NBSIR 73-314 0^

Study of Measurements of Antenna-Radiometer Parameters

Final Report on Phase I: Evaluation of Antenna Loss and

Beam Efficiency Measurements and Radiometer Calibrations

for the S-193 and S-194 Skylab Systems

A C. Newell

P.F. Wacker

O F. Wait

W.C. Daywitt

R.C. Baird

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

May 1973

Prepared for

NASA - Manned Spacecraft Center

Experiment Systems Division

Houston, Texas
II
ERRATA FOR NBSIR 73-314

Study of Measurements of Antenna -Radiomoter Parameters

Final Report on Phase 1: Evaluation of Antenna Loss and

Beam Efficiency Measurements and Radiometer Calibrations

for the S-193 and S-194 Skylab Systems

The following changes should be made in this report.

Page 6, The error estimates for given in the last three columns of

Table 1,2.3.5 should be changed to: T = 175 K ±12. 2K 11. 9K 3.5K

B

X = 350 K ± 37.2 K 18. 1 K 6.6 K

B

Page 12, In equation (2-7), the second factor in the numerator should be

( 1-522^-^) instead of (l-SnF^).

Page 46, In the fourth line of Section 3.4, change ± 14 to ± 42 K to read.

± 12 to ± 49 K.

Page 52. In equation (3-48), replace T^ with T^ . The 5th line from the bottom should read 81 K instead of 80 K.

Page 53, The last line in the second paragraph shovild give 0.96 for the

value of M^ instead of 0,81,

Page 54, The 9th line should read 372 Kelvins instead of 272,

The value of T^^ in the last line should be 372 ± 2 K instead

of. 372,2 ± 2 K,

Page 57, Insert equation nvimber (3-56) to the right of the values given in

lines 5 through 10,

In the last paragraph,

I

I = 0,025 is printed twice,

|rp I = 0, 17 instead of 0.017,

R = 1,03 ± 0,026 instead of 1,03 ± 0.027.

Page 58. Eqviation (3-58) should read

It - T' I 1. 8 K. ' AMP AMP I -

^•

In the second line of the second paragraph, delete the % sign so that a = 0. 86 ± 0. 16.

Change the last line of the second paragraph to read

"... about 0. 16 (T -t )/(aMAIN)2 ^^.^ 0.009 T^, respectively

(refer to Table 3.4, page 46)".

In the third paragraph, replace (3-56) with (3-47).

Also, in the second line of the third paragraph, delete the phrase

"listed in order of their importance".

Page 59. Replace the old page 59 with the new page 59 (attached).

Page 60. Replace the old Table 3.6 with the new Table 3.6 (attached).

2.

Table 3.5 Errors in Ante nna Brightness Temperature For the — — MATM T Typical Conditions tp=29 7K, tj^=190K, a =0.84, T^-j,= 34K, ap^=^0.8.

Parameter

Causing Error

Tg=0 K

(T^=41.7K)

Tj^=175K

(T^=184.4K)

Tg=350K

CT^=327.1K)

''A

Cal ib ration ± 12 . 3K ± 6 . IK ± 3 . 7K

a 33.6 1 . 3 31 .

1

^ •'V Deam diiciency u . U 11.0fx o . 1

R 6 .

6

2 .9 0 . 8

T

AMP

Resolution

2 .2

1 . 3

2 .

2

1.3

2 .2

1.3

Update 0 . 7 0 . 7 0 . 7

Linearity 0.4 0.4 0.4

Linear Sum ± 57.1 ±16.5 ± 43.3

Quadratic Sum ± 36.5 ± 7.6 ± 31.6

Quad, except

Cal. and T^p

± 48.8 ±12.2 ± 37.2

± 6. IK in the process of transferring the external calibration

to the internal reference generators, ± 2.9K to account for

the errors due to the mismatch between the antenna and the

radiometer versus the standard and the radiometer, and ± 2.2K

because the effective input noise temperature of the amplifier

changes when the antenna is replaced by the standard. Thus

a ± 11. 2K error component in the ± 16. 5K resultant error is

due to using a standard with an impedance different than the

antenna ' s

.

If the loss measurement errors were ± 0.02 dB (as claimed),

then these values could be used to calculate the reference

temperature T^ and T^^-, to within 2K instead of ± 3 and ± 4.2

as given in (3-54) and (3-55). Further, (3-50) could be used

instead of (3-49), to eliminate errors due to R and T^p.

Under these conditions, the errors shown in Table 3.6 would

hold and the quadrature sum should be valid. In case the old

loss measurements are not trusted, a variable impedance standard

59

Table 3.6 P robabl e Attaiiuiblc Errors in

Antenna Brightness Temperature

Parameter Tg=0 K Tg=175K Tg=350K

Causing Error (T^=41.7K) (T^=184.4K} (T^=327.1K)

a ± 6.3K ± 0.2K ± 5.8K

Beam Efficiency 0.0 0.7 1.4

Calibration 7.3 3.1 2.5

Resolution 1.3 1.3 1.3

Update 0.7 0.7 0.7

Linearity 0.

4

0 .

4

0.4

Quadratic Sum ± 9.8K ± 3.5K ± 6.6K

60

NBSIR 73-314

STUDY OF MEASUREMENTS OF ANTENNA-RADIOMETER PARAMETERS

Final Report on Phase L Evaluation of Antenna Loss and

Beam Efficiency Measurements and Radiometeter Calibrations for the

S-193 and S-194 Skylab Systems

A.C. Newell

P.F. Wacker

D.F. Wait

W.C. Daywitt

R.C. Baird

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

May 1973

Prepared for

NASA - Manned Spacecraft Center

Experiment Systems Division

Houston, Texas

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

National Bureau of Standards, Richard W. Roberts, Director
r
TABLE OF CONTENTS

Page

ABSTRACT v

1. SUMMARY 1

1.1 Program Objectives and Tasks 1 1.2 Summary of Phase I Results 2 1.2.1 Description of Phase I Effort 2 1.2.2 Summary of Section 2 -- Basic Concepts

in Loss Measurements 2 1.2.3 Summary of Section 3 -- Measurements on

the S-194 System 3

1.2.4 Summary of Section 4 -- Measurements on

the S-193 System 5 1.2.5 Combination of Errors 8

2. FUNDAMENTALS OF ANTENNA LOSS MEASUREMENTS 10

2.1 Basic Concepts 10

2.2 Measurement Methods 14

3. MEASUREMENTS ON THE S-19 4 SYSTEM 16

3.1 Loss Measurements on the S-194 Antenna 16

3.1.1 Transmission Line Efficiency (Loss)

Measurement 16

3.2 Gain Measurements on the S-194 Antenna 27

3.3 Antenna Pattern, Beam Efficiency, and

Directivity on the S-194 Antenna 33

3.3.1 Introduction 33

3.3.2 Properties of the Model Mount 36

3.3.3 Symmetry, Polarization, and Scattering 41

3.3.4 Error Estimates 45

3.4 Calibration of the S-194 Radiometer 46

3.4.1 Description of the S-194 Radiometer 47

3.4.2 The Accuracy of the S-194 Radiometer-- 52

3.4.3 Comments 58

4. MEASUREMENTS ON THE S-193 SYSTEM 61

4.1 Loss Measurements on the S-193 Antenna 61

4.2 Gain Measurements on the S-19 3 Antenna 67

iii

TABLE OF CONTENTS (Continued)

Page

4.3 Pattern Measurement, Beam Efficiency, and

Directivity of the S-193 Antenna 72

4.3.1 Introduction 72

4.3.2 General Measurement Approach 74

4.3.3 Measurement Procedure used by the

Contractor 79

4.3.4 Beam Efficiency Calculations 93

4.3.5 Error Analysis 94

4.3.6 Recommendations 105

4.3.7 Comparison of Gain, Efficiency and

Directivity 106

4.4 S-193 Radiometer Receiver Error Analysis 107

References 113

V
Final Report on Phase I: Evaluation of Antenna Loss and

Beam Efficiency Measurements and Radiometer Calibrations for

the S-19 5 and S-194 Skylab Systems

A.C. Newell, P.F, Wacker, D.F. Wait, W.C. Daywitt and R.C. Baird

Abstract

The program represents an effort to determine

the most appropriate techniques for measuring the

critical parameters of the radiometer- antenna systems

used in the NASA Earth Resources and Skylab programs.

For this first phase, the contractors' measurements

on the S-193 and S-194 Skylab systems were studied

in detail. The measured quantities included antenna

loss, antenna power gain, antenna patterns (which

yield directivity and beam efficiency) , and radiometric

noise temperatures

.

From the analysis of the contractors' data and

auxiliary information, best values and their estimated errors were determined for each of the parameters. In addition, specific recommendations were

made for easy upgrading of individual measurements,

and the errors thus reduced were estimated. For

some of the parameters, errors attainable with the

current state-of-the-art were estimated.

In the measurements of antenna "loss," both

contractors determined insertion loss rather than

the ratio of output available power to input available

power, required for radiometric determinations.

For systems with significant reflections, these two

quantities may be rather different, and the available

power ratio should always be specified.

Antenna measurements made in an anechoic chamber

showed surprisingly large wall reflections, suggesting

that such chambers should be used for cross polarization

measurements only with great caution.

Key l/ords : Antenna; antenna loss; beam efficiency;

calibration and measurement; radiometer.

vi
Final Report on Phase I: Evaluation of Antenna Loss and

Beam Efficiency Measurements and Radiometer Calibrations for

the S-195 and S-194 Sky lab Systems

A.C. Newell, P.P. Wacker, D.F. Wait, W.C. Daywitt and R.C. Baird

1 . SUMMARY

1 . 1 Program Objectives and Tasks

The objectives of this program are to determine the most

appropriate techniques for measuring the critical parameters

of the radiometer antenna systems used in the NASA Earth

Resources and Skylab programs. These parameters include

antenna and radome losses, and antenna gain, pattern, and beam

efficiency

.

The program was divided into the following two phases.

Phase I: A detailed study of measurements performed by

contractors on the S-19 3 and S-194 Skylab systems.

The purpose of this study was to determine the

best values and associated uncertainties of the

parameters measured by the contractors, and to

indicate how these results could be readily

upgraded. This report contains the results of

this study.

Phase II: Determination of the best techniques for evaluating the aforementioned parameters. Significant improvement in the accuracies of some quantities can be achieved through relatively small

efforts, as indicated in this report. Other

quantities (particularly those associated with

loss) will require additional study and research

to determine the best approaches. These efforts

will be discussed in future reports.
1 . 2 Suminary of Phase I Results

1.2.1 Description of Phase I Effort

For each system (S-193 and S-194), the contractors' determinations of the following quantities were analyzed:

- - Antenna Loss

-- Antenna power gain

Antenna patterns (which yield directivity and beam

efficiency)

Radiometer noise temperature.

The input data were obtained primarily from the contractors' test reports and from private conversations with the

engineers involved. Insofar as possible, measurement procedures,

methods of analysis, measured quantities, final calculated

parameters, and estimates of errors were all evaluated. In

cases where insufficient information concerning error sources

was available from the contractor, errors were assigned on the

basis of past experience by NBS staff members. An effort was

made to obtain all pertinent data available so that the conclusions would accurately represent the facts.

The detailed findings of this study are contained in sections 2, 3, and 4, but the main results and recommendations of

each section are summarized here as an aid in the use of the

report

.

1.2.2 Summary of Section 2 -- Basic Concepts in Loss Measurements

It became apparent early in the study that the term "loss"

as applied to antennas and transmission line components was

being used rather loosely, and, as a result, the correct quantity was not being measured. The correct loss parameter for

evaluating radiometer system performance is given in 2. The

errors resulting from use of the wrong loss parameter are most

significant when the test and/or measurement systems have significant impedance mismatches. This was particularly evident

in the S-194 analysis as is indicated in the next section.

2
The definition of the correct loss parameter (eqs . 2.2 and

2.3) should be included in future specifications of radiometer

systems. This would help ensure measurement of the correct

quantity and use of the best measurement techniques by all

contractors

,

The advantages and disadvantages of the two methods of

determining antenna loss considered by the contractors are

presented. One technique requires gain and complete pattern

measurements, from which the loss is computed as the ratio of

gain to directivity. The second method involves measuring the

loss in all readily accessible components of the feed system

and calculating or estimating the losses in those parts of the

antenna system that are not amenable to measurement.

1.2.3 Summary of Section 3 -- Measurements on the S-194 System

1.2.3.1 Antenna Loss Measurements

The contractor measured the insertion loss of the main

power divider and assumed the 8 secondary dividers to be identical to the main divider. He neglected the losses in the

radiating elements and the radome and reported the antenna loss

to be 0.2 84 dB. Due to significant mismatch problems and use

of the wrong loss parameter, there is a large error in this

reported value. Even assuming the dividers are identical and

the radiating elements are lossless, the correct loss is estimated to be 0.68 dB ^0*50

It would be difficult, if not wholly impractical, to

obtain sufficient information on this system to completely

resolve the mismatch problem. The losses in the radiating

elements and radome are also difficult to determine. It is

therefore recommended that either measurements of gain and

directivity or radiometric measurements be used to obtain a

3
more accurate antenna loss value. Using the gain and directivity values computed by the NBS (see Section 1.2.3.5) from

the contractor's data, a value of 0.37 dB ^0*2 obtained

for the antenna loss.

1.2.3.2 Antenna Gain Measurements

The major sources of error in the gain determination were

an uncalibrated gain horn, multipath signals within the anechoic

chamber, and impedance mismatches. These factors result in an

estimated error of ± 0.41 dB in the gain of the S-194 antenna.

This error could be reduced to about ± 0.20 dB by calibrating

the gain horn together with further analysis of mismatch and

multipath interference. New techniques in use at NBS could

be used to calibrate the S-194 antenna directly within about

± 0 .10 dB. •

1.2.3.3 Antenna Pattern, Beam Efficiency, and Directivity

Scattering within the chamber where the pattern measurements were performed was a problem. This scattered energy

caused significant errors in the principal polarization patterns, but the effect was partially removed by a renormalization of the patterns. The measured cross polarization patterns

of the S-194 antenna are so variable (due to the scattered

energy) that they are of little, if any, value. However, even

if the recorded patterns did accurately represent the situation, the total cross -polarized power is negligible with

respect to the power in the principal polarization and, therefore, has negligible effect on the beam efficiency and directivity. The total estimated errors due to all sources are

± 0.14 dB in directivity and 0.9% in beam efficiency.

