Reference

NBS

PUBLICATIONS

N BSI R 86-3046

A111D2

NATL INST OF STANDARDS & TECH R.I.C.

A1 11 02490798

Daywitt, William C/10-60 GHZ G/T measure QC100 .U56 NO.86-3046 1986 V19 C.1 NBS-P 10-60 GHz G/T mEASuHEMENTS

USING THE SUN AS A SOURCEA PRELIMINARY STUDY

William C. Daywitt

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

April 1986

QC

100

.056

86 - 30^6

1986

NBSIR 86-3046

NBS

research

WFORMATIOM

CEAITER

10-60 GHz G/T MEASUREMENTS

USING THE SUN AS A SOURCE—

A PRELIMINARY STUDY

William C. Daywitt

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

April 1986

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

C\J

CO^

LO

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CONTENTS

Page

1. Introduction 1

. An Estimate of the Solar Flux Density from 10 to 60 GHz 3

. Atmospheric Loss 5

. Star-Shape Correction Factor 10

. Conclusions 15

. Acknowledgement 15

7. References 15

i i i

10-60 GHz G/T Measurements Using

the Sun as a Source--A Preliminary Study

William C . Daywitt

National Bureau of Standards

Electromagnetic Fields Division

Boulder Colorado 80303

Preliminary studies show that it may be possible 1) to determine

the solar flux density incident on the earth's atmosphere using a simple algorithm with an uncertainty less than 8 percent; 2) to

overcome a deteri orati ng accuracy in atmospheric loss calculations

by using a "tipping curve" measurement, and 3) to reduce starshape correction factor uncertainty by using an equivalent solar

di ameter.

Key words: atmospheric loss, G/T, millimeter wave, solar radio

flux, star-shape correction factor, tipping curve.

1. Introduction

This report contains results from investigations using the sun as a calibrated noise source in earth terminal (G/T) measurements for the frequency

range from 10 to 60 GHz. It is a continuation of some earlier studies [1] for

the microwave region and includes 1) an estimate of the solar flux density; 2) an estimate of, and suggestions for more accurately measuring the effects of

atmospheric attenuation on the measurements, and 3) an upgraded calculation of

the solar rf diameter to be used in more accurate star shape correction factor

estimates.

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

can be expressed as

G 8,j((Y - 1)

T

)

where k is Boltzmann's constant, Y is the ratio of the power measured with the

sun in the antenna mainbeam to power measured with the antenna pointed at the

cold sky, \ is the measurement wavelength, S is the solar flux density incident on the earth's atmosphere, and k^ and k 2 are the atmospheric transmission

and star shape correction factors, respectively [2].

1
The atmospheric transmission factor accounts for the reduction in the

received flux and is due to three atmospheric phenomena [3], gaseous

attenuation, refractive spreading of the incident wavefront, and incoherent

tropospheric scattering. It does not include attenuation and scattering from

clouds, rain, fog, hail, or snow since the precision measurements envisioned

here are assumed to be performed in clear, stable weather. If xq ''s the total

zenith attenuation in nepers due to the gaseous component, then

-xg/si n0

= e (2)

where 9 (>5 degrees) is the elevation angle to the source relative to the

antenna location on the earth's surface. Details of a simplified calculation

for the gaseous component are described elsewhere [4]. Attenuation due to

refractive spreading and tropospheric scatter were estimated previously [1],

and will be ignored in this report since their effects are small (less than

0.1 dB) relative to attenuation from the gaseous absorption of the atmosphere.

The star shape correction factor accounts for variation of the solar

brightness distribution across the antenna beam pattern, and vanishes as the

ratio of the angular source diameter to the antenna half-power beamwidth

vanishes. In terms of a brightness distribution B and a normalized power

pattern P^,

/ B(Q)P (Q) dQ

" / B(q) dQ

where Q represents the polar angles of the antenna pattern, and dQ is the

differential solid angle. The integral in the denominator is equivalent to

the flux density S.

