SOME CHARACTERISTICS OF RADIO WAVES OF EXTRATERRESTRIAL ORIGIN

DISSERTATION

Presented in Partial Fulfillment of the Requirements

for the Degree Doctor of Philosophy in the

Graduate School of The Ohio State

University

By

SOL MATT, B.S., M.S.

The Ohio State University

1953

Approved by: ACKKOWUDGIXEKT

The author withes to express his sincere appreciation to

Professor J. D* Kraus for his constant encouragement and interest in the investigation of this dissertation* Grateful acknowledge sent is made to Ulss B. POx who helped in the preparation and the proof reading of the text and to Ur. J. J. Kolossi and Ur*

1* Uoore in the preparation of the graphs. The author also wishes to express his appreciation to the members of the staff of the Department of Slectrlcal Xngineering and his associates at The Ohio State University radio observatory who have offered helpful suggestions and assistance in performing the investlga* tions.

I

v TABUS Of CONTENTS

CHAPTER I - INTRODUCTION 1 a* Historical Background. 1 to. Investigations 2

CHAPTER II - RECEIVING EQUIPMENT 7 a* Original Receiving Equipment 7 b. Receiving Equipment for Present Investigations 7

CHAPTER III - ANTENNA PATTERNS POR AN ISOTROPIC POINT SOURCE 13 a* Introdoct Ion 13 b# All Elements of the Array In Phase 18 c. The Antenna Elements of the Array In Phase Opposition 26 d. The Combined In-Phase and Phassu pposition Patterns in Right Ascension 31

CHAPTER IT - ANTENNA PATTERNS FOR EXTENDED SOURCES 38 a. Introdoct ion 38 b- All Antenna Elements of the Array In Phase 38 c. The Antenna Elements of the Array In Phase Opposition 49 d. The Combined In-Phase Pattern and Phase-Opposltlon Pattern 68

CHAPTER V - THE ANGULAR EXTENT OF THE SUN AT 250 MEGACYCLES PER SECOND 69

CHAPTER VI - THE POSITION OF THE INTBTSE RADIO SOURCE IN THE CONSTELLATION OF CASSIOPEIA 74 a- Right Ascension 74 b. Declination 76 c- Slse 78

CHAPTER VII - INTERS ITT MEASUREMENTS 81 a* Introduction 81 b. Radiation Reslstanee of the Antenna 82 c. The Received Poser 85 d- Relationship of Source Temperature to Antenna Temperature 89

CHAPTER VIII - THE RECEIVED POWER FROM THE ANTENNA 91 a- Introdoct Ion 91 b* Antenna Matching 91 c* Total Pover at the Receiver Input 95 d. Temperature Calibration of the Recorder Tape 98

ii* » CHAPTER IX - LIMIT OP DETECTION

CHAPTER X - EXPERIMENTAL INTENSITY MEASUREMENTS a. Introduction b. Radio Source la the Constellation of Cassiopeia c. The Radio Source In the Constellation of Cygnus <1. Maxi ana Galactic Intensity e. The Galactic Maxinun Adjoining the Cygnus A Source f. The Intensity of the Sun g* flownry of Kxperlaent Intensity Ueasureaents with The (Riio State Uhlverslty Radio Telescope at 250 Megacycles Per Second

APPENDIX 1. Distribution of Intensity for Extended Sources 2« The Equivalent Intensity Distribution of a Spherical Source 3* Correction for Tine Delay Circuit 4* Cable Attenuation between Antenna and Receiver 5. Frequency Check by Means of the Sun*s Pattern

BIBLIOGRAPHY

AUTOBIOGRAPHY LIST 07 FIGURES

1 — The Ohio State University Radio Telescope 3

2 - An Intensity Contour Hap of the Sky at 250 Megacycles Per Second 4

3 — Schematic Diagram of the Original Receiver System 8

4 — A Record Taken with the Receiving System Su>mn in Tignre 3 9

5 — Schematic Diagram of the Receiver System for Present Investigations 10

6 — Record Taken with the Receiving System of Figure 5 12

7 — Spacing of Helices on Antenna Ground Plane 14

8 — Intensity Pattern of a Helical Beam Antenna 16

9 — A Linear Array of a Iqually Spaced Isotropic Point Sources (n Even) " 19

10 - Polar Diagram for In-Phase Intensity Patterns at 260 Megacycles Per Second for a Point Source 22

11 — Single-diObe Pattern for a Point Source 23

12 — Cassiopeia Radio Source 24

13 — Formalised Intensity Pattern in Declination for a Point Source 25

14 — SpHWLohe Pattern in Right Ascension for a Point Source 30

15 - Switching Circuit for Combining In-Phase Pattern and Phase-Oppositlon Pattern 32

16 — Combined Single-Lobe and Spllt-Lobe patterns for a Point Source 35

17 — Diagram for Determination of the Intensity patterns for Extended Sources 40

IV 18 - Single-Lobe Pattern In Right Ascension at 225 Uc/s for Xxtended Sources 46

19 - Single-Lob# Pattern in Right Ascension at 260 Mc/s for Xxtended Senrces 47

20 - Single-Lobe Pattern in Ri^it Ascension at 275 kic/s for Xxtended Senrces 46

21 — The Half Power Bean Tidth of Xxtended Source Patterns 51

22 — Split-Lebe Pattern in Right Ascension at 225 Uc/s for Xxtended Sources 55

23 — Split-Lob# pattern in Right Ascension at 250 Mc/s for Xxtended Sources 56

24 — Spllt-Lobe Pattern in Right Ascension at 275 Uc/s for Xxtended Sources 57

25 — Intensity at 6 • 0® for Horaalised Spllt-Lobe Patterns of Xxtended Sources 61

26 - The Position of Maxinua Intensity of the Split—Lobe Patterns of Xxtended Sources 63

27 — Combined Single-Lobe and Spllt-Lobe Patterns at 225 Mc/S 64

28 — Combined Single-Lobe and Spllt-Lobe Patterns at 250 lfe/8 65

29 — Combined Single—Lobe and Split-Lebe Patterns at 275 Uc/S 66

30 — Spacing Between Hull Points for the Conblned Patterns of Xxtended Sources 66

31 — Ratio: Meridian to Marlow Talus of Spllt-Lobe Pattern at 360 Uc/s for Xxtended Sources 71

32 — Spllt-Lobe Pattern of the Sun 72

33 — XqulTalent Rectangular Sise of Cassiopeia Radio Source 80

34 — The XqulTalent Circuit for the Antenna in an B a d e sure at Chi fora Tesq>erature 83

v 35 - Cable Arrangement a Between the Antenna and the Receiver 93

36 - Diagram for Theraal Volee from Cable 97

37 — Calibration Circuit for Intensity Measurements 100

36 - Cassiopeia Radio Source 108

39 - Cassiopeia Radio Star Spectrum 110

40 - Cygnus A Radio Star and Gelactic Background 112

41 - Cygnus A Radio Star Spectrum 115

42 - Equivalent Rectangular Slse of Gygms A Radio Source 117

43 — Galactic Maximum Spectrum 120

44 — Galactic Maximum Spectrum in cygnus Region 122

45 — Apparent Temperature of the Quiet Sun for One-Half Degree Diameter 125

46 - Calculated Intensity Distribution of an Extended Source at 350 Megacycles Per Second 136

47 - Diagram for Determining Xquivalent Intensity Distribution of a Sphere 128

46 — Output Time Constant Circuit 141

VI 1 CHAPTER I

INTRODUCTION a. Historical Background

Radio Astronomy had its beginning when K.G. Jansky in 1932 (1) and 1933 (2) reported his observations of radio interference or static, whose origin was extraterrestrial. He concluded that this radio noise was from the Milky Way. Further studies were made by

G. Reber (3-7) who plotted power intensity contour maps of the heavens at 160 and at 1*80 megacycles per second. In 191*5, following

World War II, the study of radio radiation of extraterrestrial origin was pursued by many others. With an interferometer type antenna system

Hey, Parsons, and Phillip (8), in 19U6 observed radiation which appeared to have its origin in a point source, referred to as a

"radio" star, in the Cygnus constellation. Many other such point sources have been found (9-15)• Simultaneously, extensive studies have been made on solar radio radiation (16-21)*

These studies are needed to obtain more information in the radio region for correlation with visual astronomical data. An advantage of the radio region over the visual region is the ability of radio telescopes to penetrate into regions obscured to visual telescopes by interstellar gases and dust, due to the fact that radio wavelengths are much longer then light wavelengths.

A radio astronomy project (22) was initiated in 1951 at The

Ohio State University under the direction of Professor J.D. Krauts*

M In 195>2 a radio telescope was put into operation. The antenna,

shown in Figure 1, for this telescope is a broadside array of helical antenna elements* Because of the low cost per unit area

of effective aperture this type of antenna is employed in preference to a parabolic reflector type of antenna or an array

of Yagi antennas which are generally used by English and Australian

observers*

The initial program conducted with The Ohio State University

radio telescope was a power intensity survey (23) of the sky at

250 megacycles per second* The result of this survey is shown

in Figure 2. b. Investigations

This dissertation treats investigations of the positions,

sizes, and intensities of celestial radio sources using The Ohio

State University radio telescope* To perform these investigations

a knowledge of the characteristics of the antenna system of the

radio telescope is necessary, since the recorded signal is a plot

of the antenna pattern. An analysis of the antenna characteristics

is given ana an outline of the receiving equipment is also included

The antenna patterns for small or point sources are calculated

The types of patterns considered are the in-phase or single-lobe pattern, the phase-opposition or split—lobe pattern, and a combina­

tion of the single—lobe pattern and the split—lobe pattern. The

results of the pattern calculations are used to determine the

location of the intense radio star in the Cassiopeia constellation* TBS OHIO STATX UKITERSITT RADIO TILSSCOP*

(Arragr of 48 Holical Aatonnao)

TIGFDRX 1 •bO

:g a s j s

0100 00 00 IJOO !oo o9'oo_ olloo

.40 ■V

^ CoMfJFi 1 10"24 «at*i/ mz/cp* f tq d*g oi 250 Me /«

AS INTENSITY CONTOUR MAP 0? THE SKY AT 250 MEGACYCLES PER SECOND (Srawiag a&de Iqr J.D. Kraus)

PIGRJRN 2

Wk- 5 For accurate determination of the source location the position

of the antenna beam is determined experimentally.

The antenna patterns for extended sources can be calculated

from the patterns for point sources. In particular, the minimum

of the phase—opposition pattern is a sensitive indication of the

size of a source whose angular extent is of the magnitude of the

beam width of the antenna. From the phase-opposition patterns

the radio diameter of the sun at 25>0 megacycles per second is

determined. In addition, for a large extended source the

calculation of the actual intensity distribution from the

observed intensity distribution is considered. The limitations

for the determination of actual intensity distributions will be

made evident by a sample calculation.

The intensities of the radiations from various radio sources

are -measured. The radiation from a source is expressed in terms

of the equivalent black body radiation according to the Rayleigh—

Jeans law. The power received by the antenna is expressed in

terms of an equivalent thermal—noise power output of a resistor

as given by the Nyquist equation. The relationship between

the radiation from a source and the received antenna power is

shown.

A procedure is described for measuring the intensity of

the radiation received from a source. The limit of detection

of the radiation received by The Ohio State University radio telescope is calculated and confirmed experimentally.

Intensity measurements are made on the most intense radio point sources in the Cassiopeia and Cygnus constellations.

Measurements are also made on the sun, the center of the galaxy, and the galactic maximum near the Cygnus radio star. For all these sources the equivalent black body radiation tenderatures are calculated. These results are used to present a spectrum for each source. 7 CHAPTER II

RECEIVING EQUIPMENT a. Original Receiving Equipment

The receiver used initially for the first intensity survey is shown schematically in Figure 3* The antenna signal is recorded for four minutes, and then the thermal-noise power output of a matched resistor at constant temperature is recorded for one minute, as shown in Figure h» Since the resistor therm&l-noise output is constant, the difference in the recorded levels of the resistor noise ana the antenna signal indicates the power received by the antenna. The intensity contour map of Figure 2 was obtained with this receiver assuming the lowest antenna signal to be a reference intensity level* Analysis of the individual system components of the receiver is given by

E* Ksaizek (2U). b. Receiving Equipment for Present Investigations

To improve the response of the system all subsequent measurements were conducted with the receiver, schematically shown in Figure 5* This circuit is based on the Dicke- differential system (2£>). In this system the antenna signal is compared 3 0 times per second with the thermal—noise output of a resistor at room temperature by means of a rotating capacitor switch* The antenna signal and the resistor noise are alternately introduced into a four-stage preamplifier which is followed by

I ANTENNA

R.F. SUPER­ OC SWITCH RECORDER PREAMP HETERODYNE AMP.

MATCHED RESISTOR RECORO

SCHEMATIC DIAQBAU 0? THS ORIGIUAL RECEIVING STOTBM

TIOOBI 3 SUN ON MERIDIAN 12i58 P.M. Aug. 6, 1952 25O Me. ANTENNA POWER GREATER THAN 16 RHH RESISTOR POWER Decl. 18° N.

