A comprehensive discussion of the
problem of the
‘‘ cosecan t-squa red”
antenna , as th is type has been
ca l ed, will be found in Chap. 14 of Vol. 12.
2.6. The Beacon Equat ion .-So far we have confined our a t ten t ion to
the “two-way”
radar problem, in which the rou te from transmit ter to
receiver is a complete round tr ip involving sca t ter ing of the energy by
some remote object . Radar beacons opera te on a differen t pr inciple. A
receiving antenna a t a remote poin t picks up direct ly energy sen t ou t
from the radar t ransmit ter . The signal is amplified and enabled to
init ia te the t ransmission of another signa l, in reply, by an associa ted
transmitter .
This signal, received back a t the radar , provides an
ar t ificia l echo which can be ut ilized in var ious ways (Chap. 8). Here
the ana logue of the radar equa t ion for rada r-beacon opera t ion will be
discussed.
It is clea r tha t we have to do with two ent irely independent processes,
each of which consists simply of one-way transmission and recept ion .
Consider th e first process, usually ca lled “in terroga t ion .” Let P, e the
power t ransmit ted by the radar , ~b the signa l power received by the
beacon antenna .
()
%=p, = )
(14)
where G, and Gb are the ga ins of the radar and beacon antennas respec-
t ively. The subsequent process of beacon reply is descr ibed by a simila r
equa t ion with the subscr ipt s b and r in terchanged throughout . If the
same nt nna or similar an tennas a re employed for transmission and
recept ion a t the beacon and likewise a the rada , as is near ly always the
ca se, th e quant ity in th e paren thesis has the same valu for in ter roga tion
and reply, and we can infer the corolla ry rela t ion
s P,
(15)
In pract ice, the ga in G, of the beacon antenna is fixed a t a rela t ively
low n umber by t he requ irem en t of som eth in g like omn idirect iona l cover -
age. The remaining factor in the paren thesis in Eq. (14) is the quant ity
G,k*which is propor t iona l to the aper tu re of the radar an tenna . This
leads one to suspect tha t long beacon ranges should be, in genera l, more
difficu t to ach ieve a t shor ter wavelengths. Antenna aper tures a re
ra rely increased in area when shor ter wavelengths a re employed: on the
other hand, ava ilable r -f power genera lly decreases markedly with
 
[SEC.!2.7
limitat ion down to wavelengths of the order of 3 cm, because ranges tha t
can be ach ieved are a lread very grea t and are limited usually by the
hor izon ra ther than by the rela t ion expressed in Eq. (14). That is to
say, the condit ion of free-space propagat ion , which we have assumed in
th is sect ion , oft en does not apply at the ext remity of the microwave-
bea con r ange.
Lon g beacon r an ges are, of cou rse, a r esult of t he en ormous advan tage
of one-way over tw~way transmission .
If we compare Eq. (14) with
Eq. (4), we see that in signal st r ength for given t ransmit ted power the
beac n process en joys the advantage of a factor of 4flJ P/G+s. It is
in terest ing to compute the limit ing free-space range for a beacon oper -
at ing in conjunct ion with a radar set of the character ist ics assumed in
our ear lier radar example. Let us suppose that the gain of the beacon
antenna is 10, and that the t ranwnit ted power and minimum requ ired
sign l power for the beacon are the same as those assumed for the radar
set . Using Eq. (14) we obta in for the maximum range, either for in ter -
r ogat ion or reply, 60,000 sta tu te miles.
In conclusion , we may poin t ou t tha t Eq. (14), a lthough it has been
wr it ten in nota t ion appropr ia te to the radar -beacon problem, applies, of
cou rse, t o any on e-wa y transmission pr oblem wh er e fr ee-space propaga-
t ion can be assumed. Applicat ions of Eq. (14) are to be found in
the fields of microwave radar relay, radar j amrning, and microwave
communication.
THE MINIMUM DETECTABLE SIGNAL
2.7. Noise.—It is well known that despit e our ability to amplify
a feeble elect r ica l signal by pract ica lly any desired factor , it is st ill not
possible to discern an arbit rar ily weak signal because of the presence of
r an dom elect r ica flu ctu at ion s, or “n oise.”
If the t rue signal en ter ing
any receiver is made weaker and weaker , it subsides even tually in to the
fluctua t ing background o noise and is lost . What is the or igin of these
fluctuat ions, and what factor s determine precisely the level a t which
the radar signal is hopelessly obscured by them?
Before we at tempt to answer these decisive quest ions, it is wor th
while to consider br iefly the limit of usefu l sensit ivity of n or inary
low-frequency radio receiver . This limit is also set by random dis-
tu rbances, but in th is case the largest random distu rbances with which
the signal must compete or igina te genera lly not in the receiver it self
but elsewhere in space. Whatever their sourc+and this may range
from a passing t rolley car to the myster ious reaches of in terstella r
spat -these distu rbances en ter the receiver by way of the antenna .
The crucia l quant ity is therefore the ra t io of the field st rength of the
 
SEC.2.7]
NOISE
29
The absolute magnitudes of signal and in ter ference power available
at the