The fact that the received power varied by 2 dB as the

antenna pair rotated with respect to the chamber indicates

4
that more care should be exercised in the future in using an

anechoic chamber for complete pattern measurements of this

type.

1.2.3.4 Radiometer System Evaluation

The contractor estimates that the S-194 radiometer can

measure brightness temperature at 175K and 350K with probable

errors of ± 2. IK to ± 4.2K respectively. Our analysis indicates

that the errors are in the range ± 14K to ± 22K for the same

temperatures. The two largest sources of error are the uncertainties in the antenna loss and in the noise standards used to

calibrate the radiometer. (See table 3.5 page 59 for a complete

listing of the sources of error in determining brightness

temperature.) There is a significant mismatch problem because

the impedances of the antenna and standards are not the same.

Alternative approaches are recommended which could be used for

this and other systems to reduce the calibration error. If

the improved calibration is used, and the uncertainty in antenna

loss is lowered to about 0.13 dB by reducing the error in

antenna gain as discussed in 1.2.3.2, the above errors would

be reduced to ± 3. IK and ± 4.7K.

1.2.4 Summary of Section 4 -- Measurements on the S-195 System

1.2.4.1 Antenna Loss Measurements

The contractor determined the loss of the S-193 antenna

by a combination of measurements and calculations. The losses

of the rectangular waveguide section and the mode transducer in

the feed were measured directly. As with the S-194, an incorrect definition of loss was used but, since mismatch errors

were small, the resulting error was on the order of a few

hundredths of a dB . The loss in the remainder of the feed

(circular waveguide, tapered dielectric guide, reflectors, etc)

5
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was determined from theoretical calculations. While this approach is probably valid for the fairly simple geometry involved, it does pose some problems. There could be flaws in

the construction of the dielectric feed which would cause

higher loss and, if no actual loss measurements are performed,

these flaws could go undetected. Also, the approximations and

assumed parameters used in the theoretical calculations may

not be completely valid. It would be desirable to actually

measure the loss of the total assembly and avoid these questions.

Gain and directivity computed from pattern measurements

could be used to obtain the antenna loss, but the existing pattern measurements for this system are not sufficiently accurate.

1.2.4.2 Antenna Gain Measurements

The major errors in this measurement were attributed to

an uncalibrated gain standard and the use of an uncalibrated

receiver for measuring the received power ratios. The resultant error of ± 0.37 dB could be reduced to about ± 0.15 dB

by calibration of the gain standard and receiver, or the S-193

antenna could be calibrated directly to within about 0.1 dB

at the National Bureau of Standards.

1.2.4.3 Antenna Pattern, Beam Efficiency, and Directivity

Complete pattern measurements were not performed on the

S-193 antenna. Patterns were measured in two of four "quadrants"

which comprise the total sphere, and symmetry was assumed to

obtain the patterns in the other two "quadrants." Analog patterns were recorded for part of the remaining region, but these

data were not used in the pattern integration. The assumed

symmetry is clearly not justified, as partial patterns for the

other two quadrants illustrate. Therefore, the lack of complete data has caused a signficant error in the calculated beam

efficiency and directivity.

7
An additional error of about 6% in the beam efficiency has

been introduced through use of an incorrect numerical integration procedure. This error could be eliminated if the integration was redone correctly. At present there is an estimated

error of about +3 ± 2.8% in the beam efficiency, which could

be reduced to about ± 2.0% by correcting the integration and

making complete pattern measurements. The remaining error is

due to a combination of receiver response error, range multipath effects, and uncertainties in the main beam boundary.

1.2.4.4 Radiometer Receiver Evaluation

Although certain simplifying assumptions were made by the

contractor in the radiometer receiver calibration, these caused

little error. The total probable error in the measured brightness temperature due to the receiver is estimated to be ± 1.5K

for a 50K incident temperature and ± 0.3K for a 350K incident

temperature

.

The errors due to uncertainty in antenna loss and beam

efficiency must be added to these numbers to obtain the total

errors which are ± 9.5K for a 50K incident temperature and

±12. 3K for a 350K incident temperature.

1.2.5 Combination of Errors

For systematic errors, worst case estimates were generally

used, and for random error, 2a values. In cases where it was

apparent that the individual sources of error were independent

with roughly normal distributions, the errors were combined by

a quadrature summation. This was true in most cases, and the

resulting combination is equivalent to a 971 confidence level.

Where the errors did not satisfy the above conditions, a direct

sum was used.

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G rH a;

O Or S U (U

0) •H 4-1 x: CO •H «J E

<-> to V)

J 0) 0) i-l

X a> c CO X G CO X X *-> bO ii

CO (U trt • H 13 4-> 3

CO 0) e to

CO bO bO bO

G rH CO o G O G •H <U X lU G G 13 rH •H •H *J E

(U (-. CO +JX 13

G o to 4-> CO G U U T-l 13

*-> «->

G 13 cO (U 4-1 0) CO rH c CO G CO X *-> ID

tfl (1> CO bO i-l e 4-> i-l • rt

to 6 a>

J

G

O to 0)

(0 0) x: to • H (J •H bOO

u f-r «-> 4-> ' 6 GC iH

u 3 <D (0X •H 3 CO

CO to o X

H X> Vh i- (U

CO 4-) 4->

XO 3 (U

G

u 0)

O 13 <+H trt j:

V to bOG cO iH JZ to G Mh CO bO (U O

*->

V •H

O

G 6 C

u o to •H •rt 0) 3 »-> o CO d) G *-> 13 MH o CO (h t/l O U G C 3

*->

X 3 -H (U CO

O

<-) o (-1 •H »-) iH •H CO 3 CO a) rH lu a. in to 4-> iH O CO X e O 0) O

JG

U 4-> 3 O trt 3 a,

4->

G to trt 13 E

•rH o 3 X

X toX

O <U 0)

U <+-( PQ PQ CO PQ rH in

CO JOO 13 9
2. FUNDAMENTALS OF ANTENNA LOSS MEASUREMENTS

2 . 1 Basic Concepts

Since a major concern of this report is to evaluate loss

measurements on a noise measuring system, it seems appropriate

to define precisely which "loss" should actually be measured,

how it is defined and influenced by other system parameters,

and how it may be measured or calculated. We will consider

first a passive, linear two-port at a temperature T with a noise generator at temperature T^ connected to one port and

a load connected to the other port (see Fig. 2-1).

i 2

Figure 2-1. Two-port with generator and load.

The power per unit bandwidth available to the load is

given by [1]

,

a£ kia^^T^ + (1 a 21 )T] . (2-1)

(In the remaining equations in this section, the power referred

to will be understood to mean power per unit bandwidth.) The

constant a^^ is defined as the ratio of available powers,

available power at port 2 a^. = ^ , (2-2)

available power at port 1

and is usually referred to as the available power ratio. This

quantity,

<^2i*

determines the reduction in available power due to

10
internal dissipation and, as shown in (2-1), determines the

amount of internal noise generated. Therefore 10 log '^l^2\

is the "loss" parameter which is required.

In terms of scattering parameters of the two port and

the termination reflection coefficient, a^-j^ is given by [2]

"^21 = J—

^

T

• ^2-3)

l^'^ll^gl^ " I *^^12^2l"^11^22^ ^g"'^22 '

'

From (2-3) it is apparent that "^^ ^ function of both the

S parameters of the two port and the source reflection

coefficient, including mismatch effects as well as S2-j^. This

means that ^'^^^ ^® measured with the proper generator

impedance in place, or corrections made for the difference

between generator impedances of the measuring and actual

system.

If the two port is reciprocal, then it can be shown [2]

that equal to ^-^2^ where ^-^2 port efficiency

for power flow from 2 to 1, i.e., in the reverse direction.

The efficiency is defined as

Net delivered power at port 1 ^-^ Tl]^2 " • (2-4)

Net delivered power at port 2 Therefore, for a reciprocal device, '^2\ ^® measured

directly, calculated from the scattering parameters, or determined by measuring ^-^2'

Since there are various other "loss" parameters of a two

port, we will give below the expressions for these in terms

of the scattering parameters and reflection coefficients of

generator and load. A more complete discussion of these may

be found elsewhere [3]

.

I (1-s r )(i-s r )-s s r r r

Insertion loss = 10 log tLJi l). g

^—

I 2ll ' g £1

^2-5)

11
Attenuation = 10 log (2-6)

Is I ^

i (i-s^^r^)(i-s^^r^)-s^^s^^r^rj^

Transducer loss = 10 log

If one of the above quantities is measured rather than a or n and used in equation (2-1) to compute noise power characteristics,

a significant error is likely to occur. For instance, take

the case where a tuned reflectionless measurement system is

used to measure the insertion loss of a two port section of

transmission line. Since the measurement system is tuned,

and are zero, and it is actually the attenuation which

is being measured. If the transmission line is now placed in

the circuit where it is actually going to be used, T and r„

will probably not be zero, and the efficiency and insertion

loss of the transmission line will not be equal to the

attenuation. The range of values that n can have for various

input, output, and generator reflection coefficients is shown

in the table below.

T ab 1 e 2.1 Possible Combinations of Attenuation and Efficiency

Measured n in dB

Sill 1 S 1

1 ^22 1

1 r 1 Attenuation (dB) Max . Min .

.1 .1 . 1 -0 . 2 -0 .129 -0 .189

.1 .1 . 1 -0 .5 -0 . 381 -0 .548

.1 .1 . 1 -1.0 -0 . 813 -1.128

.2 .2 .2 -0.5 -0 .225 -0 .469

For a multiport device the noise power relations are

similar to those for a two port, but an a must be defined for

each pair of ports. Consider a multiport at a temperature T

with independent generators on each input port at temperature

Tj . The total available power at port i is given by

P„i = k[ I

cx T + (1 - I a. )T]. (2-8)

12
Once again, each a^^ is the ratio of available power out of

port i to the available power from the generator on port j , when only the generator j has non-zero amplitude. Expressions

are available [1] which give each a^^ in terms of the scattering parameters of the multiport and the generator reflection

coefficients and, again, each a must be measured or calculated

with proper consideration for the effects of generator impedance and interaction between ports

.

The extension from a multiport to an antenna is fairly

natural. Consider a continuous brightness temperature distribution for each of two orthogonal polarizations being received

by the receiving cross section function of the antenna, where

each direction for each polarization corresponds to a "port."

The total available output power is given by

T (e,(t))-A(e,(|))

= k |/ dn . (l-a) T^ (2-9)

where Tg(e,(J)) is the brightness temperature, A(e,(|)) is the

antenna receiving cross section, T^^ is the antenna temperature, and a the factor which describes the noise generating

character of the antenna. Both Tg and A are two-vectors

with the components corresponding to each of two orthogonal

polarizations. By analogy to the multi-port case we can

identify the ot^j's for each port (direction) with the factor

a. . = ia, (2-10)

and the total a as

a = / (2-11)

The expression for a may also be derived by considering the

antenna and its load in thermal equilibrium with an incident

uniform brightness temperature T. This derivation will lead

to the same expression as (2-11).

13
If the antenna is reciprocal, then (2-11) becomes

a = - = n , (2-12)

D

where G and D are, respectively, the gain and directivity in

a given direction and n is the antenna efficiency. In this

case, n may be determined from measurements on the antenna

in either a transmitting or receiving mode. If the antenna

is non-reciprocal, then the antenna must be used in the

receiving mode when measuring a.

2.2 Measurement Methods

Both vendors have sufficient data to determine n by two

different and independent techniques. The first method is to

measure G, calculate D from the pattern data, and compute

the ratio directly. This method has a number of advantages,

especially when the pattern data are also necessary to compute

beam efficiency. Some of these advantages are:

1. This approach will account for all lossy elements

and their interactions without further calculation. This

advantage is especially significant where there may be

many elements (such as the power dividers and radiators

in the S-194) or where the phase of the reflection coefficient is unknown.

2. If the gain and pattern need to be determined for

other purposes, the efficiency may be obtained without

additional measurements.

The disadvantages of this method are that it requires

complete pattern data and computer processing to determine

D. It also requires a good range and accurate standards to

determine both gain and directivity.

14
The second method involves a conceptual decomposition

of the antenna system into segments. The loss associated with

each segment is then either measured or computed. The advantages of this approach are that it requires fairly simple

laboratory measurements and no antenna range is required. The

loss in individual components may be determined with this

method, which is an advantage in the design phase.

Some of the disadvantages of this approach are:

1. It neglects the loss in some parts of the antenna,

and therefore is really only a lower bound to the total

loss.

2. The efficiency of a given segment, which is

defined as the ratio of the net power delivered to the

load to the net input power, is a function of the scattering parameters of the segment and the load impedance . Since the load impedance of the measuring circuit may

not be the same as the load which the line sees when

used with the antenna, the correct efficiency is probably

not measured.

3. When the system is divided into a number of cascaded

elements, mismatch effects occur at each junction, and

the measurements and/or calculations should include these

effects .

It is apparent that a significant error occurred for at

least one of the systems when this second approach was used to

determine antenna efficiency. The reason for the error is that

the insertion loss rather than the efficiency was measured,

and there is a significant difference between the two for

these systems. This will be more apparent as the measurements

are examined in detail.

15
3.0 MEASUREMENTS ON THE S-194 SYSTEM

3 . 1 Loss Measurements on the S-194

The errors in both types of measurement will be analyzed

here using the data which the vendor obtained or which can

be easily obtained.

3.1.1 Transmission Line Efficiency (Loss) Measurement

In this approach, the main 8-way power dividers and the

eight secondary 8-way power dividers are assumed to be the only

lossy part of the antenna. The total efficiency of the 64-

way power divider, resulting from combining the main and

secondary dividers, is then taken to be the antenna efficiency.

Referring to the schematic shown in figure 3-1, the following notation and definitions will be used.

Pg = Net power delivered to the main power divider when

the output ports are terminated with actual loads.

(i = 1 to 8) = Net power delivered to the input of each

secondary power divider with actual loads in place. The

actual loads are the loads which will be in place when

the antenna is in use.

Q^j (i = 1 to 8; j = 1 to 8) = Net power delivered to each

radiating element.

Qq = Total power delivered to the array.

T]^ = Efficiency of main divider.

ri - = Efficiency of each the ith divider.

Total efficiency of combination 64-way divider.

