NBSIR 74-382

A STUDY OF THE MEASUREMENT

OF GA USING CASSIOPEIA A

D.F. Wait

W.C. Daywitt

M. Kanda

C.K.S. Miller

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

June 1974

Prepared for

Advanced Concepts Office

United States Army Communications Command

Fort Huachuca, Arizona 85613

NBSIR 74-382

A STUDY OF THE MEASUREMENT

OF G/T USING CASSIOPEIA A

D.F. Wait

W.C. Daywitt

M. Kanda

C.K.S. Miller

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

June 1974

Prepared for

Advanced Concepts Office

United States Army Communications Command

Fort Huachuca, Arizona 85613

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent. Secretary

NATIONAL BUREAU OF STANDARDS Richard W Roberts Director

FOREWORD

An important element of the mission of the Advanced Concepts Office of Headquarters, U.S. Army

Communications Command, is to conduct studies where

by scientific knowledge can be utilized in the solu

tion of current or foreseen problems affecting

USACC's operational capabilities. This report

investigates the problem of expeditiously measuring

the G/T parameter of a satellite communications

earth terminal as a check on the possible antennareceiver degradation of portable ground stations

after transfer from one site to another, and to

provide an overall performance test for the acceptance of new ground stations.

This study was conducted by the Noise and

Interference Section of the Electromagnetics Division of the National Bureau of Standards, Boulder,

Colorado, under ACOM Project Order SCC-411-73.

Mr. D.D. Taylor of USA-ACC-POA was the project

monitor supervising this study.

iii
CONTENTS

Page

1. INTRODUCTION 1

1.1 The Concept of, and a Working Definition for

G/X 4

1.2 The Relationship of G/T to C/n and ERP 7

1.3 The Measurement of G/T -- Advantages and Disadvantages of Using Radio Stars 9

1.4 A Brief Outline of the Radio Star Method of

Measuring G/T 11

1.5 A Brief Description of Some Important Radio

Stars 12

2. REVIEW OF THE PROPERTIES OF CAS A FROM THE LITERATURE 16

2.1 Early Measurements 16

2.2 The Location of Cas A 16

2.2.1 The Equatorial and Galactic Coordinate

- System 16

2.2.2 The Precession of the Earth's Axis 20

2.2.3 Cas A 20

2.3 Flux Density and Spectral Index 22

2.3.1 Brightness, Brightness Temperature, and

Flux Density 22

2.3.2 Flux Density and Spectral Index of Cas A 26

2.4 Secular Decay 29

2.4.1 Decay Rate 29

2.4.2 Some Measured Values of R 34

2.5 Polarization 35

2.5.1 Polarization and Faraday Rotation 35

2.5.2 Measured Polarization of Cas A 37

2.6 High Resolution Maps 39

2.7 Cosmic Background Radiation 46

2.7.1 Nature of the Cosmic Radio Background 47

- 2.7.2 Cosmic Background Contribution to the

System Noise Temperature 53

iv
CONTENTS (Continued)

Page

3. THE ATMOSPHERIC EFFECTS IN VIEWING CAS A 61

4. THE MEASUREMENT OF POWER GAIN OF A LARGE GROUND

ANTENNA FOR CALIBRATING COSMIC RADIO STARS 65

4.1 Introduction 65

4.2 Calibration of the Standard Gain Antenna by Use

o£ the Generalized Three -Ant enna Extrapolation

Technique 67

4.2.1 Introduction 67

4.2.2 Antenna Scattering Matrix Analysis 68

4.2.3 Generalized Three Antenna Measurement

Technique 72

4.2.4 Extrapolation Technique 78

4.2.5 Accuracy Consideration 80

A. Error in Mismatch Factors 82

B. Attenuator Error 83

C. Receiver Nonlinearity and Gain

Instability 83

D. Atmospheric Loss Uncertainty 84

E. Range Misalignment 84

F. Distance Inaccuracy 88

4.2.6 Summary and Concluding Remarks 88

4.3 The Calibration of a Large Ground Antenna by

the Gain Comparison Method 97

4.3.1 Introduction 97

4.3.2 Theory 98

4.3.3 Accuracy Consideration 103

A. The Power Gain of a Standard Antenna 103

B. Frequency Instability 103

C. Effective Radiated Power (ERP) 104

D. Path Loss 104

E. Polarization Mismatch 105

F. Tracking Accuracy 106

V
CONTENTS [Continued)

Page

G. Waveguide Feed Loss Uncertainty 108

H. Uncertainty in Power Ratio

Measurement 111

I. Uncertainty Due to Receiver Gain Instability and Nonlinearity 111

J. Uncertainty in Antenna System Noise

Temperature 116

K. Error Due to Change in Effective

Input Noise Temperature, Bandwidth

and Ambient Temperature 117

4.3.4 Results and Concluding Remarks 118

4.4 Summary and Conclusions 126

5. THE ACCURACY OF MEASURING THE FLUX DENSITY OF CAS A- 134

6. THE ACCURACY OF MEASURING G/T 138

6.1 The Measurement of G/T Using Gas A 138

6.2 Cas A Method of Measuring G/T Compared to the

Gain/Noise Temperature Method 138

7. G/T MEASUREMENT REPEATABILITY 146

8. CONCLUSIONS 149

8.1 The Accuracy of Measuring G/T 149

8.2 The Accuracy of the Cas A Flux Densities Cited

in the Literature 151

8.3 Proposed Future Efforts 152

8.3.1 Evaluation of the Literature 152

8.3.2 Stars Other than Cas A for G/T

Measurements 152

8.3.3 Independent Methods for Measurement of

G/T 153

8.3.4 Definitions of and Alternatives to G/T-- 153

8.3.5 Uncertainties in Antenna Gain

Measurements 153

8.3.6 Radio Star Method of Measuring G and T-- 154

REFERENCES 155

vi
CONTENTS CContinued)

Page

APPENDIX A: COMMENTS ON THE INTRODUCTORY SECTIONS-- 162

APPENDIX B: COMPUTER PRINTOUT AND PROGRAMS 164

B.l A Printout for the Practicable Accuracy of

G/T 165

B. 2 The BASIC Program for the Computation of

the Errors in the Measurement of G/T Using

Cas A 177

APPENDIX C: DETERMINATION OF ANTENNA AND RECEIVER

PARAMETERS BY NOISE -ADDING TECHNIQUES-- 183

C. l The Measurement of Antenna Parameters 185

C.2 The Measurement of System Noise

Temperature and G/T 186

vii
LIST OF ILLUSTRATIONS

Figure Page

1-1 Pictorial diagram of the system as defined for

the purpose of this report 5

1-2 Pictorial diagram for defining the carrier-tonoise density ratio 8

1- 3 The flux density spectrum of several radio stars-- 14

2- 1 The equatorial and galactic coordinate systems

superimposed onto the celestial sphere 18

2-2 The position of the radio source Cas A relative

to the visible stars in the constellation of

Cassiopeia 21

2-3 An artist's sketch of the position of the sun, and

the directions to Cas A, Tau A, and Cyg A relative

to the Milky Way Galaxy 2 3

2-4 Brightness B of an elemental radiating surface dA- 24

2-5 Elemental radiating surface dA on the celestial

surface 24

2-6 The flux density of Cas A around 7 GHz 28

2-7 Decay curve of the Cas A flux density as calculated from the shell model 30

2-8 Decay curve of the Cas A flux density showing the

relation between the differential and average

decay ratio 32

2-9 Hypothetical position angle curve for the linearly

polarized flux from Cas A 38

2-10 Brightness temperature contour map of Cas A (Epoch

AD 1950.0, 5.0 GHz). (Courtesy of Monthly Notices

of the Royal Astronomical Society , Vol . 151

,

No. 1, p. 112 , 1970) 40

2-11 Brightness temperature contour map of Cas A (Epoch

1968.4, 1.4 GHz) showing the variation of the

spectral index across the source. (After Monthly

Notices of the Royal Astronomical Society , Vol. 151, No. 1, p. 114 , 1970) 42

viii
LIST OF ILLUSTRATIONS (Continued)

Figure Page

2-12 Brightness temperature contour map o£ Cas A (Epoch

AD 1966.8, 19.4 GHz) showing (a) the brightness

temperature, (b) the linearly polarized component

of (a) amplified 20 times. (Courtesy of Astro - physical Journal , Vol. 151, p. 56, 1968; C.H.

Mayer and I. P. Hollinger; University of Chicago

Press) 43

2-13 Brightness temperature contour map of Cas A (Epoch

1950.0, 5.0 GHz) showing the distribution of

polarized emission across the source with the

average position angle of the electric vectors

superimposed. (After Monthly Notices of the

Royal Astronomical Society , Vol. 151, No. 1,

p. 116 , 19 70) 44

2-14 Mean brightness temperatue profile from the center

of Cas A outward (Epoch AD 19 50.0, 5.0 GHz).

(After Monthly Notices of the Royal Astronomical

Society , Vol. 151, No. 1, p. 118 , 1970) 4

2-15 The cosmic radio sky at 250 MHz. (After Sky and

Telescope , Vol. 16, p. 160 , 1957) 48

2-16 Brightness spectrum of the continuous cosmic

radiation as deduced from the literature 52

2-17 Cosmic radio background at 400 MHz. (After Monthly

Notices of the Royal Astronomical Society , Vol

124, No. 1, p. 74A, 1962) 54

2-18 Cosmic radio background at 960 MHz. (After

Publications of the Astronomical Society of the

Pacific , Vol. 72, No. 428 , p. 336 , I960) 55

2-19 Cosmic radio background at 1.4 GHz. (After

Publications of the National Radio Astronomy

Observatory , Vol. 1, No. 3, p. 55 , 1961)---- 56

2-20 Cosmic radio background at 3.2 GHz. (After Monthly

Notices of the Royal Astronomical Society , Vol.

129, No. 2, p. 166 , 1965) 57

2-21 Hypothetical cosmic radio background at 1.4 GHz

with effect of Cas A removed 59

ix
LIST OF ILLUSTRATIONS [Continued)

Figure Page

4-1 Antenna in the measurement coordinate system 69

4-2 Schematic o£ two antennas oriented for measurement 74

4-3 Measured data, 5 -term polynominal fit, and residuals for x-band standard horn (frequency = 7.2 5

GHz, antenna power gain 2 3 dB, major aperture

dimension of antenna = 2 3.5 cm) 81

4-4 Error in the measured antenna power gain due to

receiver non-linearity (frequency = 7.25 GHz) 85

4-5 Atmospheric attenuation versus frequency (courtesy

of Bean and Button) 86

4-6 Error in the measured antenna power gain due to

atmospheric loss uncertainty (frequency = 7.25 GHz) 87

4-7 Error in the measured antenna power gain due to

range misalignment (frequency = 7.25 GHz) 89

4-8 Error in the measured antenna power gain due to

distance uncertainty (frequency = 5 to 10 GHz,

antenna power gain = 20 to 5 0 dB, major aperture

dimension of antenna = 0.5 to 10 m) 90

4-9 Accumulated error in the measured power gain of

the generalized three -antenna extrapolation method

(frequency = 7.25 GHz) 92

4-10 Linear error accumulation for the measured power

gain of the standard antenna using the generalized

three- antenna extrapolation method (major aperture

dimension of antenna = 23.5 cm) 93

4-11 Quadrature error accumulation for the measured

power gain of the standard antenna using the

generalized three-antenna extrapolation method

(frequency = 7.2 5 GHz) 95

4-12 Quadrature error accumulation for the measured

power gain of the standard antenna using the

generalized three-antenna extrapolation method

(major aperture dimension of antenna = 23.5 cm) 96

X
LIST OF ILLUSTRATIONS (Continued)

Figure Page

4-13 Schematic for experimental gain comparison method- 99

4-14 Average power gain loss as a function of ratio of

tracking error to half power bandwidth 109

4-15 Error in the antenna power gain due to tracking

inaccuracy (frequency = 7.25 GHz, tracking inaccuracy = 5 seconds of arc, rms) 110

4-16 Error in the antenna power gain due to uncertainty

in Y = P]^/P3 112

4-17 Error in the antenna power gain due to uncertainty

in Z = P2/P4 113

4-18 Error in the antenna power gain due to uncertainty

in g2 114

4-19 Error in the antenna power gain due to uncertainty

in g^ 115

4-20 Linear error accumulation for the power gain of a large microwave antenna using the gain comparison

method (frequency = 7.25 GHz, standard antenna

gain = 30 dB nominal, effective radiated power = 10 dBW nominal) 119

4-21 Linear error accumulation for the power gain of a large microwave antenna using the gain comparison

method (frequency = 7.25 GHz, standard antenna

gain = 40 dB nominal, effective radiated power = 10 dBW nominal) 121

4-22 Linear error accumulation for the power gain of

the large microwave antenna using the gain

comparison method (frequency = 7.25 GHz, standard

antenna gain = 50 dB nominal, effective radiated

power = 10 dBW nominal) 122

4-23 Linear error accumulation for the power gain of

the large microwave antenna using the gain comparison method (frequency = 7.25 GHz, unknown

antenna gain = 60 dB nominal, effective radiated

power = 10 dBW nominal) 123

xi
LIST OF ILLUSTRATIONS (Continued)

Figure , Page

4-24 Linear error accumulation for the power gain of

the large microwave antenna using the gain comparison method (frequency = 7.2 5 GHz, unknown

antenna gain = 40 dB nominal, effective radiated

power = 10 dBW nominal) 124

4-25 Quadrature error accumulation for the power gain

of the large microwave antenna using the gain

comparison method (frequency = 7.25 GHz, effective radiated power = 10 dBW nominal) 125

4-26 Linear error accumulation for the power gain of

the large microwave antenna using the gain comparison method (frequency = 7.25 GHz, standard

antenna gain = 30 dB nominal, effective radiated

power = 30 dBW nominal) 127

4-27 Linear error accumulation for the power gain of

the large microwave antenna using the gain comparison method (frequency = 7,25 GHz, standard

antenna gain = 40 dB nominal, effective radiated

power = 30 dBW nominal) 128

4-28 Linear error accumulation for the power gain of

the large microwave antenna using the gain comparison method (frequency = 7.25 GHz, standard

antenna gain = 50 dB nominal, effective radiated

power = 30 dBW nominal) 129

4-29 Linear error accumulation for the power gain of

the large microwave antenna using the gain comparison method (frequency = 7.25 GHz, unknown

antenna gain = 60 dB nominal, effective radiated

power = 30 dBW nominal) 130

4-30 Linear error accumulation for the power gain of

the large microwave antenna using the gain comparison method (frequency = 7.25 GHz, unknown

antenna gain = 70 dB nominal, effective radiated

power = 30 dBW nominal) 131

4-31 Quadrature error accumulation for the power gain

of the large microwave antenna using the gain

comparison method (frequency = 7.25 GHz, effective radiated power = 30 dBW nominal) 132

xii
LIST OF ILLUSTRATIONS (Continued)

Figure Page

5- 1 Practicable and low bound errors in the measurement of the flux density of Cas A 135

6- 1 Practicable error in the measurement of G/T using

Cas A 139

6- 2 Practicable and lower bound errors in the measurement of G/T using Cas A 141

7- 1 G/T measurement repeatability versus frequency 148

C-1 Block diagram of the noise adding technique 184

xiii
I

I

I
A STUDY OF THE MEASUREMENT OF G/T USING

CASSIOPEIA A

This report describes a study intended to estimate the best possible accuracy of measuring the

ratio G/T (system gain to system noise temperature)

of a satellite communication ground station using

the radio star Cassiopeia A (Cas A) . The concept of

G/T and its measurement using a radio star is briefly

discussed. Results of an extensive literature search

are presented, summarizing the properties of Cas A

and its vicinity described by radio astronomers in

order to utilize this information to assess the accuracy of a G/T measurement. Consideration is given

to atmospheric effects upon a G/T measurement using

Cas A based on information available in the literature. A detailed analysis of errors for gain measurements of large ground antennas , which includes

the calibration of a standard gain antenna and the

transfer of this calibration to the large antenna,

is provided to validate radio star flux data since

this analysis is not available in the literature.

The results of these efforts are utilized to show

that the best possible accuracy of a G/T measurement

for a ground station (with practical and reasonable

specifications) having a 60 ft. diameter antenna is

in the neighborhood of ± 0.25 dB

Key words: Accuracy; antenna; calibration,

Cassiopeia A; G/T; star flux.

1. INTRODUCTION

This report describes a study that was undertaken to

estimate the best possible accuracy of measuring the ratio

G/T (gain/temperature) of a satellite communication ground

station using the radio star Cassiopeia A (Cas A) . The study

included: an extensive literature search concerning those
properties of Cas A and atmospheric attenuation relevant to

the G/T measurement; an estimate of the best possible accuracy of calibrating the gain of large ground station receiving antennas; an estimate of the best possible accuracy

in the flux density measurement of Cas A; and an estimate of

the best possible accuracy of measuring G/T.

The purpose for the determination of the best possibl

G/T accuracy was to obtain a basis for deciding whether the

measurement of G/T using Cas A could be sufficiently accurate

to justify its use in the following areas: to check on the

possible antenna-receiver degradation of portable ground

stations after transfer from one site to another; to provide

an overall performance test for the acceptance approval of

new satellite communication ground stations; and to provide

a means for building a history of ground station performance

to ascertain the degree of reduction possible in present

performance safety margins to gain a corresponding reduction

in overall system costs.

The reason that G/T is an important parameter is that

G/T, along with satellite ERP, determines the input signalto-noise ratio of the satellite - ground station communication

system. It is therefore intimately related to the system

output performance measurands such as the output signal-tonoise ratio of an analog system or the bit error rate of a digital system, and the channel capacity or upper bound to

reliable information transfer rate through the system.

This study shows that under certain conditions the

direct measurement of the G/T ratio using Cas A can be performed nearly as accurately as measuring G and T separately

and calculating their ratio. Furthermore, where the flux

density of Cas A is available, the accuracy of the direct

2
measurement of G/T using Gas A is much easier to realize

than the separate measurements of G and T. The study also

indicates that accuracies for antenna gain measurements, flux

density measurements, and G/T measurements reported in the

literature are often significantly overestimated.

This study was performed for the Advanced Concepts Office,

ACOM Headquarters, Fort Huachuca, Arizona, by the Noise and

Interference Section of the Electromagnetics Division of the

National Bureau of Standards; it is a follow-up effort by the

Noise and Interference Section of a G/T measurement project

begun at Camp Roberts, California, during June 19 72.

The report consists of eight sections and three appendices. Section 1 is of an introductory nature, describing

the reasons for the study, the concept of G/T and its measurement using a specific radio star, and the properties of

some other intense radio stars.

Section 2 presents the results of an extensive literature

search into the properties of Cas A relevant to the measurement of G/T and raises some questions apparently overlooked

in a large part of the literature.

Section 3 presents results of a literature search related to the atmospheric effect upon radio measurements of

Cas A. Although the available time did not allow an exhaustive study of this literature, some important effects are

emphasized that have been considered by only a few authors.

Section 4 presents a detailed analysis of errors for

the gain measurement of large ground antennas, and covers the

calibration of the standard gain horn used in the measurement,'

and the transfer of this calibration to the larger antenna.

This section is fairly extensive because much of the material

is new and has not been documented in the open literature.

3
Sections 5, 6, 7, and 8 present the results of an

analysis of the accuracy of the flux density measurement

of Cas A, the potential accuracy and precision of measuring

G/T, and the conclusions.

1 . 1 The Concept of, and a Working Definition for G/T

The ratio G/T is a figure of merit used to indicate the

sensitivity of the ground station antenna and receiver in a satellite communication system. The higher the ratio, the

more easily the ground station can detect a weak satellite

signal. From what follows, it can be seen that this measure

of sensitivity includes not only the effects of noise generated

in the ground station itself, but also the effects of noise

generated in the entire environment, terrestrial and cosmic,

in which the ground station antenna-receiver is immersed.

For the purpose of defining this figure of merit the

communication system is assumed to consist of those components

appearing in figure 1-1, in which the system is considered to

be functioning in its receive mode. It is clear from this

figure that the system noise includes not only the circuit

noise generated in the antenna and receiver, but noise from

cosmic and terrestrial (including atmospheric and man-made)

sources also. This system noise is characterized by a system

noise temperature [1] with a magnitude equal to the average

noise power divided by the product of Boltzmann's constant and

the limiting bandwidth of the system. The system noise

temperature can be referred to any point in the system, T-j^

,

T^ , and T^ being the system noise temperature as referred to

ports 1, 2, and 3 respectively. T-j^ is the sum of the antenna

noise temperature [2] and the effective input noise temperature [1] of the receiver. G. is the on-axis power gain of

4
o

m

•H

6

0

M

IT)

o

•M

5hO

Ph

CD

5-1

03 +->

oJ O

H

t/) i-H O

a, H 5-1 5h P

O CL, -MO <U •H ^

Pi -M

0

5-1

•H
the antenna [2] and characterizes the system gain from the

far field of the antenna to the antenna output port.

is the system gain from the far field of the antenna to

port 2, and is defined as times the available power gain

of the low noise amplifier (LNA) . is similarly defined

as times the available power gain (loss) of the waveguide

feed.

The ratio G/T has the same numerical value at any of

the ports 1, 2, or 3. That is

T3

In other words, theory predicts that G/T could be determined

at any one of these three ports with the same results

.

Therefore, G/T could be referenced to any of these ports

and the same measure of system performance would result,

indicating that the port at which G/T is defined is somewhat

arbitrary

.

From a search of the literature for an acceptable definition of the ground-station figure of merit G/T, it

appears that the authors are fairly evenly divided in their

choices of port [!> 2, or 3) to which to refer their working

definitions. The only formal definition [3] that was found

specifies port 1 (the antenna output port) . A careful

review of this formal definition is a time-consuming job

more appropriately left to a later phase of the G/T project.

Therefore, a working definition will have to suffice for

this report.

The working definition of G/T used in this report is:

the ground station figure of merit, G/T, is the ratio of the

on-axis power gain of the antenna to the system noise temperature referred to the antenna output port. With reference to

6
figure 1 this definition corresponds to

(1.2)

Henceforth, whenever G and T are used separately in this

report, they refer to G^ and respectively.

The magnitude of G/T is usually expressed in decibels

,

where the magnitude of G/T for the system under consideration

is compared to a G/T of unity. That is

CG/T)^g = 10 log^Q CG/T). CI. 3)

A few additional comments pertaining to the preceding

ideas have been left to appendix A.

1 . 2 The Relationship of G/T to C/n and ERP

The desired performance of a satellite communications

system is generally expressed as an output signal-to-noise

ratio for an analog system, or as a bit error rate for a digital system. These parameters are related to the carrierto-noise density ratio [4], C/n, at the antenna output, the

relationship depending on the type of modulation employed.

Once the desired output performance of the system is specified, C/n can be determined from equations relating it to

this desired performance. The trade-off between the

available satellite power and the ground station G/T is

determined by finding the least expensive combination of

satellite power and G/T that gives the desired C/n.

A less detailed representation than the one given in

section 1.1 of a satellite communication system in its receive mode is shown in figure 1-2. Modulated RF carriers

are radiated by the satellite and received by the ground

7
i

CD

>-oo

I— o

(-'1

CD •H

5-1 oiu

<u

•!-> n

•H

•H

CD

?-i Om o• H

+-) oi oJ u fH

03 -P H

rH

(D • H n3

5-H O 0

4-> t/5 U •H • H O

Ph

CD

5-1
station antenna. The effective radiated power (ERP) [1] is

the corresponding average power radiated in the direction

of the antenna. C is the time average power of the received carriers that is available at the antenna output

port. C is given in terms of the ERP by

C = ERPxLxG (1.4)

where L reflects the loss in carrier power caused by the

separation and the polarization mismatch between the satellite and ground station antennas, and by the atmosphere.

Under the usual assumption that the noise density kT

is much larger than the noise density from the satellite

received by the ground station, the noise density n at the

antenna output port is given by

n = kT. (1.5)

Combining eqs . (1.4) and (1.5), the ratio C/n becomes:

C = (G| ERP^lL

^,^,3

n ^T^ k

This equation shows that C/n can be increased by either

upgrading the ground station (G/T) or by increasing the

satellite ERP. It also implies an intimate relation between G/T and ultimate system performance. For example an

increase in G/T could imply a more static-free voice communication, or a more error-free data communication.

See appendix A for further comments.

1 . 3 The Measurement of G/T -- Advantages and Disadvantages

of Using Radio Stars

There are basically two approaches used to measure the

ratio G/T. In one approach G and T are measured separately

and their ratio is calculated. In the other approach

9
(sec. 1.4) G/T is measured directly in the sense that neither

G nor T is explicitly measured. It is assumed here that a radio star is employed in this direct approach.

The main advantage o£ the direct approach is that G/T

can be accurately measured using a relatively easy measurement procedure, provided the flux from the radio star is

accurately known. The relative ease of this measurement

procedure allows G/T to be measured more often and in much

less time than with the indirect approach. This point is

very important if the ground station is moved often or if a minimal allotment of time is available with which to assess

performance. Although the calibration of the radio star

itself is an undertaking at least as difficult as the indirect approach to the measurement of G/T, once the star is

calibrated the G/T of any number of ground stations can be

accurately and easily measured.

In contrast to the direct approach, an accurate determination of G/T by the separate measurement of G and T is

a major measurement undertaking which includes: (1) the

calibration of a standard gain horn; (2) the transfer of this

calibration to the system antenna; and (3) the measurement

of the system noise temperature. Even if the system antenna

is small enough for direct calibration, such a calibration

is in itself a major job.

The main disadvantage to the direct approach is that

it can only be accurately employed on a ground station whose

G/T is greater than some minimum value. As one example,

Kruetel and Pacholder [5] estimate that the G/T of a ground

station must exceed 35 dB if Gas A is to be used as the radio

star and if the probable error in G/T is not to exceed

± 0.2 dB. If another radio star is used in place of Gas A,

then the minimum G/T must be even larger.

