NBSIR 76-842

FILE COPY

BD HOT I!

ERROR EQUATIONS USED IN THE

NBS PRECISION G/T MEASUREMENT SYSTEM

W.C. Daywitt

Electromagnetic Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

September 1976

Prepared for

U.S. Army Communications Command

Fort Huachuca, Arizona 85613

NBSIR 76-842

ERROR EQUATIONS USED IN THE

NBS PRECISION G/T MEASUREMENT SYSTEM

W.C. Daywitt

Electromagnetic Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

September 1976

Prepared for

U.S. Army Communications Command

Fort Huachuca, Arizona 85613

U.S. DEPARTMENT OF COMMERCE, Elliot L Richardson, Secretary

Edward 0. Vetter, Under Secretary

Dr. Betsy Ancker-Johnson , Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Acting Director

CONTENTS

Page

I. INTRODUCTION 1

II. THE G/T EQUATION 1 III. Y-RATIO, WAVELENGTH, AND FLUX DENSITY 2

A. Y 2

B. A 3

C. S 3

IV. ATMOSPHERIC TRANSMISSION CORRECTION FACTOR (k ) 4

A. k 5 g

B. k, 6 Q

C. k 7 r

V, STAR SHAPE CORRECTION FACTOR 8 VI. BANDWIDTH CORRECTION FACTOR 9 VII. DIFFERENTIAL SYSTEM TEMPERATURE FACTOR 10 VIII. ANTENNA POINTING CORRECTION FACTOR 10

IX. POLARIZATION CORRECTION FACTOR 11

X. SYSTEM RESPONSE CORRECTION FACTOR 11

XI. RESULTS AND CONCLUSIONS 11 XII. ACKNOWLEDGMENTS 13

REFERENCES 14

iii

ERROR EQUATIONS USED IN THE NBS PRECISION G/T MEASUREMENT SYSTEM

W.C. Daywitt

ABSTRACT

Equations presently being used in the precision NBS G/T measurement system

are presented in this report. Included are the assumptions upon which these

equations are based and sample calculations showing how the measurement errors vary with antenna elevation angle

.

Key words: Error analysis; G/T; radio star; ratio precision measurements;

satellite communications.

This report summarizes the approximate error equations presently being used by NBS

in its precision satellite earth-terminal G/T (system gain/system noise temperature) measurement system [1]. These equations are the result of a four-year evolution begun in 1972

with a G/T measurement [2] of the earth terminal located at Camp Roberts, California, using

the G/T equations then available in the literature [3-8]. The equations presented here

represent the final results of a comprehensive G/T error analysis. This analysis was preceded by a thorough study [9] of the literature concerning the use of Cassiopeia A in

G/T measurements. A further study [10] of the errors involved in the absolute flux density

measurement of Cassiopeia A was subsequently performed since the literature was found to be

lacking in this respect; this study does not identify an absolute flux density value for

Cassiopeia.

The equations to be presented are approximations of "exact" equations derived in the

analysis. The ^-requirements of high accuracy and the use of models naturally narrows the

validity of the resulting equations, and although the range of validity of each equation

will be clearly stated, it should be mentioned initially that most of the equations are appropriate to the 1 GHz to 10 GHz frequency region.

Most of the financial support for these studies has come from the U.S. Army Communication Command (ACOM) Headquarters, Fort Huachuca, Arizona, and is gratefully acknowledged.

The radio star method [3,11,12] of measuring G/T involves measuring the ratio of two

noise powers at some point in the IF portion of the earth-terminal receiving system (for a complete definition of the word "system" see reference [9]). These two powers and

correspond respectively to powers received when pointing the earth-terminal antenna at and then adjacent to the calibrated radio star. The measured ratio Y is related to these

two powers by

I. INTRODUCTION

II. THE G/T EQUATION

(1)
Since the earth-terminal system gain is high, noise from the NBS apparatus attached to the

system to measure Y is insignificant, and therefore for all practical purposes eq. (1) is

exact

.

Assuming that the system has a linear power-transfer characteristic and that the noise

in the system is stationary, both and obey an equation of the form

W = / w(f)g(f) df (2)

where f is the frequency, w(f) is the spectral power available at some reference point in

the front end of the system, and g(f) is the power gain of the system from the reference

point to the output where the ratio Y is measured. Both w(f) and g(f) are integrated over

the limiting bandwidth of the system. Under these assumptions Y is related to G and T via

the equation

A

2 Sk ---k

Y = 1 + - •

. (3) T 8nk

G (for a complete definition of G and T see reference [9]) is the gain (at the earthterminal receive frequency) of the system from the far field of the antenna to the reference

point; T is the system noise temperature (at the receive frequency) at the reference point;

A is the free-space wavelength corresponding to the earth-terminal receive frequency; S is

the radio star flux density calibrated at the receive frequency; k is Boltzmann's constant;

and k^ through k^ are correction factors defined to insure the equality in eq. (3).