ANTENNA POWER LESS THAN _ RESISTOR POWER

MERIDIAN TRANSIT sawtooth record , f 1*00 P.M. 12*50 P.M. E.S.T. 12:00 Noon

A RECORD TAKEN WITH THE RECEIVING SYSTEM SHOWN IN 71 OURS 3

FIGURE 4 ANTENNA

CAPACITOR | /SWITCH -OyORUM 1/ .------PHASE SUPER­ 28CPS DC SENSITIVE HETERODYNE AMP. AMP. RECORDER RECTIFIER ~ P » /o T O R jf MATCHED I W RESISTOR PHOTOCELLS RECORD

SCHBUTIC DIAGRAM Of THE KECSITCEG ST STEM

FOB PRESE W IHYESTIGATI0H3

FIGURE 5 11 a standard superheterodyne receiver. The output of the superheterodyne receiver is amplified by a sharply tuned 30- cycle per second amplifier and then transmitted to a phase sensitive bridge circuit. The bridge arms are controlled by photocell circuits linked to the rotating switch. From the bridge circuit the signal passes through a direct-coupled amplifier to a paper-tape recorder. The signal being recorded is proportional to the difference between the signal bvel detected by the antenna and the thermal-noise level of the resistor. The response of the overall receiving system is linear within the range of operation. A record taken with

this receiver is shown in Figure 6. Analysis of the individual system components is given by E. Ksiazek (21*)* SICORD UMM fITH THI RKXZTIXC STSTItl 07 7I00BI 5

RIGHT A SC LN SION ( is N O 4305C 2)00 2 0 0 2 10) )

4 8 R H H

' C A S S I O l> E i A RADIO STAR

riOOBX 6

e CHAPTER III

ANTENNA PATTERNS FOR AN ISOTROPIC POINT SOURCE a. Introduction

The antenna of The Ohio State University radio telescope is a broadside array of U8 helical antenna (26) elements, shown in Figure 1, The antenna elements are located on a ground plane 160 feet by 12 feet with the spacings between helix centers as shown in Figure 7. The axis of the array is aligned with an east-west line. It can be rotated about the east-west axis from a declination of 90 degrees north to UO degrees south. The earth's rotation sweeps the antenna in right ascension. Thus, the antenna pattern in right ascension is recorded on a paper tape for a given antenna declination.

The antenna elements of the array are 11-turn helices, with a circumference of 15 l/U inches and a turn spacing of 10 3/h inches. To give maximum response and resolution of the antenna, all helices are wound in the same direction, namely right handed. Therefore, the helices are responsive to the right-circularly polarized component of the incident radiation.

In general, the incident radiation is random without prefer­ ence to either right- or left-circular polarization.

To match each helical element to RG - 6 3 /U cable the terminal impedance of the helix is adjusted to 120 ohms. The helical antenna element was chosen because of the small variations in 1) helix ) centers

SPACING OF HELICES ON ANTENNA GROUND PLANE

FIGURE 7 the terminal impedance over the frequency range of intended operation, 200 to 300 megacycles per second. Secondly, the current distribution along any one helix is not appreciably changed by introducing additional helices into the array.

The approximate normalized total radiation pattern of the axial mode helix is given by J.D. Kraus (26) as

_ / . n \ sin (nf/2) . E - f sin — n--- ] ) A r ■ cos $ HN [ 2n } sin ( 4* /2) where E “ normalized field intensity of a single helical HN antenna

n ■ number of turns of the helix, and (1- cos ^

with S A ■ spacing in wavelengths between turns (center to center).

The normalized power intensity of a helical antenna, P ^ * is

2 P - E HN HN

A comparison of the power intensity patterns for a helical element at 225* 250, and 275 megacycles per second is shown in Figure 8*

To obtain the total field pattern for the antenna, the principle of pattern multiplication (27) is used. A statement of the principle is as follows* ._L

T A 1 J9 N 3 1 A// d$Znv\Ncfc)M I ...1 17 •'The total field pattern of an array of nonisotropic but similar sources is the product of the individual source pattern and the pattern of an array of isotropic point sources each located at the phase center of the individual source and having the same relative amplitude and phase, while the total phase pattern is the sum of the phase patterns of the individual source and the array of isotropic point sources." (27)

Since the total field is a product of terms and the power is proportional to the square of the field, the principle of pattern multiplication is applicable in obtaining the total power intensity pattern. It is the product of the power intensity pattern of the individual source and the power intensity pattern of the array of isotropic sources.

The total field intensity of the antenna for the radio telescope is the product of the field pattern of a helical element and the field pattern of an array of isotropic point sources spaced at the helix centers shown in Figure 7* The total field pattern is calculated for the principle axes in right ascension (R.A.) (east-west) and in declination (S ) (north- south). The field pattern of a helical element is given by equation 1. The field pattern for a linear array of isotropic point sources will be derived for three arrangements of the antenna. The three antenna arrangements to be considered are the following:

1* All helical elements of the array are in phase.

2. Half of the helical elements in right ascension

are in phase opposition with the other half of

the antenna.

3. A combined pattern is obtained by the difference

of the in-phase pattern and the phase-opposition

pattern. b. All Antenna Elements of the Array In phase

The field intensity, E^, for a linear array of n (even) isotropic point sources (28) of the same amplitude and phase, shown in Figure 9, ia

Where EA - field intensity of array

o - constant Y - dy, cos * * dj. sin 6

2nd and X where X “ wavelength d - spacing between sources. A LMZAH ARRAY GBP n EQUALLY SPACE) ISOTROPIC P O U T SCXTRCSS (n IVEX)

center of array

to radio source

/ . , /' / /

/

/ / / / 3d / 0 cos Z

■* - - /

3 d cos $

T i c m x 9 30 Equation li reduces to

Jn - e E. E

-1 ^ (5) e 3 7 — e

and then

sin(n T/2) E. sin(y /2) (6)

Normalizing the result gives

v 1 sin (nV/2) ^ n sin (y /2) (7) where E„ ■ normalized field intensity for the array. The normalized power intensity, P„, of the array of isotropic point

sources is

W PN " EN

so sin (nV/2) (9) *~mN ? sin2 (V/2)

The total intensity, P, in right ascension is the product

of the array pattern and the helical antenna pattern. The equation 2 1 where E is given by equation 1 and E.T is given by equation 7. riW N The calculated power intensity pattern at 2$0 megacycles per second for 2k helical elements in right ascension is shown in polar coordinates in Figure 10.

As shown in Figure 10 a single major lobe is obtained in the total power intensity pattern. For a large number of elements in the array the major lobe of the total pattern is not appreciable different from the major lobe of the array pattern. The minor lobe structure is small except at © - 37.2 degrees. The large minor lobe is caused by the spacing being greater than one wa.relength between antenna elements in right ascension. The size of the minor lobe is limited by the helix pattern having a minimum at © - 36.9 degrees. The measured power intensity pattern has a larger minor lobe at

9 * 37*2 degrees than is shown in Figure 10, because the measured minimum value at © - 36.9 degrees of a single helix pattern is not a true null as given by equation 1.

The major lobe is used to determine the position of a radio source. Figure 11 illustrates the variations in beam width of the major lobes of the total power intensity patterns for three frequencies. A record at 2^0 megacycles per second of a point source is shown in Figure 12.

The antenna pattern in declination is obtained from the array pattern of equation 9 by letting n - 2 and multiplying by the single helix pattern. The calculated intensity patterns in declination are shown in Figure 13 for three frequencies. 2 2

n s 34

1.26° half power beaa width

37.2° 37.2° V / \ /

\ antenna plane \

Right Aeoenelon

POLAR DIAGRAM FOR IV-PRASE INTENSITY PATTERN AT 250

UEOACYCLSS PER SECOND FOR A POINT SOURCE

FI (KJRE 10 T~

4-

(Zs\ % $

0 rv . ,

■ . -

....

0 I °5 1

.... _

T------

i Right Ascension (Epoch 1950)

Declination 58*5 V

4 J — CASSIOPEIA HAD10 SOURCE.

FIGURE 12.

- 0 6 3 0 6 0 0 fit AM EST 5 3 0

£ NORMALIZE^ INTENSlT { PATTERN JN DEC UN AEON FOR A POINT SOURCi ■ I ' t ' , ! ! ' ! ;------L---

. ... "

&VO-

?7?C/U sp rnc/s- A^PS~77>t/S

6 V O \ A

AEEtNAIt w A f & ?££s) 26 The calculated half power beam width in rignt ascension and in declination Tor the major lobes at three frequencies are

summarized in TaDle I.

c. The Antenna Elements of the Array in Phase Opposition

To determine more accurately the position of a point source

in right ascension, the antenna is operated with all helices on

the west half of the antenna in phase opposition to the helices

on the east half. This is accomplished by introducing an

additional half wavelength of cable in one half of the antenna.

This arrangement gives a null in the pattern when the point

source is on the meridian.

In right ascension each half of the antenna can be con­

sidered as a single unit with twelve helices in phase. From

equation 7 the normalized field pattern, E^, for an array of 12

isotropic point sources is

1 sin (nx^x/2) 1 " nl sin (fi/2) (11)

where * 12

*f'1 - d^ sin ©

For two isotropic point sources of equal magnitude and opposite

phase (29) the field intensity, Eg, is

E2 - sin ( V 2/2) (12)

where V g “ ni^r s^n ® TABLE I

HALF POWER BEAM WIDTH IK RIGHT ASCENSION AND DECLINATION FOR IN-PHASE PATTERNS

Frequency Mc/s. H.P.B.W. in R.A. H.P.B.W. in Declination Beam Area in Square Degrees

225 l.kO° 18.9° 26.5

250 1.26° 17.h° 21.9

275 1.13° 15.6° 17.6 28 By pattern multiplication the field intensity, E^, for the

entire array is

1 sin i/2) EA ■ E 1E 2 ‘ Sin f *^2/2) (13) sin or, by substitution

_ 1 sin nx [ (dr/2) sin 9 ] r , 1 E. « — ---- — ------sin nn (d_/2) sin 0 (I4 ) A “ 1 sin [(<^2) sin e] U ^ J

By a trignometric identity (30) the field pattern for the array becomes

Jf _ 1 1-cos 2ni (W/2) A sin (*V /2) (15) or

_ 1 1-cos n (4V2) f £ EA n ■■5'in '(v/2)-- (16) where n ■ number of helical elements in right ascension

S' - dj, sin Q

The intensity, PA> of the array is

(17) '■ ■ ■** ■ i[ - a t i j p ] * The total intensity pattern is the product of the array intensity pattern, P^, and the helix intensity pattern, P^. A plot of the calculated total intensity patterns in right ascension at three frequencies for the split-lobe or phase-opposition case is shown in Figure lii*

The maximum value of the phase-opposition pattern compared to the maximum value of the in-phase pattern is independent of frequency and is a constant, whose value is 0*5>26* However, the angle at which the maximum of the phase-opposition pattern occurs is a function of the frequency. The angle, 6 -^, at mavj mum intensity is obtained by differentiation of E in equation

16* This gives

^ (0 ^ / 2 ) cos 0 ^ sin ( n f / 2 )

sin ( /2 )

1 - cos (nV/ 2 ) - (dr/2n) cos ©2_ (16) sin2 ( Y / 2 ) which reduces to

n sin ( V / 2 ) sin n (^f/2 ) + cos n (H* /2 ) - 1 (19)

Solving by trial and error with n ■ 2k gives

n ( V / 2 ) » 1 3 3 « 5 degrees - 2 * 3 3 radians (20) n 31 with

- d sin © (2 1 )

The solution for 0^ is

e . sin- 1 h f * . = P.-.^A 2 C22) 1 2hdj. dr

For three frequencies Table II lists the angles at the maximum intensities and the spacing between the maxima for the

* phase-opposition patterns. d. The Combined In-Phase and Phase-Opposition Patterns in Right

Ascension

The circuits for obtaining the in-phase or phase-opposition patterns utilize the antenna signal less than half the time.

A more efficient use of the antenna signal is attained by altering the antenna circuit and the switching circuit to eliminate the matched resistor shown in Figure This arrange­ ment is shown in Figure 15. The antenna circuit is divided into two halves and a switching circuit is inserted in the line to one half of the antenna. For half of the switching cycle the signals from the two halves of the antenna give the in- phase pattern. For the other half of the switching cycle an additional half wavelength of cable is inserted in one line to give the phase-opposition pattern. Since the remainder of the receiving circuit is unchanged, the recorded pattern is the antenna

itching network- - to preanpllfi

antenna

^-additional half ware length of cable for phase-opposition pattern

SflTCHIBG CIBCUIT TOR CCUBIIIKG IB-PHASK PATTBHH AKD

PHASB-QPPOSITIOI PATWHI

pimms 15 TABLE II

ANGLES AT MAXIMUM VALUES FOR PHASE-OPPOSITION PATTERNS

Frequency Mc/s* Location of Maximum Intensity, Spacing Between Maxima, 26^

225 1.165° 2*33°

250 1.0fc5° 2.09°

275 °.9W° 1.90°

8 difference between the in-phase pattern and the phase-opposition pattern. The calculated difference patterns are shown in

Figure 16.

The combined patterns have null points when the in-phase intensity is equal to the phase-opposition intensity. The null points are independent of the the gain fluctuations in the receiver system. For small values of 0 the single helix intensity pattern is broad and nearly unity. Thus, if © is limited to small values the total intensity pattern can be represented by the array intensity pattern. To determine the location of the null points, the in-phase pattern intensity, equation 9 , and the phase-opposition pattern intensity, equation

17, are equated. This gives

which reduces to

sin n (y/2) + cos n (y/ 2 ) ■ 1 (2h)

The first null point occurs when

n (H*/2 ) - « / 2 (25) where

y - dj. sin 0 2 and © 1 • location of first null (26) J _ CMBiNLD SINGLE LOB AND spur PAT. TERNS TOR A POINT SQURCE j "I ' L < i t '

275 tncjs 2$0 mc/s -

- 0 . 5 0

I-

8 RiGHW AS^ENSfbN Solving for 0^ gives

Q1 - sin-1 (n/n dy)

For three frequencies Table III lists the spacing between the first nulls of the difference patterns* TABLE III

FIRST NULL SPACING FOR COMBINED IN-PHASE AND PHASE-OPPOSITION PATTERNS

Frequency Mc/s. Location of First Null,©^ Spacing Between First Nulls, 2©^

225 0.785° 1.57°

250 0.7PU° 1.41°

275 0.637° 1.27°

01 -4 38

CHAPTER IV

ANTENNA PATTERNS FOi. EXTENDED SOURCES a. Introduction

It has oeen shown from observations that many sources are large in angular extent. The apparent radio si2e of an extended source can be deduced from the observed pattern. As an example, the apparent radio diameter of the sun will be determined in

Chapter V.