10
In the event that an absolute measurement o£ G/T is

less important than an intercompar ison of the G/T radio

for two similar ground stations, the accuracy of the flux

from the radio star becomes unimportant, and the direct

approach is even more appealing. Subsequently, as a greater

accuracy in the star flux becomes available, the accuracy of

the G/T for either ground station can be easily updated by

simply replacing the old value of the star flux used to

calculate G/T by the updated value.

1 . 4 A Brief Outline of the Radio Star Method of Measuring G/T

In the radio star method of measuring G/T, the ground

station antenna is first directed at the radio star. The

ground station receiver now registers an average noise

power, , that is proportional to the sum of the system

noise temperature T referred to the antenna output port and

the brightness temperature [6] of the radio star referred

also to this port, GT Q. /47t. That is

where G is the antenna gain, T^ is the brightness temperature

of the star, and is the solid angle subtended by the star.

For the purpose here it is assumed that the system noise

temperature is independent of where the antenna is pointed.

The antenna is now directed to the cold sky just far

enough to the side of the radio star that the radiated power

from the star does not contribute significantly to the

power emerging from the antenna output port. The receiver

now registers an average noise power ^2 proportional to the

system noise temperature only. That is

s s GT ^ /47T CI. 7)

(1.8)

11
Taking the ratio Y of the two noise powers in eqs

.

(1.7) and (1.8) results in

P, T + GT /47T

Y = — = . (1.9)

Solving eq. (1.9) for G/T yields

G ^ illllii . (1.10)

T T ^

s s This equation shows the basic result of a radio star measurement of G/T. Once T^ and have been established, the

measurement reduces to the relatively simple noise power ratio

(or Y-f actor) measurement.

Further comments on the radio star method are to be

found in appendix A.

1 . 5 A Brief Description of Some Important Radio Stars

There are some sources of radio frequency noise beyond

our own atmosphere. These cosmic sources include the moon,

the sun and planets, hydrogen clouds and exploding stars

within our own galaxy, and distant radio galaxies. These

sources vary in angular extent from a fraction of a second

of arc to many degrees, and in power from values well below

the minimum perceptible level of the largest and most sophisticated antenna- receiver systems to powers easily detected

by the crudest systems

.

For the purpose of this report a radio star is considered

to be a cosmic radio source whose angular extent is no larger

than a few minutes of arc. The importance of such radio

stars to the measurements of G/T stems from the fact that

their angular extent is less than the angular extent of

the main beam of the antenna currently under consideration,

allowing G/T to be measured without measuring the entire

antenna power pattern.

12
Radio star flux density is often expressed in flux

~ 2 6 imits Cf'U.)> one flux unit being equivalent to 10 watt

per meter squared per hertz. The curve of the flux density

as a function of frequency is known as the source spectrum.

Several spectra are shown in figure 1-3. The general shape

of the spectral curves indicates what physical mechanism is

responsible for the radio emission. For example, from

figure 1-3 it can be concluded that the synchrotron mechanism

(the spiraling of rapidly moving electrons around magnetic

field lines) is responsible for the radiation emanating from

Cas A, Cyg A, Tau A, and Virgo A, while radiation from the

electrons in compact ionized hydrogen clouds is responsible

for the emission from Orion A and DR 21.

Table 1-1 gives more detail concerning the radio stars

whose spectra are shown in figure 1-3. The table includes the

common star name in column one; the type of large-scale

phenomenon believed responsible for the radio star in column

two; the position of the star in equatorial coordinates

in column three; the angular size of the star in column

four; and the star's visibility from the north to south

latitudes in column five. For the purpose of this report

the visibility is defined to be that interval of terrestrial

latitudes from which a source's apparent daily path through

the sky rises to at least 20° above the horizon. This 20°

miminum assures that the source can be seen by an antenna

for at least one hour sufficiently far above the horizon to

be discernible above the atmospheric and ground noise. One.

can tell from the visibility whether a particular source is

usable in a G/T measurement at a given site. The radio

stars are arranged in a table from top to bottom according

to descending flux densities at 7.5 GHz.

13
10^

FREQUENCY (GHz)

Figure 1-3. The flux density spectrum o£ several radio stars.

14
Table 1-1. Information about several radio sources.

Radio Position Size Visibility

) SL°

11

48

75

29

57

28

Star Type* RA^ Dec° RA' X Dec ' NL°

Cas A SR 23.4 58.6 4 X 4 90

Tau A SR 5.5 22.0 3.3 X 4 90

Orion A EN 5.5 -5.4 3.5 X 3.5 65

Cyg A RG 20 .0 40 .6 1.6 X 1 90

Virgo A RG 12 . 5 12 . 7 1 X 1 . 8 73

DR 21 EN 20 .6 42 .2 < 0 .3 90

*SR = Supernova Remnant

EN = Emission Nebula

RG E Radio Galaxy

15
2. REVIEW OF THE PROPERTIES OF CAS A FROM THE LITERATURE

2 . 1 Early Measurements

The radio emission known as Cas A was discovered in

1948 by Ryle and Smith [7] while measuring rf emissions from

the Constellation of Cygnus discovered two years earlier.

In 1954 Baade and Minkowski [8] identified the newly discovered radio source with faint optical nebulosities located

near the Constellation of Cassiopeia. From optical measurements of the nebulosities Minkowski [9,10,11] concluded:

that they are traveling radially outward at a speed of

7440 km/sec; that they are approximately 11,000 light years

from the earth; and that they are remnants of a supernova

explosion, the visual evidence of which probably reached the

earth about 1700 A.D. Subsequent rf measurements [12,13]

made in 19 52 to determine the center and angular size of

Cas A helped Baade and Minkowski to positively identify the

emission with the nebulosities.

Since these first observations, many measurements of

Cas A have been made to determine its flux density and

spectral distribution, angular shape, polarization, and

stability. The following subsections contain discussions

of the results of these measurements as they pertain to the

use of Cas A as a standard source of rf noise power for the

measurement of the parameters of large antennas.

2.2 The Location of Cas A

2.2.1 The Equatorial and Galactic Coordinate System

The equatorial coordinate system is the most commonly

used system for locating the position of celestial bodies.

It is the one used in most star catalogues and will be discussed

16
in detail in this subsection. The galactic coordinate system

is often used in conjunction with the equatorial system in

locating broad regions of cosmic background radiation and

will therefore also be treated to some extent here.

Equatorial Coordinate System [6]

In the equatorial system the plane of the earth's

equator is the plane of reference; the center of the earth

is the coordinate origin; and the earth's geographic north

pole is the northern direction. The reference direction

in the reference plane is defined in conjunction with the

celestial sphere, figure 2-1. This sphere is an imaginary

spherical surface of arbitrarily large radius with the earth

as its center, and onto which the stars appear to be projected. In the period of a year, these stars exhibit very

little angular motion on the sphere and so provide a quasipermanent reference pattern for their own locations. Objects

like the sun and planets appear to move through this pattern.

The intersection of the earth's equatorial plane with this

sphere defines the celestial equator, and the earth's projected north and south poles define the celestial north and

south poles respectively. The apparent yearly path of the

sun on this sphere is called the ecliptic, which intersects

the celestial equator twice a year, once at the vernal

equinox and once at the autumnal equinox. Then, the line

drawn from the earth's center to the vernal equinox defines

the reference direction, or the direction from which the

longitude of a star of the sphere is measured.

The angle a in the equatorial plane measured eastward

from the vernal equinox to a projection of a particular

star onto the plane is the star's longitude and is called

the right ascension. It is usually expressed in hours,

minutes, and seconds, 24 hours corresponding to 360°. The

17
CELESTIAL

NORTH POLE

SUN 'S APPARENT

PATH

(ECLIPTIC)

CELESTIAL

SPHERE

TAU A

HOUR ANGLE

TO TAU A

(NEGATIVE

BEFORE

MERIDIAN

TRANSIT)

CELESTIAL

SOUTH POLE

Figure 2-1 The equatorial and galactic coordinate systems

superimposed onto the celestial sphere.

18
angle 5 measured from the reference plane to the star's position is called the star's latitude on the sphere and is

called the declination. It is expressed in degrees, arc

minutes, and arc seconds, and is positive towards the

celestial north pole and negative towards the south. For

example, Tau A is located at a = 5^ 3l"^ 30^ and 6 = 21°58'

in figure 2-1.

The angle in right ascension between the observer's

meridian (in earth coordinates) and the star is called the

star's hour angle. The hour angle is defined to be negative

before it transits the observer's meridian. For example,

h m

the Tau A hour angle to the observer's meridian (at a = 2 11 ) in the figure is approximately a negative 3^ 20"^.

Galactic Coordinate System [6]

Since 1958, the galactic coordinate system is defined

as follows. The origin is defined by the intersection of the

plane of our galaxy and the line through the center of the

earth perpendicular to this plane. Angles of galactic longitude i^^^) are measured in this plane, and angles of galactic

latitude (b''"''") are measured from this plane. The reference

direction in the galactic plane is from the origin to the

center of the galaxy in the plane.

The apparent intersection of the galactic plane with

the celestial sphere is called the galactic equator (fig. 2-1)

and provides a convenient reference circle (not a great

circle) on that sphere. The north galactic pole is the intersection (a = 12.7 and 6 = 28°) of the perpendicular from the

origin with the northern hemisphere of the celestial sphere.

19
2.2.2 The Precession of the Earth's Axis [6]

Since the earth is not a perfect sphere, the gravitational

pull exerted upon it by the sun causes a gradual precession

of the earth's axis around the pole of the ecliptic, one cycle

being completed in approximately 26000 years. This gradual

motion shifts both the celestial equator and the celestial

poles with respect to the star pattern, causing an apparent

shift in the positions of the stars. Therefore, when specifying

the right ascension and declination of a star, it is important

to specify a date (epoch) to which they refer. The change in

right ascension and declination from AD 1950.0 are given by

Aa = m + n sin a tan 6 seconds per year

A6 = n cos a seconds of arc per year

where a and 6 are the right ascension and declination for 1950.0.

m = 3.07327 seconds

and n = 20.0426 seconds of arc.

2.2.3 Cas A

Through a detailed study of the shape of Cas A [14] the

center of its rf emission is placed at

a = 23^ 2l"^ 11^

and 6 = 58°32'40"

at the epoch of 1950.0. For comparison, the optical center of

the expanding nebulosities mentioned in subsection 2.2.1 is

located at [15] 23^ 2l"^ 11.4^ right ascension, and 58°32'18.9"

decl inat ion

.

Cas A, though not visible, is located (fig. 2-2) just

west (11°) of the visible star 3 Cas. The effect of the earth's

20
00

•H O 0) M P.O

>

•H (/) +-> 0}

t—

I

fH O

(=: o

•HM

t-H D I—

I

O 0)

O

m O

u

o

• H D

0) -H m nS O -M

t/i oM ^ • H -H

t/l t/5 O -H

Oh >

I CM

0)

fHbO

•ri

PL,

(S33il93a) N0IlVNI133a

21
precessional motion upon the apparent position of the stars

from 1900 AD to 2000 AD is also indicated in figure 2-2. The

location of Cas A in our galaxy is shown in figure 2-3.

2 . 3 Flux Density and Spectral Index

2.3.1 Brightness, Brightness Temperature, and Flux Density [6]

The intensity measure of radiation from the celestial

sphere is called the brightness . The brightness of a small

surface on the celestial sphere can be related to the flux

density, S, at an antenna on the earth. This relationship

will now be developed. From figure 2-4

dw' = B dA d^^' (2.1)

where dw ' = spectral power (power per unit bandwidth) emitted

by the incremental surface dA into the solid angle watts/

Hz

B = surface brightness, watts/ (rad^ "m^ 'Hz)

dA = elemental surface area on the celestial sphere, m^

df^' = elemental solid angle, rad^

.

Thus B is a brightness whose magnitude depends upon its location on the celestial sphere, and which varies in a roughly

continuous manner over the sphere except for occasional

"bright spots" which correspond to highly localized or discrete sources of radio emissions. The broad continuous

brightness is referred to as "background radiation," and the

bright spots as radio "stars." Cas A is one of these radio

stars. Figure 2-5 is a representation of the celestial sphere

with the earth at its center, and with the size of the earth

represented by a point relative to the radius of the celestial

sphere. As seen from the earth the elemental surface area dA

22
GO

ce: o < UJ O UJ h- 1— o >- < LlJ O h- _J o O 3Z <=c <— o 1—) >. 1 \

USto W)

CD

UoC < o

•H ;3

X

+-> cfl x: • H H

If) ^ O * P.< u

CD t/l >^ ^ 03 nJ M U :2

"-H

O >^

O -M ^

I—I

+-> o

0) -H (D

inU +-1

t/l f-i

O - -H +-> 4->

(/) <D •H CD > X -H

5-1 +-> -M

03 03

!=; c (1) < o3 !-i

CD

•H

23
Figure 2-S llemental radiating surface dA

on the celestial surface

24
on the sphere (o£ radius r) subtends a solid angle , where

the area and the solid angle are related via the equation

dA = rM^. (2.2)

The spectral power (dw' of eq. (2.1)) leaving the surface dA

proceeds within the solid angle df^ ' to the earth, becoming

spread uniformly over the area dA' . Therefore the elemental

flux density (dS) that reaches the earth after radiating from

dA equals this spectral power divided by the elemental area

dA' . That is

dS = —. (2.3)

dA'

where dS = spectral power per unit area in wat ts/ (m^ "Hz) . The

area dA' and solid angle d^^ ' are related via the equation

dA' = r^d^' . (2.4)

Then using eqs (2.1), (2.2), and (2.4), eq . (2.3) reduces

to

dS = Bdr2. (2.5)

This is the fundamental equation relating the elemental

flux density (dS) arriving at the earth to the brightness B

of the area of the sphere subtended by the solid angle dO..

The flux (S) from any finite source is given by the

integral of all the elemental fluxes making up the source,

that is

S = / BdQ. (2.6)

s ource

The magnitude of the flux density is often expressed in

— 9 A

flux units (f.u.), where one unit is 10 watts/ (m^ "Hz)

.

25
The brightness temperature is a fictitious temperature

associated with the brightness . It is that temperature to

which a black-body radiator must be raised in order to have

the same brightness B. In the low- frequency approximation it

is related to the brightness through the equation [6]

Tg = (2.7)

where is the brightness temperature in kelvins ; X is the

wavelength of interest in meters; and K is Boltzmann's constant.

2.3.2 Flux Density and Spectral Index of Cas A

Among other things the flux density of Cas A is both a function of frequency and time. Therefore the time and the

frequency of its measurement must be specified. For example,

the flux density of Cas A at 7.5 GHz for the time (epoch)

AD 1965.0 is approximately 618 f.u. and is decaying at approxi-

- 2 6 mately 1% per year. One f.u. or flux unit is 10 w/(m^»Hz).

It has been found that the frequency dependence of the

flux density follows the equation

: SCf) = S^f^' C2.8)

where is the flux density at 1 GHz; a is a constant called

the "spectral index" and is defined by eq . (2.8); and f is

the frequency in GHz (the symbol a is also used to denote

right ascension). The flux density of Cas A around 7.5 GHz

is given in table 2-1 and figure 2-6. The flux densities

were transferred (see section 2.4) from the epochs in which

they were measured (column three) to the epoch AD 1965.0

(column four) by using a decay rate of 1.11 per year.

26
Table 2-1

Frequency Epoch Flux Density AD 19 65.0 Flux

(GHz) CAD) (f -uQ Density (f.u.)

5 1964.4 910 [16] 905

5.68 1968.5 740 [17] 766

6.66 1965 684 [18] 684

8 1964 590 [19] 584

9.36 1961.5 520 [20] 502

9.375 1962.7 514 [21] 502

9.38 ' 1968.5 510 [17] 528

Figure 2-6 is a log-log plot of the AD 1965.0 flux densities in table 2-1. The line drawn through the points is a least squares fit to these points and conforms in the interval

from 5 to 10 GHz to the spectral equation

S(f) = 3604 f"^ '^^^ (2.9)

where the flux density is given in flux units and the frequency

is in GHz. From this equation the flux density at 7.5 GHz

is found to be 618 f.u., with a corresponding brightness

temperature of 336 kelvins . A method such as this is often

used over a much wider frequency range to determine S at a frequency where it has not been measured, and/or to obtain a higher accuracy in S based upon the assumption that eq. (2.8)

is a correct description of how S varies with frequency.

In this context it should be pointed out that the values of

a (-0.875) and (3604 f.u.) found from this table using

only data over the restricted frequency range do not agree

with a's and S^'s generally found in the literature. This

27
28
disagreement reopens the question of whether the flux density

(at 7.5 GHz for example) can actually be more accurately

determined by a curve - fitting process on a number of measured

points close to 7.5 GHz as done in figure 2-5, by a curvefitting process over a wider frequency range or by direct

measurement of G/T at 7.5 GHz. The curve- fitting process for

finding a and S over the wider frequency range correspondingly

requires a to be constant over this larger range, a requirement that may not be met [22].

The characteristics (spectral index, polarization, decay

rate, intensity distribution, and shape) for Gas A are explained to first order [23] by an expanding shell model

wherein the rf emission is assumed to come from synchrontron

radiation within the shell. One of the predictions of this

model will be used in the next subsection where the Gas A

decay rate is discussed.

2 . 4 Secular Decay

2.4.1 Decay Rate

The shell model [23] of Gas A predicts its flux density

S at its age t. According to this model S can be calculated

from the measured flux density S measured at age t from ^ o " o the equation

S = S^Ct^/t)^ (2.10)

Where 3 is a decay constant that is related to the spectral . index a through the equation (a < o)

3 = 2(l-2a) . (2.11)

Based on eq. (2.10) the flux density S from Gas A should decay

with time as roughly indicated in figure 2-7. The (normalized)

29
S = So( t/ to)'

0 A. D 1 700 EPOCH

Figure 2-7 Decay curve of the Cas A flux density as calculated from the shell model.

30
differential decay rate, r, can be found by differentiating

eq. (2.10) and is

The decay rate calculated for Cas A using epoch AD 19 50.0

from eqs . (2.11) and [2. 12) is 21, while the measured value

is closer to II. Minkowski's [10] birth date (AD 1700) for

Cas A has been used in this calculation along with a spectral

index equal to -0.8. It is interesting to note in this regard

that Brosche [24] has drawn attention to some Korean records

that indicate a "guest star" in the region of Cassiopeia

around AD 1592, which "star," if it were the birth of Cas A,

would yield a decay rate (AD 19 50.0) of 1.3% per year, much

closer to the measured values than the rate given by

Minkowski's data.

While the shell model is not a perfect description of

the Cas A decay, it indicates in a rough way (fig. 2-7) how

the flux density should decay with time. As will be seen,

the time dependence of r as indicated in eq . (2.12) shows

that more care should be exercised in the application of

average decay rates measured over long periods

.

The decay rate predicted by eq. (2.12) decreases with

time. At the present time insufficient receiver sensitivity,

coupled with the small yearly decrease in the flux of Cas A,

prevents a short-term measurement of the Cas A decay rate.

One is forced therefore to compare the flux from Cas A over

long periods of time, a process which yields an average decay

rate instead of the differential rate. It can be seen from

figure 2-8 that this average decay rate, R, where (At = t-t^)

S - S

R = — (2.13)

SAt

31
DIFFERENTIAL

RATE

AVERAGE

RATE

Figure 2-8. Decay curve o£ the Cas A flux density showing the

relation between the differential and average

decay ratio.

32
is related to the differential decay rate, r, at age t to

first order in At/t^ by

r ^ RCl-At/t^) C2.14)

and that the differential rate is always less than the average

rate. An estimate of the magnitude of At/t^, or the relative

correction needed to reduce R to r, can be obtained by taking

the birth of the radio star to be AD 1700, t to be AD 1948, ' o and At to be 25 years. The resulting At/t^ is 0.1. In other

words the differential decay rate is 10^ less than the average

decay rate measured over the 25 year period, a difference

that should not be ignored when using the decay rate to predict the flux density of Cas A. Therefore, the model, while

not perfect, does indicate that the average decay rate (R)

used in the literature to transfer flux densities from one

epoch to another should probably be reduced, in some cases

possibly by as much as 101. Moreover, if it is assumed that

the shell velocity has not increased since the explosion that

gave rise to Cas A, then it can be easily shown that the star

birth cannot be earlier than AD 1700 under certain simplifying

assumptions in which case it can be conjectured that the difference between the average and differential decay rates is

probably greater than 10% for a 25-year measurement period.

In any case, these results derived from the shell model do

strongly suggest that the practice of using the average decay

rate to transfer flux densities from one epoch to another

should be examined more closely if a high accuracy in the

resulting flux densities is desired.

Flux densities are deduced in the literature from known

values by use of the following equation

S = S^Cl-R)^"^ (2.15)

33
where S-j^ is the flux measured at age t-^; R is the average

decay rate discussed above; and At is the time difference

between t-j^ and the time of interest t. From the preceding

discussion it is seen that a better approximation to S is

obtained when one uses r instead of R, that is,

S = S^Cl-r)^^, C2.16)

where r is calculated from R by using eq . (2.14). Even

eq. (2.16) is not exact in the sense that it is equivalent to

eq. (2.10). However, it is a sufficiently good approximation

for even the most accurate of today's measurements and has

the great advantage that 3 need not be known, and only a rough estimate of the star's birth date need be used in calculating r from eq. (2.14).

2.4.2 Some Measured Values of R

Some measured values of the average decay rate R are

shown in table 2-2.

Table 2-2

Error in

Freq

.

Decay Rate Decay Rate Epochs Year

GHz (percent) (percent) Used Span Reference

0. 082 1.06 13 1948-1960 12 Hogbom [25]

0 .082 1.29 6 1948-1969 21 Scott [26]

3.2 1.14 23 1953.9-1962. 7 8.8 Mayer [27]

1.4 1 .38 11 1965-1971 11 Findlay [28]

1-3 0.90 11 1960-1971 15 Baars [29]

These results indicate that the average decay rate is not

known to a high degree of accuracy. Add to this the fact

34
that the rates used are possibly 5% to 10% high and that

the rate possibly changes with frequency [30], and it is

easily seen that the state o£ knowledge concerning decay

rate is not at a very high level and that much more work

along this line needs to be done.

2 . 5 Polarization

2.5.1 Polarization and Faraday Rotation

Polarization [6

]

The emission from a celestial radio source extends over

a wide frequency range, and therefore within any finite bandwidth, consists of the super-position of many statistically

independent waves of various polarizations. Generally these

emissions are partially polarized, some sources tending toward

complete nonpolarization and others toward a significant

degree of polarization. Partially polarized emission can

be decomposed into a completely random wave plus completely

polarized waves. The degree of polarization d is then

defined as the ratio of the power contained in the polarized

wave to the total power in all the wave. It is this total

power, or the power contained in both the random and polarized

waves, that is proportional to the source flux density.

The "position angle" on the celestial sphere of the

polarization of a source is measured the northerly direction,

increasing in the eastwardly direction. The manner in which,

the antenna polarization and the linear source polarization

affect the available power from the antenna output port is

shown in table 2-3, on the assumption that the antenna is

pointed directly at the source, and that the source is a point

source

.

35
Table 2-3

Type o£ Antenna

Polarization

Spectral Power at

Antenna Waveguide Port

1/2 SAg(l + d Cos 29)

1/2 SA ' e

Linear

Right or Left Circular

The first column of the table shows the type of antenna

polarization assumed for the antenna receiving flux from

the sources. The second column shows the power per unit

bandwidth available at the antenna waveguide port as a result of the source flux impinging on the antenna aperture.

A^ is the effective antenna aperture [2]; d is the degree

of linear polarization of the source; and 9 is the angular

difference between the source's polarization position angle

and the antenna's linear polarization angle measured relative

to the source's north.

Faraday Rotation [6,31]

Much of the galactic medium between the earth and Cas A

is ionized and contains a small magnetic field roughly parallel

to the direction between them. Because of the presence of

the magnetic field, this medium is anisotropic and causes

the direction of polarization of a polarized wave traveling

through it to rotate as the wave proceeds. This rotation is

proportional to the square of the wavelength of the polarized

wave. Therefore, as the observed wavelength is increased,

the observed position angle of the source polarization will

increase or decrease according to whether the proportionality

constant is positive or negative respectively. This proportionality constant is called the "rotation measure," and

in the direction of Cas A is thought to be [14] approximately

-130 rad./m^.

36
2.5.2 Measured Polarization o£ Cas A

The literature [14,32,33,34] suggests that above 1 GHz

the linear polarization of Cas A is approximately 1%, and

that below 1 GHz the polarization falls to zero. Table 2-4

is representative of the values reported, and shows that the

degree of polarization and the position angle are not accurately known.

Table 2-4

Frequency Polarization Position Angle

(GHz) (Degree) Reference

1 < 1 32

3 < 1 32

5 1.4 ± 0.5 37 ± 15* 14

8.25 0.5 ± 0.2 114 ± 15 33

10 1.5 40* 32

14.5 1.2 ± 0.5 41 ± 9* 35

15.25 1.9 ± 0.2 71 ± 3* 33

15.75 2.2 ± 0.3 79 ± 3 33

19 .4 1 31* 34

*Indicates values used in figure 2-9.

The scheme depicted in figure 2-9 might be used to obtain

usable values of position angle versus frequency. The position angle values in the table identified by an asterisk have

been plotted against wavelength in the figure. The wavelength

is indicated on a squared scale so that theoretically the data

should fall along a straight line assuming the position angle

is proportional to wavelength squared. Then the least squares

fit linear curve, curve (a) in the figure, gives at least an

idea of the position angle as a function of wavelength that

37
i-HfH

_i

C\3 <U •H

iH

(D M

H

o

m

>

P

o

f 0

rH • , , bO<

Eu

zr. o

1— •H g

^-> O

•H ?-i UJ (/I _J o

p. X

>

< ,—1 1—

I

03 <+H O

•H 'TS •M 0

(U Nl ^ -H

+-> >H O o3 P^i—

1

>> o

(S33a93a) NOIlISOd

38
might be used in calculations involving linearly polarized

antennas. Curve (b) is included in the figure to indicate

the slope that corresponds to the measured [14] rotation

measure (-130 rad./m^).