All of the k factors (k^ through k^) involve integrations of the radio-star brightness

distribution with various quantities over the power pattern of the antenna. However, if the

power pattern were precisely known, G/T could be simply and accurately determined without

the aid of a radio star. This is seldom the case. Furthermore, accurate brightness distributions are difficult to obtain. The usefulness of the radio star method is based upon

three commonly present conditions: 1) for brightness distributions with angular extents

less than the antenna HPBW, the smoothing effect of the antenna allows the distribution to be removed from the integral and replaced by a disk or gaussian distribution [8,10] and a flux density; 2) the real antenna power pattern can often be adequately approximated by a gaussian pattern inside the HPBW; and 3) the k factors are often close enough to unity to allow condition 2) to be used as a perturbation calculation of these factors. For an accurate radio-star determination of G/T from eq. (3) all three of these conditions must be

met, and all three are assumed in the k-f actor equations to follow.

III. Y-RATIO, WAVELENGTH, AND FLUX DENSITY

The Y-ratio measurement is performed by an automated measurement system [14] built

around one of the most accurate power bridges known, the NBS Type II self-balancing bridge

[15].- This bridge is capable of measuring stable noise power ratios to an error no greater

2
than 0.002 dB. The resulting Y-ratio system error is assumed to be no greater than 0.004 dB

[15] . That is

= 0.1% (0.004 dB) . (4)

The corresponding error E(Y) in the determination of G/T from eq. (3) is

E(Y) = O.l L

Y

- 1%. (5) [Y - lj

In order for an accurate determination of G/T to be made the measured Y ratio should

be greater than approximately 0.25 dB. This means that the earth- terminal G/T must obey

the inequality

G 2.3 x IQ- . f

2 ^ IQ0 - 004

^ - T

> q (6)

1

where f is the receive frequency in GHz, a is the spectral index [8] of the radio star, S is

the antenna elevation angle at which the radio star is observed, and S-. is the radio-star

—26

flux density at 1 GHz in flux units (fu) (1 fu is equivalent to 10 W/m2 /Hz).

The free-space wavelength \ appearing in eq. (3) is taken to be that wavelength cor- responding to the received rf signal from the satellite even though, at the time of the

G/T measurement, the earth-terminal antenna is not pointed at the satellite and is therefore not receiving the satellite signal. The G/T error E(A) resulting from an uncertainty &X in the value of X is

E(X) = ^f- % (7)

where f is the receive frequency and of is its corresponding uncertainty, and 5f/f is

expressed in percent.

C.

The G/T error E(S) resulting from an uncertainty in the flux density S of the radio source used in the measurement is

E(S) = ^| % (8)

where 6S/S is the uncertainty in the flux density expressed in %. A number of strong extraterrestrial radio sources (all referred to as radio stars in

this report) exist whose potential flux-density accuracy is good: they are the strong

radio stars; the moon and possibly the sun. The source chosen for a particular measurement

depends on the earth-terminal G/T (eq. (6)); and on the requirement that the HPBW of the

earth-terminal antenna be greater than the angular extent of the source. The accuracy

3
SS/S to which the stronger radio stars can be calibrated [10] with present-day-not-quitestate-of-the-art equipment is approximately 5% (3a). The lower bound to the error [10]

using the best equipment of the foreseeable future under ideal conditions is approximately

2% (3a). Recent work [16] also indicates* that the moon might be used as a standard source

to a 9% accuracy. Where no other source is strong enough, even the sun might be used as a transfer standard if sufficiently monitored [17].

Considerable effort has been devoted to establishing the flux density of the stronger

radio stars [4,8,18-27]. However, comparisons among various sets of observations are often

complicated by a lack of agreement on absolute flux density scales, and, moreover, all

the observations have not been of comparable accuracy. Sometimes the problems are com- pounded by confusing accuracy with precision. Often errors less than half the lowerbound error quoted (2%) in the preceding paragraph are reported. Therefore, as regards

the radio stars, it is not clear from the literature which are the correct flux-density

values to be used in the G/T measurements (currently NBS is using the values given by

Kellerman et al. [4] with an assumed 4.46% accuracy). This situation is unacceptable where

highly accurate flux data are needed, and NBS is hoping in the near future to calibrate

some of the stronger radio stars in the neighborhood of 7.5 GHz with one of the wellcharacterized antennas at the Jet Propulsion Laboratories.