For sources comparable in size to the beam width of the antenna in right ascension, the antenna pattern is broader than the pattern for a point source. It is assumed that the angular extents of these sources are small compared to the beam width of the antenna in declination. Therefore, the intensity distri­ bution is considered to be concentrated along the principal axis in right ascension of the radio source. The signal from trie source is incoherent. Assuming the radiation to be from a distribution of isotropic point sources the total patterns are determined by the summation of the patterns for the point sources.

Three different cases will now be considered for extended sources. b. All Antenna Elements of the Array In Phase

The first case for which the pattern is calculated is with all elements of the array in phase and an extended source of angular width o( . The intensity distribution of the source is 39 assumed to be uniformly concentrated along its principal axis in right ascension. This assumption corresponds to a spherical source of constant surface intensity which is small in extent compared to the antenna beam width in declination as shown in the Appendix, section 2. As indicated in figure 17 the angle is divided into 2m equal increments, A A . Each increment is considered as a point source. In Chapter III, section b, the total in-phase intensity pattern for a point source for small values of 0 is not appreciably different from the array in-phase intensity pattern. The single helix intensity pattern is broad and nearly unity for small values of ©. Therefore, for small values of © the total in-phase intensity pattern is assumed equal to the array in-phase intensity pattern. The validity of this assumption is seen in the agreement of the patterns of extended sources calculated analytically from the array in-phase intensity pattern for a point source and calculated by graphical integration from the total in-phase intensity pattern. The normalized array intensity for a point source is given by equation 9, Chapter III, as

Cl)

For the extended source Bhown in Figure 17 the relative intensity at an angle © is the average of the intensities from the 2m point

4 40

C< Q

o< - angular extant of •ource

A A * increment of source extent

p - in te g e r p AX A angular distance of -AX increment from center of source

0 polar angle from the center of the antenna

0 © + pA A Right Ascension

DIAGRAM TOR DSTKHUINATI OR QT TRIE INTWSITY PATTERNS

TOR EXTENDED SOURCES

TI (JURE 17 41 sources, giving

p * m v 5 > sin sin (© + p a A ) 1 1 ] (2) sxn sin (© + P AA )J

Substituting 2m ■ --- and taking AA inside the summation gives A A

. s m 2 n sin (0 + p AA ) j

P ' i ^ / 2 r«rr dp 1 -i - ^A* ^ sxn sin (© + P 4A )J (3) r ZAA

In the limit as

A * — o (U) and

p — — oo (S>

the product p AX —•- X (6)

In the limit the summation becomes

dr I sin^ n 2~ sin (0 + > )J dA (7) £ sin^-jp sin (6 + A )J

j If the intensity distribution of the extended source cannot be considered uniform along the principal axis in right ascension, a distribution factor is included in the integration (See Appendix, Section 1), If the source and the major lobe are small the approximation

sin ( 0 + ? O - (@ + ^ )

is made for small values of (©+*)• Equation 7 becomes

P -

Letting

then Expressing equation 9 as a function of x, the intensity is £(e+f) p . 2 f S i S ^ Z ^ (13) °( cL n^ I sin^ x

By the trignametric identity (31)

sin2 me - 1 -c°s. 2r? (Ik)

Substituting into equation 13

2 f 1 dx (1 $) « d^n2 I 2 sin^x sin^ x

The integral of the second term is given by Peirce (32) as

cos 2nx ( sin (2 n - l)x /

-U A cos (2 n - 2)x dx - 2 f s-in- dx J J sin x + ! COS (2n -_2)x ^ (16) I sin^ x The first term on the right can now be evaluated (33) and by a

repetitive process the second term can be reduced to an integrable

form, giving n-t cos 2nx ^ \ 1 . _ 5--- dx - -2x -2 / sin2(n -m)x sin^ x / n - m / mj|

+ f cos 2(n - l)x dx (17) J sin x: Similarly, by expanding the last term another series is obtained including all the factors of the first series except the first factor. By iteration the solution is reduced to

n- I cos 2nx dx * - 2^ — -— sin 2 (n - m)x sin2 x _ n - m fl: I

- 2 nx + dx sin^x

Substituting into equation 15

p . L-z - I 1 - c ° 3 2ox- dx - 1 dx oCdjJi sin2 w dr*** sin2 x

n - 1

m dx + 2 sin 2 (n - m)x sin2 x n - m ■f. m 1

-*• 2nx

■which reduces to 45 Introducing the limits of integration

n - 1 t x d j j a \ m sin (n - m) d^C© + £) ocd n r 2 / n — m m - 1

- sin d^Cn — m)(e - \ (21)

The equation can be rewritten to give

n - 1 ex sin (n P - — £ ■ cos (n — m) dy© (22) ~a * ^ n 2 (n - m) m - 1

To check the result at one point, the value of the intensity at

oc - 0 and 8 - 0 is known to be unity* Substituting zero for oc and

6 indeed gives unity*

The intensities calculated by equation 22 are plotted for three values of oc at 22$, 2$0, and 275 megacycles per second, as shown in

Figures 18, 19, and 20, respectively* The intensity plots can also be obtained by graphical integration (34*) of the intensity pattern of a point source* The curves derived in this manner are identical with Figures 18, 19, and 20* Therefore, the initial assunption is valid for the total in-phase intensity pattern of a point source for small values of 8 being equal to the array in-phase intensity pattern* yoiQNBON UHOfd b

QtP 0 -

I,:

mi m /t o s isizuci yyi/ra/w sjounos] aios 1//1 no./ r/y/s?? iv w m fl/aoiivd a a o i-w m 'i ■ J ■ 1

T

$ 5 A/SA j'3JLNI tlWih %

£ As

becomes double and shifts from the point, 6 » 0, for CX * 3

degrees* The half power beam widths of the major lobes are

summarized in Table XV and plotted in Figure 21*

It is to be noted that the variations in beam width for

different frequencies are nearly identical for sources whose

angular extent Of exceeds the half power beam width of the

antenna for a point source*

c. The Antenna Elements of the Array In Phase Opposition

With the antenna elements connected in phase opposition

the pattern for an extended source of angular width oc is

determined in a similar manner as in section b with the antenna

elements in phase* The assumption is made that the total phase—

opposition pattern of a point source can be represented by the

array phase-opposition pattern for small values of 6* Since

the single helix intensity pattern is broad and nearly unity

for small values of ©, it is neglected* The array phase-

opposition pattern for an isotropic point source given by

equation 17, Chapter III, is TABLE IV

HALF POWER BEAM WIDTH FOR SOURCE OF ANGULAR EXTENT CX

Frequency QC m 0° ■ 1° o( * 2° • 3 Mc/S 225 1.1*0° 1.53° 2.09° 3.07°

250 1.26° 1 .ill0 2.06° 3.06°

275 1.13° 1.31° 2.06° 3.06°

8 r - • • - : • < • r~r - - * - »• - i * ;

Half Fowr IJeaafidth ! I i ! ' THS HALF POWER H&AltPOWER WI HALF THS The Angular Extent of the Source the of Extent Angular The 3 .t4 31 W W I F L 350 Ho/ 350 275 Mo/ 275 Ho/ 335

51 or expanded is 52

dr p dp 1 - 2 cos n ( y sin 8) + cos^ n (*r- sin 0) “ 2 o dp (2U> sin2 (— sin 0)

By the method illustrated in Figure 17 and applied to equation 1, equation 2h is used to obtain the intensity for an extended source of angular width Of , which is

ijj + cos^njj^ sin (0+A) 1-2 cos n v r sin (04- A »] dA (25) sin2 £^E sin ( 0 + A)j

For small angular widths

sin (0+/\)-(0 + X) (26 )

giving

r dp 1 r ^ 1 - 2 cos nj ■£- (0 + A)J + cos2 I ■j- (8 X) d?v or n* sin (27)

A 53

Let d- — (6 + A) (28) and dx - — d A

Then for

* > X . i (e+f.) (29) - 2

Expressing equation 27 as a function of x, the intensity is &(6+f)

1 - 2 cos nx + cos nx ------dx (30) o < d r n.t sin* x

The integral of the first term (35) is

dx -- - ctn x (31) f sin2 x The integral of the second term is similar to equation 18 with

n an even integer# It is n-z z cos nx 3T dx ■> 2 ctn x + nx + U / — 2 — sin (n-2m) x (32) sin* x / (n-2m) m = |

The third term is expanded to give

2 cos* nx 1 + cos 2nx , dx - £ (33) sin* x I ? * ' ^

I 5 4 This integral is similar in form to equation 15 and its aolution is

n-i cos2 nx . i 5 dx ■ - — ctn x + 2 nx + U \ K— sin 2 (n-5i) x Oh) sinc x 2 / 2 (n-p) p «i

Substituting the results in equation 30 gives

n- Z i_ P - nx + 8 sin (n — 2 m) x « d rn< n — 2m m = i n-i - \ 111 sin 2 (n - m) x (35) / n - m m -I

Introducing the limi ts of integration and then rearranging the terms, the intensity is

n-1 sin ^ m^drfy - i 2 cos (n - m) dpG (n even) n n 1 (n - m) nrt i| 5

cos c^e (36)

m -1

In the limit for « - 0° and 6 - 0°, the Intensity is zero as it should be* The calculated intensity curves for three values of « are shown in Figures 22, 23, and 2l*« It is readily observed from the figures that the relative intensity at 6 * 0 ° becomes larger as cx increases* In the range of CX from 0*5 to 2*0 degrees

I A J L i $ N 3 J . W * a 3 Z \ l V W d O N tiisAiJtiNi tfshrwioA 68 the variation of the minimum from a null is a sensitive indication of the angular width of the source. The values of the intensities at 0 » 0° for normalized patterns are summarized in Table V and shown in Figure 25. The ratio of the max-timim value of the phase— opposition pattern to the maximum value of the in-phase pattern is not constant. These ratios and the position, 0^, of the mavt mum value of the phase-opposition pattern are summarized in Table VI and shown graphically in Figure 26. d. The Combined In-Phase Pattern and phase-opposition Pattern

The circuit arrangement described in Chapter III, section d, uses the antenna signal more efficiently than the circuits for the in-phase patterns or the phase-opposition patterns. With this circuit arrangement the pattern is the difference between the in-phase and the phase-opposition patterns. The null points of the combined patterns are independent of the receiver gain fluctu­ ations. The combined patterns are obtained by subtracting the patterns of Figures 22, 23, and 2k from the corresponding patterns of Figures

18, 19, and 20, respectively. The combined patterns for sources of

angular width oc are shown in Figures 27, 28, and 29 for 225, 250, and 275 megacycles per second, respectively.

The spacings between the null points of the combined patterns for extended sources are summarized in Table VII and shown graphically in Figure 30. For a given frequency and for the same extended source 59 the spacing between the null points of the combined patterns are not greatly different than the half power beam widths of the in- phase patterns given in Table IV. TABLE V

INTENSITY AT 0 - 0° OF NORMALIZED SPLIT-LOBE PATTERN OF EXTENDED SOURCE

Frequency Of - 0° Of « 1° Of ■ 2° Of ■ 3° Mc/S 225 0 0.166 0.688 1.000

250 0 0.220 0.839 1.000

275 0 0.252 1.000 1.000

Of * angular extent of source 3°

360Uo/ 225Uo/ 275Uc/ s o u rc e s

Xateht of the Souroo s x t s h b d

or riOORX 25 riOORX A&galmr Th* rxrmms IHTEV9ITT AT O ■0° FOK U05UALXZZD SFLIT-LOBt 0

o o s 6 » M W B o TABLE VI

MAXIMUM VALUE OF IN-PHASE PATTERN RATIO t MAXIMUM VALUE OF PHASE-OPPOSITION PATTERN

Frequency Of - O' Of - 1 Of ■ 2 Of - 3

Mc/S Ratio Ratio 9_ Ratio Ratio 6.m

225 0*526 1*17 0.519 1.19 0.1*90 1.27 0.676

250 0.526 1.05 0.500 1.08 0.1*71 1.15 0.750

275 0.526 0.95 0.510 0.98 0.1*85 0.629

■ position of maximum of phase-opposition pattern

0< ■ angular extent of source

o» N

SiNGLL- 3E PATTERNS A 5 M\C/S

ANGULAR l ' / . T F ! \ 6 B W i ' v

C £ 7 W

COMBINED SINGLHQBt AND

OZ'-ANGULAR £XT£n T Of — — —SOURCE i - + - f — T}'24 -i— -i.-, -.A--'- TABLE VII

SPACINGS BETWEEN FIRST ZERO POINTS OF THE COMBINED IN-PHASE AND PHASE-OPPOSITION PATTERNS

Frequency 0< - 0° 0< ■ 1° CX * 2° OC « 3° Mc/S

225 1.58° 1.67° 2.lli°

250 1.55° 2.1ii° 3.11°

275 1.29° Ui2° 2.3ii° 3.1fc°

Cx m angular extent of source Spacing Bet won lull Points 1 ° 0 g n i c a p s

PATTHTWS PATTHTWS koi o wk t k b Ph# Angular Bxtent of the Soureo the of Bxtent Angular Ph#

l l u h t : OP OP PtOORB 30 BXTWTDBD BXTWTDBD

s t n i o p ' 1 ' !

p o p SOOPCSS

s r t

e n i b m o c

) M 4 CHAPTER V

THE ANGULAR EXTENT OF THE SUN AT 2 $ 0 MEGACYCLES PER SECOND

The svm is an intense source of radio radiation* Its angular extent is at least one-half degree (the visual diameter).

Theoretical and experimental calculations (36-40) have been made on the tender ature and intensity distribution of the sun in the radio region. With The Ohio State University radio telescope measurements on the sun can readily be made from which its apparent diameter at 250 megacycles per second can be determined.