16
—

AMPLITUDE

MEASURING

SET

r . r . i £ 1

AAA*

50^2 LOADS —^AAf

MAIN POWER

DIVIDER

SECONDARY

POWER

DIVIDER

Figure 3-1. S-194 Power Divider

17
We can write the following expressions for the

efficiencies

8 8

Z p. Z Q.

.

i = l ]_ 3 = 1

' ^i ~- ^3-1)

^0 ^i

and

= — = —8

• (3-2)

; ^ P. E p.

0 i=i 1

At this point, the contractor has assumed that the efficiencies

of each of the eight secondary dividers are identical with the

efficiency of the main divider. With this assumption eq. (Z-2)

becomes

,

The total efficiency is then determined by measuring the

efficiency of the main divider and squaring the results.

The efficiency of the main divider was measured by the

following steps

1. All of the outputs of the main divider were terminated

with low reflection loads.

2. The source was disconnected from the input to the

divider and connected to the detector of an amplitude

measuring circuit. This unit consisted of a superheterodyne

mixer with a precision attenuator in the IF line. With

the detector connected to the source, the attenuator was

set on a convenient reading and the output meter reading

noted.

3. The divider was reconnected to the source and the

detector connected to one of the output ports. The

attenuator was reset to reproduce the original meter

reading and the change in attenuator setting recorded.

18
This step was repeated for each of the other output

ports to determine the insertion loss, , for each

port

.

Referring again to figure 3-1, we will use the following

notation:

r = Reflection coefficient of source generator.

g _

= Reflection coefficient of detector.

Tq = Reflection coefficient at the input to the main

power divider.

(i = 1 to 8) = Reflection coefficient of ith output

port of divider, which is assumed to be the same for the

measurement case and in actual use.

T Ci = 1 to 8] = Reflection coefficient of the load which

the ith output port sees in actual use. This load consists

of the ith secondary divider and the attached radiating

elements

.

Dq = Power delivered to the detector when connected to the

source.

[i = 1 to 8) = Power delivered to detector when connected

to ith output.

bg = Wave amplitude which the source would deliver to a matched (ref lectionless) load.

b . = Wave amplitude which the ith output would deliver to

a matched (reflect ionless) load with the remaining ports

terminated in the actual loads and the input connected

19
to the source. This is also assumed to be the same for

the measurement case and actual use.

. Zq = Characteristic impedance of transmission line.

The measured ratio is,

= 10 log

fD.l D1 1

1^0 J °0

= log"

1

10

= R.

and the computed apparent efficiency is then

(3-4)

m

Z R. . i=l ^ (3-5)

This is not the true efficiency because of the mismatch errors

involved in the measurement. The magnitude of this mismatch

error is determined as follows. In terms of the wave amplitudes and reflection coefficients, the delivered powers are

If we let

D. =

P.

1

b r 1 - ir.r

'0 1 - r,r 1

2

d g'

gi

' d'

z 1 1 - r r 1

2

^0 1^ ^d i'

b r 1 - ir.r

^0 li-^o^gl'

b r 1 - |r„. 1

2

'0 1 £i

P.

^i = - > ^0

(3-6)

(3-7)

(3-8)

(3-9)

20
then

1 - r^r |2 (1 - |r„,|2)|i - r,r.

R. = .

' " ^i- R,;

' |i - r^r^l^ci - Irj^) |i - r^.r.|^ C3-io)

or

where

R.

1

= M.R., (3-11)

(1 - |r,.r)|i - r r rii - r r ^

M. = ^ ^ . (3-12)

is a mismatch correction in each ratio measurement.

If we assume that r. and r.. are independent of the output

port i of the main divider, then we have

n„ = Z R. = Z r! = M n' (3-13) m 1 m 1 m m' ^

where t]^ is the apparent efficiency which was determined from

the contractor's measurements, and M denotes the mismatch ' m

correction for the main divider. The contractor's measurements

on the power divider indicate that the assumption of identical

r. 's and Fp. 's is only approximately true, but is justified in

estimating limits of error.

We will assume that the same conditions are true for the

secondary dividers. That is, the output impedances and

load impedances are the same for all 64 ports. No data is

available or obtainable to support this assumption, but it is

probably justified because of the similarity of the dividers

and the radiating elements. Data are not obtainable because

there actually is no connector between the output of the

secondary dividers and the input to the radiating elements.

The dipoles are a continuation of the divider stripline and

cannot be disconnected to make reflection coefficient measurements. It will be assumed that output impedances are the

21
same as for the main divider, and that the load reflection

coefficients are somewhat higher than those of the main

divider.

It will also be assumed that the apparent efficiency of

the secondary dividers is the same as the apparent efficiency

of the main divider. This essentially means that the transmission coefficient in all dividers is the same. Again, this

is probably justified on the basis of construction and is

required for this measurement approach since direct loss measurements cannot be performed on the secondary dividers.

With the foregoing assumptions, the total efficiency is

then

riT = M M nl! (3-14)

T m s 'm' ^ ^ where is the mismatch correction for the secondary dividers.

The error in determining ri-p will then be due to the errors in

each mismat

separately.

Errors in Measuring n ^ m

each mismatch correction and n . These will now be discussed

m

The sources of error in this measurement are as follows

1. The accuracy of equipment used to measure . It

can be shown that a systematic error of AL^ dB in each

of the measured ratios will cause 10 log x\ to be in * m , error by the same amount, and therefore 10 log n-j- will be

in error by twice that amount. The precision attenuator

used to measure the ratios is probably accurate to ± .02 dB,

resulting in a .04 dB error in the total apparent

efficiency

.

2. Connector and adapter errors. The connector on the

input to the divider is a male TNC, and the connectors on

the divider outputs are different miniature coaxial female

22
types. Different adapters must therefore be used to connect

the detector to the generator and output ports. The difference in loss in these adapters will contribute an additional error which is difficult to assess. It is probable

that this error is less than .05 dB.

Errors in the Mismatch Correction

Both the amplitude and phase of each reflection coefficient must be known to completely correct for the mismatch

correction; however, part of the correction may be determined

from the amplitudes only. We can write the total mismatch correction M as the product of two factors, M = M^M^* where

1 - |rJ2 |i - r„r - r.r.P

M, = LAL, m, = . i-il-. (3-15)

1 - |r„|2

' ^ |i - r.r |2|i - r.r. P

0 ' ' d g '

' il 1

Only the magnitudes of and are required to determine . The data supplied by the contractor gives,

ITqI = 0.14 to 0.16

I r^l = 0.2 to 0.3

This would make

10 log = -0.06 dB to -0.32 dB

for the main power divider, and we will use 10 log = 0.20 dB ± 0.1 dB.

This correction can and should be applied to the

contractor's measurements to give a more accurate value for

the efficiency. It could be computed more accurately by

using the individual load and output reflection coefficients

with the corresponding measured ratio to give

Im = "2 ^ ^lih' C3-16)

but there are other larger errors which make this small

improvement pointless.

23
The value of M2 cannot be obtained without the phases

of the r's, so we can only estimate its probable value. This

uncertainty in M2 constitutes an uncertainty in the determination

of rijjj and r]j. To determine the probable value for M2 we have

taken the measured magnitude of each r, taken all phase combinations in 20° increments and computed the absolute value of the

log of M2 . This resulting distribution is shown in figure 3-2

for the following values of the r's.

^dl

= 0 .025

= 0 .025

^ol = 0 .14 - 0.16

= 0 .26

= 0 .20

The value of M2 is between zero and ± 0.53 dB , and in some

error analyses the maximum value is used. It is evident

from figure 3-2 that it is improbable that M2 would be as high

as ± 0.53 dB , but it is quite likely that the error is greater

than ± 0.30 dB. An estimate of 0.4 dB will be used for the

following analysis.

Since T and are not known for the secondary dividers,

accurate estimates of and M2 cannot be made for these

dividers. It seems probable that the r^'s will be about the

same as for the main divider. The T^^'s will probably be

larger due to the interaction between elements resulting in

a larger uncertainty for both and M2 . Because of the above

reasons, we will take

10 log = -0.2 dB ± 0.2 dB,

uncertainty in 10 log M2 = ±0.5 dB.

The individual measured or calculated quantities are

summarized below to give the total efficiency and its

associated uncertainty.

24
18

16

14

HH 12-

I—

I

I—

CO

I—o

o

10

_l I I I I I I I I 0.1 0.2 0.3 0.4 0.5

MAGNITUDE OF MISMATCH ERROR (dB)

0.6

Figure 3-2, Distribution of Mismatch Errors for the

S-194 Antenna System

25
Table 3.1 Summary of Errors in Measured Efficiency

Measured or

Calculated Value Uncertainty

CdB) (dB)

t 2 Apparent efficiency = t]^ -0 .284 ±0.09

Main divider -0.20 ±0.10

M

Secondary divider -0.20 ±0.20

Main divider ±0.40

M

Secondary divider ±0.50

TOTAL = -0.68 RSS = ±0.68

The total efficiency is then,

rij = -0.68 dB ± 0.68 dB

A number of assumptions or approximations have been made

during this discussion which were not discussed in detail.

These assumptions were necessary for this approach on this

antenna to arrive at a result, but they are not all good assump

tions . The major approximations that have been made are

summarized below to point out that the error may be even

larger due to these approximations.

1. The losses in the radiative elements and radome have not

been included, but they are probably small.

2. It is assumed that all nine dividers are identical. This

is fairly well founded, since the apparent efficiencies of

three different main dividers were quite close.

3. It is assumed that the coupling characteristics, the

r.'s, the b .'s, and r„ are unchanged when the actual loads are

1 ' gi u °

26
replaced by the 50 ^ terminations. This will not be true,

and it would have been much better to make measurements

with the actual loads in place. Since this was not done

(and apparently was not possible), an additional error was

introduced

.

4. The r.'s and r.-'s are assumed to be independent of

the output port. Data for each port of the main divider

were available where |r^| was from 0.12 to 0.35, and Ir^^^l

ranged from 0.20 to 0.30, so there is a significant difference

The difference is probably even larger for the secondary

dividers due to the cross coupling between radiating elements

.

Even when these assumptions are used, and no error

included to account for their approximate nature, this measurement approach still has an error of almost ± 0.7 dB. We

would therefore recommend that the results from this measurement not be used as an accurate value for antenna efficiency.

Due to the nature of the antenna, measurements of gain and

directivity or radiometric measurements are likely to yield

a better result.

The results of the gain and directivity measurements,

which will be discussed in the following sections, are

G = 22.13 dB ± 0.41 dB,

D = 22.50 dB ± 0.14 dB

.

These combine to give an antenna loss of 0.37 dB tg'is ^B*

If the gain error is reduced by further measurements as

recommended in section 3.2, the error in the loss would be

reduced to about ± 0.25 dB.

3 . 2 Gain Measurements on the S-194

Through discussion with the contractor the details of the

gain measurement have been determined to be as follows. Measurements were made in a tapered anechoic chamber with a

27
linearly polarized source antenna mounted at the tapered

end of the chamber. The S-194 antenna was mounted on a model

tower about 26 meters from the source, and a standard gain

horn was also on the tower pointing in the opposite direction

from the S-194. The output of the standard gain horn was connected to a waveguide-to-coax adapter which was connected to

one input of a switch by a 0.5 meter piece of coaxial cable.

The output of the S-194 was connected to the other input of

the switch through a TNC to type N adapter and a 0.5 meter

piece of coaxial cable identical to the one used for the horn.

The output of the switch was connected to a receiver through

a coaxial cable about 30 meters long.

The S-194 was positioned for maximum received signal, the

switch set to connect the S-194 output to the receiver, and

the receiver gain set to obtain a relative 0.00 dB reading on

the phase-gain indicator. The switch was then set to connect

the standard gain horn to the receiver and the mount rotated

to place the horn in position for maximum received signal.

The attenuator in the receiver was decreased in 1 dB steps to

bring the meter on scale and the difference from zero dB was

read on the phase-gain indicator.

We will use the following notation to refer to the measurement parameters

G = gain of the S-194 antenna

d = distance between source antenna and the S-194

= input reflection coefficient for the S-194

^11' ^12' ^22 ~ scattering parameters for transmission

line between the S-194 and the receiver (composed

of adapter, coax cable, switch and cable).

p = polarization ratio for the S-194. This is a complex

number equal to the ratio of the on-axis horizontal

and vertical E-fields radiated from the S-194 antenna.

28
Its magnitude would be equal to the axial ratio if the

principal axis of the polarization ellipse were aligned

along the horizontal or vertical directions.

a = available power ratio for the transmission line between

the S-194 and receiver.

= power delivered to the receiver by the S-194.

Corresponding quantities for the standard gain horn will

I t T be denoted by primes, G , d , r^, etc; and p,j, = polarization ratio for the transmitting antenna.

= Reflection coefficient at the receiver input port.

The ratio of net powers delivered to the receiver for farfield plane wave conditions is then given by,

!d_ Cl-|S22r)|l-Sl2^J^ |1-PtP|^ (IHp'I^) G^^

^d ii-\s:^^\^)\i-s^^T^\^ \i-p^p^\Hi^\p\')

(3-17)

The gain of the S-194 is then determined by measuring the

power ratio with the receiver, measuring the two distances,

knowing the gain of the standard, and making corrections for

polarization and transmission line mismatch, non- ident ical

a's, and departure from far-field conditions.

The contractor supplied the following data,

10 log G' = 16.45 dB

10 log -5- = 4.90 dB

d = 28.44 m d' = 26.0 m.

No corrections were made by the contractor for the other

terms in the gain equation, and the gain was determined to be,

10 log G = 22.13 dB

The various sources of error in the determination of G

are as follows

1. Error in Measuring Power Ratio.

29
The manufacturers specification for the receiver indicates

that an error of ± 0.10 dB can be expected for a signal change

of 5 dB.

2. Gain Standard Error.

The NBS has found from experience in calibrating standard gain horns that the actual gain may differ by 0.2 to 0.3 dB

from the values supplied by the manufacturer. Since the manufacturer's curve was used for the standard, an error of ± 0.25

dB will be assumed.

3. Distance Error.

The distance was measured accurate to ± 2 inches, which

would cause a gain error of ± 0.02 dB.

4. Transmission Line Mismatch.

With the long line between the switch and analyzer, the

reflection coefficient looking back into the line (S22 ^'^'^ S22) should be essentially the same for both antennas. This

would mean essentially no error due to transmission line

mismat ch

.