IV. ATMOSPHERIC TRANSMISSION CORRECTION FACTOR (k )

Since the calibrated radio star used in the G/T measurement is outside the earth's

atmosphere, the effects of the atmosphere upon the source flux density must be taken into

account. This effect appears in the atmospheric transmission correction factor k^, which

accounts for atmospheric absorption and scattering. The relatively high atmosphere transparency in the 1 GHz to 10 GHz microwave region [28] allows the effects of absorption and

scattering to be separated with negligible error. That is

k = k k,k (9)

1 g d r

where k^, k^, and k^ are the correction factors respectively for absorption by atmospheric

gases, diffusion by tropospheric irregularities, and refractive spreading by the continuous

component of the atmospheric ref ractivity

.

The corresponding G/T error E(k^) is thus the sum of the three component errors, E(k^)

,

E(k

d

) , and E(k

r

)

.

The effects [7] of clouds, fog, rain, hail, or snow on the attenuation cannot be

accurately calculated on a single-measurement basis. A high level of accuracy therefore

requires that the G/T measurements be performed in relatively clear weather, and no discussion of these effects will be presented here.
A. k

_£

The atmospheric gases to be considered as important absorbers in the 0.1 GHz to 50 GHz

frequency range are oxygen and water vapor [7]. For this range, calculations show that 99%

of the attenuation of energy from outside the earth's atmosphere to the earth's surface

takes place in the lower 10 km of the troposphere. The calculations reported here take

into account the first 20 km (about 20% into the stratosphere [29]) of the atmosphere above

the earth's surface with a resulting k^ error of less than 0.1% for neglecting the remaining

atmosphere

.

The oxygen and water vapor absorption coefficients (dB/km) used to calculate the

atmospheric attenuation (dB) are taken from the VanVleck theory [7,30,31] of absorption.

These coefficients are integrated along the ray path taken by the energy from the radio

star through the atmosphere to the antenna on the earth's surface. The bending of this

path by the atmosphere is accounted for by using a bi-exponential model [7,32] for the

atmospheric ref ractivity . The coefficients are functions of the atmospheric temperature,

dry-air pressure, and water vapor density, which in turn vary along the ray path. The

vertical variations of these parameters are described by average altitude profiles [28] for

various geographical locations and seasons

.

The actual values of the atmospheric variables along the ray path are not known. What

is done is to let the yearly average profiles at the location of the earth terminal

describe a uniformly stratified atmosphere for a large radius (less than 200 km (124 miles)

for elevation angles greater than 2° and a 10 km thick atmosphere) about the location.

The atmospheric attenuation is then calculated for this ficticious atmosphere by using

the profiles. The difference between the calculated and actual attenuations is assumed to be bracketed by an error equal to one half the difference between the attenuations calculated by using the maximum and minimum average seasonal profiles for the particular

location of the earth terminal.

What results from the foregoing procedure when applied to the calculation of the

zenith attenuation A is an equation of the form

g A

g

= A

1 + pA2 (10)

where A^ is the zenith attenuation (dB) due to oxygen, A^ is the zenith attenuation coefficient (dB/gm/n^) for water vapor absorption, and p is the antenna-level water-vapor

density (gm/m3 ). The calculation of atmospheric attenuations along other-than-zenith ray paths can

be performed sufficiently accurately (less than 0.3% error for elevation angles greater

than 4°) by using an equation of the form

A (6) = A • Csc 9 (11)

6 §

where ^g(^) is the attenuation for the ray path corresponding to the elevation angle 6.

5
Calculations show that for elevation angles greater than 2°, the correction factor

id the atmo: using eq. (11)

,

^ and the atmospheric transmission coefficient are equal to within 0.01 percent. Thus,

-A esc 9/10

k

g

= 10 g (12)

to better than 0.31 percent.

The total error in k using eq. (12) includes the partial errors resulting from the

8 following items: errors in and ; errors in p; errors in 6; errors caused by using

the cosecant approximation of eq. (11); errors caused by using average temperature, pressure, density, and refractivity profiles; and finally errors in the altitude of the earthterminal antenna above sea level.

For elevation angles above 4°, the G/T error E(k ) resulting from errors in k is

8 8

E(k ) = 40 (k"

1 - 1)1 (13)

8 8

B. k„

d

Atmospheric turbulence causes a random variation of the atmospheric refractive index.