2 . 6 High Resolution Maps

For the purpose o£ this report Cas A is considered to

be a discrete source with a single value assigned to its

flux density, spectral index, degree of polarization and

position angle, and secular decay rate for a given epoch and

frequency of observation. However, there have been a number

[14,34,36] of investigations made into the detailed structure

of this source which, from our point of view, are worth

examining for several reasons: 1) they aid in understanding

the nature of the background radiation in the neighborhood

of Cas A, and therefore in the interpretation of broadbeam

measurement results; 2) they help determine at what antenna

resolution Cas A can no longer be treated as a discrete

source with no structure; and 3) they can be used to obtain

more accurate source -antenna convolution corrections. The

high-resolution maps of Cas A will show that all of the

parameters of Cas A which are considered to be constants in

the broad beamwidth picture do in fact vary across the face

of the source in a highly irregular manner.

Figure 2-10 shows a brightness temperature contour

map [14] of Cas A measured around epoch AD 1969.8, where

the thick dashed curve represents the zero contour (relative to a cold area of the sky well separated from the

source), and where the contour interval is 200 kelvins

.

The brightness temperature is plotted in right ascension

versus declination, and the highly structured nature of

Cas A is clearly evident. It is also clear that the source

is well localized with a slight bulge towards the east.

39
35'

34'

8 33-

32'

31'

58*30'

0 ! ,/ —

-J •I 1

I I I I I I I Li I I I I U

30'

Figure 2-10

24' I8» 12' a

06'

23^2r

00* 54»

23h2Qm

Brightness temperature contour map of Cas A

(coordinates for Epoch AD 1950.0, 5.0 GHz).

(Courtesy of Monthly Notices of the Royal

Astronomical Society , Vol. 151, No. 1 , p . 112

,

1970 .3

40
Figure 2-11 is another brightness temperature map [14]

(epoch AD 1968.4, frequency 1.407 GHz) with a dashed zero

contour and 6 70 0 kelvins contour intervals. On this map

the numbers representing the spectral index and their locations are noteworthy. It can be seen that the index varies

from a negative -0.5 to a negative -1.2 in a highly irregular

manner. The resulting spectral index averaged over this map

is a negative -0.75, in fair agreement with Baars ' [29] negative -0.787.

Figure 2-12 [epoch AD 1966.8, frequency 19.4 GHz) shows

two profile views [34] of Gas A, curve (a) being proportional

to the brightness temperature relative to the uniform background around Gas A, and curve (b) being proportional to the

linearly polarized component (amplified 20 times) of this

brightness temperature. A characteristic "valley" of reduced polarization can be seen running from southwest to

northeast across the source. This "valley" is also evident

in figure 2-13, which show^s the distribution [14] (epoch

AD 1950, frequency 5 GHz) of this polarized component. The

bars in figure 2-13 are oriented along the electric vector

position angles, the longest bar corresponding to a brightness

temperature of about 100 kelvins. The degree of polarization

averages about 51 around the rim of the shell, with peaks of

about 10% in the southeast region and of about 61 in the northwest region. Toward the central part of the shell the polarization falls to II or less. The average polarization over

this map is 1.4% at a position angle of 37°.

To get an idea of the average shape of the Gas A,

annular rings about the center of the source 5 arc seconds

wide were extracted from the intensity map in figure 2-10,

and the intensity around each ring averaged. Figure 2-14

(epoch AD 19 50, frequency 5 GHz) shows the resulting

41
T

Figure 2-11. Brightness temperature contour map o£ Cas A

(Epoch 1968.4, 1.4 GHz) showing the variation o£ the

spectral index across the source. (After Monthly

Notices of the Royal Astronomical Society , Vol. 151, No. 1. p. 114, 1970.

42
NOIiVNnOHQ

Figure 2-12. Brightness temperature contour map o£ Cas A

(Epoch AD 1966.8, 19.4 GHz) showing (a) the

brightness temperature, (b) the linearly polarized,

component of (a) amplified 20 times. (Courtesy

of Astrophys ical Journal , Vol. 151, p. 56, 1968;

C.H~ Mayer and I. P. Hollinger; University of

Chicago Press.)

43
1 I 1

\ f1 r:^

\

\ \ r N /

, , ^

^POSITION ANGLE

t I I \ \ I I \ L.

32^ 28^ 24^ 20'' 16* 12* 08* 04* 00* 56* 52*

23^2r 23^20""

Figure 2-13. Brightness temperature contour map o£ Cas A

(Epoch 1950.0, 5.0 GHz) showing the distribution

of polarized emission across the source with the

average position angle o£ the electric vectors

superimposed. (After Monthly Notices of the

Royal Astronomical Society , Vol. 151, No. 1,

p. 116 , 1970)

.

44
RADIUS (SECONDS OF ARC)

Figure 2-14. Mean brightness temperature profile from the

center of Cas A outward (Epoch AD 1950.0,

5.0 GHz). (After Monthly Notices of the Royal

Astronomical Society , Vol. 151, No. 1, p. 118,

1970)

.

45
histogram [14]. The abscissa represents the arc radius from

the center o£ the source Qa = 23^ 21TM 11^, 6 = 58°, 32', 40",

Epoch AD 19 50), and the ordinate is proportional to the

brightness temperature relative to the uniform background

around Cas A. This histogram agrees well with other measurements which indicate that the source has an average shape

resembling a disk with an enhanced outer ring. The smooth

curve drawn through the histogram is the best -fit curve

predicted from the spherical shell model with a small radial

magnetic field. This curve or its histogram could be convolved

with the main beam of broad beamwidth antennas to obtain the

usual star size correction.

'2.7 Cosmic Background Radiation

Besides the discrete sources of radio emission like

Cas A, the cosmic or extraterrestrial radio sky contains a more or less continuous background of radiation which consists

of a thermal and a nonthermal component. In the context of

this report one needs to know this background radiation because 1) this background radiation contributes to total

system temperature of any satellite ground station -- the

contribution depending upon where the satellite is ; 2) the

background around Cas A may be different from the background

around the satellite; and 3) the background around the calibrating source (Cas A) determines where the antenna should

be pointed in the course of performing G/T ratio measurements.

46
2.7.1 Nature of the Cosmic Radio Background

The origin o£ the continuous cosmic radio background

radiation is still open to question, and it appears that a number of measurements in the microwave region and above

remain to be done.

Kraus [6] distinguishes three sources of continuous

background radiation, extragalact ic and galactic nonthermal

(synchrotron) radiation, and galactic thermal radiation

originating in the galactic HII (ionized hydrogen) regions.

The nonthermal synchrotron radiation predominates below about

1 GHz with a spectral index of from about -0.2 to -0.5, and

the thermal radiation predominates above 1 GHz. From a review of the literature one receives the impression that

above 1 GHz it is not clear what the source of the continuous thermal radiation is. Some of the references suggest

that the radiation comes from the galactic HII regions, while

others suggest a cosmic black-body origin (to be discussed)

.

In what follows it will be seen that the radio background maps

support the latter conclusion.

A radio map [6] of the cosmic radiation at 250 MHz is

shown in figure 2-15. The contours are at 6-kelvin intervals

above the coldest parts of the sky, which are at a temperature

of about 80 kelvins. Since the dotted line represents the

galactic equator it is seen that the background peaks up in

the galactic plane and falls off from this plane. Since

the measurements were done at 250 MHz, the contours are

predominantly nonthermal in nature (see fig. 2-16). Furthermore, since the contour lines run parallel to the galactic

equator, it can be implied, consistent with remarks in the

preceding paragraph, that the nonthermal radiation has a strong component associated with the galactic plane. In the

following it will be seen that the same conclusion does not

appear to be applicable to the thermal radiation above 1 GHz.

47
48
In addition to the three sources of continuous radio

emission mentioned earlier there is mention in the literature

of a possible fourth [37] source, cosmic black-body radiation. According to hypothesis it originated when the universe

was in a highly condensed and heated state, and as the

universe expanded, the cosmological red shift cooled the

radiation while preserving its thermal character. A number

of measurements [38,39,40] of the absolute cosmic background

tend to support this idea, the most convincing of which is

the set taken at Princeton [39] . Referring again to figure

2-15, the eleven numbered points along the 40th declination

represent positions where the Princeton measurements (9.375 GHz)

were made. Table 2-5 gives the values of these measurements

which, although they should be considered to be the same within

the ± 0.5 kelvin experimental error, are listed in order of

descending magnitude.

Table 2-5

Brightness

Measurement Location Temperature (kelvins)

Number (Right Ascension) at 9.375 GHz

1 23^ 40"^ 3.32

2 1^ 3.16

3 19^ 30"^ 3.14

4 18^ lO"^ 3.12

5 14^ 20^ 3.07

6 15^ 3.02

7 17^ 2.98

8 10^ lO"^ 2.89

9 18^ 30^ 2.80

10 4^ 20"^ 2.78

11 20^ 30"^ 2.76

Average 3.0 ± 0.5 kelvins

49
It is important to note from the distribution of these points

along the 40th declination that there seems to be no correlation between the position of the measured values and the

position of the galactic equator, leading to the conclusion

that the continuous radiation above 1 GHz received at the earth

is isotropic and not primarily associated with the galactic

plane. If there were a continuous increase of thermal radiation towards the galactic equator, then measurement number 11

should be considerably greater in magnitude than measurement

number 1, yet these two points represent respectively the

lowest and highest values in the table. This leads to the

conclusion that, except for HI I regions (which emit thermal

radiation) localized along the galactic equator, the continuous thermal radiation above 1 GHz is isotropic and does

not peak-up along the galactic equator like the nonthermal

case below 1 GHz (fig. 2-15). In other words, it appears that

the continuous thermal radiation is not associated with the

galactic HII regions, but that it stems from a universal blackbody radiation and is spread uniformly over the celestial

sphere. This conclusion is further supported by the contour

maps to follow. In addition to the Princeton measurement,

Penzias and Wilson [38] and Roll, et al . [39] have made measurements (averaging the absolute cosmic background along

declinations close to the 40th declination) which agree with

the Princeton measurements, and are summarized in table 2-6.

Only the direction of the contour lines in the follow^ing

maps is germane to the discussion in this section. Therefore

no attempt has been made to reconcile contour-line magnitudes

from one map to another, their values being those appearing

on the maps in the literature.

50
Table 2-6

Frequency Brightness

GHz Temperature (kelvins)

4.08 3.1 ± 1 [38]*

9.375 3.0 ± 0.5 [39]

(average of Princeton

measurements)

32.5 3.16 ± 0.2 [40]

*Th.e value quoted by Penzias and Wilson [38] is 3.5 ± 1 kelvin.

A later measurement by the same authors with a modified horn

feed mentioned by Roll, et al . [39] gave the lower (and

presumably better) value reported in table 2-6.

The preceding remarks lead to the following picture

(fig. 2-16) of the continuous cosmic radio background.

Below approximately 1 GHz the brightness (c.f. section 2.3.1)

consists mainly of synchrotron radiation [6] lying in magnitude between that emanating from the galactic center and that

from the galactic pole, and peaking up along the galactic

equator. Above 1 GHz the brightness consists of isotropic

black-body radiation at 3 kelvins. Superimposed on this continuous radiation are numerous localized HIT regions of thermal

radiation associated with the galaxy. For reference the

brightness of Gas A is included in figure 2-16. While this

picture of the continuous background seems to be consistent

with the available data and radio maps, many more measurements,

primarily in the microwave region and above, need to be

performed to adequately justify it. It is nevertheless the

most consistent picture that can be pieced together from

the available literature. With figure 2-16, the positions

of the contours with respect to the galactic equator in the

maps to follow can be easily understood and lend further

support to the conclusions drawn.

51
FREQUENCY (GHz)

Figure 2-16. Brightness spectrum o£ the continuous cosmic

radiation as deduced from the literature.

52
In addition to the map shown in figure 2-15 (250 MHz)

,

figures 2-17 [30], 2-18 [41], 2-19 [42], and 2-20 [43] show

radio maps around Cas A at 404 Mtiz, 960 MHz, 1.4 GHz, and

3.2 GHz, respectively, with the galactic equator drawn in,

and lend support to the previously drawn conclusions concerning the nature of the thermal radiation above 1 GHz.

It is apparent that in the 250 MHz, 404 MHz, and 960 MHz

maps the contours run predominantly parallel to the galactic

equator, while in the 1.4 GHz and 3.2 GHz maps this is not

the case. In fact the contours in the 1.4 GHz and 3.2 GHz

maps arise from localized HII regions around Cas A, and in

the frequency region above 1 GHz where the synchrotron radiation is expected to die out (fig. 2-16), the distinct absence

of contour lines parallel to the galactic equator indicates

a lack of continuous thermal radiation emanating from the

galactic plane. In other words, at about 1 GHz, consistent

with figure 2-16, the continuous synchrotron radiation dies

out leaving only the isotropic black-body component, with the

HII radiation manifesting in localized regions only.

2.7.2 Cosmic Background Contribution to the System

Noise Temperature

Assuming the validity of the above conclusions, the

contribution to the cosmic background on the system noise

temperature can now be predicted. When an antenna is pointed

« at a stationary satellite, the satellite appears to describe

a path on the celestial sphere along one of the celestial

declinations. In the process, the antenna beam and sidelobes

pick up cosmic radiation along this path which, in the

microwave region , is a uniform 3 kelvin black -body radiation

on which the occasional localized HII regions are superimposed.

53
o1 \ __1

•cr" Li

t^] o

^—t

<<•

«—1-

T-i- —1

«\ tHO

O •!->

AS

O

u CM

1-1

u

O -H I—1

•H +J

O

n3)

O >

05 2

>>

O rH P

•H

X <D • Ho o o o

C/3

(NI

CD

•H

tin

60

54
/—\ o

CD

O vo

+-> M-l >. I-H < -M •H VO u • o N CO

p~! • P. o o

00 oo o

IS

C to 3 < «\ O (Nl 5h <D • u I-HO ^ O > O (/) •H C O

XJ o Hm ^ -P Hu U U

•H -H a, 6

CD

O ^5, U p., 4->

00

rHI CM

•H

55
Figure 2-19. Cosmic radio background at 1.4 GHz. (After

Publications of the National Radio Astronomy

Observatory , Vol. 1, No. 5, p. 55, 1961).

56
+-> T-i < O

•HooM vO

to

rvi < t~H tn

03

+-> >^

03

O

CNI t3

CD

13 o O P

?H

O en

U

03 t/5 I—1

<DU

O •H I—1

•H +-> o

13 o >

nJ

5h

^>^ >^ o I—1 M

•H CD •Ho O o o uo

CD

•H

P-i

57
The contribution to the system noise temperature from this

background radiation varies along this path in a corresponding

manner. For example, consider what happens when the antenna

beam encounters the various HII regions along the 60th declination in figure 2-19. The contour intervals are designated

by integers which are multiples of 0.8 kelvins above a uniform background, presumably the 3 kelvin black -body radiation.

As the beam (assumed small compared to the distances between

the contours) traverses the contours along the 60th declination from right to left the antenna temperature is increased

from 3 kelvins by 1.6, 2.4, 3.2, 3.2, 2.4, 1.6, and 0.8 kelvins in succession. This gives an idea of the possible variation of the antenna temperature for a narrow-beam antenna as

it traverses a localized HII region. To know this variation

in detail a radio map along the declination traversed by the

satellite for the frequency in use is clearly necessary.

For the greatest accuracy, the preceding implies that

when measuring the ground station G/T using the direct radio

star method described in section 1.4, the offsets from Gas A

used to establish P2 or the system noise temperature should

be made to an area of the celestial sphere free from localized

HII radiation. These regions are apparent from figures 2-19

and 2-20. Furthermore, since figures 2-19 and 2-20 indicate

that there is some HII radiation surrounding Gas A, the contribution of this radiation to the system noise temperature

should be subtracted when Gas A is used as a calibrating

source. In order to do this, a good map of the HII radiation

around Gas A is needed. Figures 2-19 and 2-20 give an idea

of the problems involved in obtaining such maps at a given

frequency. The symmetry of contour lines around Gas A in

these figures strongly suggests that the high synchrotron

radiation from Gas A in the sidelobes of the antenna used to

58
59
determine these contours has distorted the resulting picture

o£ the HII radiation, and one is tempted to replace the maps

with a (hopefully) "corrected" map that might look like

figure 2-21. When this is done at 1.4 GHz, Cas A appears to

be bathed in HII radiation approximately equal to 1.2 kelvins

(1.5 X 0.8) above the 3 kelvin black -body level. Since the

brightness for the HII regions is expected [6] to be flat

above 1.4 GHz, this leads to a 0.04 kelvin (using eq. (2.8))

increase at 7.25 GHz. Thus, given the validity of the assumptions made in arriving at 0.04 kelvins, the HII background

around Cas A at this frequency should cause negligible error

(less than 0.01 dB) in the use of Cas A as a calibrating

source

.

In summary, it appears that there are many gaps in the

literature concerning the cosmic background in general, and

the background around Cas A in particular.

60
3. THE ATMOSPHERIC EFFECTS IN VIEWING CAS A

The problems associated with the effects of the atmosphere

upon the flux from Cas A passing through it are varied and complex. Therefore, within the time allotted a penetrating

review of the problems involved was not possible, and correspondingly the exposition given in this section will be

brief and somewhat incomplete. However, with this first

reading of the literature it was possible to delineate most,

if not all of these problems. As will be seen, the usual

problems concerning absorption by atmospheric constituents

(O2, ^2^* ^^i^> fog> snow, etc.) emerge. In addition, problems

associated with the distortion of the component of the flux

falling on the receiving antenna aperture by the inhomogeneous

refractive index of the earth's atmosphere also emerge. These

latter problems are overlooked by most authors, and it is not

clear which of the remaining few authors handle them correctly.

The versions of refractive distortion presented here come from

references [44] and [45].

Table 3-1 is a list of those mechanisms by which the

atmosphere affects a flux passing through. They fall into

two distinct categories: Attenuation of the flux by the

atmospheric constituents and refractive distortion and addition of noise from the atmospheric constituents. The references

included in table 3-1 are only a sampling of the papers read

during this survey and don't necessarily represent the best

possible sources of information concerning the effects they • describe.

61
Table 3-1

Mechanisms References

Attenuation

Apparent Source Solid Angle

Atmospheric Turbulence

44,45

Diffusion 45

Aperture Perturbations

0^ and H^O 46,47,48

45

Clouds, fog, rain, snow, etc. * Enhancement

Refractive Index

O2 and H^O Emission

Emissions from clouds, fog, etc. *

*It is practically impossible to make accurate measurements

during periods of bad weather. Therefore, the corresponding

literature, although accumulated, was not seriously reviewed.

According to the literature [44,45] the apparent solid

angle subtended at the antenna by the radio source decreases

with increasing zenith angle. The magnitude of this decrease

depends upon what percentage of the antenna main beam is subtended by the radio star, being greatest for a point source

and practically zero for an extended source of greater angular

extent than the beam. For example, according to the literature the flux density S from an unpolarized "point" source

appears to have a magnitude S^ when viewed by an antenna set

at a zenith angle z, where

and where 9.^ is the apparent solid angle of the source viewed

at zenith angle z, and is the true source solid angle.

The flux density S is thus seen to suffer a refractive

attenuation 9 /9 .

S = /9

z z s (3.1)

z s

62
Atmospheric turbulence causes an irregular variation in

the atmospheric refractive index, which in turn causes rays

from the radio star to diffuse and to reach the antenna

aperture with phase and magnitude perturbations. The resulting diffusive attenuation is greatest for point sources.

The largest source of flux density attenuation at

microwave frequencies is absorptive attenuation by molecular

oxygen and water vapor. The magnitude of attenuation depends

upon the temperature, pressure, and water vapor content of

the atmosphere along the path traveled by the signal and

is difficult to estimate accurately. An approximate expression for this attenuation is given by [47,48]

where (4 km) and (2 km) are characteristic heights for

the atmospheric oxygen and water vapor respectively, and where

a^ and pa^ are the frequency-dependent attenuation coefficients (dB/km) for molecular oxygen and water vapor respectively. For a standard atmosphere [49] with a water vapor

content of p = 10 g/cm^, the CCIR report [47] gives values of

0.011 dB/km and 0.00081 dB/km for a^ and pa^ respectively

at 6.4 GHz. It may be more accurate to measure this effect

than to calculate it from eq. (3.2) [50].

The relative importance of these attenuation effects for

large zenith angles can be seen in table 3-2, the values

for which were derived from measurements at 6.4 GHz of Gas A

and the moon [45] using a 22-meter antenna with a 10' halfpower-beamwidth

.

A(z) = ia I +pa a ) Sec z (dB) (3.2)

Table 3-2

Zenith

Angle (Peg.)

Absorptive

Atten (dB)

Diffusive

Atten (dB)

Refractive

Atten (dB)

60

75

86

0.1

0 .19

0.47

0.1

0.17

0 .31

0.0

0.02

0 .19

63
The surprisingly large values of diffusive attenuation

were obtained by comparing the attenuation of the flux from

Cas A with that of the moon; they follow well the predicted

frequency squared dependence of this type of attenuation when

compared with measurements at 4 GHz.

Excluding bad weather, table 3-1 lists two mechanisms

which enhance or add to the flux density: the refractive

index change from unity at the upper "edge" of the atmosphere

to n at the earth's surface [44]; and emissivity from atmospheric 0^ and H^O. When expressed in terms of the change

in the source's brightness temperature, this refractive

index change yields

ATg = (n^-l)Tg (3.3)

where ATg represents an apparent increase in the brightness

temperature, and n represents the refractive index of the

atmosphere at the earth's surface. A value of 1.0004 for

n gives a relative increase ATg of 0.003 dB

.

Tlie increase in the apparent brightness temperature of

the flux density due to atmospheric emissivity can be approximated by

ATg=0.23AT^^ (3.4)

where ATj^ represents the apparent increase, A is the attenuation (dB) given by eq. (3.2), and T is the mean temperature

ma

of the troposphere [49]. Equation (3.4) gives a relative

increase of 0.09 dB in the Cas A zenith brightness temperature at 6.4 GHz. Some of the literature indicates that this

AT^^ may be more accurately measured [50] than calculated

from eq. (3.4). Accurate versions [46] of eqs . (3.2) and

(3.4) involve a ray-path integration of the attenuation

coefficient, taking into account the atmospheric variables

along this path. A more penetrating review of this important

aspect of the problem was not possible in the time allotted.

64
4. THE MEASUREMENT OF POWER GAIN OF A LARGE GROUND ANTENNA

FOR CALIBRATING COSMIC RADIO STARS

4.1 Introduction

The strongest radio stars, Cas A, Cyg A, and Tau A have

received much attention because of their intensity in the

calibration of large antennas. One of radio astronomy's

most important and difficult problems is to determine by

use of well calibrated antennas the precise, absolute values

of the flux densities from these stars. Therefore, the

purpose of this chapter is to discuss the measurement of

the power gain of large ground-based antennas to be used

in calibrating radio stars.

The power gain of a standard horn antenna was calculated

theoretically by Schelhunoff [51] and Slayton [52]. The

theory has usually been applied satisfactorily to a relatively small standard horn antenna of fairly low-power gain.

If a low-gain, standard horn antenna is used in the calibration, then the signal-to-noise ratio associated with the

measurement is poor, and the horn's angular resolution is

low; this results in confusion between adjacent radio

sources. Moreover, the accounting for the effects of

the horn's mechanical imperfections is very difficult, and

the computation of its power gain is usually unsatisfactory.

The most common experimental method of determining antenna

gain and polarization is a substitution technique, which in- . eludes the response of an antenna under test to an incident

"plane-wave" field compared with that of one or more standard

antennas. With conventional "far- field" antenna ranges,

the plane-wave condition is attempted by using large separation distances between the transmitting and receiving sites.

65
But at large distances the errors due to ground reflections

and scattering from other objects can be significant.

Availability (in the substitution techniques when used in

medium ranges) of reliable correction procedures for proximity and multiple reflections between a large antenna and

the horn used to calibrate it would permit the use of medium

antenna ranges and reduce ground reflections. Braun [53],

Chu and Semplak [54], Tseytlin and Kinber [55], and others

have computed proximity corrections for horns separated by

medium distances. However, these computations involve approximations and idealizations which limit the accuracy of

the corrections.

In the extrapolation method of gain calibration of the

antenna [56-59] measurements are made at shorter distances

and lower tower heights than the more traditional methods.

In this method the measured variation in the received signal

with distance is then used to correct for errors caused by

both proximity and multiple reflections between antennas.

The extrapolation method gives the best accuracy currently

available for the power gain of an antenna. The extrapolation method has been implemented only for relatively small

standard gain antennas primarily because of the physical

limitations of the special extrapolation antenna ranges at

NBS. Thus it is generally necessary to determine the power

gain of a large ground antenna used to make an absolute

flux density measurement from a gain comparison with a smaller standard gain horn antenna whose gain has been

measured by the extrapolation method. This comparison can

be made directly by observing with both antennas the radiation from a satellite.

66
In section 4.2, the calibration of a small standard gain

antenna by the generalized three -antenna extrapolation method

is discussed. An analysis o£ the errors in the generalized

three-antenna extrapolation method for calibrating the small

standard gain antenna is also given.

In section 4.3, the gain transfer from a standard gain

antenna to a larger ground antenna is discussed. An analysis

of the errors in this gain comparison method is also given.

4 . 2 Calibration of Standard Gain Antennas by Use of the

Generalized Three-Antenna Extrapolation Technique

4.2.1 Introduction

The generalized three -antenna extrapolation method is

applied to the calibration of standard gain antennas with

power gains of 30 or 40 dB. This technique has the following

advantages: (1) the measurements are made at shorter distances

in order to eliminate ground reflections; and (2) it is possible to make accurate corrections for errors arising from

both proximity and multiple reflections between antennas.