As shown in Chapter IV, section c, the ratio of the intensity at the center of the phase—opposition pattern to its maximum value is a sensitive indication of the angular width of a source whose angular extent is in the region of the half power beam width of the antenna. The calculated ratios at 250 megacycles per second as a function of is shown in Figure 31. The practical range of o< in Figure 31 is limited approximately between 0.5 degrees and 2.0 degrees.

A phase-qpposition pattern record of the sun taken at The

Ohio State University radio observatory is shown in Figure 32.

From such records taken of the sun the ratios of the intensity

at the center of the phase-opposition patterns to its maximum

value were obtained. These are given in Table VIII. For the mean value of the ratios, the equivalent sun* s diameter taken from Figure 31 is 1.1 degrees at 250 megacycles per second.

This value of the sun's diameter at 250 megacycles per second is in agreement with the value quoted by Goerke (ill). VA LUE OF:, SPLlTrLOBt10: WER/Cm TO MAXIMUM VALUE OF:, SPLlTrLOBt10: A T IS O MC/S FOR EXTENDED \

aep 4-- ANGUL *R'£AT€NT SOORC SPLIT-LOEK PATTERN TABLE VIII

RATIOS OF INTENSITY AT 6 * 0° FOR NORMALIZED PHASE-OPPOSITION PATTERNS OF THE SUN AT 250

MEGACYCLES PER SECOND

Date Ratio

June 2k, 1953 0,299

June 2$, 1953 0.218

June 26, 1953 0.280

June 29, 1953 0.251*

Mean Ratio 0.266 + 0.021* 74 CHAPTER VI

THE POSITION OF THE INTENSE RADIO SOURCE IN THE CONSTELLATION

OF CASSIOPEIA

Since the discovery of a point source of radio radiation in the constellation of Cygnus (8), many other point sources have been observed. Accurate position determinations are necessary for identification of the radio sources with visually observed sources. The accuracy of the location determinations is dependent upon the resolution of the radio telescope. The resolution in turn is dependent upon the size in wavelengths of the aperture of the telescope. Because the radio wavelengths are long compared to the light wavelengths, it is impractical to build a radio telescope with the resolution of an optical telescope.

However, position determinations of discrete sources with a radio telescope can be made sufficiently accurate to identify the intense sources distinctly, a. Right Ascension

The Ohio State University radio telescope has a half power beam width in right ascension for the in—phase pattern of approximately one degree, a peak-to-peak spacing for the phase- opposition pattern of approximately two degrees, and a spacing between the first zero points of the combined pattern of approximately one and a half degrees. Either the maximum point of the in-phase pattern, the null point of the phase-opposition pattern, or the spacing between the zero points of the combined pattern can be used to determine the right ascension of a point source*

The in-phase pattern has the advantage of giving the

detail of the source and its background where either may not

be symmetrical* This is illustrated in Figure 6 which shows

the source in the constellation of Cygnus superinposed upon

the galactic background* The in—phase pattern will also

differentiate between two sources which are spaced slightly more than the half power beam width of the antenna.

The phase-opposition pattern has the advantage that a null point is more sharply defined than is the maximum of the

in-phase pattern. Also, a slowly changing background is reduced to a low level in the record*

The advantage of the combined patterns is that the zero points are independent of the receiver gain fluctuations*

The time interval between zero points can accurately be measured

since the slope of the pattern is large as it passes through the zero points*

To eliminate phase errors by the cables connecting the antenna array, records are taken on the sun over a period of days* The right ascension calculated from the record is compared to the right ascension for the visible sun as given by the ephemeris for that day. The average error is determined for the sun*s records and is applied as a correction to the right ascension measurements of a radio source. In this manner the right ascension, epoch 1950, for a radio source is measured#

A record of the intense radio source in Cassiopeia taken with The Ohio State University radio telescope is shown in

Figure 12* The tape speeds for the records are three inches, six inches, twelve inches, and fifteen inches an hour. For measurements within one—tenth of an inch the ^ime error is within 2.^ seconds for the fifteen—inches-per—hour tape and

12 seconds for the three-inches-per-hour tape. The right ascensions for 35 records are listed in Table IX# The average gives a value for the right ascension of the radio source in the constellation of Cassiopeia of 23 hours 21 minutes 23 seconds + 15 seconds# b. Declination

The declination is determined by two methods. In the first method right ascension profiles are taken for several declinations in the region of the source# From the variation of the maxima of the profiles the declination of the source is determined#

In the second method, the declination of a point source is determined from the in-phase intensity pattern. At 250 mega­ cycles per second the half power beam width of the in-phase pattern is 1.26 degrees# For a source at zero declination the time interval between the half power points is U.95 minutes#

The antenna beam at any declination always includes a sector of the same width as at zero declination# Therefore, for a source TAELS IX

RI'jHT ASCENSION OF THE CASSI3F3IA RAdO SOURCE

Date Ri^ht Ascension

hours minutes

Oc t • 12, 1952 23 21.53 Oct. 14, 1952 23 21.49 Oct. 26, 1952 23 21.75 Oct. 27, 1952 23 21.34 Nov. 1, 1952 23 22.01 Nov. 2, 1952 23 21.19 Nov. 3, 1952 23 21.70 Nov. 4, 1952 23 21.52 Nov. 5, 1952 23 21.79 Nov. 9, 1952 23 21.53 Nov. 10, 1952 23 20.93 Nov. 11, 1952 23 20.34 Nov. 12, 1952 23 20.56 Nov. 13, 1952 23 20.95 Nov. 17, 1952 23 20.46 Nov. 18, 1952 23 20.77 Nov. 20, 19 52 23 21.18 Nov. 24, 1952 23 21.10 Nov. 25, 1952 23 21.43 Feb. 24, 1953 23 21.70 June 13, 1953 23 20.78 June 19, 1953 23 21.35 June 20, 1953 23 21.59 June 21, 1953 23 21.51 June 22, 1953 23 21.69 June 23, 1953 23 21.43 June 24, 1953 23 21.53 June 26, 1953 23 21.47 June 27, 1953 23 21.36 June 29, 1953 23 21.45 July 2f 1953 23 21.54 July 3, 1953 23 21.83 July 4, 1953 23 21.63 July 5, 1953 23 22.08 July 6, 1953 23 21.91

Mean value 23 21.38 yt 0.26 at declination + £ the time interval between the half power points is increased by (cos 8 ) . From the time interval between the half power points the declination angle is found to be

£ •» + cos”1 U.95 minutes time interval between hall’ power points

For the radio source in Cassiopeia the declination is found to be North 58*7 degrees + 0,1* degrees. Table X gives the position of the radio source in Cassiopeia as found by

Ryle, Smith, and Elsinore (18) and the position determined

herein.

Tentative identification of the radio source in Cassiopeia with a visual nebula has been made by W. Baade (1*2) at The

.Mount Palomar Observatory,

c. Size

Brown, Jennison, and Das Gupta (1*3) by correlation

techniques determined the apparent angular size of the radio

source in Cassiopeia. The equivalent rectangular source of

constant surface intensity for Cassiopeia in three base lines

as determined by them is shown in Figure 33, the equivalent

area of Cassiopeia being approximately 0.003 square degrees* TABLE X

POSITION OF THE RADIO SOURCE IN CASSIOPEIA

Observer Right Ascension Declination

Ryle, Smith, and

Elsmore (16) 23h 21m 12s 58.53°

Matt 23h 21m 23s 58.7° 80

N i i

3' 30" f o f a r c 2 I 55 — II

3' 40"

EQUIVALENT RECTANGULAR SIZE OF

CASSIOPEIA RADIO SOURCE

7X0UBI 33 CHAPTER VII

INTENSITY MEASUREMENTS a. Introduction

In radio astronomy the received radiation is expressed in terms of the equivalent black body radiation. Planck's law of black body radiation gives the brigntness emitted by a black bodty in thermal equilibrium at temperature T as

S(f) Af - eChf/kT) _ i

where h • Planck's constant, 6.62 x joule-seconds —23 k ■ Boltzmann's constant, 1.38 x 10 joules per degree o c ■ velocity of light, 3 x 10 meters per second

f - frequency, cycles per second

hf • bandwidth, cycles per second

In radio astronomy the wavelengths are long andtiie thermal temperatures of the sources are small. Thus, in Planck's law hf « kT* As an example, for a wavelength of one meter and a

temperature of 101* degrees Kelvin,

hf , -6 — - 1.1* x 10 kT

Therefore, in radio astronomy Planck's law reduces to the 82

Rayleigh—Jeans law of black body radiation which ±3

lf']' B(f) Af - ^ 2 --- * f (3)

In 19iil Burgess (1U0 showed that the Nyquist thermal-noise

electromotive force of an antenna in an enclosure of uniform

temperature maybe identified with the Rayleigh-Jeans distribution

for black body radiation.

b. The Radiation Resistance of the Antenna

The antenna is the link between the receiver and the

radiation from free space. Assume the antenna is in an enclosure

at uniform temperature. It may be seen that for a temperature

corresponding to the enclosure temperature the voltage across

the radiation resistance is equivalent to the thermal-noise

electromotive force as given by the Nyquist equation.

Let the antenna have an impedance Z * R ♦ jX at its

terminals, where R includes the terminating resistance, RQ, and

the radiation resistance, Rj», at a frequency, £• Also, let

er be the mean square random-noise voltage developed at the

terminals of the antenna due to radiation in the frequency band,

A f. The mean square voltage developed by the terminating resistance at the enclosure temperature, T, is given by Nyquist * s formula as 1* k T RQ if. The equivalent circuit is shown in p Figure 3U* The mean square current, i , due to the thermal-noise JX 1------

Rc m terminating reaiatanoe of antenna

Rr ■ radiation resistance of antenna

X • reactance of antenna

er • randorv-ooise voltage due to radiation

received

\j U k T Rq a f a thermal-noise voltage from Rc

THE EQUIVALENT CIRCUIT FOR THE ANTENNA IN AN ENCLOSURE

AT UNIFORM TEMPERATURE

FIGURE 34 electromotive force developed by the terminating resistance is

i2 - ** k ^ R o ?

and the power, Prad* radiated by the radiation resistance is

U k T Ro Rr Af Prad " ±2 Rr " ---- T7

The received power, Frec> for the terminating resistance is

2 p ep Ro rec 2 Z

For thermodynamic equilibrium the total energy of the system remains unchanged. Therefore, the radiated and received powers are equal,giving

ep2 ■ 4 k T Rj. A f

For the radiation resistance the equivalent thermal-noise temperature, Tr* is equal to the enclosure temperature, T, so that the Nyquist formula gives the value of the received power.

Thus, in an enclosure of uniform temperature, T, the antenna at its terminals has an equivalent Nyquist thermal-noise electromotive force. In free space without radiation, the radiation resistance has an equivalent noise temperature of zero and at the terminals of the antenna the electromotive force is zero. 85 c. The Received Power

In general, for radiation of random polarization from an

extended source the antenna will absorb power as given by

P (8)

where A (©,♦) » antenna aperture as a function of 0 and 5

dfi. ■ element of solid angle

B (6,5) “ brightness, power per unit area of aperture per

unit solid angle per cycle per second at the

antenna as a function of 6 and 5

The factor 1/2 is introduced because the antenna can receive only-

half the random-noise power available. For the enclosure at a uniform temperature, T, the brightness is constant and indepen­

dent of the angles © and 5. Its value is given by the Rayleigh-

Jeans law. For uniform brightness equation 8 becomes

(9)

Let the integral be defined as

(1 0 ) s where Z - the average antenna aperture

The power received by the antenna from the enclosure is

P - 2 n I B(f) A f (11 ) 81 Substituting for the brightness from the Rayleigh-Jeans law,

equation 3 for the receiver power is

(12)

To satisfy thermodynamic equilibrium the received power is

equal to the power radiated by the antenna, kT Af, as shown in

section b. Equating k T A f to equation 12 gives 2 (13) which is the maximum effective aperture of an isotropic

antenna (lt£)* The power received by the antenna can be expressed

in terms of the Nyquist equation for the thermal-noise of a resistor* The received antenna power is

P - kTA a f ( l i i )

Since the bandwidth, A f, is constant for a given receiving system, it will be convenient at times to express the antenna power in terms of the equivalent antenna temperature, T^.

If the change in the brightness for extended sources over the beam width of the antenna is not large, the brightness is assumed constant* For random polarized radiation the power absorbed by the antenna is

(15) s 87 Assuming the brightness to be constant

P - \ B tf 1 A(e,*) d-a (1 6 ) 5

Hence, substituting from equation 13, the received power is

P-2nBXaf-^B>v2 4f (17)

The brightness is

The received power can also be expressed in terms of the maximum effective aperture, Aem, and the beam area (1*6),-fi. , of the antenna* For any antenna the ratio of its maximum effective aperture to its directivity, D, is equal to the maximum effective aperture of an isotropic antenna (hS), that is

(19)

The directivity expressed in terms of the beam area (1*6) is

(2 0 )

Therefore,

1 - mr (21) 88 Substituting into equation 17 the received power is

P - \ B 4 f Aem SX (. 22)

The brightness is

(23)

The product of the beam area and the maximum effective aperture of an antenna is a constant as shown in equation 21#

From a source of uniform brightness whose angular extent is greater than the beam area of the antenna, the received power

(equation 22) remains constant in spite of increases in the antenna aperture*

In the case of a source which is small compared to the beam width of the antenna

(2k)

The power absorbed is

(25)

The intensity, S, is the radial component of the Poynting vector per cycle per second from a discrete source and is

(26) s 89 From equation 2$ the intensity is

(27)

The received power is proportional to the antenna aperture.

Increasing the antenna aperture will increase the received

power as long as the beam width of the antenna is greater than

the angular extent of the source.

The dimensions for brightness and intensity are:

Brightness : energy per unit time per unit area

per unit solid angle per unit

bandwidth,

and

Intensity : energy per unit time per unit area

per unit bandwidth.