These variations can be pictured as "closely packed blobs" [33] which act as scattering

centers [34] to incident energy. In this report the attenuation due to this scattering

will be called "diffusive" after Yohoi [35]. The effect of this type of attenuation on the

antenna temperature resulting from radio noise from outer space is greatest for a point

radio source, rapidly diminishing to zero for a source whose angular diameter D is greater

than the antenna HPBW 6 u [35]. At the present time Yohoi 's paper appears to be the only source reporting diffusive

attenuation measurements for microwave energy from outer space. It can be deduced from his

paper that the resulting transmission coefficient (taken to be identical with diffusive

correction factor k^^ in this report) for power emanating from a point source takes the

form

-A, esc e/io M/ . k = 10

d (14) k

d0

iU

at least for a limited frequency range and for elevation angles greater than 5°. The

zenith attenuation A. is found to be

d A, = 0.0011 f

2 (15)

d where f is the frequency in GHz, and A^ is in decibels,

6
For antenna elevation angles greater than 5° the correction factor for a non-point

source is assumed to take the form

i i /t i \ -0.467x 2 k

d

= 1 " (1 "k

do

)e (16)

where the exponential factor is taken from the results applicable to refractive attenuation (see the next section for a more complete description) and accounts for the finite source size. The variable x is given by

x = D/1.201 9„. (17) n

where D and 6 are the source diameter and HPBW, respectively. a

Equations (14), (15), and (16) are uncertain and probably crude approximations to the correct quantitative description of the diffusive transmission coefficient. Especially

alarming is the rapid rise of the zenith attenuation (eq. (15)) with frequency, even when

restricted to the 1 GHz to 10 GHz frequency region intended here. Nevertheless, eqs . (14)

through (15) will be used in the present G/T measurements until a more complete description

of k. can be obtained,

dThe G/T error E(k^) caused by error in k^ is assumed to correspond to a 75% error in

the diffusive loss and follows the form of eq. (13). That is

E(k

d

) = 75 (k"

1

- 1)%. (18)

C. k

r

As microwave energy traverses the troposphere from outside the atmosphere, its wavefront is bent downward and spread out as it travels to the antenna. This spreading reduces

the flux density so that an antenna will intercept less energy than would be intercepted

if the atmosphere were not present. The resulting "refractive" [35] attenuation, like its

"diffusive" counterpart, vanishes as D/6 increases.

The refractive transmission correction factor k is defined here to be the ratio of

r 1) that portion of the antenna temperature due solely to energy from the extraterrestrial

radio source with the atmosphere present and neglecting gaseous and diffusive losses to

2) the corresponding antenna temperature with the atmosphere absent. For a point source

and a uniformly stratified atmosphere this ratio reduces to [35,36]

_ Cos 9 rO Cos 6' "rl (19)

36 J

where 9 and 9' are the antenna elevation angle when pointing at the source, and the true source elevation angle, respectively. For antenna elevation angles greater than 2°,

9 and G ' are approximately related by

9 - 6

1 = B Ctn 6 - C Ctn2

9 (20)

where B and C are seasonal constants calculated for a particular geographical location by

fitting eq. (20) at 2° and 20° elevation angle to the "exact" calculation [7,32]. The

resulting error in the ray bending angle (9-9') is no larger than 15% from 2° to 90°

elevation angles . 7
For a non-point source (D/6 ^ 0) the following equation for k can be used with

n r negligible error

k

r = 1 -

(1 "k

r0

)e

-0.467x2 (21)

where x is defined in eq. (17). The derivation of eq. (21) assumes a gaussian main beam.

For antenna elevation angles greater than 3°, kg can be approximated by

-1

= tt(B-2C Ctn 6)Csc 2

9 rO

1 180 * 60 (22)

The G/T error ECk.^) due to errors in k^ is given by

E(k ) = 18(k

-1

- 1)%

r r (23)

for antenna elevation angles greater than 3°, and for HPBW's determined to 3% or better.

V. STAR SHAPE CORRECTION FACTOR

The star shape correction factor V.^ accounts for the finite angular extent and shape

of the radio star. It is defined [10] as the ratio of 1) the radio-source brightness

distribution integrated over the power pattern of the antenna to 2) the brightness distribution integrated over a unity power pattern. This definition is the reciprocal of the

correction factor appearing in the literature [3,8].

The approximate equations for k^ given here assume a gaussian main beam for the antenna, and a radio-star diameter (in radians) much less than unity [8,10]:

k

2 =

1 - e l.OOlx2 (disk source)

4ft

•1/2 -1/2

1 + (Gaussian sources) (24)

where x is defined in eq. (17), D is the equivalent angular diameter [10] of the disk

source, and and are the equivalent [8] major and minor angular diameters of the

elliptically symmetric gaussian sources. The correct procedure for obtaining the diameters

is outlined by Kanda [10].

The G/T error E(k^) due to errors in k

2 for the disk source was found to be

E(k

2

) = 6(l-k

2

) + 0.1 % (25)

This equation assumes that radio star drift curves are used to measure 6 to 3% or H better, and that the D/6 U ratio is less than or equal to 0.8 [10]. Equation (25) was derived for the radio source Cassiopeia A, but it is assumed for the present to apply

to all sources used.