Section 4.2.2 describes the characterization of antennas in terms of the scattering matrix parameter. Then,

this formulation is used in section 4.2.3 to develop a generalized three - antenna technique for obtaining the power

gain and the polarization ratio. In this technique, no a priori quantitative information concerning the power gain

and the polarization ratio of any of the three antennas is

required. Although the generalized three-antenna method can

be used at the conventional far-field distances , for large

antennas more accurate values can be obtained by the

extrapolation method.

67
Section 4.2.4 briefly describes the extrapolation method,

which is based on the antenna scattering theory and detailed

mathematical constraints upon the functional relations involved

in the antenna- antenna interaction. The accuracy consideration

for the power gain of the standard gain antenna is given

last in section 4.2.5.

4.2.2 Antenna Scattering Matrix Analysis

The extrapolation method is based upon the plane-wave

scattering matrix analysis developed by Kerns [60-62], and

is covered in detail in his publications [56-59]. Therefore,

this analysis is only briefly discussed to clarify the basic

approach to the reader who may not be familiar with it.

Consider the antenna shown schematically on figure 4-1,

oriented in the coordinate system Oxyz , and let k be the

propagation vectors for plane-waves in the space surrounding

the antenna. The X, Y, and Z directions are fixed in space

and with respect to the antenna. We choose a terminal surface S^ in the waveguide feed and define a supplementary

surface S , such that S + S forms a closed surface ena a o closing the source or detector associated with the antenna

(fig. 4-1).

For simplicity we assume that only one mode need be considered in the vicinity of S^. This is also the most common

use in practice. The formulation for multimode feeds is

discussed elsewhere [63]. It is convenient to denote the

combined x and y components of the propagation vectors k

by K, so that K = K e + K e where e , e , and e are unit ^ — — X—X y—y —

X ' —y * —

z

vectors . In order to set up representations for the antenna

scattering matrix, it is assumed that a set of outgoing wave

amplitudes b^ and b^(K) in figure 4-1 is determined by a set

of incident wave amplitudes, a^ and a^(K) as shown in figure

4-1, where a and b are the incident and emergent wave

0 0

68
69
amplitudes at the surface S^, and 3l^(X) and b^C]^) are spectral

density functions for incoming and outgoing plane waves in

the K space. The index m in a^CK) and b^(K) assumes the

value 1 and 2 corresponding to the two orthogonal polarizations, and j<2 "the wave component in the XY plane,

where i<-|^ = ^ and £2 —z —1 * '^^^ plane wave antenna

scattering matix is now defined by

m=l , 2

b (K) = S,QCni,K)a + / I S^,(m,K;n,L)a (L)dL, (4.2)

n=l,2

where the antenna characteristics are embodied in the four

scattering parameters S^^, SQ^Cm,K) , S-j^Q(m,K) and S-j^-j^ (m,K ;n ,]L) , which are respectively the input reflection coefficient, and

the receiving, transmitting and scattering characteristics,

n and play the same role as m and K. This equation is

derived on the assumption that the antenna system is a passive linear system, where the relation between the set of outgoing wave amplitudes and the set of incident amplitudes is

linear

.

If the antenna is reciprocal, then the receiving characteristic SQ^(m,K) is related to the transmitting characteristic S-j^qCii^jK) by the reciprocity relation [60]

-nQSQ^(m,K) = n^(K)S^Q(m,-K) , (4.3)

where n-j^ = ooe/y and ~ y/^U are the wave admittances

associated with the polarizations and respectively,

is the wave admittance for the waveguide mode involved,

e and y represent the permittivity and permeability of the

medium, y = (k^-K^)"^, and = co^ye.

70
Antenna power gain and antenna effective area are very

useful basic quantities that are here expressed in terms of

S-|^Q(m,K) and SQ-|^(m,K^) respectively of the antenna scattering

matrix. In accord with IEEE Definitions of Terms for

Antennas (1973) [2], the power (for a transmitting) gain

is defined by

Power radiated per steradian as a function of

G(K) = ^^^^^^^Q"

.(4.4)

net power into antenna/ (4Tr)

It will follow that in terms of antenna scattering matrix

parameters, the power gain is given by

47TY k^[|S (l,K)r + |S (2,K)Y/kr]

G(K) = 5 ±^ = ^ = -, (4.5)

where is the value of /e/y for the ambient medium. It should

be noted that the power gain is a characteristic of the antenna

under consideration and is independent of the source used to

excite the antenna; also that the value of the power gain

is independent of the insertion or adjustment of a lossless

tuner in the feed waveguide, whether or not this tuner is

counted as a part of the antenna.

For an antenna functioning in a receiving mode, the

counterpart of the power gain is the effective area, A . In accordance with IEEE Standard Definitions of Terms for

Antenna (1973) [2], the effective area is defined by

The power available at the terminals of a receiving

^ _ ^ antenna

e — The power per unit area of a plane wave incident on

the antenna from a given direction which is polarized

coincident with the polarization that the antenna

would radiate, and which gives rise to the power

available at the terminals.

(4.6)

71
Then in terms of plane-wave scattering matrix parameters, the

effective area is given by

For a reciprocal antenna, the power gain and effective area

functions satisfy the well-known relation

The far-field characteristics, i.e., the power gain, the

effective area, the polarization ratio, etc., of an antenna can

be determined from S^^CK) = S^q(1,K)i<^ + S-j^^ (2 ,K) £2 • The

purpose of the extrapolation technique is, therefore, to

determine S^q(K).

4.2.3 Generalized Three Antenna Measurement Technique

There are a variety of measurement techniques that take

full account of polarization characteristics and that do not

necessarily require reciprocal antennas; namely 1) one-unknown

(and one standard) antenna; 2) generalized two identical

unknown antennas [56]; and 3) generalized three (unknown)

antenna measurement techniques [58,59]. Of all antenna

measurement methods, the generalized three -antenna measurement technique requires a minimum of a priori information

about the antennas involved in the measurements. In addition

it is the method chosen for treatment in this report because it yields the best accuracy.

In this discussion of the generalized three-antenna

technique, for convenience reciprocity is postulated for all

three antennas . There is a further generalization of the

theory to a four-antenna measurement technique [63] in which

A,CK) = (4.7)

YoCi-ISool'^

Ae® = GC-K). (4.8)

72
no antenna need satisfy a reciprocity or similar known constraint. The antenna coordinate system is defined with its

Z axis in the electromagnetic boresight direction, and with

the X and Y axes referred to arbitrary marks on the antenna

structure as shown in figure 4-1.

With the above choice of references axes , let antenna

number 1 be placed at the origin and used as the transmitting

antenna. Let one of the other antennas, number two, be placed

in a receiving orientation, i.e., located at Z = d and pointing

in the -e_^ direction. The two antennas are shown schematically

in figure 4-2 with appropriate terminal surfaces and wave

amplitudes shown. The coupling equation which relates the

received wave amplitude b^ to the wave amplitude a^ in terms

of the transmitting characteristic is given by [58] ,

a b^Cd) =

J I 'S'^Cm,K) •^S^QCm,K)exp(iTd)dK, (4.9)

1 - ^ 2 — ^

where ^SQ^(m,K) is the receiving characteristic for antenna

2 in the receiving orientation; ^S-j^Q(m,K) is the transmission

characteristic of antenna 1 in the transmitting orientation;

and and are the reflection coefficients as shown in

figure 4-2. Equation (4.9) neglects the multiple reflections

between antennas.

We consider only the on-axis values (K=0_ and k=Y) of

the antenna characteristics and refer to these quantities as the antenna characteristics. The linear and circular

components of S^q(O^) are referred to as X, Y, R and L. For

example

CO) = XVy + Yv^ = Rv"" + Lv', (4.10)

where v and v are unit basis vectors for linear polariza-

+ ' - tions, V and v are the unit basis vectors for right and

73
74
left circular polarization, and v are defined as

. .

^ _

^ (4.11)

where the time dependence is assumed to be exp(-ia3t)o Then

the transformation equations between X, Y, R and L are given

by

p = ^

- X + iY (4.13)

Using this simplified notation for S-j^q(O^) and the reciprocity

relations given in eq. (4.3) by which the change in ^Sq^(O^)

due to reorienting antenna 2 is expressed in terms of ^S^q(0_)s,

the asymptotic value of eq. (4.9) for large d is

27rilca exp(ikd)

b^(d) ^ 5 [X^X2-Y^Y2], (4.15)

(i-r^r2)d

where subscripts 1 and 2 on X and Y referred to the X and Y

components of S-j^q(0_) for antenna 1 and antenna 2 respectively.

Equation (4.15) can be rewritten as

^1^2 '*'l'^2 "

'^^^ b^(d)d(l-r^r2)exp(-ikd)

d^°°\ a 2iTik

^ o

E , (4.16)

where b^(d) is the output wave amplitude and is determinable

from measurements as explained later. Now let the receiving

antenna be further reoriented by rotating about the Z axis by

90° in the direction from X and Y; then eq . (4.16) becomes

X^Y^ + X2Y^ = lim

'b;;(d)d(i-r^r2)exp(-ikd)"

d->°°\ a 27rik

^ o

E Dj;2. (4.17)

where b|^(d) denotes the output wave amplitude for the second

orientation, and D!j|2 is determinable from measurements.

75
Equations similar to eq. (4.16) and eq. (4.17) can be

written for the other two antenna pair combinations (i.e.,

antennas 1 and 3, and antennas 2 and 3) for a total of six

complex equations in six complex unknown quantities. This

is perfectly general even for asymmetrical antennas. These

six equations may be expressed by the two general equations

for transmission from antenna m to antenna n as

and

X.X. - Y.Y. = D! .

,

ij = 1,2,3

X.Y. + X.Y. = DV. 13 3 1 13

(4.18)

(4.19)

To solve the resulting set of six complex equations we define

D . - iDV . A = -iJ ii, (4.20)

9

and

13

DI . 13

+ iDV.

LL (4.21)

Then eqs . (4.18) and (4.19) can be replaced by

and

R.R. = A. .

,

13 13

L.L. = y .

.

1 3 ^13

For example the solution for circular components gives

^21^13

'32

1/2

C4.22)

(4.23)

(4.24)

76
and

L + (4.25)

1

^ ^'32 J

where the double signs are mathematically uncorrelated . The

X and Y linear polarization components corresponding to

eqs. (4.24) and (4.25) are

where the signs are correlated vertically but not horizontally.

Which solution-pair pertains to a given measurement cannot

be determined from the equations above. With regard to the

more significant double signs within the brackets , it is

easily seen that, if one choice yields |y|^ < |X|^, then the

other will yield |Y|^ > |x|^. Thus, if it is known that one

or the other of the inequalities holds, one simply takes the

solution yielding the known inequality.

It should be noted that a variety of singular cases arise

if one or more of the three unknown antennas is nearly circularly polarized. For example if antenna 3 has a nearly

left-circular polarization, then both A^^ ^^23

nearly zero. and R2 are, therefore, indeterminate, but

and all the left components may be obtained if the other

two antennas are not circularly polarized. The most common

combinations occurring in practice are, therefore, either

three linearly polarized antennas or two linear and one

(4.26)

and

(4.27)

77
circularly polarized antenna. In the first case the gains

and polarizations are determined for all three, while in the

latter, the characteristics of only the circular antenna will

be completely determined.

Finally, using eqs . (4 .5) and (4.10) the power gain and

polarization in the boresight direction CK=0_) are unambiguously determined in terms of the linear or circular components of S^q(O^).

The power gain:

4TrY k^Clxl ^+|Yi ^)

G(0) = 5 ,

or

4TTY^k2(|L| ^ + |R| 2)

G(0) = 5 . (4.28)

The complex linear polarization factor is

The complex circular polarization factor is

= p (4,30)

The axial ratio is

The tilt angle is

A = 1^1 1^1 . (4.31)

iRl - |L|

T = 1 arg(P^) . (4.32)

4.2.4 Extrapolation Technique

The data required to determine D^^ in eqs. (4.16) and

(4.19) are the asymptotic values of b^(d)'d/a^ for large

78
d vrith the frequency and the necessary reflection coefficients.

D^^ may be evaluated experimentally in at least three ways.

1) Conventional far field measurement method.

2) Near-field scanning technique [56], [57], [61].

3) Extrapolation method [58], [59], [64].

To avoid the error due to ground reflections and to

make accurate corrections to reduce errors arising from both

proximity and multiple reflections between antennas, the

extrapolation measurement approach is employed to determine

. The extrapolation technique requires the measurement

of b^Cd)*d/a^ as a function of antenna separation distance

d. For any two essentially arbitrary antennas, the received

signal can be accurately expressed as a formal series

representation given by Wacker [64]. For the antenna pair

1, 2 considered earlier with K = 0

b '(d)

o ^

^

1

- r r

2 i

OO 00 Y exp [ i (2p+l) kd] v ^^^2p + l _t p=0 1 = 0 d^

1 - r r ^ 2 1

/ex£_ikd|A + A

01

exp 5ikd frt d3 ri°

^ exp 5ikd

11

^20-^ •

+ •

+ • (4.33)

where the A's are complex coefficients. It is clearly shown

that eq. (4.33) includes both proximity effects (in the series

A

in —^) and multiple reflection effects (in the exponential

d^

series) without approximation. For example, the first

series represents the directly transmitted wave; the second

79
series the first order multiple reflection between two antennas, and the third, fourth, etc., series the higher order

multiple reflections. In the proper application of this

technique, the antennas are sufficiently close and high

enough off the ground that ground reflections are negligible;

eq. (4.33) includes no terms due to such reflections.

It can be seen from eqs . (4.16) and (4.33) that

Thus the determination of the leading coefficient in

eq. (4.33) is the immediate measurement objective.

The basic idea of conventional far-field techniques is

to have d large enough so that other terms in eq. (4.33) are

negligible compared to the leading term, A^q, in the series.

This requires very large ranges for some antennas and even at

d = 64 where D is the major aperture dimension of the

antenna, the proximity correction for a common type of

standard gain horn is still approximately 0.05 dB . Moreover,

as the distance is increased, the. error due to ground reflection tends to increase.

In the extrapolation technique, measurements are made

as a function of separation distance, and the plotted data

points are curve fitted with as many terms of eq . (4.33)

as may be significant. When all significant terms are included, Aqq will be determined more accurately than when the

higher terms are ignored. The power gain, the effective

area, the polarization ratio, etc., will be, therefore,

determined with more accuracy when this value of A^q is used.

4.2.5 Accuracy Consideration

The general character of the averaged extrapolation

data fitted with 4 -term polynominals is shown in figure

4-3, where the abscissa is expressed in terms of the

A

00

(4.34)

Zirik

80
ID

cno

o

o

un

roo

o

o

1 >^ 1 I

• 1 1 1• I 1. o un o o un o LO o un

ir> CM o CM o Ln CM

CVJ CM CM o o o

o O O O o o o o o o

o

o

CM

o

CVJ r— Q

c_> 21<

1— o oo CM >—

1

Q

Q

UJ

r«>i

t—

(

_i

<

O

CO

Si

aio

o 2:

<Co

o

Q.

o 1—

1

C_) o

UJ

o

o

o

o

iH (=: o p •H

(/) •H N

tfl ix; O

E

•H

C • CU

ur

II +-> •H >s <U U a,

03 I—1 0)

03 3 U

C cr o

•H (U e fH 03 o ^ e

1—

1

o c: PQ o

K) 'eu M fH

1 03 •H

03

•> 03 (M

03 +-> ^( M t/i 0) II 03 is T3 T3 o 03

03 PI

03 <U

1 P

<D 03 03 ^1 M

CU O

03 O

U

P

•H

fin

(^j"j-L)(P>|L-)dxa p{p)?q

81
reciprocal normalized distance —, and the ordinate is

expressed in terms of the po\v~er ratio:

b^Cd)d expC-ikd)Ci-r^r^) ^

The difference between the measured and fitted waves is also

shown as the point plot in figure 4-3, where one point corresponds to each data point. These differences are amplified

by 500 in this figure.

The errors which have the largest effect are those which

vary with distance because the extrapolation process can

amplify the effect of small errors in the data to significant

errors in Aqq. Those errors are due to receiver nonlinearity

,

atmospheric loss uncertainty, range misalignment and

distance uncertainty. The analysis of the errors in the

measurement of the power gain of standard gain antennas is

performed using a computer program basically developed by

the Fields and Antennas Section of the Electromagnetics

Division, NBS, and is discussed below in detail.

A. Error in Mismatch Factors

As stated earlier, the power gain of an antenna is a characteristic of the antenna under consideration, and is

independent of the source used to excite the antenna. Therefore a lossless tuner in the feed waveguide, whether or not

the tuner is counted as a part of the antenna, will not change

its power gain. However, mismatch error is involved in the

measurement of b ' and a . At NBS this mismatch factor is

o o carefully taken into account by carefully measuring the

amplitude and phase of the reflection coefficients of the

antenna, the receiver and the generator using an automated

network analyzer. If the amplitudes of the reflection coefficients of an antenna, a receiver, and a generator are about

82
0.05, and the amplitude and phase can be measured to within

an accuracy of 101, then the resulting error corresponds to

about ± 0.006 dB uncertainty in the power gain of the antenna.

In calculating total errors in section 4.2.6 to follow, it

is assumed that when the amplitude and phase of the reflection coefficients of the antenna, receiver, and generator

can be measured to within an accuracy of 10%, then the mismatch error contribution to the power gain of the antenna is

around 0 .006 dB.

B . Attenuator Error

There is a large difference in wave amplitude between

b' and a . Therefore, an attenuator is used to reduce a to

0 0' o a level that the receiver can handle. Moreover, to avoid

the possible nonlinearity error associated with the receiver,

it may be desirable to further reduce the a^ signal level

to the same level as b^ by use of a calibrated precision

attenuator. A precision attenuator can be calibrated to

within an accuracy of 0.01 dB including the multiple reflections and mismatch error by the series substitution, dc

substitution, modulated subcarrier, or i-f substitution

technique [65]. In calculating errors in section 4.2.6 to

follow, it is assumed that a 0.01 dB error in the precision

attenuator causes 0.01 dB error in the power gain of the

antenna.

C . Receiver Nonlinearity and Gain Instability

The linear response of a receiving system is determined

by measuring the change in output signal resulting from a change in an input precision attenuator used to set various

receiver input power levels. Thus, the receiver nonlinearity

is determined by systematically varying the precision

attenuator over a 10-12 dB range and recording the

83
corresponding receiver output values . The resulting calibration curve is then used to correct the measured data, if

necessary. The error in the power gain of an antenna due to

receiver nonlinearity and receiver gain instability is of

the same nature and is shown in figure 4-4 as a function of

the receiver nonlinearity and/or gain instability. If the

gain instability of a receiving system is characterized as

a random uncorrelated fluctuation phenomenon, the errors due

to this source are then considered to be random and uncorrelated, and could be taken out by statistical averaging.

In calculating errors in section 4.2.6 to follow, it is

assumed that after suitable corrections, the receiver nonlinearity is about 0.002 dB per 1 dB, which contributes an

error of about 0.03 dB to the power gain of the antenna.

D. Atmospheric Loss Uncertainty

Uncertainty in the atmospheric loss between a transmitting and a receiving antenna cause an error in the measured

power gain of an antenna. This becomes particularly severe

at millimeter wavelengths where the absorption of electromagnetic power is very large and is highly dependent on frequency.

Typical atmospheric losses are shown in figure 4-5 as a function of frequency. Figure 4-6 shows the error due to

uncertainty in atmospheric loss in the calibration of the

power gain as a function of the uncertainty in atmospheric

loss. In the 5 to 10 GHz frequency range the atmospheric

loss is about 0.008 dB per kilometer. In calculating errors

in section 4.2.6 to follow, its uncertainty is assumed to be

12.51, i.e., 0.001 dB per kilometer for the analysis of the

error estimates.

E . Range Misalignment

Means must be provided for accurately aligning the two

antennas involved in a given measurement and for maintaining

84
RECEIVER NON-LINEARITY IN dB/dB

Figure 4-4 Error in the measured antenna power gain due to

receiver non-linearity (Frequency = 7.25 GHz).

85
Frequency in MH?

86
0 0.002 0.004 .006 0.008

ATMOSPHERIC LOSS UNCERTAINTY IN dB

Figure 4-6 Error in the measured antenna power gain due to atmospheric

loss uncertainty (Frequency = 7.25 Ghz)

.

87
this alignment as the separation distance is varied from

almost zero to about one or two D^/A, Assuming that in the

far- field the power gain can be very closely approximated by

^i'P) = s inc^ ^ 2 . 784(})

^ where G is an on-axis power gain,

hp °

*^hp

^^^-'-^ power beamwidth) = 70 X/D, and cj) is the misalignment angle, the error in the calibration of the power gain

of the antenna due to range misalignment is shown in figure

4-7 as a function of maximum angular misalignment. Here it

is postulated that the angular deviation is zero at the

maximum separation distance (typically 2 —) and is maximum

at the minimum separation distance (typically 0.2 —) • In

calculating errors in section 4.2.6 to follow, it is assumed

that the maximum angular deviation is about 0.01 degree

about any axis for the analysis of error estimates.

F. Distance Inaccuracy

The separation distance, d, between two antennas, or

more specifically, between terminal surfaces S-j^ and S2 of

figure 4-2 must be accurately measured. A laser interferometer is very convenient for this purpose. The separation

distance can be measured to within 0.05%. The error in the

measured power gain of an antenna due to the distance inaccuracy is shown in figure 4-8 as a function of that distance inaccuracy in percent. In calculating errors in section

4.2.6 to follow, it is assumed that the distance inaccuracy

is about 0.05% for the final analysis of the error estimates.

4.2.6 Summary and Concluding Remarks

An estimate of the best total accuracy that one can

expect for the calibration of the power gain of a standard

gain antenna using the generalized three-antenna extrapolation

88
Figure 4-7 Error in the measured antenna power gain due to range misalignment

(Frequency = 7.25 GHz).

89
0.024r0.020 -

CQ-a- 0.016 -

o

0.012-

o 0.008

0.004 -

0.02 0.04 0.06

DISTANCE UNCERTAINTY

0.08 0.10

IN PERCENT

ure 4-8 Error in the measured antenna power gain due to distance

uncertainty (frequency = 5 to 10 GHz, antenna power gain

= 20 to 50 dB, major aperture dimension of antenna

= 0.5 to 10 m)

.

90
method is shown in figure 4-9 as a function of the major

aperture dimension of the antenna. Figure 4-10 shows the

accuracy of the power gain for a standard gain antenna as

a function of the operating frequency. In these error

estimates, the following assumptions are made:

1. Amplitude (< 0.05) and phase of the reflection

coefficient are measured to within an accuracy of

101.

2. An attenuator is calibrated with an accuracy of

0.01 dB.

3. Receiver nonlinearity is 0.002 dB per dB.

4. Uncertainty in the atmospheric loss is 0.001 dB

per kilometer.

5. Maximum range misalignment is 0.01 degree about any

axis . 6. Separation distance is measured to within 0.051.

7. Random error contribution from all sources is

0.0 3 dB C3cr) . This number is based on experience

at NBS in very careful measurements, where much data

was taken and then statistically processed.

The total errors shown in figures 4-9 and 4-10 were calculated

using a linear addition of the various constituent errors,

although some of the contributing sources of error are independent and therefore satisfy the condition for quadrature

error addition. The errors due to an attenuator and the receiver linearity may not be independent and therefore may

not satisfy the condition for quadrature error addition. The

reason for this is that the receiver linearity is usually

determined by use of an attenuator. However, other sources

of errors, namely, the errors due to mismatch uncertainty,

atmospheric loss uncertainty, range misalignment, and distance

inaccuracy, are independent and do satisfy the condition for

91
0.15

D = MAJOR APERTURE DIMENSION OF ANT IN METERS

CD

CD

O

Cl.

0.10-

RANGE MISALIGNMENT (0.01 °)

ATMOSPHERIC LOSS UNCERT (0.001 dB/km)

TOTAL ERROR

ERROR DUE TO RCVR NON-LINEARITY ( 0 . 002dB/dB

)

0.05

O

0.00

Figure 4-9

ATTENUATOR ERROR (0.01 dB)

MISMATCH UNCERT (10% OF REfToeTT

7IsTrNcl"lNrCcT]RAc7 ("osT)

RANDOM ERROR (3a)

E E E E E E

un CTi UD CO oo O O CM Ln en

II II II II II II Q

1 Q

1 Q

1 Q1 Q1 Q

1 30 35 40 45 50 55

POWER GAIN OF STANDARD ANTENNA IN dB

Accumulated error in the measured power gain of the

generalized three - antenna extrapolation method (frequency

= 7.25 GHz)

.

92
0.25

POWER GAIN OF ANTENNA

0. 20 -

CO

0.15

O

CO QQ ca ca CQ 00

T3 o T3 T3 T3

CO r*. <n 00

<n CM CO ^ LO CM CM CM CM CM

II II II II II II as CD C3 t3

0.10 -RANGE MISALIGNMENT (0.01°) TOTAL ERROR

o

cm ATMOSPHERIC LOSS UNCERT (0.001 dB/km)

RECEIVER NON-LINEARITY (0.002 dB/dB)

0.05

ATTENUATOR ERROR (O.OldB)

"iTMTTTH^uTcTRTATNTY'^Tor^F REEL COEF)

'dT STAN cT "noH-Tin eTrTt y To"b 5%

)

RANDOM ERROR (3a)

5 6 7 8 9 10 n

FREQUENCY IN GHz

Figure 4-10. Linear error accumulation for the measured power

gain of the standard antenna using the generalized

three-antenna extrapolation method (major aperture

dimension of antenna = 2 3.5 cm).

93
quadrature error addition. Under these assumptions, the

limiting accuracy of the power gain of a standard gain horn

antenna using the generalized three-antenna extrapolation

method is shown in figure 4-11 as a function of the major

aperture dimension of the antenna and in figure 4-12 as a function of operating frequency.