5. Polarization Mismatch.

The magnitude of this error will depend on the polarization ratio of all three antennas. No data on polarization

ratios was taken for these antennas, so we will use some

values for similar antennas and estimate a worst case error.

Table 3.2. Possible errors due to polarization mismatch

p-p 1 Ip'I IpI worst case error (dB)

.03 . 03 .03 ± . 02

.03 .03 .10 ± .07

.10 .03 .10 ± .15

.10 .03 .03 ± .05

It is probable that the polarization mismatch error is

about 0.05 dB.

30
6. Unequal a's for the Transmission Lines.

The a's will be different due to the difference in adapters between the antennas and the coaxial line, and due to

the different "generator" impedances seen by the two lines.

The generator impedances in this case are the antenna reflection coefficients r_ and r'. The magnitude of is a a a 0.20, and r' for this type of horn antenna is about 0.03.

Substituting these values in equation (2-3), and assuming that

the S-parameters are the same gives a difference of 0.2 dB.

An additional uncertainty of 0.05 dB will be added for the

difference in adapters.

7. Multipath Errors.

The problem of scattering within the chamber, which is

discussed in detail in section 3.3.3, suggests that there could

be a sizable error in the gain measurements due to the scattering. The tapered chamber design produces a fairly uniform

field in a given plane perpendicular to the chamber axes . But

since that field is produced by the combination of the source

antenna and its images, the field strength will vary as the

source antenna is rotated about its axis, and this was observed

in the pattern measurements. Moreover, the images increase the

effective aperture of the source antenna. As a result, an inverse square law correction to account for different locations

of the test and standard antennas may be of limited accuracy.

It is very likely that there will also be a periodic variation

in the field strength along the axis of the chamber due to the

interaction of the actual source and its images. This effect

will also produce an error in the gain measurements when the

test and standard antennas are placed at different distances

from the source as in these measurements. There is a lack of

experimental data to confirm these suspected sources of error.

The pattern data show variations when the antennas were rotated

which indicate reflections no more than 20 dB below the direct
signal. However, the chamber manufacturer claimed a "quiet

zone" with reflections 40 dB below the direct signal. Where

each of these factors is taken into account, an error of ± 0.20

dB in the gain measurements is quite likely due to reflections

within the chamber.

8. Near-Zone Error.

This error is due to insufficient separation distance

between source and receiving antennas. In general it means

that the gain measured at a given distance is lower than the

actual far-field gain. The error is a function of the type and

size of the antenna and the separation distance. For both test

and standard antennas at the distances used, this error should

be less than 0.05 dB , and the net resulting error in G should

be negligible.

9. Random Error.

Random error due to alignment, signal source stability,

and receiver drift appears to have been ± 0.05 dB. The resultant

effect of these errors is summarized in Table 3.3.

Table 3.3. Summary of errors in gain measurement . Source of error Error in gai

(1) Power Ratio Measurement + 0 .10

(2) Standard Gain Horn gain + 0 .25

(3) Distance Measurement + 0 .02

(4) Transmission Line Mismatch 0 .00

(5) Polarization Mismatch + 0 .05

(6) Unequal a's ± 0 .25

(7) Multipath Signals + 0 .20

(8) Near - Zone 0 .00

(9) Random Error + 0 .05

Resultant Quadrature Sum CRSS)* ± 0 .41 <

*The expression "quadrature sum" is the square root of the sum

of the squares of the individual errors.

32
A few of these errors could be reduced without further

measurement on the S-194 antenna. The standard gain horn

could be calibrated and its axial ratio measured. This horn

could then be used to measure the axial ratio of the source

antenna, which would reduce the uncertainty due to polarization

mismatch. The reflection coefficient of the horn could be

measured, and also the characteristics of the adapters if

they are available. This information would reduce error

number 6

.

If these steps were taken, it is probable that the gain

error would be reduced to about ± 0.20 dB. If this ± 0.2 dB

gain error is unacceptable, then new gain measurements could

be made at the NBS to reduce the error to about ± 0.10 dB

.

.3 . 3 Antenna Pattern, Beam Efficiency, and

Directivity on the S-194 Antenna

3.3.1 Int roduct ion

The S-194 antenna was measured on a "model mount" using

a source antenna which is a dipole backed by a symmetrical

ground plane. In the model mount, shown in figure 3-3, the

antenna is mounted on a nominally horizontal "head" axis (z

axis) above an orthogonal (nominally vertical) "A" axis. The

antenna was mounted with its figure axis nominally coincident

with the head axis, the antenna rotated by an angle (called (J)) about the head axis and then about the vertical A axis by an

angle called 6. Care was used in aligning the antennas. Thus,

to eliminate antenna load deflection, a mirror and a weight

equal to that of the antenna (35 lbs) were mounted on the head

and adjustments made with the aid of a theodolite. Since the

rated operating load of the mount is at least 75 lbs and the

33
Figure 3-3, Model Mount Used for S-194 Antenna Measurements

34
head offset may be adjusted, deflection should have been negligible. (According to the manufacturer's specification, deflection is less than 2° at full load without compensation.)

With the test antenna on boresight (6=0), the source

antenna was rotated about the inter-antenna axis to give minimum response and then rotated by it/2 for maximum response. For

a given cut (()) value) , the orientations of the source antenna

giving maximum and minimum response on boresight (9=0) were

used to measure the "principal" and "cross" polarization,

respectively, for the entire cut. The minimum may of course

be located more accurately than the maximum because the fractional

numerical change in the slope is greater. Moreover, as will be

explained, the maxima and minima are separated by exactly tt/Z

for arbitrary polarization, neglecting scattering from the

chamber walls and imprecise alignment.

Nevertheless, anomalies did occur in the data. The

reported cross polarization was commonly maximum (only 20 dB

below the principal polarization), at or near boresight, but,

as will be explained, it should be nominally zero there.

Further, cross polarization reported on boresight varied with

the cut ((}) fixed, 0 variable), varying from 18.7 to more than

35 dB down from the principal polarization for the same

antenna. To investigate these inconsistencies, a simple

experiment was performed. With the test antenna fixed on

boresight (9 = 0) , the minimum response (cross polarization)

varied from 18 to more than 35 dB below the maximum response

(main polarization) , depending upon rotation of the antenna

pair (about the inter-antenna axis) with respect to the

anechoic chamber. Similarly, the maximum response varied by

2 dB depending upon the rotation of the antenna pair with respect to the chamber. Consequently, critical evaluation of the

data is required, using auxiliary information to resolve these

inconsistencies

.

35
3.3.2 Properties of the Model Mount

The received signal as a function of the model mount

angles must first be related to the antenna pattern and

polarization properties. Assuming far field conditions, the

complex received signal is proportional to T»R where T represents the transmitting properties of the source antenna and

R is a similar vector representing the receiving properties

of the test antenna. Both T and R are functions of the

direction of propagation and everywhere perpendicular to it.

T is proportional to the far field electric vector of the

source antenna and, if the receiving antenna is reciprocal,

R is proportional to the electric vector arising from the

test antenna when it is acting as a transmitter. Hence, we

require R, its magnitude, or the magnitudes of its components

as functions of the orientation of the test antenna, given

T on the axis of the source antenna for two different source

orientations and the received signal as a function of the

model mount angles.

First consider the right-handed rectangular coordinate

system Oxyz and the spherical polar system 0, $, r, both

fixed in the test antenna and related as shown in figure 3-4,

with unit vectors e^ , e^ , and e^^. (These angles should not

be confused with the model mount angles 6 and (^.) As may be

seen from the figure, the components are related by

1 = A (3-18)

where s and x are the column matrices {R^, R., R^} and — — 0 ip r

A =

fcC sC -S

-s c 0

cS sS C

(3-19)

and s, c, S, and C indicate sin $, cos $, sin 0, and cos 0,

respectively. Since A is an orthogonal matrix.

36
Y

z

Figure 3-4, Antenna-fixed Coordinate Systems

37
X = A s , (3-20)

where - indicates the transpose. The components R , R , and

X y

R^ relative to the antenna- fixed rectangular coordinate

system are required in terms o£ the experimental data.

It is assumed that: (a) the head and A axes intersect

and are perpendicular to each other, and (b) the axis of rotation

of the source antenna passes through their intersection and

coincides with the head axis for 6=0. For the initial model

mount configuration (6 = ({) = 0), y and z of Oxyz (the antennafixed system) are coincident with the A and head axes, respectively, and Oxyz is coincident with the space-fixed coordinate

system OXYZ. Then, as may be seen from figures 3-3 and 3-4,

rotation of the head axis by (}> = followed by rotation about

the vertical axis by 6 = 9 yields the relations

R3(0,$) = R^(e,(f)), R^(0,$) = Ry^[Qy<^)y and R^(e,$) = R^iQy<^)y

(3-21)

where R^^, Ry, and R^ are the components of R in the indicated

directions in the space- fixed coordinate system after the

above rotation by 9 and ({> . Since the source antenna is also

rotated by cj) =

where

s ='- ^

= B

' c s

0"

B = -s c 0

L 0 0 1,

(3-22)

(3-23)

and X and x' are the components of R in the coordinates fixed

in space (3-21) and the source antenna, respectively. Hence,

t -=BX=Bs=BAxEMx, (3-24)

38
where

M = fc^C + s sc(C-l)

V cS

sc(C-l)

s^C + sS

-cS

-sS

C

(3-25)

Since A and B are orthogonal, so is M and

X = M x' . (3-26)

Since R = 0 in the far field, the bottom row of (3-19) gives

R in terms of R and R Substituting this value of in

(3-24), one obtains an alternative expression for M, namely

M' =

c^E + s sc(E -1)

0

sc(S-l)

+ c

0

(3-27)

where S represents sec 0. Since M' has no inverse it may not

be used in (3-26) but a similar simplification results from

the fact that the last column of M may be ignored since R , Thus, (3-24) and following relate the components of R for the

coordinate system fixed in the test antenna to those for

the system fixed in the source antenna. In particular.

= 0

R = 0 and, for a calibrated linearly polarized source

antenna, R , and R ,, i.e. , the dot product of a row of

X y

(3-25) or (3-27) with x, may be considered as known.

The qualitative character of M is shown by its behavior

on meridian cuts (fixed $) corresponding to the E plane

($ = 0 or it) , the H plane ($ = 7t/2 or 3it/2) , and the two

diagonal planes ($ = 7t/4, 37t/4, 5Tr/4, or 77t/4) . The corresponding M's are respectively:

' c 0 +S"

0 1 0 (3-28)

0 c

39
0

0 c +s

±s

(3-28) —(C-1)

e (C-1)

^

S

/I

-H. S c

If 0 = 0, all three matrices reduce to the unit matrix.

In (3-28) e, f, and g are each ± 1 depending upon the individual

angle; fg = e; and, for the first two cases, the upper signs

hold for $ = 0 or 77/2 and the lower signs for $ = it or 37t/2 . The alternate M's (corresponding to (3-27)), are obtained byreplacing the last row and column by zeros and the remaining

C's by 2's. On the E and H planes, only one element of each

row of M is non-zero and that element is equal to C, 1, or

± S; hence, R^, R^., and R^ may be determined by a single measurement with a linearly polarized antenna. Further, on these

planes , their absolute values may be determined without a phase measurement. For the diagonal and most other planes

the components are mixed so that phase measurements must be

made to obtain the individual components for 6/0, although

the magnitudes of R and R may be obtained to fair accuracy

X y

without phase measurements if 0 is small. The magnitude of

R (without reference to polarization) may of course be obtained

without phase measurements.

Commonly the principal and cross polarizations are not

referred to a direction fixed with respect to the antenna

but rather, for each orientation of the test antenna in its

mount, chosen perpendicular to the line of antenna centers,

40
say vertical and horizontal. Such a description depends

upon the mount and the manner in which the antenna is

mounted on the mount, but is quite practical if it is given

in terms o£ the mount and mounting used with the antenna in its

eventual application. However, it is commonly given in terms

of the mount and antenna mounting used for measurement. (The

discrepancies may be small for directions not far from boresight.) In the absence of information concerning the mount

to be used, the measurement mount is treated. For the model

mount, manner of antenna mounting, and coordinate systems used

here, the principal and cross polarizations could have been

taken to be Rq and respectively. These polarizations would

have been obtained directly with a linearly polarized antenna

if the source had not been rotated. However, since the source

antenna was rotated, s_ = Bx' (3-22) and x' = B s_. For the

cases described by equation (3-28) , B reduces to

(±1

0

I 0

0

0' '0 ±1 0" 3//2 0' ±1 0 ^1 0 0 , and -6//2 a//2 0 (3

0 1 .0 0 1 [ 0 0 1 J respective ly> where a and 3 are ± 1 depending upon the angle.

3.3.3 Symmetry, Polarization, and Scattering

Determination of the antenna polarizations on boresight

and evaluation of chamber scattering require a careful

interpretation of the data and its anomalies together with

a priori considerations. The source antenna and the S-194

antenna each have two orthogonal planes of nominal material

symmetry and are nominally excited (in the transmitting mode)

so that one plane (the E plane) is a plane of field symmetry

and the other (the H plane) is a plane of field antisymmetry.

Field symmetry is used here in the vector-pseudovector sense.

41
i.e., reflection o£ an electric field vector E (solid arrow in

Fig. 3-5) in a plane perpendicular to the vector reverses its

direction, while reflection of a magnetic field pseudovector

H (dashed arrow in Fig. 3-5) in a plane perpendicular to the

usual arrow leaves the field unchanged, i.e., the pseudovector

H behaves like the elementary current loop associated with H.

In this sense, the E field

I

1>

>

t

> — >

<

1' igure 3-5. Antenna Field Symmetries

and the associated H (more

precisely magnetic induction

B) field (as functions of position) have identical symmetry

properties. For an antenna

with such symmetry, on the E

plane there can be no E component normal to the plane and

on the H plane there can be

no E component in the plane.

Thus , any antenna with such

symmetry must be linearly

polarized with no cross polarization on the two planes and doubly so on their intersection

(boresight) . These statements apply to (a) the radiated field

(a function of position) , (b) the complex vector radiation

pattern T (a function of direction) , (c) the complex vector

receiving pattern R, and (d) the corresponding power patterns.

Moreover, if the anechoic chamber in which the antennas were

measured had two planes of material symmetry and the source

antenna was symmetrically positioned and oriented, then the

total radiation incident upon the test (S-194) antenna (including the radiation scattered from the chamber walls) had the

aforementioned polarization character (linear, no cross

polarization). Moreover, must be zero in the E plane

and Rq must be zero in the H plane.