8
The work by Kanda [10] indicates the possibility of treating all sources of whatever

shape (disk, gaussian, double point, etc.) in terms of an equivalent disk model with no

significant increase in the G/T error. This possibility apparently stems from the smoothing

effect the antenna has upon the source distribution for D/6 ratios less than unity.

n

VI. BANDWIDTH CORRECTION FACTOR

The G/T ratio is a single-frequency f igure-of-merit referenced to the earth-terminal

receive frequency, while the measurement represented by eq. (1) is the ratio of two noise powers whose spectra occupy the entire passband of the earth-terminal receiver.

The conversion from this "passband" measurement to the single-frequency G/T ratio is

accomplished by the bandwidth correction factor k^ which accounts for the variation of all

the frequency-dependent parameters of the system across the receiver passband.

The "exact" expression for k^ involves integrals whose order of magnitudes are proportional either to: 1) the difference in system noise temperatures between when

the earth-terminal antenna is pointed at the calibrated radio star and when it is pointed

at the cold sky; or to 2) the product of the radio-star brightness temperature [37] and its own solid angle [37] divided by the antenna solid angle [37]. Which one of these integrals

predominately determines the final form of k^. For sources like Cassiopeia A where the

temperature-difference integral predominates k^ becomes

k

3 = 1 + (Af/2f) 2 (26)

where Af is the noise bandwidth [37] of the system passband, and f is the receive frequency

to which the G/T is referenced. The assumptions leading to the second term in eq. (26) are:

1) that the system noise temperature difference is due entirely to cosmic radio noise [37];

2) that the average cosmic background in which the calibrated radio star source is immersed

is due to ionized hydrogen in addition to the 3-Kelvin blackbody noise [38] and that the

ionized hydrogen emits radiation proportional to the reciprocal of the frequency squared

from 1 GHz to 10 GHz; 3) that the cosmic region to which the antenna is pointed after pointing

at the radio star emits only 3 Kelvin blackbody noise; 4) that the average background within

one bandwidth of the radio source has an average noise temperature around 1 Kelvin; 5) that

the system bandpass is roughly rectangular; 6) that Af is less than 500 MHz; and 7) that the

earth-terminal antenna gain is less than 70 decibels.

For small antenna-earth terminals only the sun or moon [39] emit sufficient radiation

to allow a G/T measurement to be made (see eq. (6)). Equation (26) probably does not apply

to these terminals

.

The G/T error E(k^) due to errors in k^ is assumed to be

E(k ) = 50(Af/2f) 2 %. (27)

9
VII. DIFFERENTIAL SYSTEM TEMPERATURE FACTOR

In a G/T measurement the earth-terminal antenna is first pointed at the cosmic radio

source, and then a few degrees in azimuth to the side. The system [9] noise temperature

is conceivably different for these two antenna positions, and this difference is accounted

for in the differential system temperature factor k^. This factor is given by

0.004 T k = 1 + ^ (28)

k

1k

2 S

where T is the average noise temperature of the cosmic background within one antenna

AVE

beamwidth (the main lobe) surrounding the radio star, 6 U is the antenna HPBW in arc-minutes,

k^ and k^ are correction factors previously described, and S is the radio source flux density in fu. The assumptions leading to eq . (28) are: that the system temperature difference

is due solely to changes in the cosmic background between the two antenna positions and that

the system temperature difference is equal to the average temperature T^^ divided by the

frequency in GHz squared.

The maximum G/T error E(k^) due to errors in k^ is assumed for all the strong radio

stars to be

°' 4 TAVE

9 H

E <V = k^s % - (29)

VIII. ANTENNA POINTING CORRECTION FACTOR

During that part of the G/T measurement when the star is being used, the center of

the earth-terminal antenna mainbeam and the center of the radio source should be coincident.

Any angular spearation between these two centers will cause a reduction in the power entering

the antenna. This reduction is accounted for by the antenna pointing correction factor k^

given by

. 2(£n 2)x2 (e/100) 2

, S

= 1 ^—; °0)

e - 1

where x has been previously defined, and e is the pointing error in percent of the antenna

HPBW. The resulting G/T error E(k<_) is taken to be

= 0.014 x? £

2 %m (31)

J x i e - 1

In the event that the pointing error is large (e > 6%) a radio-source drift method [10]

is available which will give k^ to a 0.5% error or less.