In conclusion, using the extrapolation technique, it

seems possible to calibrate the power gain of a standard

gain antenna, with a typical power gain of 40 dB and whose

major aperture dimension is approximately 1.6 m, to within

linear accumulation error of 0.08 dB for 3a limits or a quadratic accumulation error of 0.04 dB for 3a limits. The

typical length of the extrapolation range required for the

extrapolation measurements is approximately 120 m, and the

separation distance (for D = 1.6 m and f = 7.25 GHz) is to

be varied from typically 0.2 that is 12 m, to 2 —, that

is 120 m. In principle, it is possible to calibrate the

power gain of a larger standard gain antenna, say, with

power gain of 50 dB whose major aperture dimension is approximately. 5.3m using this method. However in order to achieve

the separation distances varying from 0.2 to 2 —, the required length of an extrapolation range is approximately

1.4 km. In practice, it is very difficult to construct and

maintain such a long extrapolation range with good stability

and alignment. Therefore, it is generally necessary to

calibrate the power gain of a relatively small standard gain

antenna, typically with power gain of 40 dB and major aperture

dimension of 1.6 m at 7.25 GHz by use of the extrapolation

method, and then to determine the power gain of a larger

ground antenna, typically with power gain of 60 dB and major

aperture dimension of 16.6 m by a gain comparison technique

which uses a radiation from a satellite as a common source.

This gain comparison method is discussed in the next section.

94
LL. O

z:oI—

I

LU

LU

<co"-3

III o

iiie-9=Q -

ujg • L = a -

Lug-o=a -

L

Lf) o

o

Ln

o

• H (U

rt +-*

ct!

J_l 1

<L) D

O >H

fl. 1 ' 1

p—' '

' to •H N

03 i-i K

:z <D cd o

I—

1

<D LO <c

f' CD • —

1

LiJ

1

~ t1) II Vi/ II 2: O

t-M 4-) ti.. Q »—1 ^^^^ 1-^ oW fli t~-* SI/ <a; • H •H 3 Q

J3 <U

•=x. 3 Cd tL, CO e d *—

'

' I—

<

u. U <U 13 o (J 4J Q

rrt p; (-;

»—

I

ct w ^

CJ3

K-i p; QC

UJ

(U o J-i +-> nj 3 I/) '—

i

+j o

rt <D Ph

C/ O <D o

CO

o O

CVJ o o

o

I

(^e) ap Ni NIV9 y3M0d vnnbinv ni yoay3

95
0 .05

D

CD

o

en

0 . 04

0 .03

0 .02

0.01

G = POWER GAIN OF ANTENNA

CQ

a

.CO

II o

CQo

CVJ

II C3

00

I

CQ"O

cy> roCM

II

CD

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CO

inCM

II C5

7 8

FREQUENCY IN GHz

10

Figure 4-12 Quadrature error accumulation for the measured power gain

of the standard antenna using the generalized threeantenna extrapolation method (major aperture dimension

of antenna = 23.5 cm).

96
4 . 3 The Calibration of a Large Ground Antenna by the Gain

Comparison Method

4.3.1 Introduction

Utilization o£ an accurately calibrated large ground

antenna with 60 dB power gain is typically required for an

accurate calibration of Cas A [see section 6) . Unfortunately,

accurate calibrations of large antennas are very difficult.

There are various methods in common use which yield fairly

accurate gain figures, but which may require elaborate technical

preparation. Some of these methods are: gain comparison,

pattern measurements and subsequent integration, extrapolation

measurements, planar or spherical scanning techniques.

It is found in general that the extrapolation method

gives best accuracies for the power gain of relatively small

standard gain antennas, but is not suitable for large antennas

as indicated in section 4-2. Therefore the decision is often

made to calibrate the power gain of large ground antennas

by the gain-comparison technique, utilizing a standard gain

antenna. In this method, a received signal is successively

measured with the standard gain antenna whose absolute gain

is accurately known and then with the large ground antenna

under test, both being connected to the same receiving

systems . The ratio of the received powers is then related

to the ratio of the power gain of a standard gain antenna

to that of the large ground antenna under test.

In this part of the report we discuss the gain comparison method and assume that the calibration signal is stable

and is transmitted by a geostationary satellite. The major

advantages of the gain-comparison method are: 1) the signal

source is in the far- field of even larger ground antennas

97
because the distance between a satellite and a ground station

is typically 35,000 kilometers; and 2) the power radiated by

a typical satellite is approximately 10 dBW or higher (dBW

means dB above one watt) and is strong enough to acquire with

even a low- gain standard antenna.

In the gain-comparison method the total power received

from the satellite is measured in rapid succession: first

with the large ground antenna under test, then with the

standard gain antenna. These two measurements are then repeated without the satellite signal. The setup for the gaincomparison measurement is shown in figure 4-13. The advantages

of this technique are: 1) a priori knowledge of the following

is not required: satellite performance characteristics,

effective radiated power from the satellite, path loss between the satellite and the ground antenna, the system

temperatures when the standard gain antenna or the large

ground antenna under test are connected to a receiver, the

bandwidth of the receiver, etc.; and 2) it is possible to

perform the measurements of power ratio with more accuracy

than measurements of absolute power.

Referring to figure 4-13, the total power delivered to

the receiver output port is symbolized by P. For a large

ground antenna while receiving a signal from the satellite

4.3.2 Theory

Pi = ((—'ERP '(l-L ) 'M -t -A +k

1 u^ u-^uuu

u

+k* (1-a , ) -T , -B,

^ ul'^ oul 1

T T 'B,] 'a T+kT tB, aul 1-* ul el 1

(4.35)

98
SATELLITE

ERP

/ \

/ \

/ \

/ \

LARGE GROUND

ANTENNA

/

POWER GAIN = G

EFFECTIVE ^ . AREA

\V

WAVEGUIDE

SWITCH

STANDARD GAIN

ANTENNA

POWER GAIN = G.

EFFECTIVE ^ . AREA

OUTPUT PORT

RECEIVING SYSTEM i

Figure 4-13 Schematic for experimental gain comparison method

99
and for a standard gain antenna,

^2

+k» (1-a ^ ^) •! ^'B^ •go- (4.36) S2-' os2 2

For the ground antenna under test when the antenna is

pointing away from the satellite,

P3 = '^•[Te3^T^u3-W(l-"u3)-Tou3]-B3-g3. (4.37)

and similarly for the standard gain antenna

P4 = k-[T^4.T^3,-a^^.(l-a^^).T^^,].B4.g^. (4.38)

Here, A is the wavelength,

ERP is the effective radiated power of the satellite,

L is the path loss between the satellite and a ground

antenna, expressed as a power ratio,

M is the polarization mismatch factor,

t is the tracking factor that takes tracking inaccuracy

into account,

A is the effective area of the antenna,

k is the Boltzmann's constant,

is the antenna noise temperature referred to the

antenna output port and includes external noise and

noise due to antenna loss,

B is the bandwidth of the receiving system,

g is the available power gain of the receiving system,

a is the ratio of the available power at the antenna

output port to the available power at the receiver

input port,

is the physical temperature of the waveguide, etc.

between the antenna output port and the receiver input

port,

and is the effective input noise temperature of the receiver.

100
The subscript "u" denotes factors associated with the measurement when the system is connected to the ground antenna,

and the subscript "s" denotes factors associated with the

measurement when the system is connected to a standard gain

antenna.

The effective area of the ground antenna is then given

by

A^'ERP • (1-L ) 'M -t

A = A

u s u

as2

-ERP • (1-L ) 'M -t

u u" u u ul

!2

§1

XZ_

Y

"3 ^2

^u

(4.39)

where

(4.40)

(4.41)

"2 '3 M (4.42)

[T^ ^+T ^-a ^+(l-a ^) -T ^]«B^-[T .+1 .'a . + (l-a J 'T J'B. e2 as2 s2 ^ s2^ os2-' 2 e4 as4 s4 ^ s4^ os4-' 4

s4-^ 0S4-' 4

(4.43)

and

[T^T+T T + (l-a J 'T t]'B,-[T -+T -'a ^+(l-a „)'T ^]*B_

_ *- el aul ul ^ ul^ oul-* 1 *- e3 au3 u3 ^ u3^ ouS-* 3

[T _+T -'a ,+(l-a _)'T 72*B_ a3 su3 u3 u3'^ ou3 3

^^-^

It should be emphasized that the ratios X, Y, and Z should

nominally be measured rather than the absolute powers , ?2> Pj* and P^. The expression for the effective area of

a ground antenna given in eq. (4.39) applies to the very

general case where the effective radiated power, antenna

101
temperature, path loss, front-end loss, gain of receiving

system, bandwidth, etc. , are assumed to change during the series

of four measurements. It is useful only for the purpose of an

error analysis. For actual measurement purposes, however,

one assumes the following to hold during the measurements

1. Operating frequency stays constant.

2. - ERP stays constant.

3. Antenna temperature stays constant for each antenna.

4. Path loss is the same between the satellite and

each antenna and stays constant.

5. The polarization mismatch between the incident wave

from the satellite and both antennas is the same.

6. Tracking factor is the same for both antennas.

7. Losses between the antennas and the receiver

system are equal for both antennas.

8. The gain of the receiving system stays constant.

9. The physical temperature of the antennas and between the antennas and the receiving system is the

same for both antennas.

10. The effective input noise temperature of the receiver stays constant.

With these assumptions, eq. (4.39) simplifies to

P - P

A = A — X_l_l = A — ^ . C4.45) u

^ Y Z - 1 ^ P2 - P4

It is easy to see that the factor Y - 1 is the signal-tonoise ratio for the large ground antenna when receiving the

signal from the satellite. Similarly, Z - 1 is the signalto-noise ratio for the standard gain antenna when receiving

the signal from the satellite.

102
For a reciprocal antenna, the power gain is obtained

from

G = — A, (4.46)

and the final analysis o£ the error estimate is discussed in

terms o£ the power gain o£ the large ground antenna.

4.3.3 Accuracy Consideration

The power ratio measurements cause the largest uncertainty

in the calibration of the power gain of the large ground antenna under many circumstances, and should be carefully noted.

In this section the various sources of error in the gaincomparison method are discussed.

A. The Power Gain of a Standard Antenna

The summary of the power gain accuracy of the standard

gain antenna using the extrapolation technique is given in

section 4.2.4. Typically the power gain of a 40-dB standard

gain antenna can be determined to within a linear accumulation

error of 0.08 dB for 3a limits by use of the extrapolation

technique, or to within a quadrature accumulation error of

0.04 dB. This error in the power gain of the standard gain

antenna reflects directly on the error in the measured power

gain of the ground antenna.

B . Frequency Instability

The receiving system is assumed to be tuned to the frequency of the signal from the satellite. The signal from the

satellite used for calibration is assumed to be CW so that

its bandwidth is much narrower than that of the receiving

103
system. It is possible to control the frequency of a satellite

signal and of a receiving system to within one part in 10^ with

a good synchronizer. Therefore the error due to this source

is negligible.

C . Effective Radiated Power (ERP)

According to IEEE standard definitions of terms for

antennas [2] , the effective radiated power is defined as ERP = in given direction, the power gain of a transmitting antenna multiplied by the net power

accepted by the antenna from the connected

transmitter.

It is assumed for the purpose of the present error

analysis that the effective radiated power from a satellite

is either 10 dBW or 30 dBW. It should be noted that the

value of ERP is needed only for the error analysis and does

not need to be known for the measurement of the power gain

of the ground antenna, provided ERP is stable during the

measurements. In practice, an assumed 0.01 dB instability

of ERP exists during the power measurements and causes an

uncertainty of again 0.01 dB in the measured power gain of

the ground antenna.

D. Path Loss

The path loss consists of the free-space loss and the

loss due to atmospheric absorptions. The free-space loss

is the loss between two isotropic antennas in free space,

expressed as a power ratio [2]. The free-space loss is usually

expressed in decibels and is given by 20 logC4TTr/A) where r is the distance between two antennas. For a typical distance

of 35,000 km between a satellite and a receiving antenna, the

free-space loss at 7.25 GHz is approximately 200 dB.

104
The terrestrial atmosphere causes radio wave attenuation,

which usually divides into three different types: absorptive,

refractive, and diffusive attenuation. Absorptive attenuation

is caused by a resonance in the oxygen and water vapor molecules and is about 0.1 dB at a 40° elevation angle. Smooth

variations in the refractive index of the atmosphere cause

refraction of the radio wave from a satellite, and irregular

variations in the refractive index of the atmosphere due to

turbulence cause diffusion and distortion of a radio wave.

The attenuation due to refraction and diffusion (as sensed

by the antenna) is dependent on the aperture dimension of

the antenna [66].

The average atmospheric loss at 7.25 GHz is about

0.008 dB per kilometer as previously shown in figure 4-5.

Path loss instability between satellite and ground introduces

an error which is assumed to be 0.01 dB to the power gain of

the ground antenna.

E . Polarization Mismatch

To determine the mismatch between the polarization

patterns of the signal from the satellite and that of the

receiving ground antenna (or the standard gain antenna) it

is necessary to know the on-axis polarization characteristics

of each antenna and the polarization characteristics of the

field incident from the satellite.

The polarization mismatch factor, M, is defined here

as follows (M relates to a specific receiving antenna and

the on-axis component of a specific incoming wave) : M is

given by the ratio of the power at the antenna output port

when an arbitrarily polarized and oriented wave is being

received, to the same output power when a wave that is

polarized and oriented for optimum reception is being received.

105
The expression for M that holds when either field or antenna

is elliptically or circularly polarized is given by [67]

(R. R^±l)^ cos^ 0 + (R +R^)2 sin^ 9

M = —^-^ ^ ^ ^ . (4.47)

(R^+1)(R^+1)

R^ and R2 are the electric field axial ratios (maximum

divided by minimum) for an antenna and an incident electric

field, respectively. 6 is the polarization mismatch angle,

i.e., the angular difference between the major axes of two

polarization ellipses.

In eq. (4.47) the plus sign is used when the polarizations of the antenna and the incident electric field from

the satellite are in the same sense, and the minus sign

applies when both polarizations are in the opposite sense.

When one of the polarizations is linear, the polarization mismatch factor, M, becomes

(R2+1) + (R2-1)cos 29

M = . (4.48)

- v 2(R^+1)

When both polarizations are linear, M is simply given by

cos^ 6. When the electric field axial ratios of the elliptically polarized incoming wave from a satellite and of

a ground (or standard horn) antenna are assumed to be 1.2 and

can be measured with 0.1% accuracy, the error for the gain

calibration of a ground antenna due to this source is about

± 0.005 dB. Similarly, when the polarization mismatch angle

or orientation of the major axis of the polarization pattern

can be ascertained to within 1 degree, the resulting error

is 0.005 dB.

F. Tracking Accuracy

The tracking accuracy is the accuracy with which an

antenna can track a source. The tracking error is a measure

106
of tracking accuracy and is defined as the instantaneous

space angle difference, (}>, between the directions of the

power pattern maxima of a receiving antenna and a (satellite)

transmitting antenna. The tracking error is usually specified

in terms of its rms value, which is usually normalized to halfpower beamwidth, in this case that of the ground antenna.

To estimate the error introduced in the measured power

gain by the tracking error, it is reasonable to assume that

the tracking error has a normal probability distribution [68]

,

namely.

exp

hp hp

TT < ()) < IT (4.49)

where 6 is the rms value of the tracking error normalized

to the half -power-beamdwidth of the ground antenna. At

far-field distances, the power gain of the antenna can be

very closely approximated by the sine x function. Knowing

that the function sinc^ x = 0.5 when x = 1.392 radian, the

power gain can be given by

G((f)) = sinc^(-5 -)

° "hp

The expected value of the power gain is then

(4.50)

TT E{G((t))} =

/ G((i))p((t))d(})

-TT

/ZtT 6

'hp

/ sine'

-TT

2.784({)

'hp

exp

26^0

hp

dcf). (4.51)

The expected reduction in measured power loss due to tracking

inaccuracies is given by the ratio of the expected values of

107
the power gain and ;

E{G(e)} 1 — = f 2f2.784(j)

J sine -

G /Ztt 60^ -TT ^ exp A.

hp " ""hp ^hp

dc|). C4.52)

The numerical computation o£ the integral was performed by

Zolnay [68] and the result is given in figure 4-14. Using

the expression for half-power beamwidth,

V = (4.53)

where 6^^^ is in degrees, D is the major aperture dimension

of the antenna, and X is the wavelength. The power gain of

an antenna is

G = ilA= if n^Ag, C4.54)

where X is the wavelength, A is the effective area of the

antenna, is the aperture radiation efficiency and is

the geometrical aperture area. The expected reduction in

measured power gain due to tracking inaccuracy is given as

a function of power gain and of antenna diameter in figure

4-15.

In calculating total error in the measured power gain

discussed in section 4.3.4 to follow, it is assumed that the

tracking error is 5 seconds of arc.

G. Waveguide Feed Loss Uncertainty

The uncertainty in the difference between losses arising

between the ground antenna output port and the receiver input port and losses arising between the standard gain antenna output port and the receiver input port contributes an

error to the measured power gain of the ground antenna. It

is assumed in section 4.3.4 that this difference is 0.01 dB

,

which in turn causes a 0.01 dB error in the measured power

gain of the ground antenna.

108

0.07 r—

0.06

0.05

T3

CD

O

0.04

0.03

0.02

eno

on 0.01

D E MAJOR APERTURE DIMENSION

OF ANTENNA

o

II II Q

CO

Ln

II oII Q

ID

CO

ID

II Q

(D

MO

30 40 50 60 70

ANTENNA POWER GAIN IN dB

80

Figure 4-15 Error in the antenna power gain due to tracking

inaccuracy (frequency = 7.25 GHz, tracking inaccuracy

= 5 seconds of arc, rms).

110
H. Uncertainty in Po\fer Ratio Measurement

One of the most significant errors in the calibration

of the power gain of a ground antenna is due to the uncertainty

in the power ratio measurements. This is especially true when

the effective radiated power (ERP) from the satellite and/or

the power gain of the antenna is small. Figure 4-16 shows

the error in the power gain of an antenna due to the uncertainty in Y as a function of uncertainty in Y, and figure

4-17 shows the error in the power gain due to uncertainty in

Z as a function of uncertainty in Z. The ratios Y and Z are

defined in eqs . (4.41) and (4.42). It is clear from this

figure that the ratio of the power measurement for a standard

antenna receiving a signal to that without a signal should

be performed with great care in order to minimize the relatively large Z related error.

I . Uncertainty Due to Receiver Gain Instability and

Nonlinearity

Receiver gain instability and nonlinearity are often

significant sources of error in the calibration of the power

gain of a ground antenna. In order to minimize these measurement errors, extremely good receiver stability and

linearity are required, especially during the power measurements when the standard gain antenna is connected.

The gains of the receiving system during the power

measurement with the standard gain antenna are g2 and g^ in

eq. (4.39). Figures 4-18 and 4-19 show uncertainty in the

measured power gain of the ground antenna due to uncertainty

in g2 and g^ as a function of uncertainty in g2 and g^

respectively

.

To avoid the nonlinearity errors that result from widely

different levels it may be desirable to reduce the signal

level from the larger (ground) antenna to the same level as

111
0. 01 5|-

T3

<

O

o

a.

LU

0.010

0.005 - o

q:

a;UJ

ERP = EFFECTIVE RADIATED POWER FROM

SATELLITE

Gu = POWER GAIN OF ANTENNA UNDER TEST

(ANTENNA SYSTEM NOISE TEMP = 30K)

0.01

UNCERTAINTY IN Y IN dB

0.02

Figure 4-16 Lrror in the antenna power gain due to uncertainty

in V = P1/F3

112
0.025 r0.020 -

-a

- 0.015-

UJo

a.

EFFECTIVE RADIATED

POWER FROM SATELLITE

POWER GAIN OF STANDARD

ANTENNA (ANTENNA SYSTEM

NOISE TEMP = 30 K)

0.010 -

eno

a:

a:

0.005 -

0.01

UNCERTAINTY IN Z IN dB

0.02

Figure 4-17 Error in the antenna power gain due to uncertainty in

Z = P2/P4

113
0.025

0.020 -

GQo

^ 0.015-

o

a.

0.010 -

a:o

q:

a:

0.005 -I

Gs-POWER GAIN OF STANDARD ANTENNA

J

0.002 0.004 0.006 0.008 0.010

UNCERTAINTY IN IN dB

Figure 4-18 Error in the antenna power gain due to uncertainty in g2

114
0.025|-

0.020 -

CD

-a

CD

O

CL.

0.015 -

0.010 -

o

a:

0.005 -

ERP = EFFECTIVE RADIATED POWER

FROM SATELLITE

POWER GAIN FOR STANDARD

ANTENNA

0.002 0.004 0.006 0.008 0.010

UNCERTAINTY IN IN dB

Figure 4-19 Error in the antenna power gain due to uncertainty in

115
that from the smaller (standard gain) antenna. This is

accomplished by the use of a calibrated directional coupler

and/or a precision attenuator. This technique introduces

an additional error due to the coupler and/or the attenuator.

Moreover, since this technique degrades the signal-to-noise

ratio of the receiving system as used with the large antenna,

the error due to the power ratio measurements (Y) becomes

large just as in the case of the smaller antenna. Therefore,

the use of a coupler and/or attenuator may not reduce the

total measurement error.

If receiver gain instability is regarded as a random

phenomenon, the resulting error is also random and can be

minimized by statistical averaging. However, the uncertainty

due to receiver nonlinearity should still be included as a systematic error.

J. Uncertainty in Antenna System Noise Temperature

The noise temperature, T^ , represents the available power

at the output port of a hypothetical lossless antenna. T^ is

due to noise sources external to the antenna aperture and is

given by

G

\ ^ ^ T(e,cl))f(0,(}))d((), (4.55)

where T (e,(j)) is the temperature distribution on the sphere

surrounding the antenna and f(G,4)) is the antenna power

normalized to the on axis power gain , and is the antenna

radiation efficiency. The external noise consists of sky

noise (cosmic noise plus noise due to atmospheric absorption)

and ground noise (usually around 290K)

.

116
The antenna noise temperature, i.e., the noise temperature

appearing at the output port of the antenna feed, consists

of both the (lossless) antenna noise temperature, , and

noise introduced by the antenna and waveguide feed losses.

The antenna noise temperature, T^, can be stated in terms of

the following equation

T^ = T^a + Cl-a)TQ, (4.56)

where T^ is the (lossless) antenna noise temperature (K)

referred to the lossless antenna output port, a is the ratio

of the power entering the antenna aperture to the available

power at the output port of the waveguide feed, and T^ is

the ambient temperature.

It should be noted that the antenna noise temperature

changes drastically with elevation angles (9) , particularly

at the lower elevation angles between 0 and 10 degrees , and

reaches almost 290K at zero elevation angles. However, at

elevation angles larger than 40 degrees the antenna noise

temperature is relatively constant and is about 30K,

The instability or changes in the antenna noise temperature while on- and off -satellite measurements are being made

with any one antenna cause an error in the measured power gain

of the ground antenna. It can be assumed that when the

sky noise temperature is about 5 degrees or less, as is usually

the case, the antenna noise temperature does not change much

during the measurements. Therefore the error due to this soufce

is assumed to be negligible.

K. Error Due to Change in Effective Input Noise

Temperature, Bandwidth, and Ambient Temperature

The effective input noise temperature, the limiting

bandwidth of the receiving system, and the ambient temperature

at various points of the system are assumed to be stable

117
provided measurements are carried out rapidly. This rapid

measurement process also minimizes the errors caused by chang

in the receiver gain and ERP. Thus, errors due to changes

in the effective input noise temperature, bandwidth, and

ambient temperature are negligible.

i- 4.3.4 Results and Concluding Remarks

The estimated errors incurred in the course of the gain

comparison method used to calibrate power gain of a large

ground antenna are summarized below.

In this estimate we assume that:

1) satellite ERP is 10 or 30 dBW;

2) antenna noise temperature of the ground antenna

is 30K, and that of a standard gain antenna is

40K;

3) path loss is 200 dB

;

4) bandwidth of the receiving system is 40 MHz;

5) gain of the receiving system is 100 dB;

6) differences in loss between the antenna output port

and the receiver input port are 1 dB for the

standard gain antenna and 2 dB for the large

ground antenna;

7) the ambient temperature is 290K.

Only the errors not judged to be negligible have been listed

here

.

Using a 30 dB standard gain antenna, the linear sum of

all errors as a function of power gain of a ground antenna

is given in figure 4-20. As expected, although the error

in the measured power gain of the standard gain antenna is

quite small (0.08 dB) , the uncertainty in the measurements

of power ratio, Z, and that due to stabilities in gains

118
o

<

o

o

UJ99 L=a

mS 2S = a

ni9'9L=Q

•rJ

<D o 13 +->

1 Jh 03 e 03-H

•H o Id U a 03

03 fH •H to 0

0) 03 >

O Kl •!-> ^ U 0

^-) m

LO <4^ -M bficNi 0

C •

J-( •H O t/i I—

1

m 3 11 03C

03 >s-H o cue • H ceo +J 0 0 !=; rH

03 03 T—

1

o3 0 13 •H 6

;=! <D O O

o id u 03 03 ^ II o o

O U +-> -H H 0 03 O

0) 0 C 03 II M o c

03

0) OS -H 0 0

I—1 5-1 -M •H 03 C o

hJ o3 Ph o3

CD

(Nl

(oe) 8P Ni NIV9 a3M0d VNNBiNv Ni aoyy3

0

•H

119
§4 will contribute large errors because of the poor

signal-to-noise ratio for a standard gain antenna.

It appears that this problem can be reduced by use of

a standard gain antenna with higher gain. Figure 4-21 shows

the linear accumulation of all errors as a function of the

power gain of a ground antenna using a 40 -dB standard gain

antenna. The errors due to Z and instabilities in gains g2

and g^ are indeed reduced by use of a larger, in this case

50 dB, standard gain antenna, as shown in figure 4-22. Unfortunately, the power gain calibration of a 50-dB standard

gain antenna is easier said than done: the near-field

scanning or extrapolation ranges needed for accurate calibration of 50-dB antennas do not exist. Furthermore, the

alignment accuracy and stability necessary for such an

extrapolation range are at best very difficult to build in

view of a length requirement of approximately 1.4 km. Therefore, larger standard gain antennas are impractical at least

for the present.