42
The reported cross polarization on the H plane cut is

consistent with the nominal symmetry, being at least 35 dB

down on boresight and at least 30 dB down for every value

of 6. However, the cross polarization reported for the

E plane and diagonal cuts are maximum on or near boresight

(0 = 0), being only 18.7 to approximately 20 dB down from

the principal polarization on boresight. The latter measurements are not only inconsistent with the nominal symmetry

but at wide variance with the other values on boresight.

Further, these boresight differences must be due to the

difference in the field scattered by the anechoic chamber.

To estimate the ellipticity of the polarization of the test

antenna and the radiation incident upon it, the boresight

measurements are used, particularly the fact that for one

pair of orientations the minimum response was more than

35 dB below the maximum response. (Recall that no ambiguity

arises from the model mount behavior for 0=0. See (3-28).)

For two antennas, each in the far field of the other and one

rotating about the line connecting the centers of the antennas,

the received power (proportional to |T»R|^) may be shown to be

2 2 2 2 proportional to (1-tr) cos a + (t-r) sin a, where a is the

angle between the major axes of the two polarization ellipses,

r is the ratio of minor axis to the major axis for the receiving antenna, and t is the corresponding ratio for the transmitting antenna. (The ratios are allowed to assume negative

as well as positive values to account for the senses of rotation.) For antennas which are even approximately linearly

polarized, t and r are small enough compared to unity that the

2 2 minimum response will be proportional to (t-r) , not (1-tr) . Due to the difference in the character of the two antennas, r/t

will not be even roughly +1 except by chance. Thus, the small

2 magnitude of (t-r) is probably not due to cancellation so

2 2 that t and r are probably no more than a few dB greater than

(t-r)2.

43
The scattered field (and therefore the total radiation

incident upon the test antenna) depends only upon the orientation of the source antenna and so upon ^ but not 6; however

the effect of the scattered field may depend upon 6, say as the main beam points toward a scatterer. The data for the

2 H plane cut indicates that r for the test antenna on the

2 boresight and t for the composite radiation field when the

source antenna is horizontally oriented are probably no greater

2 than -30 dB . Hence, the large values of (t-r) for the source

antenna oriented vertically or diagonally must be due es2 sentially to the effective t which is therefore approximately

-18 or -20 dB for these source orientations.

Further, the reported cross polarization on or near boresight must be due primarily to scattered radiation except for

the H plane measurements. The fact that the maxima for other

source orientations occur on or near boresight is in agreement

with this conclusion since the reflection coefficient tends

to increase as the incident radiation approaches a grazing

angle. (For an infinite plane wave incident upon an infinite

plane surface, both the perpendicular and parallel reflection

coefficients approach unity as the grazing angle is approached,

the perpendicular coefficient being fairly large for angles

well off grazing.) Moreover, the fact that little if any

"cross polarization" occurs for |0| > 14° indicates that the

direction of the scattered radiation does not deviate far

from the line of antenna centers. It should be noted that

the reported values of cross polarization do not indicate the

magnitude of the total scattered power but only a rough lower

bound; the scattered power is probably significantly larger

than the bound, particularly when the source antenna is

polarized roughly horizontally or vertically. The circumstance

with the anechoic chamber may be much more common than is

generally realized. The reflection coefficient was reported

44
to be down by at least 40 dB , and therefore scattering was

considered to be negligible. Such values are of course for

normal incidence and may be of limited significance for a tapered anechoic chamber.

3.3.4 Error Estimates

Since the preceding analysis indicates that the measurements of cross polarization have little if any value, the following discussion is limited to the total received power as a function of direction. The following sources of error are

considered

1. Non-linear polarization of the test antenna and

composite source on boresight. The previously estimated magnitudes of r and t (0.03 and 0.10), give rise to an error of

± 0.03 dB in the directivity and ± 0.14% in the beam efficiency.

2. Receiver non-linearity. Assuming a non-linearity

of 0.02 dB/dB yields an error of 0.08 dB in the directivity

and an error of 0.241 in the beam efficiency.

3. Scattered signal. To estimate the error due to

scattered radiation, the reported cross polarization for the

source antenna vertically polarized was used as a measure of

the scattered radiation. The resulting errors in the directivity and beam efficiency were found to be 0.87 dB and 0.6%,

respectively. To the extent that the total radiation incident

upon the test antenna propagates parallel to the line of

antenna centers, renormalization of the values for each cut

to yield the same value on boresight yields correct relative

pattern values. Using the same estimate for the scattered

radiation, which estimate assumes off -axis scattered radiation, errors of 0.03 dB and 0.5% were estimated for renormalized measurements as carried out by the contractor.

The total scattered signal could not be determined from

the available data, so the following two assumptions were

45
made. (1) That part of the scattered signal for which there

was a change of polarization was used as a lower bound, yielding a rough lower bound for the error due to scattering.

(2) As a measure of the scattered signal with the change of

polarization, the maximum value was used, namely that associated

with vertical polarization of the source antenna. (For other

orientations of the source antenna, actual values of the

scattered signals with change of polarization were less.)

It is hoped that these two assumptions, the first leading to

a low error estimate and the second toward a high estimate,

will roughly cancel each other.

Table 3.4. Summary of Errors in Directivity and Beam Efficiency

Source of Error AD Ae

Polarization ± 0.03 ± 0.14

Non-linear Receiver ± 0.08 ± 0.24

Scattered Power ± 0.03 ± 0.50

Total ± 0 .14 dB ±0.881

3 . 4 Calibration of the S-194 Radiometer

Briefly, it is the contractor's estimate that the S-194

radiometer can measure brightness temperature with a probable

error of ± 1 . 7 to ± 6 . 3 K . We feel that the errors are in the

range from ± 14 to ± 42 K. The difference in estimates is due

primarily to the uncertainty assigned to the accuracy in measuring antenna efficiency and in the accuracy of the standards

used to calibrate the radiometer.

In the S-194 radiometer analysis, some concern was expressed

by Hartsfield about the mathematics of joining an antenna to a receiver, or even if a satisfactory expression existed. To

answer the quesions raised, a more rigorous joining equation than

the one presented by the contractor is included and utilized in

the error analysis.

46
3.4.1 Description of the S-194 Radiometer

A diagram of the S-194 system is shown in Fig. 3-6. Radiation is incident on the antenna with brightness temperature Tg.

A digital output, A^, is obtained that is linearly related to

the incident radiation; viz.

f n where the slope K*" and the intercept Tq are determined in

part by removing the antenna and utilizing standard noise

generators. To protect the calibration against internal gain

changes, a comparison radiometer of the switching type was

selected; and to protect against time varying internal noise

contributions, hot and cold internal reference standards and

various temperature -monitor ing sensors are available for an

update calibration routine. The accuracy to which Tg is

known for a given A^ depends on (1) the radiometer's resolution, (2) the initial accuracy of the calibration for the

radiometer, (3) the stability and/or the accuracy of the update corrections, and (4) the accuracy of characterizing the

antenna

.

When the antenna is replaced with standard noise generators,

"^STD " ^STD "^O* (3-31)

The values for K and Tq depend on the reflection coefficients

of the standards rgrj,^, in addition to the circuit between the

reference planes A and X (Fig. 3-6). To evaluate this dependence, note that the output d.c. voltage, E, at X (see fig.

3-6) is related to the power available at the antenna input

at A by

E = QXA^STD * '5xf(®FA-^TaMp'' (3-32)

where

, V°ltage at X

^ ^3 ^3^

Power available at i

47
and i refers to the reference planes A, F and R. T^]^p is the

effective input noise temperature of the amplifier system, and

0 FA is the radiation (in degrees kelvin) originating in the

front end of the radiometer and available to the amplifier at

F. When the radiometer is switched to the reference generator,

the dc voltage at X is adjusted via the binary attenuator to

equal E in (3-32)

,

E = QXR^R ' QXF^^FR ^ TaMP^> (3-34)

where the symbols have meanings similar to those in (3-32).

The double prime implies the switch is connecting the reference

source. Using the available power ratio coefficients defined

in (2-2) ,

^XR ^XF°'fR

"

Voltage at X ] ( Power available at F

^Power available at F

and (3-34) becomes

^Power available at R

i

(3-35)

E = Q^p[a

^Fr'^R ®FR '^AMP (3-36)

Equating (3-36) with (3-32), comparing with (3-31), and

noting that Qya/Q XA' ^XF " °^FA

K =

via a relationship similar to (3-35) ,

(3-37)

a a FA

and

To = a[0 FA "^AMP

+ T

AMPa a FA

(3-38)

where a and b are defined by the linear relation between ^^jy)

and the binary attenuation controlling the voltages at X; namely

48
^STD " ^"^^Xp/^XF^ " ^' (3-39)

If the isolation between ports on the diode switch is adequate,

then the terms within the square brackets are independent of

the impedance at the input to the radiometer, and the change

of K and to K' and T^, due to a changed input impedance is

governed by

K' = R K. (3-40)

Hence

t' = R T * ^^FA'^FA^ ^^^AMP-^AMP\ (3.413

o o 1

a FA

where R e o^p^/otpy^* ^.nd the prime indicates the parameters

associated with a new impedance. If we use a more convenient

form of (2-3), namely

(i-ir.r)is..r

a.. = ^ ^ ^ , (3-42)

(i-|r.r)|i - s..r.r

where r. is the reflection coefficient looking away from the

3 ^ two-port at port j, and is the reflection coefficient looking into the two-port at port j , then

!

R = . (3-43)

I ^ANt' I '"^STD^Swl ^ I ^pl

The unprimed parameters correspond to the impedance of the

standards used to calibrate the radiometer and the primed parameters to the impedance of the antenna. Tp is the reflection

coefficient looking into the filter at reference plane P;

Tcm^ is the reflection coefficient of the standard: T.^tt is STD ' ANT

the reflection coefficient of the antenna; and Fg^ is the

reflection coefficient looking towards the switch at reference

plane A (see Pig. 3-6).

49
O O

o oa 1

Z Q£ 3 LU O O O 1-

a: oo O Z

1 =)

LU UJ o. o

r) <j

Ofo o cc: z o

< O 1-

Of — cc: o

3: LU O 1— Z LU

z: >- o

I

a:

•a: o

\ LUo

o

tD O

i-i o

o

>- 1-

oc <: <c =3

CD LU

=3 QO LU t—

h- I— =3

•-« <: s

3 q: s:

</) o

a;2

o

LU z: -1 <

3 O O Q

o

t— 1—

</1 o

s:

LU ^

1— 1—

LU K

r O

o

<x. a

z

<c

I—

o

o: i-i

<_> LU to

I— > o

«>o o oO

to

f-.

(/) Li.

1 < LU 1jj Qu t— ( <i. —

_i =««= 3 u. O U. I1- _J Ll_

i

z

Q£ < O

O o O 1— —

1

1— >—

4

sC o CD

—1 a LU O

o _i _1 1 o LU O CO

i k /

LU 31 b; Q CJ LU o t— z

1-1 1—

1

Q 3 tLO

o

1—

JURE 1

t—

<_> t—

LU C£. tJ O

Z LU 1— z

_J LU o s:

3:

UA Ut <t. q: «a: o: «t a: LU t— OL

h- LU n: LU -<

LU Z Z3

o; t—

Ll. Q. Z

LU LU

CC CD

EMP O tr) <C

LU (— s:

CO w

•Mso

•H

nJ

CO

CD A(->

a

bc Q

u

0

i-H

I

bc

•H

50
To evaluate the second term in (3-41) note that 0p^ is

the available power which originates in the front end of the

radiometer between the reference planes A and F. It contains

black-body radiation terms from the losses, leakage through

the switch from the other switch ports, and shot noise generated by the switch. The shot noise contribution was measured

by the contractor to be less than 1 K, and the variation of

this contribution with change of impedance cannot be corrected

without further information. It is likely that the variation

of this 1 K contribution with the radiometer input impedance

is negligible, but tests to verify this would be worthwhile.

The isolation between switch ports insures that the leakage

contribution to 0p^ is small, and variations due to input impedance should be negligible. The only remaining contribution

to 0p^ left to consider is the black-body radiation from the

front-end losses. This contribution is [1]

®FA ^ " ^'fA^^D' (^3-44)

where t^ is the physical temperature of the front end at the

time of measurement. Thus (3-41) becomes

t; = R T„ - (l-R)tj, * (T;^5,-Tamp)/°'fa- t3-45)

We are now in a position to express Tg in terms of the parameters calibrated using the standard noise sources. Assuming

that Tg is constant over the main antenna beam, one finds from

(2-9) and (2-11) that the power available from the antenna at

A is

^A - ^ ^ANT» C3-46)

where

"^ANT ' (^-^^^i * "^SIDE' (3-47)

51
MAIN

a is defined in (2-11), a is obtained from (2-11) where

the integral is only over the main beam, t^^ is the physical

temperature of the antenna, and Tg-j-^g is the radiation entering through the antenna side lobes available at A. The radiometer response to this available power is

= k' - T^, (3-48)

where the primed parameters correspond to the antenna's impedance. Using (3-40) and (3-45),

MAIN '

' Tg = (1/a )WT^-t^) - CT^MP-^AMP^/^^FA ^^D'^ANT^^' (3-49)

where

The parameter T^ is the temperature that a generator (having

the same impedance as the calibration standards) would have in

order to produce the output A^. If the radiometer is calibrated

with standards having the same impedance as the antenna, then

(3-49) simplifies to

= ^^A " ^ANT^/°^^^^- ^3-50)

3.4.2 The Accuracy of the S-194 Radiometer

To address the question of accuracy, we have a somewhat different view of the radiometer than the contractor. It seems to

us that the two internal standards should be thought of as providing two reference noise amplitudes sent through the radiometer

system to calibrate out any long-term drift in the output display

words. The initial calibration using the external standards

at 372 K and 80 K, etc., is used to identify those brightness

temperatures that correspond to these two reference amplitudes.

The output of the radiometer is digital so that the brightness

temperature of the radiation can vary over a range of about

one degree before the output display word would change. In

52
addition, however, the internal noise contributions can change

over a one degree range before the output display word would

be recalibrated. Thus the temperature that a particular output display word represents is in principle ambiguous over a two degree range. Ideally one would identify the center of

this range for each output word so that the uncertainty would

be plus or minus one degree.