10
IX. POLARIZATION CORRECTION FACTOR

Some of the stronger radio stars are known to possess a small component of linear

polarization [19]. The reduction in the power received by the earth-terminal antenna re- sulting from a mismatch between this component and the antenna polarization is accounted for

in the polarization correction factor k, [10]. It is assumed in this report that the anD tenna polarization is circular to within 3° of 45° [10]. This assumption allows k^ to be

taken as unity with a corresponding G/T error E(k^) no greater than 0.1%. That is

k

6 = 1 (32)

and

E(k,) = 0.1%. (33)

D

Equations (32) and (33) may not apply to radio star Taurus A.

X. SYSTEM RESPONSE CORRECTION FACTOR

Instabilities in the earth-terminal receiver gain and a long system response time can limit the accuracy of a single G/T measurement. However, with the present instrumentation

the response-time effect is negligible, so that only the effects of gain instabilities have

been incorporated into the system response correction factor k^ . This factor is taken to be

k

? = 1 (34)

with a single-measurement G/T error E(k_,) given by

E(k

?

) = Y - 11 g

% (35)

where Y is the ratio in eq . (1), and 6g/g is the percentage relative gain instability of

the earth-terminal receiver.

Gain instabilities encountered in the G/T measurements performed at Camp Roberts [2],

California, and at Fucino [40], Italy, were 0.45% and 1.27%, respectively. The resulting

single-measurement error in k^ was 4% and 16%, respectively. These large errors were re- duced by measuring the G/T many times at a number of antenna elevation angles and fitting

a smooth curve to the results. A more desirable method to reduce the error can be obtained

by adding noise [41] through the side arm of a directional coupler into the front end of

the earth-terminal receiver system, and monitoring changes in magnitude changes that occur

in this added noise after it has been amplified by the system.

XI. RESULTS AND CONCLUSIONS

The use of the previous equations is illustrated in table I where the results of four

sample calculations (one at each of the four antenna elevation angles, 5°, 15°, 30°, and

90°) are presented. The variables appearing in the table are those needed to determine the

11
G/T ratio from eq. (3). The values of the parameters used in the equations were: f, 7.5 GHz

6f/f, 0; Af, 10 MHz; 6g/g, 0.46%; e„, 9.2 arc minutes; e, 5%; S.. , 3090 fu (Cassiopeia A);

a, -0.765; D, 4.6 arc minutes; B, 1; C, 0.013; A , 0.038 dB; A

2

, 0.00035 dB m

3 /gm; and p, 8.5 gm/m3

. These values are typical of those which might be encountered in an earth terminal located in the Continental United States, having an antenna gain of 60 dB and a system

temperature of 100 kelvins . The use of these values in eq . (6) indicates that a reasonably

accurate G/T measurement could be expected for an earth terminal with a G/T as low as 33.4 dB

The table shows that of the correction factors (k, through k,) only k , k,, k and k n 1 ° 1

J g' d r 2 are important, the others being close to unity magnitude. Excluding the rest (k^ through

k^) will not cause a significant additional rms error. Of the "important" correction factors k^ and k^_ have not previously appeared in the literature.

The table further illustrates the tendency of the total G/T error E(G/T) to decrease

rapidly from low elevation angles, encountering a "knee" in the neighborhood of 15° elevation with a much reduced fall-off thereafter. The error below the "knee" at higher elevation angles compares very favorably with the G/T error encountered using the best of other

methods than the radio-star method examined here. This condition strongly recommends the

radio-star method of G/T measurement because other accurate methods require considerable

skill and highly qualified personnel to perform.

The "E(G/T)-without E(S)" row indicates the possible accuracy in relative G/T measurements, where a highly accurate value for the radio-source flux density S is not needed.

This kind of measurement is of value where only relative values of G/T are needed for

quality comparison between various earth terminals.

Two sets of errors stand out in the "Resulting Error" columns of the table, those

arriving from the flux density S and the diffusive correction factor k^. The 4.46% G/T error due to the flux density is examined in an earlier report [10] from which it can be

concluded that, at least for the present, it will be difficult to reduce this error further.

It should be again pointed out that it is not clear from the literature which, of all the

flux density values reported, is the best value to use in the G/T measurements.

The G/T error resulting from k, reflects the fact that at the present time few

investigations concerning the diffusive attenuation of microwave noise from radio stars have

taken place. Some work along this line would probably reduce this error considerably.

The values of the parameters (D, D^, and D^) used to calculate the other "important"

factor k^ for the strong radio sources should be determined [10] by minimizing the difference beween 1) the k^ calculated from a brightness distribution map of the source, and

2) the k^ calculated using the source's equivalent shape. When this was done for the radio

star Cassiopeia A treated as a uniformly bright disk of angular diameter D, D was determined

[11] to be 4.6' in distinction to the 4.3' value appearing in the literature. The additional G/T error incurred by using 4.3' instead of 4.6' in eq . (24) is 1.1%, a value too large to ignore. Similar determinations for the other radio sources still need to be

performed.