For data included herein the units are:

Brightness s watts per square meter per square

degree per cycle per second, and

Intensity : watts per square meter per cycle

per second, d. Relationship of Source Temperature to Antenna Temperature

Consider a source which subtends a solid angle, to, and has a black body temperature, Tg, The power received by the antenna is proportional Tgto, The power absorbed by the antenna can be described in terms of the beam area, Cl , times the 90 maximum value of the radiation intensity over the beam area.

The equivalent Nyquist temperature for the maximum radiation intensity is defined as the antenna temperature, T.. For A random radiation the antenna can absorb only half of the available power. The power absorbed by the antenna is

TA ^ " \ TS“ (28) and

t s n (29) 2 TA •

Therefore, if the angular size of a discrete source is known, the equivalent black body temperature of the source can be determined from the antenna temperature of the source. 91

CHAPTER VIII

THE RECEIVED POWER FRO}.: THE ANTENNA a. Introduction

To have maximum sensitivity for the radio telescope, the maximum antenna power is transmitted to the receiver. This is accomplished by matching the transmission lines from the antenna to the receiver. Since the transmission lines have attenuation, a portion of the power at the receiver input is contributed by the thermal-noise of the transmission line resistances. The proportion of the total power at the receiver input which is antenna power is calculated. From these calculations the intensities of received radiations are determined. b. Antenna Matching

To obtain the maximum antenna power at the receiver input, the transmission lines from the antenna to the receiver are matched. The terminal impedances of the 1*8 helical antennas of The Ohio State University radio telescope are adjusted to

120 ohms. RG-63/U cable (120 ohms) connects each helical antenna to impedance matching transformers located on the back side of the antenna ground plane. Six helices are paralleled at the input of each transformer, whose output impedance is

50 ohms. The output of each of the eight transformers is brought by RG—17/U cables (50 ohms) to the receiver. The cables are paralleled and the output impedance is adjusted to

50 ohms with a double stub tuner. RG-8/U cable (50 ohms) is

used for the remainder of the radio frequency transmission

line. The signal then passes through the capacitor switch

whose output is adjusted to 50 ohms. The output of the

capacitor switch is connected to the 50—ohm input of the

preamplifier sections.

The power delivered to the receiver is a function of the

antenna and is independent of the paths of the matched trans­

mission lines to the receiver. This may be demonstrated as

follows.

Let PQ be the power received by each of n helical

antennas. This is power radiated from an incoherent source.

Consider first the n helices paralleled at the terminals and

connected to the receiver by a single cable with an attenuation

as shown in Figure 35a. The antenna impedance is matched to

the cable impedance by a lossless matching network. The portion of the antenna power, nP0, reaching the receiver

input is p nPQ*

An alternate circuit arrangement is shown in Figure 35b.

Each helix has a separate cable path with attenuation ^ to

the receiver. The cables are paralleled at the receiver and then matched to the receiver input. The power from each helix, P0, reaching the matching network is (3 PQ. The total power at the receiver input is nftPo# Thus, either circuit 1 2 3 O o g D D i

nP.

Lossless nP, £nP, Hatching Heteork

(a)

* * 0 A, 06. Loealaoa c Matching Raoelver Hatvork P * o

n - nunbar of halloas In antanna array *o " power received by one halls /} * cable attenuation

0ABL1 IHRAVOnrOtTS BKTfKKM THS JUTOSHA

AVD THS HSCSIVXR

PIOURS 36 arrangement of Figure 35a or b delivers the same power to

the receiver*

The antenna power which reaches the receiver can also be

deduced from voltage considerations. The signal, P , to each helical antenna is from a single random source. The mean 2 square voltage, ejjj , developed across the terminal resistance,

Ra, of each helix is

em " po R a

With all the helices having the same phase, the voltages at the helix terminals are in phase. Consider the helices paralleled at their terminals as in Figure 35a. The voltage applied to the receiver cable is e^, and the impedance is H&/n

The power delivered to the cable is

2 2 em ne m _ ----- m - B n P „ Ra/n Ra

With a cable attenuation of |3 the antenna power reaching the receiver is ^ nP^. In the alternate arrangement the power from each helix is transmitted by a separate cable (with identical characteristics for a!1 cables) to the receiver.

With a cable power attenuation of p the voltage from each helix at the receiver is ^ e^. Paralleling the cables at the receiver the output voltage is -fff e and the impedance is R /n \ m a The antenna power available at the receiver is 95

(3)

To transmit maximum power from the antenna to the receiver , paralleling the helical antennas at either their terminals or

at the receiver is immaterial if the parallel cables are identical. c. Total Power at the Receiver Input

The antenna with an equivalent temperature, V is the link between the source and the receiver. The cable from the

antenna to the receiver has a total attenuation of (3 (Appendix,

section U). The cable temperature is taken as the room temper­

ature, Tq. Since the power is proportional to the temperature

as given by the Nyquist's formula, temperature equations shall be written in place of power equations.

The proportion of the antenna temperature at the receiver input is ^ T^. There is an additional signal at the receiver input caused by the cable attenuation. If the attenuation

constant per unit length of cable is oc and the length is L then,

let

e (U)

the attenuation. For a cable at temperature, T^> the thermal— noise power from an increment, dx, of the cable as shown in 96

Figure 36 is

_ - 0 4 x m -«(x+dx) T o e -T oe

The total tfaennal-noise pcnrer from the cable, T , at the receiver c input is found by integrating over the cable length, giving

T - r T e-*x I l-e~“dX CIO u (S) J o

Expanding to a first order approximation the integral becomes

Toe ~ * x [ l - (1 - or dx)] - Toe~*x dx (6) Tc J J

The solution of the integral is

Tc - To ( 1 - e'*'L) - T0 (1 - f ) - (7)

The total power, T , at the receiver input is then,

p *. + ( i - a ) t - t (8) v r . °J reo antenna signal cable noise

for an ideal cable, that is, ^ • 1, the contribution of power from the cable is zero, and the total antenna power is transmitted to the receiver input. For infinite attenuation constant, that dx Antenna

L • total cable length

x * distance from receiver

dx - inorement of cable length

DIAGRAM FOR THURMAL-NOISE FROM CABLE

FIOURX 36 is, |3 ** 0, no antenna power reaches the receiver. To transmit

the maxi mum antenna power to the receiver, the cable attenu­

ation should be kept as small as possible*

The temperature recorded on the tape is T • If the tape rec is calibrated, T is known, and the antenna temperature from 1*GC equation 3 is

Treo - a - p ) To T ------—J------(9) f

The portion of the antenna temperature caused by a point source,

T*, superimposed on the general background is A i n»i Arec ta - --- <10>

where T 1 - the recorded temperature caused by the point source* rec

d. Temperature Calibration of the Recorder Tape

To calibrate the recorder tape, the antenna system is replaced

by a resistor matched to the receiver input. The temperature

of the matched resistor can be varied above find below room tem­ perature. From the theory of the preceding section the tempera­

ture recorded on the tape for the resistor at a temperature T is K

P r ^ ( 1 " P r > To - Trec 99 where 6 is the attenuation of the cable from the resistor I R to the receiver input.

For various values of T . the corresponding value of T R* rei is noted on the recorder tape. Within the temperature range of operation, the scale deflection is proportional to the temperature variation. The required ran;;e of temperature in the calibration resistor for a given recorder deflection is not as large as the antenna teller a ture variation, since the cable attenuation between the matched resistor and the receiver is less than the attenuation between the antenna and the receiver.

A circuit arrangement which gives a reference level on the recorder tape is shown in Figure 37. The antenna system is replaced by the calibration resistor at room temperature at intervals to give the reference level which corresponds to

T , since in equation 11, T_ « T , and, therefore, T - T • o' J R o' 9 rec o The antenna circuit and the calibration resistor should be matched identically to the high frequency relay. After the relay, the circuit is the same for the antenna signal and the thermal—noise output of the calibration resistor. Therefore, the two signals are treated identically. antenna / rotating capacitor switch

high-frequency relay -VWV reference level resistor w w — J calibration resistor

CALIBKATION CIHCDIT FOR INTENSITY MEiStlREMENTS

nm a 37 101

CHAPTER IX

LIMIT OF DETECTION

The signals received by the antenna from extraterrestrial sources are generally incoherent except for the abnormal sun1 s activity which is strongly polarized at frequencies under 100 megacycles per second (21). The limit of detection of the low levels of power is a function of the bandwidth, the noise figure, and the output time constant of the receiver. As will be shown, it is possible to detect powers of one one—thousandth of the noise level since the ability to measure a difference in the noise level is the limiting factor. The detectable differ­ ence in the noise level is dependent upon the fluctuation of the noise level.

From statistical analysis the deviation of n readings of a random signal from the mean is proportional to n"“^ / ^ * For an input bandwidth of df^, A f^ independent readings per second are taken, and these are averaged over t seconds, the output time constant. The number of independent readings is the product of the input bandwidth and the output time constant:

n - A f ± tQ (1) The variation from the mean is then

n- . - tf:input bandwidth time output time constant (2)

d 103

For a receiver noise temperature T and an antenna temperature R T., the detected signal T equals T + T • From the preceding A A R paragraph the antenna signal variation & T which can be detected is

AT, 1 1 (3)

The smallest change in the antenna signal which can be detected is

(h)

Increasing n is limited by the desire to observe changes in the intensity of radiation over short intervals for position determinations and for spectrum analysis• In addition the input bandwidth oust be kept m a n to exclude local interference* In the receiving system of The Ohio State University radio telescope the overall bandwidth is one—half megacycles per second, and the output time constant is usually between 25 and 75 seconds* The noise figure of the receiver is less than 3*0* Therefore, the equivalent receiver temperature is 600 degrees Kelvin* From equation ii the detectable change in the antenna temperature neglecting cable attenuation for two values of the output time constant is

(1) for t0 ■ 25 seconds

A ■ 0*17 degrees Kelvin (5) 103

and (2) for tQ • 75 seconds

aTA " 0,3-° degrees Kelvin (6)

With a change of six degrees Kelvin in the tenperature of the calibrating resistor, the receiving system can be set to give a one inch deflection on the recorder tape for an output time constant of 25 seconds. Assuming that one-tenth of an inch can be distinguished on the record, the detectable variation in tenperature is 0,6 degrees

Kelvin,

The maximum sensitivity of the receiving system used in the intensity measurements of the radio sources given in Chapter X is a 30-degree Kelvin change in the tenperature of the the receiver input signal gives a deflection of one inch on the recorder tape.

The detectable variation of the receiver input signal is about 3-0 degrees Kelvin, The actual sensitivity is less than the theoretical limit of sensitivity because of equipment instability and local interference. The variation in the intensity measurements is about

10 per cent, which is also observed in the measurements given in

Chapter X, 104 CHAPTER X

EXPERIMENTAL INTENSITY MEASUREMENTS

a* Introduction

As seen in Chapter VIII, section d, the calibration of the recorder tape is accomplished most easily in terms of tempera­ ture* The recorded powers are measured in terms of temperature and then converted to brightness or intensity of the source*

The measured equivalent temperatures correspond to the tenperatures in the Rayleigh-Jeans law. In spectrum analysis the brightness or intensity variation with frequency is assumed to be f*. By the Rayleigh-Jeans law, Chapter VII, equation 3, the brightness is

B (f) ~ f2 T (1)

If from the spectrum analysis the brightness is

B ( f ) ~ f X (2) then the tenperature variation with frequency is

(3)

From the antenna tenperature measurement the power received by the antenna as given by equation LU, Chapter VII, is

P - k T A A f (10 The power per unit bandwidth is

P (5)

From equation 23, Chapter VII, the brightness of an extended source is

(6)

and from equation 27, Chapter VII, the intensity of a discrete source is

(7)

For measurements made with The Ohio State University radio telescope the maximum effective aperture, A ^ , is assumed to be equal to the physical aperture, 179 square meters* The beam area, 1^, of the radio telescope is 21.9 square degrees at 2£0 megacycles per second* Expressed in terms of the antenna temperature the brightness of an extended source is

(8)

or

B ■ 7*05 x IQ"2? T^o watts per square meter per (9)

square degree per cycle per second 106 [he intensity of a discrete source is

S . 2 k T*— (10) ^em

or

*2 S o S * 1.5h2 x 10“ T watts per square meter per A cycle per second

The intensity measurements of discrete and extended sources presented herein are obtained with The Ohio State University radio telescope consisting of ii8 helices. For all measurements the frequency is 250 megacycles per second, b. Radio Source in the Constellation of Cassiopeia

Measurements were made on the Cassiopeia radio source, which is the most intense discrete source known. The procedure for the measurements is described in Chapter VIII, section d.

The antenna temperatures obtained for the Cassiopeia source are listed in Table XI. The minimum background or sky tenperature at a declination of North 58.5 degrees is also tabulated. A record is shown in Figure 38. The mean value of the antenna temperatures is 21*7.5° + 5 .5° Kelvin. The mi ni mum observed background tenperature is 272 degrees Kelvin. The background tenperature appears to be extraterrestrial in origin. The records were taken from 10*00 P.M. to 8*00 A.M. local time. TABLE H

ANTENNA TEMPERATURES FOR CASSIOPEIA RADIO SOURCE AT 250 MEGACYCLES PER SECOND

Date Antenna Temperature Minimum Background (Sky) Tenperature for Casaiopeia Source at Declination North 58*5

June 18, 1953 286° K

June 23, 1953 253.5° K _____

June 26, 1953 2iiO° K _____

June 27, 1953 2i*9° K 272° K o CASSIOPEIA RADIO ®SOURCE 1 0 8 § JUNE 23, 1953 2 5 0 M C / S 4 6 R M H . o Tape Calibration 28. 2ViJ£ Cable Temperature 3 0 0 °K Antenna Temperature for Star 2 54*ic Declination N 5 8 .5 ^ o R. A. 23h 2 l # 4 3 m § Si*^ fr %

o »

3 0 0 * K § re fe re n c e level V 254*K

-j \ o o c pi CT R

5 : 4 0 A.ME : E . f T r a o CM . CM 8 -/V

j L q

3 0 m :£3fa (Sin RIGHT ASCENS tOtf lePQCTt; IS S O JIt'

-- -*■ — i > j 109 Five records of the Cassiopeia radio source taken in

September, 1952, give the mean value of the antenna tenperatures

for the radio source as 250 degrees Kelvin or 2.5 degrees Kelvin

greater than the value of antenna temperature listed in Table XI.