Although the objective of the radiometer is to measure

the brightness temperature Tg , the errors in measuring (see

Eqn. (3-49)) was given special attention by the contractor; and

for comparison purposes, the errors in knowing will be discussed before continuing on to the problem of determining Tg.

Although the contractor defines (i.e. power available at

plane A from a generator having the same impedance as the calibration standards) , they analyze relative to Tg^, which is a delivered noise temperature, and thus is related via Tg^ = M^T^

where

M, E ^ ^

(3-51)

1 1 -r r I ^

where r^rp is the reflection coefficient looking toward the

antenna, and Tg^ is the reflection coefficient looking toward

the switch at the reference plane A. The mismatch factor

is about 0.81 for the S-194, so errors in Tg^ and T^ are

comparable

.

3.4.2.1 The Accuracy of T^

The accuracy of determining T^ depends on the resolution

error (± IK already discussed), the calibration accuracy of

the two reference amplitudes, linearity of the output, and

errors in updating the reference amplitudes.

Calibration Error . The calibration by the contractor assumes that

their hot and cold sources are 372 ± IK and 81 ± IK, respectively,

53
including a reduction in available power due to an adapter from

the standard's connector to the radiometer's connector. After

contacting the manufacturer of this standard, and because an

unevaluated adapter was utilized, we estimate at least a 4K

error for the cold source and 2K for the hot source. For assurance this adapter needs to be evaluated. This is to say that

the standards which were used have not received an evaluation

comparable to NBS noise standards that have about ±- IK accuracy.

Furthermore, because it is questionable that 81 Kelvins or 272

Kelvins are the most probable noise outputs, these errors should

not be used in quadrature with other errors.

Using the standards and T^^-. which give rise to the

output display words A^ and A^^ , and using (3-31), the coefficients K and T are evaluated,

o

'

^AH ~ "^AC

K = -T 3—T—, (3-52)

^AH ^AC

and

^ ^AC'^AH " '^Ah'^AC

T = ^ . (3-53)

° ^AH ^AC

Using these values for K and T , the "calibration temperature"

"^AH

^^'^ ^AC ^'^^ assigned to the output display words A^j^ and A^^

produced by the two internal reference noise generators. The

uncertainties in T^ and T^^^ are proportional to the uncertainties

in T^ and T^^-. plus an additional error because this calibration procedure does not identify where within the one degree

resolution zone the reference noise voltage is. Although the

internal noise causes the digital output to oscillate between

two states when amplitudes are close to a transition voltage,

how close the reference voltages were to a particular transition

voltage was not established. Thus the full one-degree resolution error should be added to the uncertainties in T^ and T^^--

Using T^^ = 81 ± 4K, and T^ = 372.2 ± 2K, we conclude for

the S-194 radiometer

54
* T.„ = 369.4 ± 3K, (3-54)

= 200 ± 4.2K. (3-55)

The resulting errors in due to calibration limitations are

shown in Fig. 3-7. For readability, the errors are magnified

by a factor of 10. Thus, a display output of 650 implies that

for T^ = 14K a calibration error of ± 12K occurs.

Linearity Error . Based on private communication with the

test engineer, it is understood that linearity checks were

made during an acceptance test for the radiometer over the

range 90K to 250K. Due to the accuracy of the attenuator

utilized, it was possible to verify that deviations of less

than 2K occurred over the 90 to 250 range. It seems probable

that the nonlinearity errors are due primarily to the uncertainty in the binary attenuator calibration. The error due

to the binary attenuator was estimated to be on the order of

0.3K. A better linearity check needs to be performed in order

to verify that the 0.3K estimate is reasonable.

The equivalent T^'s corresponding to the two internal

calibration outputs depend on the temperature of the internal

standards, internal losses, and internal temperature distributions. The temperatures of the internal standards are monitored

and are stabilized within 0.1°K. This stabilization of the

noise generators should also stabilize the associated loss

distributions adequately. Thus no additional error is expected

due to the minor temperature changes of the internal standards.

The calibration of the radiometer takes place with the

coaxial transmission line between the antenna and radiometer

switch at room temperature. In operation, the antenna will

typically be at an ambient temperature near 190K. This results

in a decrease of about 2K for the thermal radiation from the

cable losses for the operating situation compared with the

55
Figure 3-7. Effective Antenna Temperature vs Radiometer

Output with Calibration Error

56
calibration situation. The contractor estimates a 25% uncertainty in the measurement of the cable loss, or a ± 0.5K error

in calculating the equivalent calibrated values. The contributions to the error in T^ are summarized as follows.

Resolution ± IK

Calibration ± 3 at 370K

± 4.2 at 200K

± 12.5 at OK

Linearity ± 0.3

Update ± 0.5

The linearity, resolution, and update errors are probably

in quadrature (i.e., independent, equally likely to be positive

as negative, and more likely to be small than large). Thus

the resultant linearity, resolution and update error is ± 1.2K.

Our estimates for the errors in T^ near OK, 200K and 370K are

± 13. 7K, ± 5.4K and ± 4.2K, respectively, compared with estimates

of ± 1.7, ± 0.9, and ± 1.3, respectively, made by the contractor.

3.4.2.2 The Accuracy of Tg

From T^ one can obtain Tg using (3-49). Additional

errors occur because of uncertainty in R, because of the change

in the amplifier noise temperature, , and because of unMAIN certainties in the antenna parameters a and T^,j,.

Accuracy of R . The parameter R is given in (3-43) . For the

S-194 radiometer iTg^jjl was not measured but is probably less

than 0.05, | | = 0.17 ± 0.02, |rg^| = 0.02 5, and |rg^| = 0.025, and |rp| = 0.017. No phase information was obtained. It

is estimated that (1 - |rp|^)/(l - |rp|^) = 1 ± 0.007 so that

R = 1.03 ± 0.027. (3-57)

57
Change in Amplifier Noise Temperature . The change in | Tp | o£

0.01 as the antenna replaces the calibration noise source will

change the amplifier's effective input noise temperature T^j^p

on the order of 0.4%. Thus for a 4.1 dB noise figure amplifier,

this implies

Tamp " '^mv ~- ^-s^- C^-ss)

Uncertainties in Antenna Parameters . For the S-194 radiometer,

MA TN

we have estimated a = 0.86 ± 161 and a ^ = 0.98a. If we

neglect uncertainties of the radiation entering the antenna

via the side and back lobes, then from (3-47) and (3-49) the

errors due to the uncertainties in the antenna loss and beam

efficiency are about 0.16(T^-tj^) and 0.009 Tg, respectively.

Resultant Error in Tg. Using (3-49) and (3-56), the errors in

Tg are shown in Table 3.5, listed in order of their importance,

for Tg in the center of its expected range. Both the linear

sum and the quadrature sum are listed. The appropriate error

lies between these limits. Insofar as the sources of error

are independent, and the most probable values for each parameter are used in the calculation, then the appropriate error

will lie nearer the quadratic sum. In our opinion, the calibration error and the error due to a change in T^jyjp do not

satisfy the conditions for quadratic addition. The last entry

in Table 3.5 lists the error if the calibration error and the

error due to the changing T^p are added linearly, while the

remaining errors are added quadrat ically

.

3.4.3 Comments

The calibration procedure used by the contractor contributes a large error. In particular, for Tg = 175K, the use of

an external standard to calibrate the radiometer contributed

58
Table 3.5 Errors in Antenna Brightness Temperature For the

MA TN Typical Conditions tQ=297K, tj^=190K, a^-^^^=0.84, T^^=34K.

Parameter Tg=0 K Tg=17SK r*n »v ^ T /" Tg=350K

Causing Error (T^=34K) CT^=167K) (T^=300K)

Calibration ± 13. 7K ± 6.2K ± 1. 9K

a 25.0 3.7 17.6

Beam Efficiency 0 . 0 1 . 6 3.1

R 7.1 3.5 0.1

"^AMP 2.2 2.2 2 . 2 Resolution 1.3 1 . 3 1.3

Update 0.7 0 . 7 0.7

Linearity 0.4 0.4 0.4

Linear Sum ± 50. 4K ±20 . OK ± 27. 3K

Quadratic Sum ± 29. 5K ± 8.7K ± 18 .2K

Quad, except ± 41. 9K ±13. 9K ± 22. IK

Cal. and T^^p

± 6.8K in the process of transferring the external calibration

to the internal reference generators, ± 3.5K to account for

the errors due to the mismatch between the antenna and the

radiometer versus the standard and the radiometer, and ± 2.2K

because the effective input noise temperature of the amplifier

changes when the antenna is replaced by the standard. Thus

a ± 12. 5K error component in the ± 14. 3K resultant error is

due to using a standard with an impedance diffferent than the

antenna's.

If the loss measurement errors were ± 0.02 dB (as claimed),

then these values could be used to calculate the reference

is it temperature T^ and T^^ to within 2K instead of ± 3 and ± 4.2

as given in (3-54) and (3-55). Further, (3-50) could be used

instead of (3-49) to eliminate errors due to R and T^j^ • Under these conditions, the errors shown in Table 3.6 would

hold and the quadrature sum should be valid. In case the old

loss measurements are not trusted, a variable impedance standard

59
adjusted to equal the antenna impedance might be used with comparable results. Matching the antenna impedance across the

pass band of the amplifiers might not be practical so that

some mismatch error would still remain. In any case, (3-49)

should be adequate as a joining equation to use in estimating

these errors. This is to say, (3-49) accounts for the multiple

reflection and correlation terms which the contractor and

Hartsfield were concerned about. It is also apparent from

Table 3.5 that the antenna parameters need to be measured more

accurately. Table 3.6 shows the uncertainties probably

attainable by the use of improved antenna loss and beam

efficiency measurements together with improved radiometer

calibration, using either accurate loss measurements on the

radiometer components or an adjustable impedance standard.

Table 3.6 Probable Attainable Errors in

Antenna Brightness Temperature

Parameter Tg=0 K Tg=175K Tg=350K

Causing Error (T^=34K) (T^=167K) (T^=300K)

a ± 4,.8K ± 0..7K ± 3,.4K

Beam Efficiency 0,.0 0,. 7 1

,

.4

Calibration 6 .8 2 ,.5 2 ,.5

Resolution 1,.3 1,.3 1

,

.3

Update .7 .7 .7

Linearity .4 1.4 .4

Quadratic Sum ± 8.. 5K ± 3.. IK ± 4,.7K

60
4.0 MEASUREMENTS ON THE S-193 SYSTEM

4 . 1 Loss Measurements on the S-195 Antenna

The antenna and its associated switching circuits are

shown in figure 4-1. The numbered terminal ports are at

important waveguide junctions and will be used in the following discussion.

There is a problem for this antenna when defining

how much of the switching assembly should be considered a part of the antenna, and then making measurements at the

appropriate junctions. Leakage and cross-talk within

circulator G affect the cros s -polar izat ion response of the

antenna and, therefore, the gain and pattern measurements

should definitely be taken at some terminal which includes G as a port of the antenna system.

The output of circulator G would be the best place to

make these measurements; but it is not possible to get at this

connection, so pattern measurements have been made at terminal

IV. Gain measurements (to determine antenna efficiency) should

also be made after circulator G, since the on-axis cross polarization is significant. If these gain measurements are made at

terminal IV, they will include the efficiency of the antenna

structure plus all of the waveguide switching assemt^ly. However in operation, the switching assembly will be at a different temperature than the antenna, so the efficiency of each

assembly must also be measured separately. The contractor was

aware of this problem and therefore made pattern measurements

at terminal IV, computed or measured the loss of the antenna

to terminals II and III, measured the loss from terminals II

and III to IV, and made gain measurements at terminals 0 and

0'. The pattern measurements have therefore included the

effect of the first circulator, while the gain measurements

have not. The antenna efficiency determined from the ratio

61
WAVEGUIDE

(HOR. POL.) jj

I

FEED ASSEMBLY

MODE TRANSDUCER

III VII

1 \ (d

I

1 Vly '

(VERT. POL.) WAVEGUIDE

WAVEGUIDE SWITCHING ASSY

IV

^ VI

Figure 4-1. Schematic of S-193 Antenna and Switching Assembly

62
of gain to directivity will therefore have a small error due

to this difference in measurement points.

Loss Computed from An tenna - Component Data . The contractor

determined the loss of the antenna by measuring or calculating

the loss in the individual components which make up the antenna

input and feed assembly. These components are shown schematically in figure 4-2.

The components for both ports are composed of a 2-inch

straight section and a combination of bends of WR-62 waveguide plus the orthomode transducer. The losses of these components were measured in a re fleet ionles s ins ert ion - loss measuring system, and therefore attenuation rather than efficiency

was determined. However, the loss was less than 0.20 dB in each

case, so the difference between the two quantities is quite

small. The other error in these measured attenuations is due

to the inaccuracy of the measuring system. For the small losses

measured, the error for the type of system used is about ± 0.02

dB. The measured data and associated errors are listed below.

Table 4.1 Errors in Measured Efficiencies of Antenna

Input Components

Component

Measured

Attenuat ion

(dB)

System

Error

(dB)

Efficiency vs

.

Attenuation Error

(dB)

2 in. Straight Section - .04 ±.02 + .02

Vert. Port Bends - .06 ±.02 + .02

Hor. Port Bends - .06 ± .02 + .02

Orthomode Transducer

Vert. Port

- . 03 ± .02 + .01

Orthomode Transducer - .08 ±.02 + .03

Hor. Port

The errors, listed as efficiency

tained by using the magnitudes of (a)

63

vs. attenuation, were obthe attenuation, (b) the
64
input and output reflection coefficients for each section, and

(c) the reflection coefficient of each preceding section as

the source reflection coefficient r . The efficiency (or a)

was then computed from equation (2-3) using all realizable

phase combinations for the r's.

The losses of the 12.920 inch long circular waveguide and

the following tapered section with its tapered dielectric were

determined by calculation. The calculation for the straight

circular section is straightforward using formulas available

in standard texts [6] . These calculations give a loss of

0.01 dB with an estimated uncertainty of ±0.01 dB. The

tapered section geometry is approximated for purpose of calculation. It was assumed that the waveguide was of uniform

circular cross section uniformly filled with the fused silica

dielectric. The dielectric constant of the fused silica is

3.8 with a loss tangent of 2 x 10 ^. The calculated loss of

this section using available formulas [7] is 0.16 dB.