12
XII. ACKNOWLEDGMENTS

This report forms only one part of a broad effort in the accurate G/T measurement area, including error analyses, and software and instrumentation development. The key personnel

associated with this effort are Mr. W.C. Daywitt, Mr. L.D. Driver, Dr. M. Kanda,

Mr. C.K.S. Miller, Mr. G.R. Reeve, Dr. D.F. Wait, and Mr. J. P. Wakefield.

13
REFERENCES

[I] Wait, D.F., "NBS Measures G/T of a Satellite Earth Terminal," submitted for publication

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Ratio for the Satellite Ground Station at Camp Roberts," Unpublished report of measurement results prepared for the Commanding General, U.S. Army Strategic Communications Command, Fort Huachuca, Arizona (Aug. 1972).

[3] Kreutel, R.W. , Jr. and A.O. Pacholder, "The Measurement of Gain and Noise Temperature

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[4] Kellermann, K.I., I.I.K. Pauling-Toth, and P.J.S. William, "The Spectra of Radio Sources

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[5] Kuz'min, A.D. and A.E. Salomonovich , "Radioastronomical Methods of Antenna Measurement,"

(Academic Press, New York, 1966).

[6] Croom, D.L., "Naturally Occurring Thermal Radiation in the Range 1-10 Gc/s," Proc. IEEE,

Vol. Ill, No. 5 (May 1964)

.

[7] Bean, B.R. and E.J. Dutton, "Radio Meteorology," Nat. Bur. Stand. (U.S.), Monogr. 92,

271 pages (March 1966).

[8] Baars, J.W.M. , P.G. Mezger and H. Wendker, "The Spectra of the Strongest Non-Thermal

Radio Sources in the Centimeter-Wavelength Range," Astrophysical J. Vol. 142, 122-134

(1965)

.

[9] Wait, D.F., W.C. Daywitt, M. Kanda, and C.K.S. Miller, "A Study of the Measurement of

G/T Using Cassiopeia A," NBSIR 74-382 (June 1974); also published under same title as U.S. Army Communication Command Technical Report No. ACC-ACO-2-74 (June 1974).

[10] Kanda, M. , "Study of Errors in Absolute Flux Density Measurements of Cassiopeia A,"

NBSIR 75-822 (Oct. 1975).

[II] Mattes, J.E., "Verification of the Figure of Merit of Earth Stations for Satellite

Communications," Proc. IEEE, Vol. 61, No. 4, 77 (April 1973).

[12] CCIR XII Plenary Assembly, New Delhi, 1970, "Fixed Service Using Communication

Satellites (Study Group 4)," Vol. IV, Part 2, published by the International Telecommunication Union (1970).

[13] Boyle, D.R., F.R. Clague, G.R. Reeve, D.F. Wait, and M. Kanda, "An Automated Precision Noise Figure Measurement System at 60 GHz," IEEE Trans. I&M, Vol. IM-21, No. 4,

543-549 (Nov. 1972).

[14] Larsen, N.T. and F.R. Clague, "The NBS Type-II Power Measurement System," 1970 ISA

Annual Conference Proceedings (Philadelphia, PA), Paper No. 712-70, Vol. 25, Part 3 (Oct. 1970).

[15] Wait, D.F., private communication.

[16] Linsky, J.L., "The Moon as a Proposed Radiometric Standard for Microwave and Infrared

Observations of Extended Sources," Astrophysical J., Supplement Series No. 216, Vol.

25, 163-204 (Feb. 1973).
[17] NASA Sun Patrol Program, National Oceanographic and Atmospheric Administration, Boulder

Colorado 80302.

[18] Allen, R.J. and A.H. Barrett, "Absolute Measurements of the Radio Flux From Cassiopeia

A and Taurus A at 3.65 and 1.94 cm," Astrophysical J., Vol. 149, No. 1, Part 1, 1-13

(July 1967).

[19] Baars, J.W.M. , "The Measurement of Large Antennas with Cosmic Radio Sources," IEEE

Trans, on A&P, Vol. AP-21, No. 4, 461 (July 1973).

[20] Baars, J.W.M. and A. P. Hartsuijker , "The Decrease of Flux Density of Cassiopeia A

and the Absolute Spectra of Cassiopeia A, Cygnus A, and Taurus A," Astron. & Astrophys. J., Vol. 17, No. 2, 172-181 (1972).

[21] Broten, N.W. and W.J. Medd, "Absolute Flux Measurements of Cassiopeia A, Taurus A,

and Cygnus A, at 3200 Mc/s," Astrophysical J., Vol. 132, No. 2, 279-285 (Sept. 1960).