The type of record is illustrated in Figure U. The values were

determined by assuming the minimum background temperature to be

the same as found by the measurements listed in Table XI.

From equation 11 the intensity of the Cassiopeia radio

source at 2$0 megacycles is 0.38 x 10“^ watts per square meter

per cycle per second. The minimum background brightness is

1.9 x 10“^ watts per square meter per square degree per cycle

per second.

Ryle, Smith, and Elsmore (ill) measured an intensity for the no Cassiopeia source of 2.10 x 10 “ watts per square meter per

cycle per second at 81 megacycles per second. A spectrum based

on the preceding measurements is shown in Figure 39* From the

spectrum the variations in the intensity and the equivalent

tenperature with frequency over a range of 80 to 250 megacycles per second for the Cassiopeia source are

(12)

and

T ~ f-3»50 (13) 110 CASS/OA^/A /?A £/£ S7A/? S/D£'£77?M 4 i ■ - ■ . /■- - T ! j ;■.: T’ .. I ... • ..■ i --- : 1 .■ j ' • • j : . . " I - ; ■ , | : : - !■ ■ i i- 1 ! — -- ill -I ‘ ' 4 - ! . -l i ■; — — t Z . j r JEH. 4 *::JX i r 1 t1 f *...... :: : S W A T 7 ~ ■ — — t :::' ...... :

i ■*? : : : : ; J : ■ . : :■ : ; = : i : . 1 . j.. 1 ' f r f \ ...: l i i : *; ■: :!ii i?::n ■ : .i;.: : -1 ::ii ‘.4.. ! . .. j " ] . : I .•* • • • i • • N , . • * H TH: , ; : j i : . : . ■ ■ *— i g i ■ * i ■■ : : * ■ * ...... ■...... — . .. I 4 ■ ♦- ■ 1 . . : . .. i. t. 44 ■ i ' -■ ,.j - ‘i.i :::: V; ...... ; !;.;■ .... ■ : ..... - . . . ' r * * ; ‘t i . i . ■ :.u; . ■ ■ ■ * * 1 ■ . ■ ------10. S A. r * c r . : ! . . ' 1 . ; : + f': .1- : 1 t-i - ^rr l-t: s t . ?. T“ .: ^rrrs . ! , . L' . ... 7 : : J r : . \ T * ; —.r 7! t ii'r " *: :*rrti: + : r t;:: 'i-: ui: imrrrtJ : t; e. i-’ M ■ *rr A r r r i b :r - "I, T . V B V ^ f :rHr:iL: i i :: ::ZT ” ‘ ii': E i r S J h \ 7, f P t ii- ■ .- ,, j. . ■ 4 ...... * 1' j*ii JU 1.^,1 1,1 ....mmmmm »•••* ;£ ;in n ^ r “ : -* :::: :t • • ...... ^r: HI •i;; - -:'r. - - ..-I •r:. i .* ■ • * t r*;r •--4 z i b. *v r :! " : . : : . • ■ I .:l! / r y U:- -ii n t - : r ‘ i! .ii . : r . T ' ; ^ f? : ‘•it -L. . ! . : : t . ; *j . r-.. ; ;: ;> ; ::; ;;r4 '.'4 ■' rrrr : r? . : ;;n :t: ; : ; . ■ : r ' i-r *Lt! r:: - ^V.\\ \\\ :: ' i L.. ' ‘ ■, i ■ if ; t t - r f r r r r T: ~ r t r r : -i i i . i. T ^rt - : u v .:: ~ '... . : .rt : i i ;• ■-**r . T . i *Tp : i 4 i L i d n : : 1 : _.! ...7 f - M ' + +-t- * j ::r + ♦ * * - " :: rr: ...... : : -.+1 . . )i 4 — ■ ■ ■ t — r" ■ rsr ffr- ■ i ■:*!..? ■ T r r r r r r ! ■! 1 1 ;. ■ kr*r I : ■ ...r \ : : ’ f Tl' :! ": ; ... •: : : ' -■ ,-r- ■ i i •;v ;!ll ■. : t: :.----- r; ' — ■ Ii-.. . 1 ; ; i ^ ; ^ — ,— Lii. ; • V ... r ■ : : * • • ; _ !■. [i ■ j; ■1■i •-ft: t ; ;; i.Li.;*'

.;f; . ; ■iV7"!* i i-i'ZJH ; lh -1 t I - ■ u p - ! : • - • f a r . T.. ‘ T r 1::. , . .4 . . ... ,.. * 4*K > iri..P . i. i % t: n: , . * r • . 'ir n r ! i: : ± ". t * . r\:: ♦ u *- .' i.l. ■r .: l.V lll.l .}«* ...... :i!r f? .- if' i*—4*. * # » * A *• + • Zv - *— • •» - * ■ " ;r **■ -< 'ii: 4 r ■ . . * . . i i . *J.,.I+Jl ■ ■ ;:.4 j*. • • + ! * * '-i r r HJl a t s o * 1 ...... 4— • - - ■ - 1 * * ' ■*— ■ 1 i^. ■ I ...... r " ; I 1 .5 2 .5 .1 7 8 9 10 1 .5 2 .5 Ill Assuming constant surface intensity, the apparent size of the Cassiopeia source has been found from Chapter VI, section c,

to be approximately 0.003 square degrees. From equation 29,

Chapter VII, the equivalent tenperature for the source is

S co or

Ts ■ 3*6 x 106 degrees Kelvin at 2$Q Me/s. (Ii*)

Temperatures of the above magnitude are not likely to be thermal

temperatures. Thus, other means of radiation other than thermal

radiation must also be present in the radio source, c. The Radio source in the Constellation of Cygnus

Intensity measurements were made at 250 megacycles per

second on the Cygnus A radio source. The calibration of the intensity scale is the same as for the Cassiopeia source. The

Cygnus source is the second most intense discrete source. As

seen in Figure UO this source is superimposed upon the galactic plane. The antenna temperatures measured for the source are recorded in Table H I . Also recorded are the minimum background

temperatures observed at a declination of North i*0 degrees. The mean value of the antenna temperatures for the Cygnus source is

207° + 6° Kelvin. The minimum observed background or sky tenpera­

ture at a declination of North 1*0° is 118 degrees Kelvin. The o o o N- N CYGNUS Tope Coljbration 30.2°K/in. RA. -J9h 57.9 m Cygnus Antenna Temperature2 0 7 ° K Cotoatic Moximum 622°K Declination N4£° 0 - - c -O to © ~ o Juty 12, t953 i I"- > 2 5 0 MG/S 48 RHH OALAXT . -RA 20tr18'5m U- -V o O r O 10 : . 3 P g K © T A- reference level •--* .. a

o \ . O *

i.i t:20 EST * t? ■ n J*- 2 Oh 15m 2 0 h 0 0 m RIGHT ASCENSION (EPOCH 1950.0)-:

CYGNUS A RADIO STAR A NO GALACTIC BACKGROUND o o o CJ nan* 40 TABLE XII

ANTENNA TEMPERATURES FOR CYQNUS A RADIO SOURCE AT 2$0 MEGACYLES PER SECOND

Date Cygnus A Antenna Minimum Background (Sky) Tenperature at Temperature a Declination of North liO°

June 25, 1953 217.5° K

July 9, 1953 199° K

July 10, 1953 201° K 186° K

July 11, 1953 210.5° K 118° K

July 12, 1953 207° K 13l*° K

July 13, 1953 208° K

Mean value 207° + 6° Kelvin

& M 1X4 records were taken between 10*00 P.M. and 8*00 A.M. local time.

Measurements from two records of the Cygnus source taken in September, 1952, give an average of 201 decrees Kelvin for the antenna temperature, or six degrees less than the mean antenna temperature given in Table XII. These values were determined by assuming the minimum background temperature as given in Table XII.

From equation 11 the intensity of the Cygnus A source is pp 0.32 x 10_<1<1 watts per square meter per cycle per second. The minimum background brightness is 0.60 x 10“^ watts per square meter per square degree per cycle per second.

Intensity measurements of the Cygnus A source at other frequencies have been made oy other observers. A spectrum for the source is shown in Figure hi. From the spectrum the frequency variations of the intensity and the equivalent tenperature from

1*0 to 250 megacycles per second are

S ~ f-1.30 and

T ~ f-3*30 (16)

Stanley and Slee (13) plot a frequency spectrum of the

Cygnus source from hO to 160 megacycles per second. From their spectrum the variation of the intensity with frequency is f —1 17 • 115 CAGA/Of A AAA/O S7A/? S A fC TtftW

J-S-J7MAZ*y JS£A >? - >91 Y?7* - I'WS’ m -jiam M.r ~ "••: 1 ■ ■:"

rr

tt

2.5

* 116 This value is in fair agreement with the value determined herein.

The variation of the intensity of the Cygnus A source with frequency is less than the Cassiopeia source. This indicated that probably the origin of the radiation is different in the two sources. The Cygnus A radio source also has been tentatively identified with a visually observeu source by W. 3aade (U2).

Baade's observations show the Cassiopeia source and the Cygnus

source to be different types of sources. The Cassiopeia source is a nebula of filamentary structure. The gas in the filaments

is moving at high velocities, over a thousand kilometer per

second. The Cygnus source, on the other hand, appears to be

two galaxies in collision.

The equivalent size of the Cygnus A radio source in terms

of a rectangular source of constant surface intensity is given by Brown, Jennison, and Das Gupta (U3) along three base lines

as shown in Figure U2. The area is approximately 0.22 x 10"^

square degrees. From equation 29, Chapter VII, the equivalent

temperature of the Cygnus radio source is then

or

Tg « Ul.2 x 10^ degrees Kelvin (17) 11?

34 —4 2'2 I0‘ I' of arc

EQUIVALENT RECTANGULAR SIZE OF CYGNUS A RADIO SOURCE

riaoBi 4 2

4 118 d. Maximum Galactic Intensity

The radiation observed by Jansky has its origin at the center of our galaxy, or Milky Way. Several observers (5,7, k7 - 50) have mapped intensity contours of the region about the galactic center. The maximum intensities at the galactic center for various frequencies have been determined. Measure­ ments have been made with The Ohio State University radio telescope at 250 megacycles per second of the intensity at the galactic maximum. The equivalent temperature is found to be

2320 degrees Kelvin at right ascension 17 hours 1±3*5 minutes and the antenna declination at South 28.5 degrees. From equation 9 the brightness at the galactic center is 8.2 x 10”^* watts per square meter per square degree per cycle per second.

A spectrum of the galactic center is shown in Figure it3* The intensities correspond to the maximum value found be each observer. All positions of the galactic center for different frequencies lie along the galactic equator out vary in galactic longitude. From the spectrum the frequency variations of the brightness and the equivalent tenperature from 100 to

1*80 megacycles per second are

(18) and

(1?) 119

Stanley and Slee (13) determined the frequency variation

of the temperature of the galactic center at f~2*65 ^ ^he

frequency range of 1*0 to 160 megacycles per second.

In Figure i*3> the spectrum of the galactic center, two

values by other observers fall below the assumed spectrum.

This may have been caused by optimistic estimates of their

antenna performances.

e. The Galactic Maximum Adjoining the Cygnus A Source

The galactic maximum adjacent to the Cygnus A radio source

is shown in Figure 1*0. The spectrum of the galaxy at two

different positions can be compared. With The Ohio State

University radio telescope measurements of the equivalent

temperature of the galactic maxj nrum adjoining the Cygnus source

have been made. The temperatures are listed in Table XIII.

The mean value of the equivalent temperature is 61*2° ♦ 57°

Kelvin. From equation 9 the brightness is 2.3 x 10”^ watts per square meter per square degree per cycle per second. A

spectrum for the galactic maxi nrum adjoining the Cygnus source

is shown in Figure 1*1*« From the spectrum the brightness and

equivalent temperature variations with frequency from 80 to

1*80 megacycles per second are

B ~ f-0«87 (20)

and

(21) iso GAIXCT/C' MAXZ/PfUH

AS~ At- £ W .A'kiL-J?a/r A.wj H,?r.rx>n/A as a - - - .

o. M

3 0 € 0. n o £ 5 0

2.5 2.6 TABLE XIII

THE GALACTIC MAXIMl ADJOINING THE CYGNUS EALIO SOUHCE

AT 250 MEGACYCLES PER SECOND

Date Equivalent Temperature

July 9, 1953 750° K July 10, 1953 590° X

July 1953 650° X

July 12, 1953 622° X

July 13, 1953 600° X

Mean value 642° £ 57° K /AC 7/t M4X//P16M S/%rC77?Wf /A/ C>&t€/S

XT' s & M t rr a , u p i c s *

z&razrzrzttirajim ix

0 5

SO € 0 l O O \ :-

2,5 123 The brightness variation with frequency, f-0«87^ approximately /*N O l the same as the frequency variation, f * , at the galactic maximum. It may, thus, be concluded that the relative distri­ bution of radio sources for the galaxy in the Cygnus region is

similar to the distribution of radio sources at the galactic

center. f. The Intensity of the Sun

Many observations have been made on the sun. In particular,

the abnormal variations, such as bursts and flares, have been

studied (16, 19 - 21). Of importance, also, is the intensity of the quiet sun.