The contractor has added an additional 0.02 dB loss in

the reflector cap and parabolic reflector. The total antenna

loss is then tabulated below.

Table 4.2 Summary of Loss Components on S-193 Antenna

Horizontal Mode

Input waveguide and

orthomode transducer

Components Loss (dB)

0.18

Estimated error (dB)

+ .06

- .12

Circular guide 0 .01 ±0.01

Dielectric taper 0.16 + .05

- .10

Reflector cap and

Parabolic reflector

0.02 ± .02

Total 0 .37 + 0 .14

-0.25

65
Vertical Mode

Components Loss (dB) Estimated Error (dB)

Input waveguide and 0.13 + .06 • orthomode transducer - .12

Circular guide 0.01 ±0.01

Dielectric taper 0.16 + .05

- .10

Reflector cap and 0.02 ±0.02

Parabolic reflector

Total 0.32 +0.14

-0 .25

The total errors for the input waveguide and orthomode

transducer combination are an arithmetic sum of the values in

the first table. They were not added in quadrature since the

system error would be the same for all three components, and

the efficiency vs. attenuation errors are all positive.

For an incident brightness temperature of Tg and an

antenna temperature of T , the resulting error in antenna

output noise temperature dT^ is given by.

For values of da of +0.03, -0.06 (which correspond to +0.14

and -0.25 dB , respectively), a temperature difference (Tg-T^) of

100 Kelvins would produce an error of + 3 and - 6 Kelvins,

respectively

.

Loss Measurements from Gain and Directivity . Although the

contractor has not used the pattern data to compute directivity,

it should be very simple to complete this calculation. This

could then be used with the measured gain to compute the antenna

efficiency and therefore obtain this, parameter by two independent

methods. This would serve as a check on both the loss measurements and the pattern measurements, and we recommend that this

be done.

66
4 . 2 Gain Measurements on the S-195

There was no documentation of the gain measurements

available, and so the information and data referred to here

have been obtained from discussion with the engineer who performed the measurements

.

Two sets of measurements were made of the antenna gain.

In the first set, the gain standard was connected to terminal

I via a 12-inch section of guide and the receiver was connected

to terminal IV. Due to high wind conditions during the measurement and other factors, the random error in this measurement

was ±0.4 dB. Since a more accurate measurement was performed

later, the first measurement will not be examined in detail.

The second gain measurement was done at the outputs of

the orthomode transducer, ports 0 and 0'. The standard gain

horn was mounted on the rotator pedestal so that it was

pointing 90° in azimuth away from the dish. When the horn

was rotated into receiving position, it was at approximately

the same location as one quadrant of the test antenna. Four

readings were taken for each position of the horn, and it

was then changed to another quadrant and four more readings

taken. The resulting sixteen measurements were averaged to

give one value for received power ratio which was used in the

gain calculation.

Each power ratio measurement was made using the instrumentation shown in figure 4-3. The measurement procedure consisted

of placing the test antenna in the receiving position, connecting the load to its output port, and adjusting the rotator for

peak received signal. The gain of the receiver was then adjusted

for a zero dB reading on the SWR meter. The standard gain horn

was then rotated into position, and the load connected to its

output port. The rotator was again positioned for maximum received signal, and the change in signal level was read on the

SWR meter. The test antenna was rotated back into receiving

67
68
position, the load replaced on its output port, and the SWR

meter read again. Values of power ratio were therefore

obtained going from test to standard and from standard to

test, and these two values were averaged to reduce the effect

of drift and random error.

The data obtained from these measurements are:

f = 13.9 GHz

Gain of Standard = 10 log G' = 24.10 dB

Power ratio (average of 16) = 10 log P^/P^ = 17.0 dB

Separation distance, d = d' = 1432 m.

= 0. 05

t = 0. 03 to 0. 05

= 0. 05

P-p 1 = 0. 01 to 0. 03

Pgl = 0. 01 to 0. 03

= 0. 08 to 0. 10

Since the same load circuit, consisting of the output

attenuator and mixer, was used with each antenna, and no

waveguide was used between the antennas and the load,

equation (3-17) becomes,

p, Ci-|r„|')|i-r'r |2 | i-p p| ^ (i+| 1 2) ^'^ g

-f = T — (4-2)

Pd ^l-lTgl') |l-rjJ2 |l-p^p' |'(i+|p|') G'

The sources of error in determining G are then as follows:

1. Error in Measuring Power Ratio. The manufacturer specifies

the error in the receiver to be ± 0.25 dB. This is also about

the error which would result if the uncalibrated attenuators

were used to measure the power ratio.

2. Gain Standard Error. Since an uncalibrated gain standard

was used, its error is estimated to be ± 0.25 dB.

69
3. Distance Error. The long-range distance used makes

probable distance errors insignificant.

4. Transmission Line Mismatch. If the amplitude and phase

of each reflection coefficient were known, a complete correction could be made for the mismatch. Since only the magnitudes are known, we can estimate a worst case error of ± 0.04

dB due to mismatch.

5. Polarization Mismatch. The source antenna and standard

gain horn have axial ratios of 30 to 40 dB. Due to the crosstalk in the first circulator, the axial ratio of the test

antenna is only 20 dB. This combination of polarization ratios

would produce an error of 0.06 dB.

6. Unequal a's for the Transmission Line. This error does not

apply for this measurement because a was the same for both

antennas

.

7. Multipath Error. The multipath effect is reduced by

moving the horn to the four different positions and averaging

the results. A residual multipath error of ± 0.05 dB is

probable

.

8. Near-Zone Error. The very long-range distances again

make this error negligible.

9. Random Error. From the sixteen measured power ratios for

one gain computation the random error was ± 0.05 dB

.

10. Ground Reflection Error. In the comparison technique this

error occurs only if the two antennas have significantly different patterns. It was considered negligible here.

The resultant effect of these errors is summarized

in Table 4.3. This error could be reduced without further

measurement on the S-193 antenna by calibrating the gain standard and the detector -rece iver used to measure the power ratio.

If this were done, the gain error could be reduced to about

± 0.15 dB.

70
Table 4.3 Summary of Errors in Gain Measurements .

Source of Error Error in Gain (dB)

CI) Power Ratio Measurement + 0 .25

(2) Standard Gain Horn Gain + 0 .25

(3) Distance Measurement + 0 .00

(4) Transmission Line Mismatch + 0 . 04

Polarization Mismatch + 0 .06

unequal ot s

+ 0 . u u (7) Multipath Signals + 0 .05

(8) Near- Zone + 0 .00

(9) Random Error +

0 .05

RSS = + 0 .37 dB

71
4 . 3 Pattern Measurement, Beam Efficiency, and Directivity

of the S-193 Antenna

4.3.1 Introduct ion

The purpose of the pattern measurement is to determine

the beam efficiency and directivity, and to use the directivity

with the previously measured gain to determine the antenna

efficiency (loss)

.

The following notation will be used in this section to

refer to measured and computed parameters.

G = antenna gain in the boresight direction.

D = antenna directivity in the boresight direction.

$'(a,S) = radiation intensity (power per unit solid

angle) transmitted by the antenna in the direction defined by the angles a and 3.

$^ = radiation intensity in the boresight direction.

Prp = total power radiated by antenna.

P^ = power radiated in main beam.

Pg = power radiated in all side and back lobes.

P^ = net power delivered to antenna input.

£ = antenna beam efficiency,

n

= antenna efficiency (loss) .

Q. = solid angle.

AZ = rotator mount aximuth angle.

EL = rotator mount elevation angle.

Since only relative pattern measurements are made and

required to compute beam efficiency and directivity, we

may use relative rather than absolute values for the above

power quantities. Using the radiation intensity in the

boresight direction as the normalization factor, and denoting

the absolute quantities by primes, the relative quantities

are

72
o _ 1, (4-3)

P P=_I p=J!l p =

O -, O

_s (4-4)

(4-5)

The $ quantities are dimensionless , and the normalized powers

have the units of steradians.

In terms of the above quantities, the following relations exist.

477 $

G

=

47T

477 $

, D =

477 P^

Tl = P P — = - £ = — m

P + Pe

m S

m

1

-

= eP^, Pg = (l-e)P^, Pt = ^S'

(4-6)

(4-7)

(4-8)

The errors in e and D due to the errors in the two partial

powers are

de _ (l-£) rdP

dP

eP

dD

D

T

dP

m

m

dP.

— dPc; = (1-e)

P^T

m

dPg]

f dP

m

m

dP

+ (1-e)

m

(4-9)

(4-10)

For antennas with e > 0.90, the error in side lobe power has

little effect on the directivity, and the effect of errors

in both partial powers on the beam efficiency is reduced

by the factor (l-£).

73
4.3.2 General Measurement Approach

The first step in the measurement is to define a set

of coordinate axes which are fixed in the antenna. The

vector components of the E-field are then defined with

respect to these coordinates, and the scheme used to measure

these components must be consistent with the chosen coordinate

system. In other words, the axes and angles defined in the

antenna coordinate system will be appropriate for a specific

type of rotator (AZ/EL, EL/AZ or model mount) and orientation

of the antenna on the rotator. The same angles will probably

not be appropriate if the type of rotator or antenna orientation on the rotator is changed.

Let us define two coordinate systems, one fixed in

space and denoted by 0 X Y Z, and one fixed in the antenna

and denoted by oxyz. The Y and Z- axes of the space system

are shown in figure 4-4. The X-axis is coincident with the

elevation axis of the azimuth/elevation rotator used by

the contractor. If the antenna is to be placed on the rotator

as shown in figure 4-4, then the azimuth rotation will always

rotate the antenna about its own y-axis (except for a slight

parallax error) . One angle in the antenna coordinate system

should therefore be defined as a rotation about the y-axis.

The angle a shown in figure 4-5 is this angle. The

angle 3 is defined as a rotation about the x' axis (which

becomes the x-axis for a = 0) . Every direction of propagation

denoted by the propagation vector k(a,3) relative to the

antenna is defined by these two angles a and 3 through the

relations,

~ I— I ^ ^

= |k| sin 3 |k|= il (4-11)

k = I k I cos 3 cos a. At a large distance from the antenna, the total electric

field transmitted by the test antenna is contained in the plane

74
Y

1

Figure 4-4, Rotator with Space and Antenna Coordinate

75
Figure 4-5. a-3 Coordinate System Used with the S-193 Antenna

76
of and e_g , and the components o£ E will be denoted by

E (a, 3) and E„(a,3). The unit vectors e and e„ are related

to the unit vectors in the x, y and z-directions by the

relations,

e = cos a e_ - sin a e_ (4-12)

e_o = - sin a sin 3 e_ + cos 3 e_ - cos a sin 3 e_ . (4-13)

p X y z

If the antenna is placed on the rotator as shown in

figure 4-4 and the rotator moved through the angles,

azimuth = -a, elevation = -3, it is evident from figure 4-5 that

the vector k(a,3) will be coincident with the space T-axis;

e_g will be coincident with the space Y-axis; and e^ will

be coincident with the space X-axis. If we let and Sy

denote the far-field on-axis X- and Y-components of the E-field

from the source antenna, then the signal received by the test

antenna will be given by

b^(-a,-3) = C[SYEg(a,3) - S3^E^(a,3)]

= C'E^(a,3) [l-PsP^(a,3)] , (4-14)

where p^p and Pg are complex polarization factors given by

h E^(a,3)

Pg = — , P.p(a,3) = , (4-15)

Sy EgCa,3)

C is a constant for fixed separation distance, and

If either polarization factor is zero, then the output

signal is proportional to the 3-component of the electric

field in the direction defined by a and 3- Since in most

cases neither factor is zero, the term, 1 - pgPrj,(a,3),

represents an error in the measurement of E^ due to cross

polarization.

77
Since only relative power patterns are to be measured,

b^(-a,-3) is normalized by the power in the boresight direction, giving

b^(-a,-3) ^|Eg(a,e) [l-PsP^(a,3)]

|Eg(0,0) [1-P5P^C0,0)]

(4-16)

Measurement of for a = 0 to 360° and 3 = +90° to -90°

can yield complete relative power patterns for the 3-

component of the field if the polarization factor is unity.

If the source antenna is now rotated about its axis by

90°, the normalized received signal will be given by

|E (a,3) [1 + p^/pT,Ca,3)] |'

. • B^(-a,-3) = — ^—^ (4-17)

|Eg(0,0) [1 - P5P^(0,0)] |2

Measurement of B2 for the same range of angles as B-j^ will give complete relative power patterns for the a-component

of the electric field. These will also be in error due to

the polarization error factor unless the amplitudes and

phases of pg and prp(a,3) are known.

In the following discussion, the polarization error

factors in (4-16) and (4-17) will be neglected. This is what

usually done, and what the contractor did in determining the

radiated powers from the measured data. The error caused by

this assumption will then be evaluated in the section on

errors

.

The total and main beam powers contained in the 3-

component of the field are then given by

27T 7T/2

P-Pg = / / B^(a,3) cos 3 d3 da, (4-18)

o -Tr/2

and

P

g = / / B^(a,3) cos 3 d3 da, (4-19)

main

beam

78
with similar relations for the a-component

.

Since measurements are made at discrete points, the

integration is carried out by an approximate numerical technique

such as the trapezoidal rule. If we assume that B-j^ was measured at uniform spacings in the a and 3 directions given by

Aa = —, a. = iAct, A3 = J, 3j = j A3 , (4-20)

then the total power is given by,

^ 2 N M

P = ^ I I B^(a-,3i) ^i- • C4-21)

NM j=li=l

4.3.3 Measurement Procedure used by the Contractor

The last section has briefly described the steps which

should be followed to obtain beam efficiency and directivity

from measured power patterns. The actual procedure used by

the contractor on the S-193 antenna is a modification of the

described procedure, which in some cases has introduced errors

into the results. The steps in the measurement procedure will

now be described for the case of the vertical output port. The

case for the horizontal port is similar. These measurement

procedures and some of the data have been obtained primarily

from discussion with the engineer who performed them. There

is very little documentation of the measurement procedures.

The coordinate system definition for the antenna is such

that the y-axis is in the direction of the principal component

of the electric field in the boresight direction. The z-axis

is along the boresight direction, and the x-axis is orthogonal

to y and z. The angles a and 3 are defined as in figures 4-4

and 4-5 with the y-axis as the a-axis.