The linear accumulation of errors in the measured power

gain of a large (60 dB) antenna as a function of power gain

of standard gain antennas is shown in figure 4-23. Figure

4-24 shows the same errors for a larger (70 dB) antenna.

Some of the contributing sources of error are independent

and satisfy the condition for quadrature error addition.

For example, errors due to the standard gain antenna, ERP,

path loss, waveguide feed loss, polarization mismatch, and

tracking inaccuracy are independent and can be added in

quadrature. However, uncertainties in the measurements of

X, Y and Z are not independent of each other. Similarly,

the uncertainties due to nonlinearity and instability in g-j^

,

^2* ^3* ^"'^ ^4 independent. These should be added

linearly. Figure 4-25 shows the total quadrature error

in the measured power gain of a ground antenna, calculated

in the fashion just described as a function of power gain

of the unknown antenna.

120 !
0.4

D= MAJOR APERTURE DIMENSION OF ANTENNA

•ERROR DUE TO (O.OOldB)

ERROR DUE TO (O.OOldB)

0.3

TRACKING ERROR

(5 SEC OF ARC)

c

CO

CQo

ERROR DUE TO (O.OOldB)

o

a.

ERROR DUE TO X (0.002dB) ERROR DUE TO g^ (O.OOldB)

0.2

ERROR DUE TO Y (0.002dB)

ERROR DUE TO Z (0.002dB)

o

0.1

POLARIZATION MISMATCH UNCERTAINTY (O.OldB)

UNCERTAINTY IN FRONT END LOSS - UNKNOWN ANTENNA SIDE (O.OldB)

UNCERTAINTY IN FRONT END LOSS - STANDARD ANTENNA SID E (O.OldB)

INSTABILITY IN PATH LOSS (O.OldB)

INSTABILITY IN ERP (O.OldB)

ERROR IN STANDARD ANTENNA ( 0 . 082dB )( 3 o)

E

CO

II

50

Figure 4-21

II Q

_L

II Q

_L

II

60 70

POWER GAIN OF UNKNOWN ANTENNA IN dB

80

Linear error accumulation for the power gain o£

a large microwave antenna using the gain comparison method (frequency = 7.25 GHz, standard

antenna gain = 40 dB nominal, effective radiated

power = 10 dBW nominal)

.

1 21
T3 m CQ r— -O "O O CM

uJ99L = a _

uJ9'9l=a -

uj£-g=a -

(oe) gp NI NIV9 a3H0d VNNHiNV NI doaa3

m 1 o

a

•H +J CD

V5 >

•H

-P

5h

OJ E CD

15 (D U "+H O X

pU+J Lf) 0)

CSl CD • ^ • fi I>- 1-1 1—

\

M •H 03 rH

II a 03

fi •H O •H

03 o o

o

n n CD

CO o CD 3 PQ

• H +->

+-> PI CD pq

nJ fH O 'd

I—

1

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(NEGLIGIBLE)

o

II o

D = MAJOR APERTURE DIMENSION OF ANTENNA

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(NEGLIGIBLE)

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(NEGLIGIBLE)

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•ERROR DUE TO g^ (O.OOldB)

-TOTAL ERROR

II II

ERROR DUE TO Z (0.002dB)

Instability and/or

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] polarization mismatch etc.

v^ljO.OSdB)

ERROR IN STANDARD ANTENNA (3a)

I I 20 30 40 50

POWER GAIN OF STANDARD ANTENNA IN dB

Figure 4-23. Linear error accumulation for the power gain o£

the large microwave antenna using the gain

comparison method (frequency = 7.2 5 GHz, standard antenna gain = 60 dB nominal, effective

radiated power = 10 dBW nominal)

.

123
2.0

1 . 6

1 .4

1 .2

1 .0

0.8

0.6

0.4

D ^ MAJOR APERTURE DIMENSION OF ANTENNA

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(NEGLIGIBLE)

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(NEGLIGIBLE)

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-(NEGLIGIBLE)

0.2

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ERROR DUE TO g^ (O.OOldB)

ERROR DUE TO

X & Y

TOTAL ERROR

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flNSTABILITY AND/OR

JUNCERTAINTY IN ERP PATH

"^LOSS, POLAR MISMATCH ETC

(0.05dB)

ERROR IN STANDARD ANTENNA (3<t)

-J I 20 30 40 50

POWER GAIN OF STANDARD ANTENNA IN dB

ure 4-24. Linear error accumulation for the power gain of

the large microwave antenna using the gain comparison method (frequency = 7.25 GHz, unknown

antenna gain = 40 dB nominal, effective radiated

power = 10 dBW nominal)

.

124
1 .2

o

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T3

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30dB ( D = 0. 5ni)

G 5 s D = STANDARD ANTENNA POWER GAIN

MAJOR APERTURE DIMENSION OF ANTENNA

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Figure 4-25

= 40dB (D 1 .6ni)

G^ = 50dB (D 5 . 3m)

_L 60 70

POWER GAIN OF UNKNOWN ANTENNA IN dB

80

Quadrature error accumulation for the power gain

of the large microwave antenna using the gain

comparison method (frequency = 7.25 GHz, effective radiated power = 10 dBW nominal)

.

125
If a higher ERP is available, the error in the measured

power gain of the ground antenna can be reduced. Therefore

let us assume an ERP of 30 dBW, but assume that other parameters

are the same as mentioned above. Then the results are shown

in figures 4-26, 4-27, and 4-28 for 30, 40, and 50-dB standard

gain antennas as a function of the power gain of a ground

antenna. When a satellite with 30 dBW ERP is available, the

use of a 50-dB (instead of 40-dB) standard gain antenna reduces the error in the power gain by only 0.01 dB. Figures

4-29 and 4-30 show the linear accumulation of the errors in

measured power gain for 60 and 70 dB ground antennas as a function of standard antenna gain. Quadrature error in measured power gain based on the assumptions mentioned above is

shown in figure 4-31 as a function of the ground antenna power

gain.

In summary it seems possible to calibrate a 60 or 70-dB

ground antenna to within a 0.18-dB linear error or a 0.06-dB

quadrature error. These results assume a 40-dB standard gain

antenna, the gain comparison method, and an ERP of 30 dBW.

4.4 Summary and Conclusions

The calibration of the power gain of large antennas to

be used primarily for the purpose of calibrating Cas A has

been described. First, a practical, generalized three -antenna

method of determining the power gain of a relatively small

standard gain antenna has been discussed. It has been found

that using the extrapolation method the power gain of a 40-dB standard gain antenna can be calibrated to within a linear accumulation error of 0.08 dB for 3a limits or

quadratic accumulation error of 0.04 dB

.

Although it is in principle possible to calibrate

standard gain antennas with a power gain of 50 dB or higher,

a 1.4 km-long extrapolation range is required for separation

126
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MAJOR APERTURE DIMENSION OF ANTENNA

-TRACKING ERROR (Ssec OF ARC)

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RROR DUE TO (0.004dB;

ERROR DUE TO (0.004dB)

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ERROR DUE TO (0.004dB)

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ERROR IN STANDARD ANTENNA {3a]

oII Q

OII a

E

CO

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20 30 40

POWER GAIN OF STANDARD ANTENNA IN dB

50

Figure 4-29. Linear error accumulation for the power gain of

the large microwave antenna using the gain comparison method (frequency = 7.2 5 GHz, unknown

antenna gain = 60 dB nominal, effective radiated

power = 30 dBW nominal)

.

130
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0. 20

5 POWER GAIN OF STANDARD ANTENNA

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s

II II O

E

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50 60 70

POWER GAIN OF UNKNOWN ANTENNA IN dB

80

Figure 4-31. Quadrature error accumulation for the power gain

of the large microwave antenna using the gain

comparison method (frequency = 7.25 GHz, effective radiated power = 30 dBW nominal)

.

132
D2 distance to be varied from 0.2 to 2 j—. In practice, it is

almost impossible to construct and maintain such a long extrapolation range with sufficiently good stability and alignment.

The planar or possibly the spherical scanning technique

promises better power gain calibration accuracy than the

extrapolation method, particularly for larger standard gain

antennas, if the necessary planar or spherical scanner is

available. Although an error analysis has not yet been performed, it is estimated that the power gain of a 50-dB standard gain antenna with major aperture dimension of typically

5.3 m can be determined to within 0.1 dB by the planar nearfield scanning technique.

It will be found from section 5 that a 60-dB ground antenna is required for calibrating Cas A. Therefore, it is

generally necessary to use the gain comparison method to

determine the power gain of a ground antenna which is intended

for flux density measurements of Cas A. This procedure has

established a lower bound on the error in the measured power

gain of a typical, high-quality antenna, in which a 3a random

error estimate has been included along with various systematic

errors. By use of a 40 -dB standard gain antenna, it is possible to measure the power gain of a 60-dB ground antenna

to within a linear accumulation error of 0.18 dB for 3a limits

or quadrature accumulation error of 0.06 dB for 3a limits;

this assumes use of the gain comparison method, and an ERP of

30 dBW. Therefore, 0.06 dB is a good estimate of the lower

bound of the uncertainty within which a 60-dB ground antenna

can be calibrated.

133
5. THE ACCURACY OF MEASURING THE FLUX DENSITY OF CAS A

In this report the term "practicable error" refers to

calculations based upon the assumption that the measurement

has been performed under careful but not quite state-of-theart conditions; and the term "lower-bound error" refers to

calculations based upon a best guess of the foreseeable

state-of-the-art and ideal measurement conditions. In

calculating practicable and lower-bound errors, the antenna

gain error contributions are taken to be their linear and

quadrature sums respectively. For example, the antenna-gain

error contribution in Tables 5-1 and 5-2 are ± 0.18 dB (from

figure 4-30) and 0.06 dB (from figure 4-31), which represent

linear and quadrature error sums respectively in the calculation of the antenna gain errors. It should be pointed

out that this procedure represents the particular viewpoint

adopted in this report and not necessarily a standard procedure. A decision of how to sum error contributions depends

heavily upon measurement conditions and the intended use of

the error analysis.

Quadrature-sum estimates of the accuracy of measuring

the flux density of Cas A are shown in figure 5-1 assuming

that a noise-adding technique (appendix C) is used. The errors

shown are obtained from computer printouts like the one in

appendix B. For the estimate of practicable errors, the

antenna gain was restricted to be less than 60 -dB in order

to avoid difficult, star-shape corrections. The contributions

to the measurement errors at 7.25 GHz are listed in Tables 5-1

and 5-2. The best accuracy (lower-bound error) noted in the

2 to 16 GHz range in figure 5-1 is 1.4%. Therefore, the fluxdensity uncertainty of about ± II quoted in the recent literature is clearly not realistic.

134
10

FREQUENCY (GHz)

j Figure 5-1 Practicable and lower bound errors in the measurement of

the flux density of Cas A .

f

135
Table 5-1. The practicable error of measuring the flux

density of Cas A at 7.25 GHz.

The following assumptions were used in calculating the errors

The system temperature referred to the output port of the

antenna is 100 K; antenna beam efficiency is 55%; the HPBW

(half power beamwidth) of the antenna is 70° divided by the

diameter of the antenna expressed in free-space wavelengths

(70° X/D).

Error Contribution

Source of Error to Measuring Flux

1. Antenna gain (fig. 4-30) 4.14%

(59 ± 0 .18 dB)

2. Temperature calibration standard 0.20%

(± 0.2%)

3. Temperature rise due to Cas A 0.90%

(22.2 ± 0.2 K)

4. Sky background 1.33%

(6 ± 0.3 K)

5. Atmospheric transmission 1.02%

(.98 ± 0.01)

6 Star shape correction, 0.72%

(.933 ± 0.007)

7. Antenna pointing 0.65%

(± 5% HPBW)

Quadrature sum 4.6 7%

136
Table 5-2. The lower bound error of measuring the flux

density of Cas A at 7.25 GHz.

The following assumptions were used in calculating the errors

The system temperature referred to the output port of the

antenna is 100 K; antenna beam efficiency is 55%; the HPBW

of the antenna is 70° X/D.

Error Contribution

Source of Error to Measuring Flux

1. Antenna gain (fig. 4-31) 1.341

(59 ± 0.06 dB)

2. Temperature calibration standard 0.20%

(± 0.2%)

3. Temperature rise due to Cas A 0.45%

(22.2 ± 0.1 K)

4. Sky background 0.89%

(6 ± 0.2 K)

5. Atmospheric transmission 0.10%

(0.98 ± 0.001)

6. Star shape correction,

(0.933 ± 0.0034) ^ 0.36%

7. Antenna pointing 0.10

(±2% HPBW)

Quadrature sum 1.73%

I 137
6. THE ACCURACY OF MEASURING G/T

The primary concern in this section is the accuracy o£

measuring G/T using Cas A. For comparison purposes, a few

remarks will be addressed to the accuracy o£ determining G/T

by separate measurements o£ gain and noise temperature.

6.1 The Measurement of G/T Using Cas A

•' The practicable accuracy of measuring G/T using Cas A is

given in figure 6-1 in terms of quadrature error. The magnitude of this error depends on the magnitude of the G/T being

measured. The measurement assumptions and the origin of the

error contributions are tabulated in Table 6-1 for the frequency 7.25 GHz. The errors listed are estimates based on the

assumption of reasonable, but not exceptional measurement

conditions. The same information as given in figure 6-1, but

using antenna diameter as the parameter, is shown in figure

6-2. The computer program and printout on which this figure

is based are given in appendix B.

Estimates of the lower bound errors (best possible accuracy) are also shown in figure 6-2, and the origin of the

error contributions are tabulated in Table 6-2. In this table

a best guess of the foreseeable state-of-the-art under ideal

measurement conditions is assumed, and in cases of doubt, the

error has been underestimated.

6 . 2 Cas A Method of Measuring G/T Compared to the Gain/Noise

Temperature Method

The practicable errors in the separate measurements

of noise temperature, Tg^j^^> S-^id effective receiver input noise

temperature, T , are independent of frequency for the frequency

138
139
Table 6-1. The practicable error of measuring G/T at

7.25 GHz using Gas A.

The following assumptions were used in calculating the errors:

The system temperature referred to the output port of the

antenna is 100 K; antenna beam efficiency is 551; the HPBW

of the antenna is 70° X/D.

Error Gontribution to G/T in dB

Antenna diameter = G/T = G =

llm(37 ')

36 dB

56 dB

18mC58 ')

40 dB

60 dB

28m(93')

44 dB

64 dB

Source of Error

1. Flux Density of Gas A

700 fu ± 4.6 7%

0. 194 0 .194 0.194

2 . Secular decay (6 mos.)

1.1 ± O.lSVyr

0 .004 0 .004 0 .004

3. Sky background

6 ± 0 .3 K

0 .101 0 .043 0.019

4. Atmospheric transmission

0.98 ± 0.01

0 .044 0 .044 0.044

5. Star shape factor CK2=.965) (K2=.916) CK2=.807)

± (1-K2)0.1 0 .016 0 .040 0.104

6 . Bandwidth effect

1 ± 0 .001

0 .004 0 .004 0.004

7. Antenna pointing

± 5% HPBW

0 .028 0 .028 0.028

8. Y-f actor

± 0.01 dB

0 .089 0 .043 0.025

9. Resolution

± 0.01 dB

0 .089 0 .043 0.025

Quadrature Sum 0.248 dB 0.218 dB 0.2 30 dB

140
2 4 6 8 10 12 14 16

FREQUENCY IN GHz

Figure 6-2 Practicable and lower bound errors in the measurement of

G/T using Cas A.

141
Table 6-2. The lower bound error of measuring G/T at

7.25 GHz using Cas A.

The following assumptions were used in calculating the errors:

The system temperature referred to the output port of the

antenna is 100 K; antenna beam efficiency is 551; the HPBW

of the antenna is 70° X/D.

Error Contribution to G/T in dB

Antenna diameter = G/T = G

=

llm(37')

36 dB

56 dB

18mC58')

40 dB

60 dB

28mC93')

44 dB

64 dB

Source of Error

1. Flux of Cas A

700 fu ± 1.73

0.0 75 dB 0.0 75 dB 0.075 dB

2. Secular decay (6 mos.)

1.1 ± 0.151/yr

0.004 0 .004 0 .004

3. Sky background

6 ± 0.2 K

0 .068 0 .029 0.013

4. Atmospheric transmission

0.98 ± 0 .001

0 .004 0 .004 0.004

5. Star shape factor (K2=.965) (K2=.916) (K2=.807)

K2 ±(1-K2)0.05 0 .008 0 .020 0.052

6. Bandwidth effect

1 ± 0.001

0 .004 0 .004 0 .004

7. Antenna pointing

± 1% HPBW

0.005 0 .005 0 .005

8. Y-f actor

± 0.003 dB

0.027 0.013 0.008

9. Resolution

± 0.005 dB

0 .045 0 .022 0 .013

Quadrature Sum 0.114 dB 0.0 86 dB 0.094 dB

142
ranges considered here. The use o£ frequencies at which

NBS calibration services are available has an advantage in

practice. The practicable errors in measuring T and T ^ ^ e ant

are noted in Tables 6-3 and 6-4. The error components of

T^ are taken from reference [69] and for T . from reference

e ant

[70]. Because the output port of the antenna may be defined

at one of several reference points in the system, error contributions for two different values of T are shown in

e Tables 6-3 and 6-4.

For the best accuracy of the measurement of T , there ^ sys

is some advantage in defining the antenna measurement plane

as close to the preamplifier as possible. The practicable

Table 6-3. The practicable accuracy of measuring T . The

basic measurement equation used to determine T^

is T = (T, . - Y T Tj)/(Y - 1) where Y is the

e ^ hot cold^ ^

^ ratio of power at the receiver output port when

T, . then T respectively are connected to hot cold ^

^ the receiver input port. For the measurement

of T_ we assume T = 300 ± O.IK, and

T

e " "hot

= 80 ± 0.2K, that the reflection coeffi cold - cient of these standards differs from that of the

antenna such that |r .-r.,|<0.05, and that ' ant std'

the antenna to the receiver such that

ant rec

< 0 .1 [71] .

Parameter uncertainty

causing the error

Error Contribution to T in K

e T = 30K T = 70K

e e

0 .05 K 0 .07 K

Tcold' * 0 . 30 0 .34

Y-factor, ± 0.01 dB 0 .38 0 . 58

Receiver gain, ± 0.1% 0 .17 0 .25

Connector loss variation = 0.005 dB 0 .38 0 .42

Mismatch induced error 0 .39 0 .91

Quadrature sum 0.75 K 1.23 K

143
Table 6-4. The practicable error of measuring T^^^. It

is assumed that a compensated radiometer with

an effective input noise temperature of 100 K

and a resolution of 0.005 dB is used to measure

T

ant *

Error Contribution to T ^ in K ant

Source of the Error

ant

= 70K ant

= 30K

T ^ . = 80 ± 0 .2K

s td 0. 20K 0 20K

Extrapolation error [0.23% 0. 02 0 .09

of temperature difference)

Resolution error 0 34 0 .26

Quadrature sum 0.39K 0.34K

Table 6-5. The practicable accuracy of measuring G/T for

frequencies near 7.25 GHz by separate measurement

of antenna power Ggain G^^^, and system noise

temperature, T^^^^ = "^ant^

"^e

* basic measurement equation is G/T = Gg.nt'^'^sys t * assumed that a satellite with an ERP of 1000 W

is available for the gain transfer calibration,

and that T ^ = 100 K.

sys t

Source of Error Error Contribution to G/T

ant

(fig. 4-30) 0.18 dB

T . ant

= 70 ± 0.39K 0.017

T = 30 ± 0.75K 0.033

e Quadrature sum 0.184 dB

144
error components in a G/T determination by separate G and T

measurements are tabulated in Table 6-5, where the practicable

antenna gain error from figure 4-27 has been used. Table 6-5

can be compared with figures 6-1 and 6-2 to judge how an ideal

G/T measurement using Gas A compares with an ideal measurement

of G ^ divided by the ideal measurement of T . For a 60-

ant ^ sys

foot antenna and for frequencies near 7.2 5 GHz, the measurement

error of G/T using Gas A differs in accuracy from the error

in a measurement of G and T separately by less than 0.05 dB

.

145
7. G/T MEASUREMENT REPEATABILITY

The use o£ Gas A to monitor ground station G/T changes,

or to compare G/T ratios for separate but similar ground

stations, requires only relative (not absolute) G/T determinations . The purpose o£ this section is to estimate to what

repeatability these comparisons can be made for 60' antenna

ground stations. The word "repeatability" as used here distinguishes between the usual G/T measurement precision (measurement scatter for a number of similar measurements performed

over a short period) and how closely the averages of two sets

of G/T measurements performed six months apart agree, assuming

the G/T has not changed during this period. The repeatability

estimated in this section will then be a limit beyond which two

G/T measurements performed six months apart on a 60 '-antenna

ground station must differ if it is to be concluded that the

ground station G/T has changed. This repeatability also gives

an idea of how meaningfully relative G/T measurements between

two similar 60 '-antenna ground stations can be compared.

Table 7-1, which is an example of how the repeatability

was estimated at 7 GHz for 33'- and 52'- antenna ground

stations, gives a list of parameters that affect the repeatability. Similar estimates were performed to generate

figure 7-1, which shows the repeatability for 33'- and 52'-

antenna ground stations as a function of frequency. Although

a similar graph for a 60 '-antenna ground station was not

generated, it can at least be inferred from figure 7-1 that

the repeatability is better than 0.1 dB for frequencies less

than 8 GHz. Therefore, for a 60 '-antenna ground station with

specifications similar to those in the example, G/T changes

greater than 0.1 dB over periods less than or equal to six

months can be positively identified.

146
Table 7-1. 7 GHz G/T measurement repeatability using Gas A.

The following assumptions were used in calculating the repeatability: the system temperature referred to the output of the

antenna is 100 K; antenna beam efficiency is 55%; the HPBW

of the antenna is 70° A/D.

Error Gontribution to G/T in dB

Antenna diameter = G/T = G =

16mC52 ')

38.7 dB

58.7 dB

10mC32 ')

34.8 dB

54.8 dB

Source of Error

J.1 • k^J ^ Cl J. CX X Li-CV^dV \J O « J 1.1 ± 0.15%/yr

0 004 dB U • U VJ T- LI JJ

2 . Sky background

6 ± 0.2K

0 .035 0 .083

3. Atmospheric transmission

0.98 ± 0.002

0.009 0 .009

4. Antenna pointing

±5% HPBW

0.028 0.028

5. Y-factor

± 0.01 dB

0.051 0.108

6. Res olution

± 0.01 dB

0 .051 0.108

Quadrature sum 0.085 dB 0.176 dB

147
148
8. CONCLUSIONS

As will be seen the use of Cas A to measure G/T is clearly

the measurement technique that should be used in certain frequency and G/T ranges. Listed below are some of the prospects

and problems concerning accurate G/T measurements.

8 . 1 The Accuracy of Measuring G/T

Several graphs and tables showing the lower-bound error

(best possible accuracy) the practicable error of measuring

G/T by the Cas A method have been presented and compared

(section 6) with the accuracy of measuring G/T by a method

in which antenna power gain and system noise temperature are

measured separately from each other. We concluded (figure 6-2,

Table 6-5) that for a 60 '-antenna system operating at less

than 8 GHz,

the practicable error (Cas A method) = ± 0.25 dB

the practicable error (gain-noise temperature method) =

± 0.18 dB

the lower bound error (Cas A method) = ± 0.10 dB

the lower bound error (gain-noise temperature method) =

± 0.0 7 dB

the repeatability (section 7) (Cas A Method) = ± 0.10 dB

.

For this case, the potential accuracy of the gain -temperature

method is a little better than the Cas A method, but we

seriously doubt whether this advantage is often realized.

This is because the gain-noise temperature method, as it

is usually implemented, is a very difficult measurement: the

difficulty is that the worst possible measurement plane,

namely, the antenna output reference plane, is used for

measuring system noise temperature. At this plane mismatch

149
errors are difficult to control, and noise temperatures to be

measured have small magnitudes . Sometimes these measurements

are further degraded when the temperature contributions of

the diplexer and/or the antenna lead are calculated from

data obtained in separate loss measurements . Better noise

temperature measurements at a different measurement plane

would alleviate these objections.

As seen in figure 6-2, lower-bound error for the 60'-

antenna system is roughly one-third of the practicable error.

Although we can visualize some of the practicable error contributions being reduced to their lower bound values, some

errors not easily accounted for, making it unlikely that the

total error can be reduced much below the practicable curve.

Examples of possible causes of such errors are antenna gain

and pointing hysteresis, harsh climatic conditions, antenna

surface warping due to wind or temperature gradients, oxidizing,

and antenna stress relief. To a certain extent, these timedependent effects can be monitored within the repeatability,

± 0.1 dB (section 7), of the G/T measurement.

For half -power beamdwidths of 8.6' and larger, the antenna

power gain pattern is sufficiently constant across the Gas A

profile to permit using the flux density in calculating the

antenna temperature with Gas A in the main beam. For smaller

beamwidths, however, the antenna response must be calculated

from a brightness contour map like figure 2-10 instead of

using the flux density. (Restricting the beamwidth to twice

the star width, or 8.6', is to a certain extent arbitrary, but

to be more exact requires a convolution of the star map with

the antenna power gain pattern.) Therefore, the use of Gas A

is restricted to 8.6' HPBW (or greater) antennas, thereby

setting an upper limit to the G/T (41 dB for a 100 K system

noise temperature and a 0.55 antenna aperture efficiency)

150
that can be measured using Cas A. It can be seen from figure

6-1, that for less than 8 GHz, G/T ratios greater than 36 dB

up to 41 dB maximum have about the minimum G/T error. This

G/T range corresponds to ClOOK noise temperature, 0.55 antenna

aperture efficiency) antenna diameter from 37' to 65' for

systems operating at 7.2 5 GHz. Therefore, G/T ratios can be

measured most accurately (for systems operating at 7.25 GHz)

for antenna diameters from 37' to 65'.