The measurement technique [12] leading to eq (1) is suitable for personnel with less expertise than that required to determine the G/T ratio by

separate G and T measurements. This radio star technique for measuring G/T

assumes the availability of predetermined solar flux data and a relatively

simple method for determining atmospheric attenuation. It is in the spirit of

this personnel constraint that the study reported here was performed. Thus,

section 2 describes a simple method for obtaining the solar flux density

incident on the earth's atmosphere. This technique is still in the proposal

stage and needs further experimental verification. An apparently viable.

2
simple method for obtaining atmospheric loss is discussed in section 3. In section 4 an equivalent disk model for more accurate evaluation of the star

shape correction factor, k 2 , is discussed.

2. An Estimate of the Solar Flux Density from 10 to 60 GHz

Solar radio emission is the result of three superimposed sources of

radiation [5], the quiet, slow, and burst components. The quiet sun emission

comes from unlocalized, thermal sources in the solar atmosphere (chromosphere

and corona), and is constant over periods of months to years. The slow component is also thermally generated and originates in local sources in the

vicinity of sunspots and chromospheric plaques. These partially polarized

sources have periods of days, weeks, or months. The burst components are the

results of thermal, synchrotron, and plasma radiation from transient sources

such as flares, and are partially polarized. Their recurrence frequency and

period are small for the quiescent portion of the solar cycle, increasing to

two or more per a 10-hour viewing day during the active portion, and suggest

the possibility of making G/T measurements without encountering a burst during

the process.

Figure 1 depicts the average solar flux density spectrum incident on the

earth's atmosphere [6] with an insert [7] indicating the duration of the burst

spectrum from 10 MHz to 30 GHz. The quiet component of the solar emission

dominates above 5 GHz, at which frequency most of the burst components have

disappeared and the slow component is falling off. The insert shows that the

duration of the remaining burst continuum is short. Thus, the solar emission

above 5 GHz is relatively stable from day to day as long as the type IV bursts

are avoided. Superimposed on the graph of figure 1 are three sets of hashmarks representing monthly averages of AFGL (Air Force Geophysical Laboratory)

flux density measurements [8] from January 1979 to May 1982. As expected, the

measurement values approach the quiet sun values between the "sunspot (s.s.)

max" and the "s.s. min" curves as the frequency increases. Thus, it appears

that the average of the quiet sun curves might be used to determine the incident flux density. Following is an approximate equation giving this average

that was derived by a quadratic least-square fitting of the data in table 1 from reference [6]

log S = 1.20 + 1.10 (log f) + 0.179 (log f)2. (4)

3
Solar

Flux

(W/m^/Hz)

Frequency (GHz)

Figure 1. Solar radio spectrum.

4
Table 1. Logarithm to the base. ten of the average flux density S(W/m^/Hz)

vs frequency for the quiet sun radiation. (From Allen [6].)

QUIET SUN RADIATION

FREQUENCY (GHz) Log S

10 2.48

20 2.93

50 3.57

100 4.125

200 4.69

500 5.47

The error in using eq (4) is tentatively estimated to be 8 percent [1], but is

in need of further verification and/or upgrading. In fact, further investigation may show that periodic measurements at least at one frequency between

10 and 60 GHz are necessary to obtain sufficiently accurate coefficients for

eq (4).

3. Atmospheric Loss

An estimate [4] of the zenith attenuation through the atmosphere as a function of frequency is given by the solid curve in figure 2 for a water

vapor density of 7.75 gm/m . The dashed curves and the right-hand scale show

the corresponding error in (approximately 95(l-ki)) two elevation

angles (30° and 90°), and indicate that above 10 GHz another method must be

found for determining the loss if a tolerable G/T measurement accuracy is to

be maintained. A number of versions [9,10,11] of the "tipping curve"

technique (to be described) have been used to measure the loss and appear to

give good accuracy. For example, Ulich [10] reports an error (20(l-ki))

nearly five times less than that obtainable from the proceeding calculation

[4]. Therefore, since the present earth terminal measurement system (ETMS)

[12] accumulates tipping-curve data automatically during a G/T measurement.