At 250 megacycles per second it was shown in Chapter V,

that the equivalent diameter of the sun, assuming uniform

intensity distribution, is 1.1 degrees. Measurements on six

records with The Ohio State University radio telescope indicate

little variation in the intensity of the quiet sun. The

antenna temperature for the sun was found to be 3665 degrees

Kelvin. Observations by The Bureau of Standards on 167 megacycles per second of the sun's activity, indicated no

abnormal disturbances during the recording periods. For a

diameter of 1.1 degrees, from equation 29* Chapter VII, the equivalent sun's tenperature is 1814,000 degrees Kelvin. On the basis of the visual size of one-half of a degree for the diameter,

the equivalent sun's tenperature is 820,000 degrees Kelvin. The intensity for a diameter of 1.1 degrees is 5*65 x 10 watts per square meter per cycle per second. Other observers have measured

the equivalent temperature oi the quiet sun at other frequencies

for an assumed diameter of one-half of a degree. Tabulation of

the values are given by Van De Hulst (51). A curve of the quiet

sun's equivalent temperature at various frequencies for an

assumed diameter of one-half of a degree is shown in Figure u5»

The equivalent temperature of 0.82 x 10^ degrees Kelvin at 250 megacycles per second for a diameter of one-half of a degree

lies close to the curve, shown by the circle in Figure U5.

The actual distribution across the surface of the sun has

not been measured directly at wavelengths longer than 50

centimeters. The difficulty has been to obtain the resolution

necessary to distinguish variations in intensity for small

sectors of the surface. Christiansen, Yabsley, and Mills (38)

observed at 600 megacycles per second a nearly total eclipse of

the sun. The results indicate two possible distributions. One

conclusion, is that "limb-biightning" is present with half the

total radiation originating near or beyond the visible limb or

in the corona region. The alternative conclusion is that the

emission is from a disk of uniform apparent temperature having

1.3 times the diameter of the visible disk. Smerd (36) in a

theoretical discussion predicts "limb-brightning" due to high

corona temperatures• However, Stainer (39) did not find

"limb-brightning" at 500 megacycles per second. He, however, APPARENT TEMPERATURE ~ DEGREES KELVIN I01 10 DIAMETER DEGREE ONE-HALF SUNFOR PAET EPRTR O TE QUIET THE OF TEMPERATURE APPARENT 10' 3 0 1 5 0 0 0 100 50 20 10 5 2 WAVE LENGTH - LENGTH WAVECENTIMETERS yiOURS 46 yiOURS osu

0 0 5 125 126 concluded that one—third of the total radiation is from outside the visible disk.

Covington and Broten (52) have shown that ''limb-brightning** occurs at 10.3 centimeter wavelength. However, they conclude that ” limb-brightning*1 is not present at much longer wavelengths.

J'achin and Smith (53) have observed at 80 megacycles per second the Taurus radio source as the sun passes between it and the earth. The observations showed refraction and absorption of the radiation from the Taurus source to a distance greater than ten times the sun's visible diameter. A general conclusion is that radio radiation takes place in the sun's atmosphere outside the visible disk and with '•limb-brightning11 present for the higher frequencies, that is, above 2000 megacycles per second. SUMMARY I

g. SUMMARY OP EXPERIMENTAL INTENSITY MEASUREMENTS TTITH TEE OHIO STATE UNIVERSITY

RADIO TELESCOPE AT 250 MEGACYCLES PER SECOND

Section Radio Source Intensity or Preq. Range Frequency Equivalent Brightness for Spectrum Variation, f"x Source Temp. Mc/S. x Deg. Kelvin

b. Ca»»iopela(area- 0.38 x 10"22 w/a2/cps 80 - 250 1.50 3.5 x 10° 0*003 sq. deg.)

c« Cygnua(area- 0*00022 aq* deg*} 0.32 x 10~22 w/m2/cps 40 - 250 1.30 41.2 x 106

f. Sun (1.1 deg. diameter) 5*65 x 10~22 w/m2/cps 0.82 x 106

d* Maximum at Galactic Center 8.2 x 1 0 ^ 4 w/m2/sq deg/cpa 100 - 480 0.91 2320

e* Galaxy in Cygnus Region 2.3 x 10~24 w/m2/sq deg/cpB 80 - 480 0.87 642 1 2 8

APPENDIX

SECTION 1 - DISTRIBUTION OF INTENSITY FOR EXTENDED SOURCES

Extended sources which can be considered to have a uniform

Intensity distribution concentrated along the principal axis in right ascension have been discussed in Chapter IV. The antenna patterns were calculated for the extended sources. From the patterns the sun's equivalent radio diameter at 250 megacycles per second was determined in Chapter V.

A general problem in radio astronomy is the determination of the true distribution of intensity of a source from the observed distribution pattern. The integral equation for the observed patterns of extended sources, similar to equation 7, Chapter IV, is

(1) where g(P) « the observed Intensity at the point P

f(Q) • the true distribution of the source intensity

at the point Q

#(8) = the antenna pattern for a point source

6 * the angle between the radii to points P and Q,

The antenna pattern for a point source and the observed pattern for the extended source are known. By solving the Integral equation the true distribution f(Q) Is then obtained.

The solution of the Integral equation has been considered by 129

A. P. Calderon (54) who has discussed the problem ar.d expressed a theory as follows:

"In the theory of the radio telescope with rotational symmetry about its axis one encounters the following integral equation

where f and £ are functions defined on the spherical surface with

'’enter at 0, 8 is the angle between the radii OP and OQ,, and dQ denotes the element of area.

"This integral equation can be discussed easily an account of the following relationship. If Yn is a surface harmonic of degree n, ?m(x) *a tlje Legendre polynomial and r is the radius of the sphere then

(2)

This formula can be found in the literature (see for Instance,

Hobson, Spherical and. Ellipsoidal Harmonica, p. 145). Let now

f « 8 * Z % 7n (Q)

e(P) = ? T>n 7n*(P) O be the expansions of f and £ in surface harmonics Yn (Q^ and Yn*(P) denoting normalized harmonics of degree n , and 130 the expansion of 0 In Legendre polynomials. Then equations (1' and (2) give

D - — ■— ■ r211 ^ 2 a c (3) n 2n / 1 n 11

"This formula allows to discuss equation (1) completely and to find _f for any given g. Theorem: Given a quadratically integrable function 0 and a function g a necessary and sufficient condition in order that equation (1) have a solution jf of integrable square is that bn = 0 for all _n for which c„n ~ 0 and that

OP z *n n < 0 0 (4) I cn

A necessary and sufficient condition in order that the solution be unique is that cQ / 0 for all n* If

= I V T. (5) then

(6).» (54) f = 1 - r T» © a The form of the solution as given by Calderon is applicable for the expansion of the functions f and g in any set of orthogonal functions. In particular, for the cases considered herein, Fourier series are appropriate*

It is assumed that the functions f, g , and 0 can be expanded 131 into Fourier series. Thus, referring to Figure 17 let the true distribution be

<30 f(Q) - aQ / Z cos m©2 / d sin m©„ (2) ^ " I ^ where ©_, = © / A X/ the observed distribution be CO g(F) = b / Z b cos n© e sin n© (3) o n -, n n tnd the antenna pattern (which is eycnietrical) for a point source be Oo 55(A) s c 4- H c cos p a (4) p=i

Then

ft

The solution of the first integral is fT a c d©0 = 2 Tf a c (6) 0 0 2 0 0 I iT and the second Integral is Tf

J j 1 cp (co‘ p0 cos p8g / ®*n P® ®ln -TT (a^ cos jn02 ^ ®ln ^®2

s TrCa* cm cos m© J* dg, cB sin b0) (7) 132

Therefore,

/ f(e,0 0(a ) d9- - 2tta c / n X - (a cos m9 / d sin m0> 14, 4, 00 1DT71 •'^TT (8)

The integral is also equal to the observed pattern Thus,

S ~ ^ Z <*n coa nB ^ en sin nB^

= 2 w »0 °o* Tr^ cn co3 n9 0 ^ sin n0) (9) or equating term by term the coefficients of the true distribution are

a = b° , a = ^2— and cL = ~ ° 2Vc_'n “ ~tt ’ c_n “ ire. n

The necessary and sufficient condition that a solution fcr

the true distribution f exists is the same as in Calderon*s theorem, that is, b and e be zero for all n for which c_ is zero and that ' n n — n CD I L *n •n 2 I < o o (11) o ■ °n cn

The solution is applicable to symmetrical or unsymmetrical distributions of the source intensities.

A limitation in the solution for the true distribution is that of obtaining a sufficient number of terms in the series expansion

so that the series will be sufficiently convergent. As an example, a solution is found for the actual intensity distribution at 250 megacycles per second from the observed pattern of a constant 133 intensity source of angular width tv s 2 degrees. The calculated observed pattern 1b shown in Figure 19. The Fourier series for the antenna pattern of a point soorce at 250 megacycles per second is obtained graphically from Figure 11 by the 24—ordinate scheme (55) and is given in Table XIV* The Fourier series for the observed pattern of the extended source in Figure 19 is also obtained by the 24-ordinate method and 1b given in Table XIV. The range of 9 in Figures 11 and 19 is from —3° to /3°* The solution for the actual intensity distribution of the extended source calcu^ lated from equation 10 is also given in Table XIV* The Fourier series for the known true intensity distribution Is calculated and given In Table XIV*

From Table XIV the coefficients of the Fourier series to the fourth harmonic terms of the actual intensity distribution are in agreement. The coefficients of the higher harmonic terms have large errors because these coefficients result from the small differences of large quantities. A plot of the actual Intensity distribution and the Intensity distribution obtained from the first five terms of the Fourier series is shown in Figure 46* If the accuracy in determining the coefficients of the higher harmonic terms is improved, better agreement can be obtained between the two curves* The method discussed in this section is applicable for calculating the actual intensity distribution of an extended 1 3 4 source, If reasonable accuracy can be obtained in the determination of the coefficients of the Fourier series. TABLE XIV

COEFFICIENTS OP THE FOURIER SERIES

Y(x) * y0 / Z yn cos nx

y0 *1 y2 y3 y4 y5 y6 y 7 y 8 y9

1. Antenna pattern of 0.224 0.365 0.246 0.134 0.026 -0.001 0.C01 -0.003 C.C03 0.003 a point source

2* Observed pattern 0.360 0.485 0.162 0 -0.009 0.002 -0.001 0.001 -O.ooi 0.C01 of extended source

3. Calculated true 1.00 1.65 0.82 0 -0.45 -1.47 -o.ee -0.18 -0.23 0.10 distribution from (Relative values of coefficients) 1. and 2.

4. Known true 1.00 1.65 0.83 0 -0.41 -0.33 0 0.24 0.21 c distribution (Relative values of coefficients) - 4-

j .

1-

pALcmATO ipTwanrr juaipMBtnpcK ofjis; m —* ——------—---*—■'-!■ • i —— —— „--- ♦ I I ----- 1 I ■ . I I I SOtJHCK AjF 360 pBOACtbl^S pjsR

j&h£tilajr •xtept of urtiforjn ln tn m ilty »onr&»

TXJ±4as:ia$uTtxm

m h- - 4 APPENDIX

SECTION 2 - TME EQUIVALENT INTENSITY DISTRIBUTION OF A SPHERICAL SOURCE

Some r;--dio sources such as the sun are nearly spherical in shape and others may presumably be so. If the radio source is small in angular extent compared to the beam width of the antenna in declination, the intensity car be considered concentrated along the diameter of the source in right ascension. Consider a small spherical source whose radiation is from a uniform surface intensity. The eouivalent intensity distribution alone the diameter in right ascension will now be calculated. In Figure 47 the surface is divided into sections perpendicular to the diameter. The circumference of a section is

2Tra cos $ Cl) where a =■ radius of the sphere

0 * azimuth angle.

The surface area of the section on the sphere is

2TTa2 cos 0 A $ (2)

The increment, Ay, along the diameter is equal to

a cos 0 (3)

Therefore, the area of a section on the sphere as a function of A y is

2 tra A y (4) and is a constant. Thus, if the radiation of a sphere is from a uniform surface intensity, the equivalent intensity distribution 138 Z

a sin * a a* A y * a cos * A*

a * radius of sphere a cos * ■ radius of section 2na cos ♦ ■ circumference of section 2aa^ cos * a * ■ area of section on sphere surface 2na Ay » area of section on sphere surface na^ cos^ * u p • volume of section na^ cos * Ay ■ volume of section

DIAQHAM FOR DETERMINING EQUIVALENT INTENSITY

DISTRIBUTION OF A SPHERE

FIOUHS 47 139 along a diameter is a constant.

The radiation from a volume intensity distribution of a sphere is also considered. Assuming the radiation from any volume increment to be a constant, the equivalent Intensity distribution along a diameter will be calculated. From Figure 47 the radius of any section is

a cos 0 (5)

The volume of the section is

a2 cos2 0 (a & 0) (6)

The increment & y as a function of 0 is given in equation 3. The volume of a section as a function of Ay is

a2 cos 0 ay (7) If a sphere has a uniform volume intensity distribution, the equivalent intensity distribution along a diameter varies as the cos 0•

For a uniform intensity distribution from a spherical shell the variation of the equivalent distribution along a diameter lies between the two cases considered. 140 APPENDIX

SECTION 3 - CORRECTION TOR TIME BELAY CIRCUIT

To Increase the output tine constant of the receiver, a time

delay circuit is Introduced following the phase sensitive rectifier*

In so doing a lower noise level can he detected as shewn by equation

2, Chapter IX, which increases the sensitivity of the receiver.