[22] Findlay, J.W. , "The Flux Density of Cassiopeia A at 1440 MHz and its Rate of Decrease, 1

Astrophysical J., Vol. 174, 527-528 (June 1972).

[23] Findlay, J.W. , H. Hvatum and W.B. Waltman, "An Absolute Flux-Density Measurement of

Cassiopeia A at 1440 MHz, " Astrophysical J., Vol. 141, No. 3, 873-884 (1965).

[24] Medd, W.J., Absolute Flux Density Measurements at Centimeter Wavelengths," Astrophysical J., Vol. 171, 41-50 (Jan. 1972).

[25] Medd, W.J. and K.V.V. Ramana, "Flux Density Measurements at 3.15 Gc/s," Astrophysical J., Vol. 142, No. 1, 383-386 (July 1965).

[26] Pawsey, J.L., "A Catalogue of Reliably Known Discrete Sources of Cosmic Radio Waves,"

Astrophysical J., Vol. 121, No. 1, 1 (Jan. 1955).

[27] Penzias, A. A. and R.W. Wilson, "Measurements of the Flux Density of Cas A 4080 Mc/s,"

Astrophysical J., Vol. 142, No. 3, 1149-1155 (1965).

[28] Valley, S.L. (Editor), "Handbook of Geophysics and Space Environments," Air Force

Cambridge Research Laboratories, Office of Aerospace Research, United States Air

Force (1965).

[29] Jacchia, L.G., "The Earth's Upper Atmosphere-I , " Sky and Telescope, 155 (March 1975).

[30] VanVleck, J.H., "The Absorption of Microwaves by Uncondensed Water Vapor," Phys. Rev.,

Vol. 71, 425-433 (April 1947).

[31] VanVleck, J.H., "Theory of Absorption by Uncondensed Gases," Propagation of Short

Radio Waves , pp. 646-664 (McGraw-Hill Book Co., Inc., New York, N.Y., 1951).

[32] Bean, B.R. , B.A. Cahoon, C.A. Samson, and G.O. Thayer, "A World Atlas of Atmospheric Radio Ref ractivity , " ESSA Monograph 1 (1966).

[33] Booker, H.G. and W.E. Gordon, "A Theory of Radio Scattering in the Troposphere,"

Proc. IRE, Vol. 38, 401-412 (1950).

[34] Wheelon, A.D. and R.B. Muchmore, "Line-of-Sight Propagation Phenomena — II. Scattered

Components," Proc. IRE, Vol. 43, 1450-1458 (Oct. 1955).

[35] Yokoi, H. , M. Yamada and T. Satoh, "Atmospheric Attenuation and Scintillation of

Microwaves from Outer Space," Pub. Astron. Soc. of Japan, Vol. 22, No. 4, 511-524

(1970)

.
[36] Howell, T.F. and J.R. Shakeshaft, "Attenuation of Radio Waves by the Troposphere Over

the Frequency Range 0.4-10 GHz," J. of Astrophys. & Terr. Phys . , Vol. 29, 1559-1571

(1967).

[37] Kraus, J.D. , "Radio Astronomy" (McGraw-Hill Book Co., New York, N.Y., 1966)'.

[38] MSR, "Cosmic Background Radiation Reveals its Blackbody Shape," Physics Today,

17 (July 1975).

[39] Johannsen, K.G. and A. Koury, "The Moon as a Source for G/T Measurements," IEEE Trans. on A&E Systems, 718-727 (Sept. 1974).

[40] Wait, D.F, "The G/T Ratio of the Scientific-Atlanta 10-Meter Fucino Earth Terminal,"

unpublished report (April 1975).

[41] Stelzried, C.T., "The JPL Total Power and Noise Adding Radiometers," NBS High Frequency

and Microwave Noise Seminar, unpublished note (May 1970).

16
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U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBSIR - 76-842

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Error Equations Used in the NBS Precision G/T Measurement

System

5. Publication Date September 1976

6. Performing Organization Code

276.06

7. AUTHOR(S)

Daywitt, W. C.

8. Performing Organ. Report No. NBSIR 76-8U2

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

IU. Fro ject/Task/Work Unit No. 2766488

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

U. S. Army Communications Command

Fort Huachuca, Arizona 85613

13. Type of Report & Period Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

Equations presently being used in the precision NBS G/T measurement system

are presented in this report. Included are the assumptions upon which these equations are based and sample calculations showing how the measurement errors vary with

antenna elevation angle.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Error analysis; G/T; precision measurements; radio star; satellite communications.

: 643 4

18. AVAILABILITY TJ Unlimited

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' For Official Di stribution. Do Not Release to NTIS

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Springfield, Virginia 22151

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