5
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this data can be used to obtain a more accurate loss estimate. What follows

is the description of a slightly different version of the tipping-curve method

using "noise add" which is appropriate to the type of data collected by the

Figure 3 shows a measurement system consisting of an antenna, a crossguide coupler, a receiver, and a power meter. A noise source that can be

rapidly turned on and off is attached to one arm of the coupler. The slanted,

cross-hatched area at the left of the diagram represents the atmosphere

extending down to the antenna at the earth's surface, and that is viewed at an angle 0 (the elevation angle) relative to the horizontal. at the far left

(above the atmosphere) represents the incident isotropic, cosmic background

temperature [13]. is an average atmospheric temperature [9] that allows

the sky brightness temperature to be accurately calculated by the formula

where is the slant height loss (neper attenuation) through the atmosphere

and is related to the elevation angle (x = csc0) and the zenith loss tq The

equati on

The curved, dashed line around the antenna aperture representing the incident

sky flux is a reminder that the flux is considered to be constant over the

antenna beam. In effect, the antenna is assumed to be in an isothermal cavity

of brightness temperature T^^. a represents the noise efficiency [14] of the

antenna-coupler combination. The receiver noise, including the noise from the

ohmic losses in the antenna and coupler, is represented by T^. The attenuated

noise temperature due to the sky, and appearing at the receiver input is given

by aT^, while the noise from the noise source (when the source is turned on)

appearing at this same point is represented by T^. The correspondi ng downconverted powers at the power meter are Pg, p^, and p^, respectively.

In performing a measurement at a particular x, two powers are measured;

one with (P^ ^

^n^ without (P^ + Pg) the noise source in figure 3

turned on; and the following Y-factor ratio is calculated;

ETMS

( 5 )

X

X To ( 6 )

y

= Pn

( 7 )

7
ATMOSPHERE 8

Figure

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for

the

atmosphere

and a

satellite

earth

terminal

receiving

system.
from which the radiometer calibration equation (eq (8)) is obtained (errors

due to receiver gain variations are 'removed from the measurement by taking the

ratio in eq (7) [15,16]):

( 8 )

where a and b are functions of the antenna system parameters and the noise add

signal T^. In terms of noise temperatures, "a" is equivalent to the noise add

signal referred to the antenna aperture, T^/a, and "b" is equivalent to the

receiver noise referred to the aperture, Tg/a.

Tg can be determined in one of two ways: the two constants, a and b, in

eq (8) can be determined from two known values of T^; or from one value of

and the use of an absorber of known temperature (T^ in fig. 3) in the antenna

aperture. Since tq is initially unknown, the second or tipping curve scheme

is used in a manner [11] similar to the following simplified description. The

antenna is pointed to zenith (some other elevation angle could be used) and

the Y-factor, y^, is measured, correspondi ng to which a preliminary value of

zenith loss is assumed and a preliminary brightness temperature

calculated. An absorber is inserted into the antenna aperture and the Y-factor

y^ measured. These values are then used to obtain an initial estimate of the

constants in eq (8). A number of other Y-factors are measured at various

elevation angles, for which their correspondi ng brightness temperatures are estimated from eq (8). Using these estimates the following equation is

plotted as a function of x (see eq (5)):

T

X

= ^n (-

T - T

T

m

(9)

where the circumflex accents above and T^ indicate that these values are preliminary estimates. A straight line is fit th ough the resulting points,

and extended to the ordinate. Equations (5) and (6) imply that the resulting

intercept should be at the origin. If this is not the case, the preceding

steps are repeated until the extended line passes through the origin, at which

point the assumed value of zenith loss is the correct one, and the atmospheric

loss has been determined.