8 . 2 The Accuracy of the Cas A Flux Densities Cited

in the Literature

The most recent literature [29] quotes the uncertainty

in Cas A flux density as about ± 1%. This uncertainty is comparable to some of the most accurate electromagnetic measurements made by the Electromagnetics Division at NBS ; in particular it is better than the best noise temperature and

antenna power gain measurements ever made at NBS. Because

a flux density measurement intrinsically contains both a noise measurement, and an antenna power gain measurement under

difficult field operations, the 1% value quoted above seems

unrealistic

.

There are many difficulties with obtaining an accurate

flux density value for Cas A, namely: (1) accounting for flux

density decay from the time of last measurement; (2) correcting for the difference between the measurement frequency

and the frequencies at which Cas A data is available; (3)

the star-shape correction -- there are hints that different

portions of the star have different spectral indices (figure

2-11); (4) corrections for cosmic backgrounds -- especially

when a background map is not available at the measurement frequency or when the antenna to be measured must be pointed to

a location near Cas A because of the satellite location;

(5) accounting for atmospheric effects -- diffraction, diffusive attenuation, apparent solid-angle, correction.

151
absorption, reradiat ion , temperature and humidity corrections,

and [6) availability o£ equipment or personnel capable of

the best measurement techniques

.

Because there are many problems related to using published

Cas A data for G/T measurements, a substantial effort is required to determine by a study of the published papers which

of the experimenters have properly minimized their errors and

have properly accounted for the various sources of uncertainty

in their error estimates.

8 . 3 Proposed Future Effort

Several areas in which future effort seems to be needed

have been uncovered during this study. These are discussed

below

.

8.3.1 Evaluation of the Literature

Some of the published radio astronomy papers are much

too optimistic in estimating the accuracy of Cas A flux

density measurements. More reliable flux density values can

possibly be obtained by reanalyzing the various experimental

results where presented in the literature so that the resulting accuracies conform to more realistic error appraisals.

8.3.2 Stars Other than Cas A for G/T Measurements

The use of Cas A looks very promising for the measurements of G/T. Still, other stars, the sun and the moon

should also be examined to determine their utility. Their

advantages as regards G/T, if any, should be tabulated.

Cas A is not visible from some southern hemisphere ground

stations. For certain measurements on small antennas, the

moon and/or sun should be useful, and for larger antennas,

smaller and weaker stars look interestingly useful.

152
8.3.3 Independent Methods for Measurement of G/T

It would be worthwhile to measure the G/T of a ground

station by two independent methods. This approach almost

always uncovers unsuspected errors and greatly increases the

confidence placed in a particular method. The two methods

discussed in this report Qi.e., the Gas A method and the gain

noise temperature method) when used on one ground station,

would be suitable for the purpose.

8.3.4 Definition of and Alternatives to G/T

There is a real need for a figure-of -merit performance

parameter for a ground station, be it G/T or a substitute

parameter. G/T is a useful figure -of -merit of a ground

station, but the difficulties in its accurate determination

must be recognized. It therefore seems worthwhile 1) to

examine the details of the definition of G/T in order to

determine whether an improved definition (from a measurement

accuracy point of view) can be generated, and 2) to examine

other possible figures -of -merit with regard to their suitability as substitutes for G/T that are amenable to more

accurate measurement.

8.3.5 Uncertainties in Antenna Gain Measurements

The error budgets of flux density and G/T measurements

are dominated by the uncertainty in measuring the power gain

of standard gain antennas . This error source is therefore a key to improved G/T measurements. In the antenna analysis of

this report we assumed the use of the extrapolation technique

because it is currently the best implemented technique at NBS

The planar-near-field calibration technique and the spherical

near-field technique look promising especially for large

153
antennas for improving gain accuracy. The planar technique

has been developed, and a near-field planar scanning range

that can accommodate 40 -dB standard gain antennas at 7.25 GHz

has recently been constructed at NBS. The spherical technique

is in its early stages of development; no spherical range has

ever been built, and there is therefore no experimental

experience with it. Further development and analysis of

these techniques would be very valuable in further reducing

the major error source in G/T measurements.

8.3.6 Radio Star Method of Measuring G and T

It would be useful to examine the separate measurements

of G and T by use of radio stars. Although the measurements

proposed are independent, the topics are related. Some of

the theory for such measurements is contained in appendix C.

This theory should be extended to measurements of G and T by

techniques that do not require breaking into the antenna

system. If this were done, the resulting technique would have

the same measurement convenience as the Gas A method of measuring G/T. This becomes possible if one chooses the measurement reference plane to be at the aperture of the feed horn

in the antenna instead of at the output of the antenna.

Acknowle dgment

The authors appreciate the extensive and critical technical

review given this report by Dr. H. M. Altschuler. His criticism

was very helpful.

154
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161
APPENDIX A: COMMENTS ON THE INTRODUCTORY SECTIONS

Section 1.1

1. The system as defined in section 1.1 is time varying,

and care must be taken to insure that the state of the system

at the time its G/T is measured is adequately specified. At

least the following parameters should be specified or implied

when reporting a value for G/T: the epoch and time of day

when the measurements were taken; the longitude and latitude

of the antenna site; the measurement frequency or frequencies;

the antenna polarization; and, if the antenna is steerable, its

pointing angles.

2. The on- axis power gain of the antenna is the maximum

of the antenna power pattern which is assumed to be measured

in the far field of the antenna with all attenuation effects

of the atmosphere removed, i.e., the gain assuming no atmosphere.

3. It should be recognized that the power gain of an

antenna is a transmitting concept and can be used for a receiving antenna only if the antenna is reciprocal. However, a quantity can be defined for a non -reciprocal receiving antenna that is analogous to the power gain of a transmitting antenna. This point needs to be expanded in a later phase of the G/T project, and the results should

properly be included in any formal definition of G/T.

4. It should be noted that the system noise temperatures defined in section 1.1 are combinations of real noise

temperatures and effective input noise temperatures.

5. The IEEE defines G/T [2] as the ratio of antenna

gain to antenn a noise temperature. In contrast, the G/T

ratios discussed in section 1.1 are antenna gain to system

noise temperature ratios, and are consequently more appropriate measurands of ground station performance.

162
Section 1.2

It is implicitly assumed throughout these introductory

sections that the noise radiated by the satellite is insignificant compared to the noise associated with the ground

station which includes the cosmic and terrestrial noise. It

should be expressly noted that the system noise temperature T

includes only the latter noise contributions and not the

satellite noise.

If the ground station noise does not predominate over the

radiated satellite noise, then n of section 1.2 includes the

satellite noise and the following expression [72] for the

carrier-to-noise ratio must be used:

C ^ CG/T) (ERP)

L

n k + CG/T)ngL

where n^ is referred to the satellite and corresponds to the

satellite noise. The other parameters are defined in section

1.2.

Section 1.4

1. A number of assumptions were made in section 1.4 to

simplify the presentation. These assumptions include: the

radio star is treated as a point source of unpolarized radiation; the atmospheric attenuation of the power from the radio

star is zero; and the radio star is positioned in the center

of the antenna main beam during the first part of the measurement . 2. The brightness temperature of the radio star is that

thermodynamic temperature to which a black body of the same

angular extent and position as the star must be raised in

order for its flux density to equal that of the radio star.

163
APPENDIX B: COMPUTER PRINTOUT AND PROGRAMS

The error contributions to the total error in the measurement of the Cas A flux density and a ground station G/T

have been completed for various sets of parameters. The

computer printouts for G/T are included here in appendix B.l

some computed errors of which have been used in section 5.

Appendix B.2 gives the basic program for the G/T error compu

tations , and since this program is only slightly more compre

hensive than the program for the flux density error computations, the latter has been omitted.

164
B . 1 A Printout for the Practicable Accuracy of G/T

This printout lists the input variables and assumptions

first. The errors contributed to measured values of G/T by the

nine error sources listed are tabulated in the last four

columns. The meaning of the information in the first three

columns (three deep) is as follows:

Heading Meaning

G/TCDB) The value of G/T assumed in the calculation.

YCDB) The Y-factor of eq. Cl«9) expressed in decibels.

G(D) The power gain of the antenna.

FLUX(FU) The magnitude of the flux density of Gas A that has

been assumed for the calculation expressed in flux

units 1 F.U. = 10 2 6 Watts/mVHz

.

+-LINE

K2

HPBW

+

- QUAD

TCSTAR)

DIAM

The linear accumulation of the nine error contributions to the error in measuring the flux density.

The star-shape correction factor computed assuming

Gas A has a disk intensity distribution [22]

.

The half-power beamwidth of the antenna expressed

in minutes.

The quadratic (root mean square) accumulation of the

nine error contributions.

The noise temperature rise at the output of the

antenna caused by Gas A.

The diameter of the antenna.

165
The meaning o£ the last four columns is:

Heading Meaning

E-G Error contribution from the antenna gain.

E-DT Error contribution from the output noise temperature

di f ference

.

E-T(STAR) Error contribution from inability to completely

resolve star measurement.

E-Sky Error contribution from cosmic radio background.

E-Kl Error contribution from atmospheric transmission.

E-K2 Error contribution from star-shape correction.

E-Polzn Error contribution from polarization mismatch between

star and antenna.

E-BW Error contribution for receiver bandwidth.

E-Point Error contribution from imperfect antenna tracking

of star.

Table 6-1 is based on this printout.

166
MEASUREMENT OF G/T USING CAS A

QUANTITY UNIT VALUE UNCERTAINTY

1 FLUX AT 1 GHZ( 1974 > F.U. 3185

2 SPECTRAL INDEX -.765

3 SECULAR DECAY X/YR 1 .

1

4 SKY BACKGROUND K 6

5 KKATM TRANS) .98

6 K2<STAR SHAPE) LISTED

7 STAR POLARIZATION % 1 8 K3C BANDWIDTH EFFECTS) I 9 ANT POINTING % HPBW *

10 Y-FACTOR DB *

11 GAIN INSTABILITY DB * 12 MEASUREMENT RESOLUTION DB *

LISTED

0

I- .15

+ - .3

+ - .01

+-(K2-1 )*(

+ - .01 +- .001

- 5 + - .01

•».- 0

+ - .01

1 )

ASSUMPTIONS; T<SYST)= 100 K

DATE OF MEASUREMENT IS 1974.6

HPBW OF CAS A= 4.3 MIN

ANT BEAM EFFICIENCY^ 55 X

ANT POLARIZATION RAT 10= 0

######################################################################

FREQ* 7.25 GHZ

FLUX« 700 F.U.

FLUX UNCERTAINTY* 4.67

G/T(DB)+-LIM

-QUAD

Y(DB) G(DB)

K2 HPBW

T(STAR) DIAM

TERROR CONTRIBUTIONS TO G/T IN DB3

E-FLUX E-INDEX E-DECAY E-SKY

E-Kl E-K2 E-POLZN E-BW

E-POINT E-Y E-GAIN E-RESOL

22 +- 5.723

3.164

24 +- 3.879

1- 2.091

26 2.64

+- 1.38

28 1.817

+- .913

30 +- 1.277

.612

.02

.999

.52

.04

.998

.82

.06

.997

1 .31

.09

.994

2.06

• 14

.991

3.26

42

67.4 • 7.3 FT

44

53.6 • 9.2 FT

46

42.6 • 11.6 FT

48

33.8 • 14.6 FT

50

26.8 • 18.4 FT

. 194

.044

.028

. 194

.044

.028

. 194

.044

.028

. 194

.044

.028

• 194

.044

.028

0

.001

1.93

0

. 001

1.223

0

.002

.776

0

.002

.494

0

.004

.317

. 004

0

0

. 004

0

0

.004

0

0

.004

0

0

.004

0

0

1 .587

.004

1 .93

1 . r58

.004

1 .223

.812

.004

.776

.551

.004

.494

.366

.004

.317

167
FREQ= 7 .25 GHZ

FLUX« 700 F.U.

FLUX UNCERTAINTY' 4.67 %

G/T<DB)+-LIN

+-QUAD

Y(DB> G(DB)

K2 HPBW

TCSTAR) DIAM

CERROR CONTRIBUTIONS TO G/T IN DB]

E-FLUX E- INDEX E-DECAY E-SKY

E-Kl E-K2 E-POLZN E-BW

E-POINT E-Y E-GAIN E-RESOL

32 .929

+- .426

. 22

. 986

5.14

52

21.3 • 23.2 FT

. 194

.044

.028

.006

.204

004 .239

• 004

.204

34 +- .707

+- .317

36 +- .569

+- .258

.34

.978

8.08

.52

.965

1 2.65

54

16.9 • 29.2 FT

56

13.5 • 36.7 FT

. 194

. 044

.028

. 194

. 044

.-028

0

.01

.134

0

.016

.089

. 004

0

0

*

. 004

0

0

. 1 55

.004

.134

.101

.004

.089

38 4-- .486

.229

.78

.946

19.64

58

10.7 • 46.2 FT

• 194

• 044

.028

0

.025

. 061

• 004

0

0

• 065

.004

.061

40 +- .443

.218

1.14

.916

30. 14

60

8.5 • 58.2 FT

. 194

. 044

.028

0

. 04

.043

• 004

0

0

• 043

.004

.043

42 +- .431

.217

1 .63

.871

45.44

62

6.7 • 7 3.3 FT

. 194

.044

.028

0

.064

• 032

004 • 028

• 004

• 032

44 +- ^448

^23

2^22

• 807

66^66

64

5^4 • 92^3 FT

. 194

• 044

• 028

0

. 104

.025

004

0

0

• 019

.004

.025

168
FREQ" 2 GHZ

FLUX" 1874 F.U.

FLUX UNCERTAINTY* 4.32 %

C ERROR CONTRIBUTIONS TO G/T IN DB3

E-FLUX E-INDEX E-DECAY E-SKY

E-Kl E-K2 E-POLZN E-BW

E-POINT E-Y E-GAIN E-RESOL

G/TCDB)*-LIN YCDB) 6CDB)

+-QUAD K2 HPBW

TCSTAR) DIAM

22 .46 .73 42 . 18 0 • 004 . 07

+ - .22 • 999 67.4 • .044 • 001 0 • 004

18^33 26^6 FT • 028 .065 0 .065

24 .395 1*11 44 • 18 0 . 004 . 044

• 203 .998 53^6 • • 044 .001 0 • 004

29.02 33^4 FT • 028 .044 0 .044

26 .354 1 .64 46 . 18 0 • 004 .028

.195 .997 42.6 • .044 .002 0 .004

45.94 42.1 FT .028 .032 0 • 032

28 • 328 2.37 48 • 18 0 . 004 • 018

• 191 .994 33.8 • .044 .002 0 • 004

72.66 53 FT • 028 .024 0 • 024

30 • 313 3.32 50 • 18 0 . 004 • 01 1 *- • 19 .991 26.8 • • 044 . 004 0 .004

1 14.78 66.7 FT . 028 .019 0 .019

32 • 305 4.49 52 . 18 0 . 004 • 007

-«>- • 189 • 986 21.3 • .044 . 006 0 • 004

180^97 84 FT .028 .016 0 • 016

34 f- • 302 5.85 54 . 18 0 . 004 .005

f- .189 .978 16.9 • .044 .01 0 • 004

284.48 105.8 FT .028 .014 0 .014

36 • 303 7 • 36 56 . 18 0 . 004 .003

+ - • 189 .965 13.5 .044 • 016 0 • 004

445.08 133.1 FT • 028 .012 0 .012

38 • 31 8.98 58 • 18 0 . 004 • 00*2

• 19 .946 10.7 • .044 • 025 0 • 004

691 . 17 167.6 FT .028 .011 0 • 01 1

40 + - .323 10.65 60 . 18 0 . 004 .001

• 192 .916 8.5 • .044 • 04 0 .004

1060.91 21 1 FT .028 • 011 0 .011

42 .347 12.3 62 . 18 0 • 004 .001

.199 .87 1 6.7 • • 044 • 064 0 .004

1599.42 265.7 FT .028 .011 0 .011

44 + - .386 13.88 64 . 18 0 .004 .001

.215 .807 5.4 • .044 . 104 0 .004

2346.09 334.5 FT .028 .01 0 • 01

169
FREQ« 4 GHZ

FLUX- 1 i03 F.U.

FLUX UN CERTA INTYa 4.3 3 %

G/T<DB)+-LIN

•f-QUAD

Y(DB) G(DB)

K2 HPBW

T(STAR) DIAM

[ERROR CONTRIBUTIONS TO G/T IN DB3

E-FLUX E-INDEX E-DECAY E-SKY

E-Kl E-K2 E-POLZN E-BW

E-POINT E-Y E-GAIN E-RESOL

22 +- 1 .458

.717

.12

.999

2.7

42

67.4 • 13.3 FT

. 18

. 044

.028

0

.001

.381

004 .435

.004

.381

24 1.035

.486

.18

.998

4.27

44

53.6 • 16.7 FT

. 18

.044

.028

0

.001

.244

. 004

0

0

.28 5

.004

.244

26 "»•-

•f

.763

.345

.28

.997

6.76

46

42.6 • 21.1 FT

. 18

. 044

.028

0

.002

. 158

• 004

0

0

.185

. 004

.158

28 .589

.266

. 44

.994

10.69

48

33.8 • 26.5 FT

.18

.044

. 028

0

• 002

. 1 04

. 004

0

0

. 1 19

.004

.104

30 .479

.225

.68

.991

16.89

50

26.8

33.4 FT

. 18

.044

.028

. 004

.069

.004

0

0

.076

.004

.069

32 +- .41 1 .2051 .03

.986

26.62

52

21.3 • 42 FT

. 18

.044

.023

0

.006

.048

.004

0

0

.048

.004

.048

34 +- .369

. 197

1 .52

.978

41.85

54

16.9 ' Sa.9 FT

. 18

. 044

.028

0

.01

.034

.004

0

0

.03 1 .004

.034

36 +-

+ - .347

. 193

2.19

.965

65.43

56

13.5 • 66.6 FT

. 18

. 044

.028

.016

.025

. 004

0

0

.02

.004

.025

38 .338

. 192

3.05

.946

1 01 .68

58

10.7 • 8 3.8 FT

. 18

. 044

. 028

0

.025

.02

. 004

0

0

.013

.004

.02

40

+ - .342

.194

4.08

.916

156.07

60

8.5 • 105.5 FT

. 18

. 044

.028

0

.04

.016

. 004

0

0

.008

.004

.016

42 .3 59

.2

5.25

.87 1 235.3

62

6.7 • 132.8 FT

. 18

.044

. 023

0

.064

.014

. 004

0

0

.006

.004

.014

44 ^•- + - .395

.216

6.48

.807

345. 1

4

64

5.4 • 167.2 FT

. 18

. 044

.028

0

.104

.013

. 004

0

0

.004

. 004

.013

170
FREQ« 6 GHZ

FLUX- 809 F.U.

FLUX UNCERTAINTY- 4.45 X

CERROR CONTRIBUTIONS TO G/T IN DBl

G/T<DB)-»-LIN Y<DB) GCDB) E-FLUX E-INDEX E-DECAY E-SKY

-QUAD K2 HPBW E-Kl E-K2 E-POLZN E-BW

TCSTAR) DIAM E-POINT E-Y E-GAIN E-RESOL

22 ».- 3.667 .04 42

+- 1.973 .999 67.4 • .88 8.9 FT

24 2.494 .06 44

1.301 .998 53.6 • 1.39 11.1 FT

26 1.716 .09 46

.859 .997 42.6 • 2.2 14 FT

28 1.207 .15 48

•»-- .576 .994 33.8 • 3.48 17.7 FT

30 +- .877 .23 50

*' .401 .991 26.8 * 5.5 22.2 FT

32 +- .667 .36 52

*' .299 .986 21.3 * 8.68 28 FT

34 .536 .56 54

.244 .978 16.9 • 13.64 35.3 FT

36 -f- .455 .84 56 - .218 .965 13.5 * 21.34 44.4 FT

38 .41 1 .24 58

.206 .946 10.7 • 33.14 55.9 FT

40 •».- .39 1.79 60 - .202 .916 8.5 * 50.87 70.3 FT

42 -I-- .393 2.47 62

».- .206 .871 6.7 • 76.69 88.6 FT

44 - .419 3.27 64 - .221 .807 5.4 * 112.49 111.5 FT

. 185 0 . 004 1 • 10

.044 .001 0 .004

.028 1 .148 0 1. 14

. 185 0 . 004 .77

.044 .001 0 .004

• 028 .729 0 .729

. 185 0 .004 .521

.044 .002 0 .004

• 028 • 464 0 .4 64

. 185 0 . 004 .344

.044 • 002 0 .004

.028 .297 0 .297

. 185 0 . 004 . 225

.044 .004 0 .004

.028 .192 0 • 192

. 185 0 . 004 • 145

.044 .006 0 • 004

.028 . 125 0 • 125

. 185 0 . 004 .093

. 044 .01 0 .004

.028 .083 0 .083

• 185 0 • 004 • 06

.044 .016 0 • 004

.028 .057 0 • 057

. 185 0 • 004 .039

.044 .025 0 • 004

. 028 .04 0 • 04

.185 0 • 004 • 025

.044 .04 0 • 004

• 028 .03 0 .03

• 185 0 • 004 .017

.044 • 064 0 .004

.028 • 023 0 .023

. 185 0 • 004 .012

.044 • 104 0 .004

.028 .019 0 .019

171
FREQ« 8 GHZ

FLUX* 649 r.U.

FLUX UNCERTAINTY* 4.7 9 X

CERROR CONTRIBUTIONS TO G/T IN DB3

/T<DB)+-LIN T CDB) G (DB) E-r LUX E- INDEX E- DECAY E-SKY

-QUAD K2 HPBW E-Kl E-K2 E-POLZN E-BW

T<STAR) DIAM E-POINT E-Y E-GAIN E-RESOl

22

• 7,212 .02 42 . 199 0 .004 1.87

4 .044 .999 67.4 • .044 • 001 0 .004

• 4 o . 6 FT . 02o 2.531 0 2. 53 1

24 4.888 .03 44 . 199 0 • 004 1.404

o til .998 53.6 • • 044 .001 0 . 004

• 63 8.4 FT • 028 1 . 602 0 1 . 602

26 »- 3.319 . 04 46 . 199 0 . 004 1 . 007

+ - 1 .766 .997 42.6 • .044 • 002 0 .004

.99 10.5 FT .028 U016 0 1.016

28 2.269 .07 48 . 199 0 .004 • 696

•f

1 . 167 .994 33.8 • • 044 • 002 0 .004

1 .57 13.3 FT . 028 • 646 0 • 646

30 U576

^776

. 1 1 .991

2.48

50

26.8 • 16.7 FT

. 199

.044

.028

0

.004

.413

• 004

0

0

• 468

• 004

• 413

32 +- 1.125

.528

. 17

.986

3.92

52

21.3 • 21 FT

. 199

.044

.028

0

. 006

.265

004

0

0

.309

.004

.265

34 .836

.377

. 26

.978

6. 16

54

16.9 • 26.4 FT

. 199

. 044

• 028

0

• 01

• 172

• 004

0

0

.202

• 004

.172

36 +- .654

.292

• 4

.965

9.63

56

13.5 • 33.3 FT

.199

.044

.028

0

.016

. 1 14

004

0

0

.131

.004

. 1 14

38 +- .543

.249

• 61

.946

14.96

58

10.7 • 4 1.9 FT

. 199

.044

.028

0

.025

.077

.004

0

0

• 085

• 004

• 077

40 "»•- .482

.229

.9

.916

22.96

60

8.5 • 52.8 FT

. 199

. 044

.028

.04

.054

• 004

0

0

• 056

.004

.054

42 +- .458

.225

1 .29

.871

34.62

62

6.7 • 66.4 FT

. 199

.044

.028

0

.064

.039

.004

0

0

.037

. 004

.039

44 +- .4 68 +- .235

1 .78

.807

50.77

64

5.4 • 83.6 FT

. 199

• 044

.028

0

. 104

• 03

004

0

.026

.004

• 03

172
FREQ« 10 GHZ

FLUX- 547 F.U.

FLUX UNCERTAINTY* 5.49 %

G/T(DB)-e-LIN Y(DB) GCDB)

+-QUAD K2 HPBW

TCSTAR) DIAM

CERROR CONTRIBUTIONS TO G/T IN DBl

E-FLUX E- INDEX E-DECAY E-SKY

E-Kl E-K2 E-POLZN E-BW

E-POINT E-Y E-GAIN E-RESOL

22 12.206

7.094

• 01

.999

.21

42

67.4 • 5.3 FT

.226

.044

.028

0

.001

4.682

004

0

0

2.535

. 004

4.682

24

+ - 8.268

4.663

.01

.998

.34

44

53.6 • 6.7 FT

.226

.044

• 028

0

• 001

2.961

.004

0

0

2.039

.004

2.961

26 5.614

3.083

.02

.997

.54

46

42.6 • 8.4 FT

.226

.044

.028

0

• 002

1 .874

• 004

0

0

1 . 558

.004

1 .874

28 <•-- •f- 3.821

2.041

.04

.994

.85

48

33.8 • 10.6 FT

.226

.044

.028

0

.002

1. 189

004 1 . 134

• 004

1 .189

30 2.617

1 .352

.06

.991

1 .34

50

26.8 • 13^3 FT

• 226

• 044

• 028

0

• 004

• 756

• 004

0

0

• 794

• 004

• 756

32 +- 1 ^819

• 901

• 09

• 986

2^1 1

52

2U3 • 16.8 FT

• 226

• 044

• 028

0

• 006

.483

004 .54

• 004

• 483

34 +-

+ - U298

.614

.14

.978

3.32

54

16.9 • 21.2 FT

.226

.044

.028

0

.01

.311

. 004

0

0

.36

.004

.31 1

36 -t-- .964

.438

• 22

.965

5.2

56

13.5 • 26.6 FT

.226

.044

.028

0

.016

.202

004

0

0

.237

.004

.202

38 .755

.338

.34

.946

8.07

58

10.7 • 33.5 FT

.226

.044

.028

0

.025

.134

• 004

0

0

• 1,5 6

• 004

• 134

40

+ -

42

+-

• 631

.287

.566

.266

.51

• 916

12.39

.74

.871

18.68

60

8.5 • 42.2 FT

62

6.7 • 53.1 FT

.226

.044

.028

.226

.044

• 028

0

.04

.091

0

.064

.064

. 004

0

0

.004

0

.103

• 004

• 091

.069

.004

.064

44 4- .551

.267

1 .05

.807

27.4

64

5.4 • 66.9 FT

.226

.044

.028

0

. 104

.047

004

0

0

.047

.004

.047

173
FREQ" 12 GHZ

FLUX- 476 F.U.