However, the time delay circuit changes the wave shape and the magiitude of the observed pattern. The distortion of the wave shape

is a function of the null point beam width of the pattern as well

as the resistance-capacitance combination. The circuit is shown in

Eigure 48a. The equivalent circuit for the 30-cycle component of

the signal is shown in Figure 48b. The circuit can be further reduced

to the diagram in Figure 48c. The voltage applied to the R—C network

is proportional to the antenna signal at any instant. Since the

superheterodyne receiver gives square law detection, a good ap­

proximation to the antenna intensity pattern (voltage variation to

E*-C network) for a point source Is E(1 - coswt). Thus, the half

power angular width is twice the null power angular width. The

differential circuit equations are

E(1 - cos Uft) - 128 x 103 ij - 54 x 103 ig (1) and

(3) PHOTOCELLS =37K (b) INPUT 6 ACE UPT IE OSAT CIRCUIT CONSTANT TIME OUTPUT 6AC5 27K 27 K W W ■ „ V V V ' 13 9 K I39K i riOUBX 46 riOUBX Id) 27 K 2 7 K ? s < i L 74K -A/VW v • W V I 3 K 9 139 K >1 N

K s 4 3 T c (C) p 1 1 i

278 K 278 AMPL D.C. 141 143

The so lutio n fo r is

2 ~ t l„ = 1.367 I 10"6 £_ I e " - l.se’ x 10"6 S cos b t 4 0) Z2 1 (2) idlers R • 309,200 ohms

Z2 - P.2 / X2

X - J_ Ul C

0 = tan "1 (X/R)

Solving for the voltage across the capacitor which Is the Input to the direct-coupled amplifier gives

ec * 0.420E £ 1 - (X/Z) cosjwt / (0 - y-)} - (R2/ ^ ) e " &C (4)

This equation is valid for the range

0 * ujt 2 tr (5)

Since the period for the signal is from six to twenty minutes, and generally, X*R, the exponential term decays rapidly. The maximum value of voltage occurs at

cot / $ -ILsTT or u>t m — $ (6)

Without the delay circuit the maximum rould occur at u»t * TT.

The angular shift in the maximum caused by the delay circuit is

S ( tot) - jS = “ tan"*1 (X/R) « cot"1 (x /r) *» c o t"1 (l/*»CR) (?) The time delay is

t d • (1 /*«) c o t"1 (1 /m iCR) (8) 143

From eq^iatior 4 the peak value of the voltage is

C®c'm a x * °*420 E f1 ^ {X/Z)J C9) as coatpared to 2E for the input voltage to the delay eirduit. The half power beam width measurement is the time interval between points of l/£ /(X/zV| of the magnitude of the peak. The maximum value is dependent on the beam width, and it is slowly varying.

The values of capacitances used were 78.7 and 240 microfarads.

The half power "beam width for the antenna in right ascension is

1.26 degrees or (4.95/ cosS ) minutes, where S is the angle of declination of the point source. A comparison of the shift in the peak is listed in Table XT. The shift in the peak Is almost the

R—C time constant. The differences increase with increasing capacitance or decreasing period. TABLE XV

CORRECTION FOR TIME RELAY CIRCUIT

Capacitance Time Between Null R-C Time Constant Time Correction for Maximum Points Point of Pattern, Equation 8

78.7 microfarads 11 minutes 24.3 seconds 23.9 seconds

78.7 microfarads 22 minutes 34.3 seconds 24.2 seconds

240.0 microfarads 11 minutes 73.3 seconds 64.5 seconds

240.0 microfarads 22 minutes 73.9 seconds 71.4 seconds 146

APPENDIX

SECTION 4 - CABLE ATTENUATION BETWEEN ANTE1UIA AND HECEITER

The attenuation of thr antenna signal by the cables linking the antenna to the receiver vast be calcvJLated for accurate determination of equivalent antenna temperatures. Three types or cables are used in series to connect the antenna to the receiver. The two higher less cables are used for short runs because of convenience in har.I’lirg.

The attenuate or per hundred feet of cable is supplied by the manufacturer. The cable types, lengths, and attenuations are shown in Table XVT. TABLE XVI

CABLE ATTENUATIONS AT 250 IFCACYCLES PET. SECOND

Type Length Attenuation

RG—6o/U 9 1/3 ft. 0.298 db.

RG-I7/U 80 ft. 1.250 db.

AG-8/U 21 ft. 0.771 db.

Total 2.319 db.

Thus, the portion of the antenna porrer, Pant , which reaches the input of the receiver i3

2.319 - 10 log (1) p rec and

p a n t “ l*30o P rec (2) 146

APPENDIX

SECTION 5 - IPXqUENCY CHECK BY MEANS C7 THE SUN'S PATTERN

With the spacing in right ascension between elements of the array greater than one wavelength at 250 megacycles per second, a

large minor lobe for the in-phase pattern appears at © • 37.2° in

Figure 10. The large minor lobe is also found at the same angle ©

for extended sources. The results of the records taken on the sun

to obtain the minor lobe spacings from the major lobe in right ascension is given in Table XVII. The mean value of the angle is

37.2° £ 0.7°.

The measured position of the large minor lobe agrees with the calculated position* From the measurements the frequency is 250 megacycles per second with a variation of less than two per cent* 147

TAELS XVIT

MINOR LOBE SPA CINQS OF THE SKI'S PATTERN

Late Mi’nor Lobe Preceding Minor Lobe Subsequent

Major Lobe to Major Lobe

-Jure 20, 1953 - 37.2° June 21, 1953 36.C° 37.6°

June 22, 1953 37.2° -

June 29, 1953 - 36.4°

July 3, 1953 37.5° 38.8°

July 4, 1953 37.0° 37.0°

July 5, 1953 38.9° 37.2°

Mean value 37.2° £ 0.7° 148

BIBLIOGRAPHY

1. Jansky, K. G. "Directional Studies of Atmospherics at High

Frequencies." Proc. I.R.E., 20 (1932), p* 1920.

2. Jansky, K. G. "Electrical Disturbances Apparently of Bxtra—

Terrestrial Origin." Proc. I.R.g., 21 (1933), p. 1387.

3* Reber, Q. "Cosmic Static." Proc. I.R.3S., 28 (1940), p. 68.

4. Reber, G. "Cosmic Static." Proc. I.R.E., 30 (1942), p.367.

5. Reber, G. "Cosmic Static." Astrophysics Jour., 100 (1944), p. 279.

6. Reber, G. "Solar Radiation at 480 Mc/S." Nature, 158 (1946),

p. 945.

7. Reber, G. "Cosmic Static." Proc. I.R.E., 36 (1948), p. 1215.

8. Hey, J.S., Parsons, S. J., and Phillips, J.W. "Fluctuations in

Cosmic Radiation at Radio-Frequencies." Nature, 158 (1946), p. 234.

9. Bolton, J.G., and Stanley, G.J. "The Variable Source of Radio-

Frequency Radiation in the Constellation of Cygnus." Nature,

161 (1948), p. 312.

10. Bolton, J.G. "Discrete Sources of Galactic Radio—Frequency Noise."

Nature, 162 (1948), p. 141.

11. Ryle, U., and Smith, F.G. "A New Intense Source of Radio-

Frequency Radiation in the Constellation of Cassiopeia."

Nature. 162 (1948), p. 462.

12. Bolton, J.G., Stanley, G.J., and Slee, O.B. "Positions of Three

Discrete Sources of Galactic Radio—Frequency Radiation." Nature, 149

164 (1949), p. 101.

13. Stanley, G.J., and Slee, O.B. H Galactic Had! at Ion at Radio-

Frequencies * II. Discrete Sources." Aust. Jour. Sci. Rea.,

3 Ser. A (1950), p. 234.

14. Ryle, M., Smith, F.G., and Elsinore, B. "A Preliminary Survey of

the Radio Stars in the Northern Hemisphere." Mon. Not. Roy. Astro.

Soc., 110 (1950), p. 508.

15. Brown, R.H., and Hazard, C. "Radio Emission from the Andromeda

Nebula." Mon. Not. Roy. Astro. Soc., Ill (1951), p. 357.

16. Ryle, M., and Vonberg, D.D. "Solar Radiation on 175 Mc/s."

Nature, 158 (1946), p. 339.

17. Fawsey, J.L. , Payne-Scott, R., and McCready, L. "Radio-Frequency

Energy from the Sun." Nature, 157 (1946), p. 158.

18. McCready, L., Pawsey, J.L., and Payne-Scott, R. "Solar Radiation

at Radio-Frequencies and Its Relation to Sunspots." Proc. Roy.

Soc., 190 Ser. A (1947), p. 357.

19. Covington, A.E. "Microwave Solar Noise Observations During the

Partial Eclipse of November 23, 1946." Nature, 159 (1947), p. 405.

20. Ryle, U., and Vonberg, D.D. "Relation Between the Intensity of

Solar Radiation on 175 Mc/S. and 80 Mo/s." Nature, 160 (1947),

p. 157.

21. Ryle, M-, and Vonberg, D.D. "Investigations of Radio-Frequency

Radiation from the Sun." Proc. Roy. Soc. London, 193 Ser. A

(1948), p. 98. ICO 22. Kraus, J.D. "The Ohio State University Radio Telescope." Shy

and Telescope, (April, 1953), p. 157.

23. Kraus, J.D., and Matt, S."Galactic Survey and Discrete Source

Observations at 250 Megacycles." U.R.S.I. conference, Washington,

D.C., April 26-30, 1953.

24. Ksiazek, 5. "Analysis and Application of a System for Receiving

Electromagnetic Radiation of Extraterrestrial Origin." master's

thesis, The Ohio State University, 1953.

25. Dicke, R.H. "Thermal Radiation at Microwave Frequencies."

Rev. Sci. Instr., 17 (1946), p. 263.

26. Kraus, J.D. Antennas. New York: McGraw-Hill Book Co., Inc.,

1950, p. 173.

27. Ibid., p. 67.

28. Ibid., p. 76.

29. Ibid., p. 60.

30. Dwight, H.B. Tables of Integrals and Other Mathematical Data.

New York: MacMillan Co., 1947, p. 73.

31. Ibid., p. 76.

32. Peirce, B.O. A Short Table of Integrals. Boston: Ginn and Co.,

1929, p. 50.

33. Ibid., p. 50.

34. Whittaker, E., and Robinson, G. The Calculus of Observations.

London: Blackie and Son, Lim. . 1944, p. 132.

35. Peirce, op. cit.f p. 40.

36. Smerd, S-F. "Radio-Frequency Radiation from the Qjiiet Sun."

4 151

Aust. Jour. Sci. Res., 3 Ser.A (1950), p. 34.

37. Ryle, M. "The Significance of the Observation of Intense Radio-

Frequency Emission from the Sun." Proc. Fhy. Soc., 62 Ser. A

(1949), p. 483.

38. Christiansen, W.N., Yabsley, D.E., and Mills, B.H. "Eclipse

Observations of Solar Radiation at a Wave-Length of 50 Cm."

Kature, 164 (1949), p. 569.

39. Stanier, H.H. "Distribution of Radiation from the Undisturbed

Sun at a Wavelength of 60 Cm." Nature, 165 (1950), p. 354.

40. Machi’i, K.E. "Distribution of Radiation Across the Solar Disk

at a Frequency of 81.5 Mc/S." Mature, 167 (1951), p.889.

41. Goerke, V.H. personal communication, National Bureau of

Standards, Boulder, Colorado, 1953.

42. Baade, W., conference paper, National Acadeiqy of Science,

Washington, D.C., April 29, 1953.

43. Broim R.H., Jennison, R.C., and Das Gupta, U.K. "Apparent Angular

Sizes of Discrete Radio Sources." Nature. 170 (1952), p. 1061.

44. Burgees, R.S. “Noise in Receiving Aerial Systems^' Proc. Physical

Soc., 53 (1941), p. 293.

45. Kraua, op. cit., p. 53.

46. Kraus, op. cit., p. 24.

47. Bolton, J.G., and Westfold, K.C. "Galactic Radiation at Radio

Frequencies. I, 100 Mc/s. Survey." Aust. Jour. Sci. Res., 3 Ser* A (1950), p. 19. 153

48. Allen, C-W*, and Gum, C-S* "Survey of Galactic Radio-Noise at

200 Mc/s." Aust. Jour. Sci. Res., 5 Ser. A (1950), p. 234.

49. Bolton, J.G., and Westfold, X.G. "Galactic Radiation at Radio

Frequencies. III. Galactic Structure." Aust. Jour. Sci. Res.,

5 Ser. A (1950), p . 251.

50. Hey, J.S., Parsons, S.J., and Phillips, J.T7. "An Investigation

of Galactic Radiation in the Radio Spectrum." Proc. Roy. Soc.,

192 Ser. A (1948), p. 425.

51. Van De Hulst, H.C. A Course in Radio Astronomy. Leiden,

Netherlands: Leiden Observatory, 1951, Chap. VI.

52. Covington, A.E. and Broten, N.W. "Some Characteristics of Solar

Radio Emissive Regions at a Wavelength of 10.3 Centimeters."

U.R.S.I. conference paper, Ottawa, Canada, October 5, 1953.

53. Machin, K.E. and Smith, F.G. "Occultation of a Radio Star by

Solar Corona." Nature, 170 (1952), p. 319.

54. Calderon, A.P. "An Integral Equation in the Theory of the

Radio Telescope." private communication, 1953.

55. Pipes, L.A. Applied Mathematics for Engineers and Physicists.

New York: McGraw-Hill Book Co., Inc., 1946, p. 58.

56. Whittaker and Robinson, op. cit., p. 273. 153

AUTOBIOGRAPHY

I, Sol Matt, was born in Cleveland, Ohio, September 3, 1923*

I received my secondary school education in the public schools of the city of Cleveland Heights, Ohio. My undergraduate training was obtained at Ohio University, from which I received the degree

Bachelor of Science in 19l4i* After military service I was appointed an instructor in the Department of Electrical Engineering and in the Department of Mechanics at Ohio University and taught there for

one academic year, 19U6-U7* I then began graduate studies at the

California Institute of Technology from which I received the degree

Master of Science in 19U8. I remained at the Institute for two years as a research assistant* I pursued further graduate studies in 1990 at The Ohio State University in the Department of Electrical Engi­ neering* In 19911 received an appointment as a research assistant for one year on the radio telescope project under the direction of

Dr. John D* Kraus* The following year I received an appointment as an instructor in the Department of Electrical Engineering at The

Ohio State University.