The usefulness of the above technique is limited by the system noise

which masks changes in the antenna noise temperature caused by the tipping9
curve procedure. Assuming a minimum useful change of 0.1 * in the antenna

temperature between x = 1 and x = 3, the tipping-curve method appears to work

up to a zenith attenuation of about 1.04 dB for a of 800 K. Thus, the

dotted lines in figure 2 indicate that a direct application of the tippingcurve technique at the frequency of interest should be useful up to some frequency between 40 GHz and 50 GHz. Above this frequency a dual -channel

approach [11] in conjunction with calculations might be used to determine the

atmospheric loss.

4. Star-Shape Correction Factor

For antenna half-power beamwidths (HPBW) greater than about five angular

source diameters, examination of eq (10) below shows that the ratio in eq (3) can be replaced by unity with an error less than 1 percent. However, to use

the celestial source method of measuring G/T accurately when the HPBW is less

than five source diameters requires an estimate of the variation of the source brightness distribution across the antenna mainbeam, as indicated in eq (3).

For sources with stable and predictable distributions and antennas with

Gaussian mainbeams, this can be accomplished by replacing the ratio in eq (3)

by a simple formula [17] depending only on the ratio of HPBW to source diameter. Furthermore, if the source diameter is properly chosen, the formula

will provide an accurate estimate of the correction factor for any HPBW/

diameter ratio above unity [18,19]. As will be seen there is reason to expect

that this technique will also work for the sun, even though the solar brightness temperature is continuously changing.

For a Gaussian mainbeam and a source resembling a circular disk, eq (3)

leads to (note that x is redefined)

dg'is an equivalent angular disk diameter for the source, and 9|^ is the

antenna HPBW. The diameter is chosen to minimize the difference

_

1 - e

2 " x2

( 10 )

where

( 11 )

1 - e -x2

/ B(Q) P (Q) dQ

n

/ B(Q) dQ

( 12 )

10
for e^/d greater than unity, where d is the apparent or optical solar angular

diameter. The same expressions (eqs (10) and (11)) hold for an elliptical

disk with d^ replaced by the product of the major and minor source diameters. No significant reduction in the difference in eq (11) is achieved

with this latter model, however, even though the solar brightness distribution

shows a decided ellipticity [5].

Figure 1 shows that, except for the burst components which are assumed to

be missing during the G/T measurement, the quiet sun emission plays an increasingly dominant role in the total emission above 5 GHz where the slow

component begins to fall off. Furthermore, observations of the solar brightness distribution in the decimeter, centimeter, and millimeter wave frequency

regions reveal that, although the effective brightness temperature varies with

the solar cycle, the distributions remain relatively constant [5]. It is this

constant part of the brightness distribution that will presumably be amenable

to the technique of the previous paragraph, with fluctuations in the result

coming from the more variable slow emission component. The degree of success

will depend upon how minor these fluctuations turn out to be, but hopefully at

least some accuracy in k 2 will be gained below five source diameters. This

question can only be decided after a number of actual distributions at various

frequencies and at various times during the solar cycle have been convoluted

with the antenna beam pattern. To date this has not been done.

The equivalent disk diameter described here was calculated from an approximation (fig. 4, dashed curves) to the solar atmosphere tabulated in Allen

[6] (fig. 4, solid curves) using the dynamical equations described by Smerd

[20] to obtain the solar brightness temperature. The resulting disk diameter

(normalized by the apparent solar diameter) is shown in figure 5 for the frequency range from 1 to 100 GHz. As a matter of interest, the disk diameter

obtained using Smerd's earlier atmosphere is also shown in the figure (dashed

curve)

.

The uncertainty in k 2 due to using the apparent diameter (d^ = d) to

calculate the star shape correction factor via eq (10) is shown in figure 6 as

a function of the ratio of antenna half-power beamwidth to apparent diameter.

After minimizing this uncertainty per the discussion surrounding eq (12) and

using the resulting equivalent diameter (d^ = 1.0342d), the uncertainty in

using eq (10) to estimate the integral in eq (12) is negligible.