FLUX UNCERTAINTY- 6.7 X

G/T<DB)-^-LIN Y(DB) G(DB)

-QUAD K2 HPBW

T(STAR> DIAM

C ERROR CONTRIBUTIONS TO G/T IN DB3

E-FLUX E- INDEX E-DECAY E-SKY

E-Kl E-K2 E-POLZN E-BW

E-POINT E-Y E-QAIN E-RESOL

22 - 18.88

1 1.37

.01

.999

.13

42

67.4 • 4.4 FT

.273

.044

• 028

0

.001

7.746

004

0

3.035

.004

7.746

24 +- 12.726

7.393

.01

.998

• 2

44

53.6 • 5.6 FT

.273

. 044

.028

0

.001

4.895

. 004

0

0

2.581

.004

4.895

26 8.635

4.859

.01

.997

.32

46

42.6 • 7 FT

.273

.044

.028

0

.002

3.096

.004

0

0

2.088

.004

3.096

28 - 5.^82

3.216

.02

.994

.5 1

48

33.8 • 8.8 FT

.273

• 044

.028

0

.002

1.961

.004

0

0

1.604

• 004

1.961

30 4.022

2. 135

.04

.991

.81

50

26.8 • 11.1 FT

.273

• 044

• 028

0

. 004

1 .245

• 004

0

1. 174

• 004

U245

32 -1- 2^773

U421

.06

.986

1 .28

52

21.3 • 14 FT

• 273

• 044

• 028

0

• 006

• 793

• 004

0

• 826

• 004

.793

34 1 ^945

• 956

.09

.978

2.01

54

16.9 • 17.6 FT

.273

• 044

.028

0

.01

.508

. 004

0

0

• 565

• 004

• 508

36 1 .405

.661

• 13

• 965

3^ 14

56

13.5 • 22^2 FT

• 273

• 044

• 028

0

• 016

• 329

• 004

0

0

• 379

• 004

• 329

38 1 .06

.483

.21

. 946

4.88

58

10.7 • 27 . 9 FT

.273

. 044

.028

0

• 025

• 215

004

0

0

• 252

• 004

• 215

40 •«--

•f

• 848

• 385

• 31

• 916

7^48

60

8.5 • 35.2 FT

.273

.044

• 028

0

• 04

• 144

• 004

0

0

• 167

• 004

• 144

42 +-

- .727

.337

• 46

• 871

1 U28

62

6.7 • 44^3 FT

.273

• 044

.028

0

.064

.099

.004

0

• 1 12

• 004

.099

44

- a676

.322

.67

.807

16.55

64

5.4 • 55.7 FT

.273

.044

.028

0

. 104

.07

• 004

0

• 077

• 004

• 07

174
FREQ* 14 GHZ

FLUX« 423 F.U,

FLUX UNCERTAINTY- 8.8 X

6/T<DB)*-LIN Y(DB) 6<DB)

+-QUAD K2 HPBW

T<STAR) DIAM

C ERROR CONTRIBUTIONS TO G/T IN DB]

E-FLUX E- INDEX E-DECAY E-SKY

E-Kl E-K2 E-POLZN E-BW

E-POINT E-Y E-QAIN E-RESOL

22 *-- 27.538

17,I13

0

.999

• 08

42

67.4 • 3.8 FT

.351

.044

.028

0

.001

1 1 ,858

004 3.389

• 004

1 1 .858

24 18.418

11.017

.01

.998

. 13

44

53.6 • 4.8 FT

.351

.044

.028

0

.001

7.49

004 3.004

• 004

7.49

26 12.453

7.175

.01

.997

.21

46

42.6 • 6 FT

.351

.044

.028

0

.002

4.737

004 2. 547

• 004

4.737

28 8.484

+- 4.724

.01

.994

.33

48

33.8 • 7.6 FT

.351

.044

.028

.002

2.998

004 2.053

.004

2.998

30 5.811

+- 3.135

.02

.991

.53

50

26.8 • 9.5 FT

.351

.044

.028

0

• 004

1 .902

004 1.57 2

• 004

1.902

32 4.007

2.091

.04

.986

.83

52

21.3 • 12 FT

.351

.044

.028

.006

1.21

004 1 . 149

.004

1.21

34 »•- 2.797

•«•- 1.406

.06

.978

1.31

54

16.9 • 15.1 FT

.351

.044

.028

0

• 01

.773

. 004

0

0

• 809

• 004

.773

36 1.998

-»•- .964

.09

.965

2.05

56

13.5 • 19 FT

.351

.044

.028

0

• 016

.498

• 004

0

• 554

• 004

• 498

38 1.479

+ - .69

.14

.946

3.18

58

10.7 • 23.9 FT

.351

.044

.028

0

.025

.324

004 • 374

.004

.324

40 1.152

+- .532

.21

.916

4.89

60

8.5 • 30.1 FT

.351

.044

.028

0

.04

.215

• 004

0

0

• 251

• 004

• 215

42 +- .957

.449

.31

.871

7.37

62

6.7 • 38 FT

.351

.044

• 028

0

• 064

.146

.004

0

0

.17

• 004

.146

44 -»-<- .858

+- .414

.45

.807

10.81

64

5.4 • 47^8 FT

• 351

. 044

.028

• 104

.103

• 004

0

0

• 1 17

• 004

• 103

175
FREQ« 16 GHZ

FLUXa 382 F.U.

FLUX UNCERTAINTYa 11.87 X

G/T(DB)+-LIN Y(DB) GCDB)

J-QUAD K2 HPBW

T(STAR) DIAM

[ERROR CONTRIBUTIONS TO 6/T IN DB1

E-FLUX E- INDEX E-DECAY E-SKY

E-Kl E-K2 E-POLZN E-BW

E-POINT E-Y E-GAIN E-RESOL

22 38.479

24.53

0

.999

.06

42

67.4 • 3.3 FT

.461

.044

.028

0

. 001

17.151

004

0

0

3.636

• 004

17.151

24 +• 25.531

15.684

0

.998

.09

44

53.6 • 4.2 FT

.461

. 044

.028

0

.001

10.834

. 004

0

3.32

.094

10.834

26 +- 17. 158

10. 125

• 0t

.997

. 1 5

46

42.6 • 5.3 FT

• 461

.044

.028

0

.002

6.848

004

0

0

2.919

. 004

6.848

28 +• 1 1 .662

6.617

.01

.994

.23

48

33.8 • 6.6 FT

.461

.044

.028

0

.002

4.333

.004

0

0

2.452

.004

4.333

30 + 7.996

4.374

.02

.991

. 37

50

26.8 • 8.3 FT

.461

• 044

.028

0

. 004

2.747

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0

0

U958

• 004

2^747

32 + 5.526

2,919

.02

.986

.58

52

21.3 • 10.5 FT

.461

.044

.028

0

.006

1.746

004

0

0

1 .487

• 004

1 ^746

34 +'+ • 3.86

1 .966

. 04

.978

• 91

54

16.9 • 13.2 FT

.461

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0

.01

1.114

.004

0

0

1 .081

• 004

1 • 1 14

36 +- 2.747

1 ^347

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1 .42

56

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.461

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• 716

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0

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• 759

• 004

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.09

.946

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58

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.461

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.028

.025

464

.004

0

• 521

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40 1 .548

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.14

.916

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60

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.461

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.306

.004

0

0

• 354

• 004

• 306

42 »•. 1 .26

.602

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62

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.461

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.206

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0

• 242

• 004

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7.47

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0

0

• 168

• 004

• 144

1 76
B . 2 The BASIC Program for the Computation of the Errors in

the Measurement of G/T Using Cas A

In this section the computer program which was used to

produce 'the printout in section B.l is given. The remarks

in this printout starting with step 5851 identify many of the

parameters used.

177
100 PRINT "DW26.2 (74 JAN 12) NBS 6514"

102 REM SWITCH 0i BYPASS R-PRINTOUT OF INPUT DATA

103 REM MODIFIED TO ALLOW VARIABLE FLUX ACCURACY PER 29.2 P6442

106 DIM EC123

108 DIM DC41

110 DIM SC 12x n

112 DEF FNA<X)« INT (1000* ABS (X/. 23026) -i-. 5 )/ 1 000

114 DEF FNB(X)« INT (1000* LOG X/ LOG (10)+.5)/100

120 READ Q5>G5,G6>G7,Y1 ,Y2,T

122 READ N

125 READ A1>A2,A3,A5*A6

130 FOR 1*1 TO 4

135 READ DC I 1 140 NEXT I 150 FOR 1=1 TO 12

155 READ SCI> 03>SCI>11

160 NEXT I 162 CALL 1 I, 0,V2

164 IF V2=l GOTO 510

172 PRINT

173 PRINT

175 FOR 1=1 TO 70

176 PRINT "#••;

177 NEXT I 178 PRINT

179 PRINT

180 PRINT > "MEASUREMENT OF G/T USING CAS A"

185 PRINT

190 PRINT QUANTITY"; TAB Ai;"UNIT";

195 PRINT TAB A2; "VALUE"; TAB A3; "UNCERTAINTY"

200 PRINT

205 LET M9 =M9+10

207 LET 1 = 1 210 PRINT " 1 FLUX at";q5;"ghz("Yi;")"; tab ai;"f.u.";

215 PRINT TAB A2;SCU 0 3; TAB A3; "LISTED"

220 GO SUB 201 5

230 PRINT "SPECTRAL INDEX";

240 GO SUB 2000

250 PRINT "SECULAR DECAY"; TAB Ai;"X/YR";

260 GOSUB 2000

27 0 PRINT "SKY BACKGROUND"; TAB Ai;"K";

280 GOSUB 2000

284 PRINT "KKATM TRANS)";

286 GOSUB 2000

290 PRINT "K2(STAR SHAPE)"; TAB A2; "LISTED";

295 PRINT TAB A3;"-i--(K2-l ) * ( "SC I > 13 ; " ) " 300 GOSUB 2015

330 PRINT "STAR POLARIZATION"; TAB Ai;"X";

340 GOSUB 2000

350 PRINT "K3( BANDWIDTH EFFECTS)";

360 GOSUB 2000

370 PRINT "ANT POINTING"; TAB Ai;"X HPBW"; TAB A2;" *";

380 GOSUB 2010

178
390 PRINT "Y-FACTOR"! TAB Ai;"DB"; TAB A2;"

400 GOSUB 2010

410 PRINT "GAIN INSTABILITY"; TAB Al;"DB"; TAB A2J" *";

420 GOSUB 2010

430 PRINT "MEASUREMENT RESOLUTION"; TAB Ai;"DB"; TAB A2;"

440 GOSUB 2010

450 PRINT

460 PRINT " assumptions; "*"T<SYST)=";T;"K"

470 PRINT >"DATE OF MEASUREMENT IS";Y2

480 PRINT ,"HPBW OF CAS A«";SC6, 03;"MIN"

485 PRINT >"ANT BEAM EFFI CIENCY»";

1

00*N; "%"

490 PRINT ,"ANT POLARIZATION RATIO«";P

500 PRINT

502 FOR I»l TO 70

504 PRINT "#";

506 NEXT I 507 LET M9«M9-»-20

510 PRINT

580 READ Q2^F

600 GOSUB 3000

770 FOR G2«G5 TO G6 STEP G7

778 LET SCUn«F*SCU 03/100

780 LET Gl«10t (G2/10)

790 LET GaGl*T

800 GOSUB 5900

805 LET Y»1+R4*G1

810 LET Q4«SC 1 ^ n*lE-26

820 GOSUB 5984

830 LET ECn«l-R4/R6

840 LET Q4» 0

850 LET Q7 = SC2>n

860 GOSUB 5984

870 LET EC23al-R4/R6

880 LET Q7« 0

890 LET R2»K2*SC5* 03*((1-(SC3> 03-SC3> 1 3 )/100)t (Y2-Y1 )

)

900 GOSUB 5984

920 LET EC3 3«1-R4/R6

925 GOSUB 5900

930 LET Et43«l-R4/(R4+St4>13/G)

950 LET EC53«SC5> 1 3/SC5, 03

960 LET EC63a( 1-K2)*SC6^ 1 3/K2

1000 LET EC83«SC8, 13/SC8> 03

1010 LET X9«(2.784*SC9, 1 3/100)

1020 LET EC93»l-< SIN (X9)/X9)t2

1050 FOR I»10 TO 12

1060 LET ECI 3«(SCI > I 3*.23026*Y)/<Y-1

)

1070 NEXT I

1 100 LET Xla 0

1110 LET X2« 0

1120 FOR I«l TO 12

1130 LET Xl«Xl+Eri3

1140 LET X2-X2-I.ECI 3t2

1150 NEXT I

17D
1200 PRINT G2;"+-"; FNACXl);

1210 PRINT TAB A5; FNB(Y);

1220 PRINT TAB A6; FNB(G);

1230 FOR I»l TO 4

1240 PRINT TAB DCI3; FNACECn);

1250 NEXT I 1255 PRINT

1260 PRINT " -I.-"; FNA( SQR CX2>);

1270 PRINT TAB A5; INT ( 1 000*K2+ . 5 ) / 1 000;

1275 PRINT TAB A6; INT ( 1 0*X3-»- . 5 ) /1 01 " • "J

1280 FOR 1=1 TO A

1290 PRINT TAB DC n; FNA<ECI+43);

1300 NEXT I 1310 PRINT

1350 PRINT TAB A5; INT < 100*G*R4-f.5)/100;

1360 PRINT TAB A6; INT <3.13« SQR (G/N ) /Q2+ .5 ) / 1 0; "FT"

1380 FOR 1*1 TO 4

1390 PRINT TAB DCIi; FNA<ECl+83);

1400 NEXT I 1410 PRINT

1420 PRINT

1430 LET M9«M9^4

1440 LET M8=64

1445 IF M9<M8-5 GOTO 1500

1450 FOR I»M9 TO M8>8

1460 PRINT

1470 NEXT I 1480 LET M9«3

1490 GOSUB 3000

1500 NEXT G2

1600 FOR I«M9 TO M8-I-8

1610 PRINT

1620 NEXT I 1625 LET M9«3

1630 GOTO 510

2000 REM INPUT DATA PRINT SUBROUTINE

2005 PRINT TAB A2;SCI> 03;

2010 PRINT TAB A3; "-" ; S C I >

H

2015 REM

2020 IF I«12 GOTO 2050

2030 LET 1=1+1

2040 PRINT i;" ";

2050 RETURN

3000 PRINT

3002 PRINT

3003 LET G«l

3004 GOSUB 5900

3005 PRINT "FREQa";Q2;"GHZ"

3007 PRINT "FLUX="; INT ( Q3*( Q2/Q5 > t Q6* 1 0t < 26) +. 5 ) ; "F.U.

3009 PRINT "FLUX UNCERTAINTY^"; F; "X"

3010 PRINT

3020 PRINT TAB DCn;"CERROR CONTRIBUTIONS TO G/T IN DB3"

3030 PRINT "G/T(DB)+-LIN";

180
3040 PRINT

3050 PRINT

3060 PRINT

3070 PRINT

3080 PRINT

3090 PRINT

3100 PRINT

3110 PRINT

3120 PRINT

3130 PRINT

3140 PRINT

3150 PRINT

3160 LET M9

3170 RETURN

4926 LET K2

5850 REM

5851 REM

5852 REM

5853 REM

5854 REM

5855 REM

5856 REM

5857 REM

5858 REM

5860 REM

5861 REM

5862 REM

5863 REM

5864 REM

5867 REM

5870 REM

5872 REM

5874 REM

587 5 REM

587 6 REM

5877 REM

5878 REM

5900 LET Q3

5905 LET Q4

5910 LET Q6

5915 LET Q7=

5920 LET Rl

5922 LET X3

5924 LET Xa

5926 LET K2

5930 LET R2

5975 LET K»

5980 LET R4

5982 RETURN

5984 REM

5990 LET R6

5995 RETURN

7000 DATA

TAB A5;"Y<DB)"1 TAB A6;"G<DB>";

TAB DC n;"E-FLUX*'l TAB DC 23 ; "E- INDEX"J

TAB DC3i;"E-DECAY"; TAB DC4i;"E-SKY"

• -QUAD"; TAB A5;"K2";

TAB A6J"HPBW"; TAB DCn;"E-Kl";

TAB DC23;"E-K2"; TAB DC 3 3

5 "E-POLZN";

TAB DC4];"E-BW"

TAB as; "T< STAR)"; TAB A6;"DIAM";

TAB DC 1 3;"E-P0INT"; TAB DC2];"E-Y";

TAB DC33;"E-GAIN"; TAB DC4] ; "E-RESOL"

tM9 + 10

< 1 - EXP (-X«X) )/<X*X)

^iHtm** G/T COEFFICIENT SUBROUTINE ****

Q2

Q3

Q4

Q5

Q6

Q7

Rl

R2

R4

R6

R5

K

FREQ

STAR

sSC

a 0

»SC

as 0

«SC

-II

SC6

«< 1 «K2

2.9

aRl

1

FLUX

" " ERROR

FLUX FREQUENCY

SPECTRAL INDEX

ERROR

ATMOSPHERIC TRANSMISSION

FINITE STAR CORRECTION AND STAR DECAY FACTOR

DT(STAR)/G

" " (MAX) BUT NO ATM OR FINITE STAR ERB

ERROR IN FREQ

Ct2/8 PI K

K2«K2<STAR SHAPE)

F«X ERROR IN FLUX

G«G

G 1«G/T

G2«G/T<DB)

N«BEAM EFFICIENCY

X3=ANT HPBW IN MIN

Y1«YR FLUX MEASURED

Y2=YR G/T MEASURED

03*i0» (-26)

2> 0]

5^ 0]

448/ SQR (G/N)

, 01/< 1 .2012*X3)

- EXP (-X*X))/Xt2

*SC5* 0]*(1-SC3, 03/100)t <Y2-Y1

)

97 93E+8T2*lE-18/(8*3. 141 59*1 .38046E-23)

*R2*K*Q3*(Q2/Q5) tQ6/Q2t2

*** R6 IS THE MAXIMUM DT(STAR)/G **

sRl *R2*K*<Q3+Q4)*<(Q2-R5)/Q5)t CQ6+Q7)/<Q2-R5)t2

1

181
7 01 1 01 f V I V PCM ^T rtP . C^ITO AAA

UA 1 A

O O /I /I o

r>AT A 1 07 A . 1 Q7 A ft 7 CI 01

r 1o o V HAT A 1 0101 1 lOlO

r O ^ DATA • ^ ^ 7 01/1 01

1 10** \o n AT A Offl 07 . /i7

r IC J - n r A

1

7 om «^

f loo o rv AT A 10, 1 «> OA^4, 'X^ 00, Ilh 44, f\'X Oo, f\0 0^

O 1L/ lO i HAT A T18«^. '^C1.--7ft'^. 01 O 10 10 o HAT A

800S \J Xj XJ -J DATA . 98 . .01. A. 3. .1

KJ xj YJ 1 DAT A 1, .01, 1, .001

8W 00Q XJ X/ 7 DATA 0, 5, 0, .01

RO 01 t 1 10 I 1 r> AT A 0, 0, 0, .01

8 100 REM FREQUENCY, FLUX ERROR PAIRS

8110 DATA 7.25, 4.67, 2, 4.32, 4, 4.33 , 6, 4.45,

8120 DATA 10, 5.49, 12, 6.7, 14, 8.8, 16, 11.87

182
APPENDIX C: DETERMINATION OF ANTENNA AND RECEIVER PARAMETERS

BY NOISE-ADDING TECHNIQUES

Parameters such as antenna gain (when measured with the

Cas A method), antenna noise temperature, system noise

temperature, and gain to noise temperature ratio, are sometimes obtained by use of a noise-adding circuit such as that

shown in figure C-1. The noise-adding circuit consists of

a directional coupler with the sidearm terminated with a variable noise source. The purpose of this section is to

discuss such a noise adding measurement system and its possible applications.

The output from port 2 of the directional coupler expressed

in terms of noise temperature is given by [73]

\2 ' "21^1 * * Vamb' C^.l)

where ql^-^ arid 0^23 available power ratios for the

directional coupler and depend on and r^,

^2'''amb

'^^ thermal energy originating within the three port. The

parameters o'j^j (i - 1>2,3; i ^ j = 1,2,3) represent ratios

of the power available from port i to the available power

of a signal source attached to port j. If T^ is changed

and Tj is simultaneously adjusted so that T^2 remains unchanged, then

AT^ = -(a23/a2^)AT3. (C.2)

That is, a (plus) one kelvin change in (^2 3'^°^21'' "^3 ^^^^^^^

the available noise temperature at port 2 in exactly the

same way as a (minus) one kelvin change in T-j^

.

Two noise sources of known temperatures (say room-temperature and liquid nitrogen) successively placed at port 1 calibrate (0^23/ "^21-^ ^^3 P^O'^i'i^d T|32 held constant by adjusting

183
184
the attenuator on the sidearm. Once the system is calibrated,

any change AT^ can be calculated from eq. (C.2) once the corresponding ATj has been determined.

The calibration parameter '^23'^ ^^21 ^ function of

and r^, and of the scattering parameters of the directional coupler [73] . It follows that once this parameter

has been determined, care must be exercised to maintain

and close to their original values in the course of

subsequent measurements.

C. 1 The Measurement of Antenna Parameters

The antenna parameters of interest are antenna gain

and noise temperature.

Antenna gain can be deduced from the measured change in

s t ar noise temperature, (AT^) , referred to the antenna output

port, when a radio star drifts across the antenna beam;

G = CAT^)^^^^/^. CC.3)

Here C is defined by ^ = (X^/8tt) k^k2S , where S is the star

flux density at measurement wavelength X incident from outside the earth's atmosphere; and k2 are correction factors

for atmospheric effects and for the finite extent of the star

in relation to the antenna power-gain pattern. For example,

^ is of the order of lO'^K for Cas A at 4 GHz.

Antenna temperature can be deduced from the change in

measured noise temperature (AT^)^^^ when the antenna

is removed from port 1 and replaced by a cold standard

noise source T ^j; s td

Tant ' ^std * C^T^^" CC.4)

Then a ratio method as will be seen below (the Y-factor

method) can be used to determine system noise temperature and

G/T.

185
C. 2 The Measurement of System Noise Temperature and G/T

In order to determine the system noise temperature, T,

the ratio of the power at the receiver output port is

measured for a known change AT^ , determined in a separate

measurement based on eq. (C.2). T equals the sum of the an

tenna temperature, T_

noise temperature, T

tenna temperature, T^^^, and the receiver effective input

e

= (AT-j^ + T)/T. (C.5)

Inverting eq. (C.5) to obtain T results in

T = AT^/(Y^ - 1). (C.6)

If T^^^ is known from separate measurements and eq. (C.4),

then T equals T minus T

e ^ ant

To obtain G/T, the same star-drift measurement described

in connection with eq. (C.3) can be used, except that in this

case the ratio Y of the total power at the system output port

is measured. It can be seen that

Y E (AT^^^^ + T)/T, (C.7)

and with eq. (C.3) in mind, that

G/T = (Y - 1)/?. (C.8)

1

186
.-0

R

M NBS-n4A (1-71) U.S. DEPT. OF COMM. 1. PUBLICATION OR REPORT NO. 2, Gov't Accession

BIBLIOGRAPHIC DATA ..^ott. -? a qoo

SHEET NBSIR 74-382

3. Recipient's Accession No.

.TITLE AND SUBTITLE

A STUDY OF THE MEASUREMENT OF G/T USING

CASSIOPEIA A

5. Publication Date June 1974

6. Performing Organization Code

7.AUTH0R(S)

D. F. Wait, W. C. Daywitt, C. K. S. Miller, M. Kanda

8. Performing Organization

I PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10 Proiprr/Ta<;lf/WorW Ilnir Nr> 2766482

11. Contract/Grant No. P.O. No. SCC-411-73

', Sponsoring Organization Name and Address

advanced Concepts Office

Jnited States Army Communications Command

'ort WJ~ ^ Huachiica 1 1 UUW 1 1 \mf CL . Ai"i 7nna RRfil f

J_ _1_ ^^1 Id V_J ^ V_J _i_ J

13, Type of Report & Period

C overe d

5. SUPPLEMENTARY NOTES

i6, ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

|This report describes a study intended to estimate the best possible

iaccuracy of measuring the ratio G/T (system gain to system noise temperature) of a satellite communication ground station using the radio

star Cassiopeia A (Cas A) . The concept of G/T and its measurement using

}a radio star is briefly discussed. Results of an extensive literature

search are presented^ summarizing the properties of Cas A and its vicinity

described by radio astronomers in order to utilize this information to

assess the accuracy of a G/T measurement. Consideration is given to

atmospheric effects upon a G/T measurement using Cas A based on inforMtion available in the literature. A detailed analysis of errors for

gain measurements of large ground antennas, which includes the calibration

if a standard gain antenna and the transfer of the calibration of this

tandard to a large antenna, is provided to validate radio star flux data

;ince this analysis is not available in the literature. The results of

|hese efforts are utilized to show that the best possible accuracy of

i G/T measurement for a ground station having a 60 ft. diameter antenna

and both practical and reasonable specifications is in the neighborhood

bf ± 0.25 dB.

^. KEY WORDS (Alphabetical order, separated by semicolons)

Accuracy; antenna; calibration; Cassiopeia a; g/t; star flux.

p. AVAILABILITY STATEMENT

(Xl UNLIMITED.

1 1 FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

1

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

21, NO. OF PAGES

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

22. Price

USCOMM-DC 66244-P71


U.S. GOVERNMENT PRINTING OFFICE 1974 • 677-234/1214 REG. 8



!