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Figure 5. Equivalent disk diameter d^ in units of the apparent solar

diameter d as a function of frequency using 1) data from

Allen [6], solid curve; and 2) data from Smerd [20], dashed

curve.

13
3

HPBW/d

Figure 6. Uncertainty in the star shape correction factor vs HPBW (in

units of the apparent solar diameter) due to using the

apparent solar diameter in eq (10). When an equivalent disk

diameter equal to 1.0342d is used, the uncertainty is

negl i gibl e.

14
An accurate description of the solar brightness temperature at cm- and

mm-wavelengths requires accounting for the chromospheric fine structure [21].

The resulting two-component solar atmosphere [22] includes radiation from both

the chromospheric spicular and the i nterspi cul ar regions and their variation

with height. These details have not been included in the preceeding calculations of the equivalent diameter.

5. Conclusions

Equation (4) is an algorithm for calculating the solar flux density

incident on the earth's atmosphere, with an estimated uncertainty of 8 percent. Experiments need to be performed to see if this uncertainty can be

reduced and/or to improve the coefficients in eq (4). Furthermore, it may be

necessary to periodically measure the solar flux density and update the coefficients.

It may be possible to overcome the deteriorating accuracy in earlier

atmospheric loss calculations [4] by i ncorporati ng a tipping curve measurement

into the ETMS G/T measurement scheme. If this improvement is not possible,

on-site measurement of the loss by more sophisticated instrumentation [11]

will be required.

Simple and accurate calculations of the star shape correction factor

using eq (10) may be possible, but need to be verified by experimental data.

Although strai ghtforward, the effects of chromospheric fine structure still

need to be incorporated into the calculation of the equivalent solar disk

di ameter.

6. Acknowledgement

The author wishes to thank the Air Force Satellite Control Facility at

the Sunnyvale Air Force Station for support of these studies.

7. References

[1] Daywitt, W. C. A preliminary investigation into using the sun as a source for G/T measurements. Nat. Bur. Stand. (U.S.) Int. Rpt. 84-3015;

1984 August.

15
[2] Daywitt, W. C. Error equations used in the NBS precision G/T measurement

system. Nat. Bur. Stand. (U.S.) Int. Rpt. 76-842; 1976 September.

[3] Yokoi, H.; Yamada, M.; Satok, T. Atmospheric attenuation and

scintillation of microwaves from outer space. Publ. Astr. Soc. Japan.

22(4): 511-524; 1970.

Yamada, M.; Yokoi, H. Measurements of earth-space propagation

characteristics at 15.5 GHz and 31.6 GHz using celestial radio sources.

J. of the Inst, of Electronics, and Communication Engineers of Japan. 57-

B(2) ; 1974 February.

[4] Daywitt, W. C. Atmospheric propagation equations used in the NBS earth

terminal measurement system. Nat. Bur. Stand. (U.S.) Int. Rpt. 78-883;

1978 April

.

[5] Kundu, M. R. Solar radio astronomy. New York: Interscience Publishers;

1965.

[6] Allen, C. W. Astrophysical quantities. London, England: The Athlene

Press/Uni versity of London; 1976.

[7] Mangis, S. J. Introduction to sol ar-terrestial phenomena and the space

environment services center. NOAA Tech. Rpt. ERL 315-SEL 32; 1975

January

.

[8] Coffey, H. E., ed. Solar-geophysical data: prompt reports. No. 470,

Part 1; 1983 November.

[9] Falcone, V. J., Jr.; Wulfsberg, K. N.; Gitelson, S. Atmospheric emission

and absorption at millimeter wavelengths. Rad. Sci. 6(3): 347-355; 1971

March.

[10] Ulich, B.; Davis, J. H.; Rhodes, P. J.; Holis, J. M. Absolute brightness

temperature measurements at 3.5-mm wavelength. IEEE Trans, on Ant. and

Propag. AP-28(3); 1980 May.

[11] Guirand, F. 0.; Howard, J.; Hogg, D. C. A dual-channel microwave

radiometer for measurement of precipitable water vapor and liquid. IEEE

Trans, on Geosci. Elect. GE-17(4); 1979 October.

Hogg, D. C.; Guirand, F. D.; Westwater, E. R. Emission measurements of

31.6 GHz absorption by atmospheric water vapor. Rad. Sci. 18(6): 1295-

1300; 1983 November-December.

[12] Wait, D. F. Precision measurements of antenna system noise using radio

stars. IEEE Trans, on I&M. IM-32(1): 110-116; 1983 March.

[13] Penzias, A. A.; Wilson R. W. A measurement of excess antenna temperature

at 4080 mc/s. Astro. J. 142: 419-421; 1965.

[14] Daywitt, W. C. Design and error analysis for the WRIO thermal noise

standard. Nat. Bur. Stand. (U.S.) Tech. Note 1071; 1983 December.

16
[15] Ohm, E. A.; Snell, W. W. A radiometer for a space communications

receiver. The Bell System Technical Journal; 1963 September.

[16] Stelzried, C. T. Total power and noise adding radiometers. From notes

for high-frequency and microwave noise seminar. Nat. Bur. Stand. (U.S.);

1970 May.

[17] Baars, J. W. M.; Mezger, P. G.; Wendker, H. The spectra of the strongest

nonthermal radio sources in the centimeter-wavelength range. Astr. J.

142: 122-134; 1965.

[18] Kanda, M. Study of errors in absolute flux density measurements of

Cassiopeia A. Nat. Bur. Stand. (U.S.) Int. Rpt. 75-822; 1975 October.

[19] Daywitt, W. C. An error analysis for the use of presently available

lunar radio flux data in broadbeam antenna system measurements. Nat.

Bur. Stand. (U.S.) TEch. Note 1073; 1984 February.

[20] Smerd, S. F. Radio-frequency radiation from the quiet sun. Aus. J. Sci

.

Res. A3(34): 34-59; 1950.

[21] Fu'rst, E. The quiet sun at cm- and mm-wavelengths . Radio Physics of the

sun. M. R. Kande and T. E. Gergely, eds. STATE D. Reidel Publishing

Company; 1980.

[22] Bray, R. J.; Longhead, R. E. The solar chromosphere. London: Chapman & Hall; 1974.

U S GOVERNMENT PRINTING •' 17
NBS«n4A (REV. 2 -ec) U.s.S DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NBSIR 86-3046

2. Performing Organ. Report No. 3. Publication Date

| April 1986

4. TITLE AND SUBTITLE

10-60 GHz G/T Measurements Using the Sun As A Source--A Preliminary Study

5, AUTHOR(S)

William C. Daywitt

6. PERFORMING ORGANIZATION (If joint or other than NBS, see in struction s) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

NBSIR 1985-1986

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State. ZIP)

Department of the Air Force

HQ Air Force Satellite Control Facility (AFSC)

Sunnyvale Air Force Station, P.O. Box 3430

Sunnyvale, California 94088

10, SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FIPS Software Summary, is attached.

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

bi bliography or literature survey, mention it here) Preliminary studies show that it may be possible 1) to determine the solar flux

density incident on the earth's atmosphere using a simple algorithm with an uncertainty less than 8 percent; 2) to overcome a deteriorating accuracy in

atmospheric loss calculations by using a "tipping curve" measurement, and

3) to reduce star-shape correction factor uncertainty by using an equivalent

solar diameter.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

atmospheric loss; G/T; millimeter wave' solar radio flux; star-shape correction

factor; tipping curve

13. AVAILABILITY

[5[X Unl imited

1 1 For Official Distribution. Do Not Release to NTIS

1 1 Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

24

15. Price

USCOMM-DC 6043-P80


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