For future reference, it will be helpful to represent

the range of directions defined by a and 3 in a rectangular

coordinate system, with a ranging between -tt and it, and 3

79
ranging between -7t/2 and 7t/2 as shown in figure 4-6. The

numbering o£ the quadrants will be used to identify the

regions over which digital and analogue data were taken.

This designation of direction space by a quadrant number is

the same as was used by the contractor in their reports. It

must be kept in mind that this diagram represents directions

with respect to the antenna coordinate system and not the

space system. Therefore, to measure the patterns in quadrants

2 and 3 which correspond to negative values for 3 and k^.

,

without reorienting the antenna on the mount, the elevation

angle of the rotator mount is positive.

Table 4.4 Elevation Increments in Pattern Measurements

Elevation Angles Elevation Angle Increment

0°-5° 0.5°

6°-10° 2.0°

10°-20° 5.0°

20°-80° 10.0°

The antenna was placed on the azimuth/elevation rotator

as shown in figure 4-4 such that for the azimuth and elevation

angles both equal to zero, the space and antenna coordinate

systems were coincident. (Actually due to physical limitations, the origins cannot be made coincident, and corresponding

axes of the two systems are only parallel.)

Due to large ground reflections when the antenna was

pointed towards the ground (negative elevation angles) , reliable

data could only be taken for positive elevation angles. There

were also significant reflections on one side of the range,

and this limited the motion of the mount to positive (counter

clockwise) azimuth angles. The result of these two restrictions was that digital data were taken for only one quadrant of

the mount's total motion without reorientation of the antenna

on the mount. With the antenna oriented as in figure 4-4,

rotation of the mount in positive azimuth and elevation angles

80
2

0

QUADRANT 4 QUADRANT 1

QUADRANT 3 QUADRANT 2

0 ^

Figure 4-6, a-P Direction Space and the Four Measurement Quadrants

81
produced data only in quadrant 3. The elevation angle was

incremented and cuts taken along lines of constant elevation.

The increments varied with the distance from boresight as shown

in Table 4.4 and in figure 4-7. In addition to the digital

data taken in quadrant 3, analogue data were taken for both

polarizations in quadrants 3 and 2. These data were taken at

the same time as the digital data but extended 30° into quadrant

2 for each elevation step. On the basis of the analogue data it

was assumed that the patterns were identical (or at least that

the total powers were identical) in quadrants 3 and 2.

Figures 4-8 and 4-9 are samples of the analogue plots in

quadrants 3 and 2. From these and similar plots contained

in the "Calibration Data Report, Flight Hardware, Volume 11,"

it appears that the patterns are quite symmetrical between

3 and 2. For amplitudes down to about -30 dB the differences

are only a few tenths of a dB , and there is general agreement

between -30 dB and -50 dB. Thus it would appear that the

assumption of 3-2 symmetry is fairly good.

No analogue plots or digital data have been available to

justify an assumption of symmetry between quadrants 1 and

4, and yet this is implicit in the approach which was

made. Perhaps some analogue plots were taken which showed

the same basic characteristics as those in figures 4-8 and

4-9, or else the 3-2 symmetry was assumed sufficient to

justify 4-1 symmetry. Whatever the reason, we do not have

sufficient information to evaluate this assumption.

With the assumption of 3-2 and 4-1 symmetry, and data

in quadrant 3, the total power pattern can be obtained by

either justifying 2-1 and 3-4 symmetry or obtaining digital

data in quadrants 1 or 4.

With the antenna in its initial orientation on the

rotator, as shown in figure 4-4, pattern measurements in

quadrants 1 or 4 would require pointing the antenna towards

82
0

6°

10°

30°

80'

6

QUADRANT 4 QUADRANT 1

—— — —

QUADRANT 3 QUADRANT 2 n T P T X A 1 0 UlblTAL &

ANALOGUE

ANALOGUE ONLY

INITIAL

ANTENNA

ORIENTATION

30'

0 —I

6°

10°

30°

80'

QUADRANT 3

QUADRANT 2

DIGITAL &

ANALOGUE

QUADRANT 4

QUADRANT 1 ANALOGUE ONLY

SECOND

ANTENNA

ORIENTATION

Figure 4-7. Measurement Schemes for the Two Antenna Orientations

83

Figure 4-9. Pattern Cuts for the S-193 Antenna
the ground. Because of the ground reflection problem, the

antenna was reoriented on the rotator so that data could be

obtained in quadrants 1 and/or 4 without pointing the antenna

towards the ground. The reorientation consisted of rotating

the test antenna and the source antenna about their z-axes

by 90° in a clockwise direction as viewed from the rear of

the test antenna. In this orientation, azimuth cuts with

positive elevation angles provided data in quadrants 2 and 1.

Counter-clockwise rotation in azimuth and up in elevation

would provide data from quadrant 2 in the "low reflection

region" of the range.

IVhile the reorientation did make low-reflection measurements possible in quadrant 2 and close to boresight in

quadrant 1, it also produced another small problem. The

problem is, that due to the reorientation of the antenna

on the mount, only principal plane cuts give strictly the

same field components as were measured before reorientation

along similar lines in "direction space." For instance, if

the source antenna is linearly polarized in the 7-direction

for the initial antenna orientation, azimuth cuts at a constant elevation angle will yield patterns of the 3-

component along lines of constant 3 (along straight lines

in the direction space representation of figure 4-6). When

the test antenna is reoriented as described above, and the

source antenna is linearly polarized in the X direction, azimuth

cuts at a constant elevation angle do not measure the gcomponent along lines of constant a. The component measured

is a combination of a and 3, and the path in the direction

space of figure 4-6 is curved. The total radiated power in

quadrant 2 can be correctly determined from the sum of the

powers in the two measured components but, strictly speaking,

the measured major component powers in quadrants 2 and 3

should not be combined to give the power in the principal

component. The same is true for the cross component power.

86
Fortunately, for this antenna with its narrow beam, the

effect due to reorientation is small over the significant

part of the pattern. If we denote the measured components

and rotator angles in the reoriented case by primes, (E^, E^,

AZ ' , EL'), and similar quantities in the original orientation

without primes, we have

e' = -E^Ccos^ EL'+sin^ EL' cos AZ ' ) - E sin AZ sin EL

3 3

^ a (4-22)

for the case where

EL' = AZ and AZ ' = EL. (4-23)

When either EL' = 0 or AZ ' = 0, = E_ ; even at the edges

of the significant part of the patterns where EL = AZ - 12'',

E^ = -0.9990 Eg + .04 E^. (4-24)

Since the difference between E^ and Eq is small, and only E_

p p p data is available in quadrant 2, the following discussion

will assume that they are equal. We will then estimate the

error due to this assumption in the section on error analysis.

Analogue azimuth cut plots were taken in this new orientation at 0.1° elevation increments between zero degrees and

6° elevation, over the range from -5° to +5° azimuth. This

was done for both polarizations, apparently to determine

the symmetry between quadrants 2 and 1. Samples of these

plots are shown in figure 4-10. It is apparent from these and

similar patterns at other elevation angles that there is

significant non-symmetry here for both measured components.

For the principal component, amplitudes are generally higher

in quadrant 2 than in quadrant 1. This is especially true

for azimuth angles greater than ± 1° where some differences

are 5 dB or more. The null of the cross component is shifted

off boresight into quadrant 2, and the peak is also slightly

lower in quadrant 2. Therefore there is a significant difference in the cross component powers in these two quadrants.

87

Again there are no patterns available between quadrants

3 and 4. Apparently it was assumed that the symme tryproperties there were the same as between 2 and 1. Even

with this assumption, the significant 2-1 non-symmetry would

require that digital data be taken at least in quadrant 1.

However, digital data were not taken in quadrants 1 or 4.

Instead digital data were taken in quadrant 2. In view of the

symmetry shown by figure 4-9, these data should give results

quite similar to that obtained in quadrant 3. But without

any data in quadrants 1 or 4, 2-1 and 3-4 symmetry must be

assumed to obtain total powers and beam efficiency, and this

symmetry assumption is clearly not justified. It would have

been much better to rotate the antenna on its axis by 180°,

rather than 90°, to obtain actual a- and |3-component data

in quadrant 1. Since this was not done, we can expect a significant error due to the assumed symmetry. The magnitude

of this error will be estimated in the error analysis section.

With the necessary 2-1 and 3-4 symmetry assumptions,

the total power in each component is then given by twice

the sum of the power for that component in quadrants 2 and

3. Thus,

Since the limits of integration (or summation) for each partial

power are different than for the total spherical integration

implied in (4-18) and (4-19), these quantities are modified

slightly to give

This integral was evaluated by the trapezoidal rule. Summation

over the azimuth cuts yields

TT Tr/2 = / / B^(AZ,EL) cos EL dEL dAZ

.

(4-26)

(4-27)

89
and further summation over the elevation increments gives

N-1

In the above equations,

7T AAZ = -, AEL = —, AZ^ = iAAZ, EL. = jAEL,

M 2N

(4-28)

(4-29)

and S2g(ELj) is the result o£ summing one azimuth cut as expressed in (4-27). In the measurements, both the azimuth

and elevation measurement intervals varied over the area of

measurement (see Fig. 4-7). This results in a further modification of equations (4-27) and (4-28) to account for the end

points and AAZ or AEL of each interval. For instance the

summation for each cut where there are two spacings is given by

23 (EL.) = cos EL

^[B(0,ELj)-HB(AZ^,ELj)] AAZ.^

2

[B(AZj^,EL.)+B(7T,EL.)]AAZ2

2

M-1

+ AAZ . Z BTAZ( .

. .EL^ , .) + AAZ^

i=l ^

^ where (4-30)

,EL,)

AZ

AAZ.

M

AZ

AAZ,

M

M K

(4-31)

A computer printout of the summation for the zero degree

elevation cut in quadrant 2 for the horizontal port was provided by the contractor. The first page of this printout is

shown in table 4-5. The power column is identical to B^(AZ^,ELj),

and the "weighted P" column is equal to the power times

AEL cos EL for that cut. The AEL factor has therefore been

included in the summation of (4-27) rather than in (4-28).

Although the AEL for this run was 0.5 degrees, a value of 0.25

90
Table 4.5 Computer Summary of Trapezoidal Rule Integration

ELEVATION ANGLE =0-0 DEGREES

FOR DOMINANT POLARIZATION

AZIMUTH

ANGT F DATA DFC J-/ J_f \^ TRFT -L U 1^ Lj 1^S POWER WEIGHTED P A r r HM

. 083 -1 - .07 .98363 . 24591 .02049

.167 -1 - .07 .98363 .24591 . 04098

.250 -1 - .07 .98363 .24591 . 06148

. 333 -4 - .29 .93611 .23403 . 08147

.417 -7 - .50 .89088 .22272 .10051

.500 -9 - .65 . 86195 .21549 . 11876

.583 -13 - .93 .80638 .20172 .13615

.667 -21 -1.51 .70707 . 17677 .15192

.750 -25 -1. 79 .66189 .16547 . 16618

.833 -33 -2.37 .58002 .14500 .17911

. 917 -41 -2 . 94 .50827 .12707 .19045

1.000 -55 -3.94 .40340 .10085 .19995

1. 083 -61 -4. 37 . 36536 .09134 .20796

1.167 -70 -5.02 . 31493 .07873 .21504

1 .250 -82 -5.88 .25834 .06458 . 22101

1.333 -99 -7.10 .19513 . 04878 .22574

1.417 -109 -7. 81 .16544 . 04136 .22949

1. SCO -124 -8 . 89 .12915 .03229 . 23256

1.667 -138 -9.89 .10251 .02563 .23739

1.750 -155 -11.11 .07743 . 01936 .23926

1.833 -168 -12 . 04 . 06247 . 01562 .24072

1.917 -181 -12 .97 . 05041 .01260 . 24190

2 .000 -196 -14 . 05 .03935 .00984 . 24283

2 . 083 -213 -15 .27 .02972 .00743 . 24355

2 .167 -227 -16 .27 .02359 .00590 .24411

2.250 -241 -17.28 . 01872 . 00468 . 24455

2 .333 -258 -18 .49 . 01414 .00354 . 24489

2 .417 -282 -20.22 .00952 . 00238 . 24513

2 .500 -294 -21. 08 .00781 .00195 . 24532

2 . 583 -312 -22 .37 .00580 .00145 . 24546

2 . 667 -333 -23.87 .00410 .00103 . 24556

2.750 -360 -25.81 . 00263 .00066 . 24563

2.833 -373 -26 .74 .00212 .00053 .24568

2 . 917 -393 -28.17 . 00152 . 00038 . 24572

3.000 -421 -30 .18 .00096 .00024 . 24574

3. 083 -445 -31 .90 .00065 .00016 . 24576

3.167 -457 -32 . 76 .00053 .00013 . 24577

3.250 -472 -33. 84 .00041 .00010 . 24578

3. 333 -486 -34.84 .00033 . 00008 . 24579

3.417 -504 -36 .13 .00024 .00006 . 24580

3. 500 -515 -36 .92 .00020 .00005 . 24580

3. 583 -523 -37.49 .00018 .00004 . 24580

3. 667 -525 -37.63 . 00017 .00004 . 24581

3.750 -515 -36 .92 .00020 .00005 . 24581

3.833 -504 -36 .13 .00024 .00006 . 24582

3. 917 -490 -35 .13 .00031 .00008 . 24582

91
was used, which apparently is to account for the fact that this

sum is for one of the end points in the sum over the elevation direction.

To obtain the values in the "accum" column, we multiply

the weighted P values by the appropriate AAZ and add to the

preceding sum. This column represents the value of the

summation as a function of the azimuth angle and points up

one significant error in this summation. The error is that

the end points of the summation interval have not been handled

properly. Equation (4-30) states that the powers at the end

points of each subinterval should be divided by two and

then multiplied by the AAZ for that subinterval before

being summed. It appears from the computer printout of

table 4.5 that the first point of each cut, the B(0,ELj) point,

has not been added in at all , and that the boundary point

between sub intervals , B(30°,ELj), and the end point, B(180,ELj),

have been added in as regular points of one subinterval. The

engineer who performed the measurements and computations has

indicated that the azimuth angle given in column 1 of table 4.5

is actually one increment ahead of the data. Therefore, the

first row is actually for AZ = 0°, and instead of being left

out, the first point has been added in as a regular point.

Each cut summation is therefore in error by the amount 6,

given by

^sumtELj) = S-CELj) - SCEL.)

sum

B(0,EL.)AAZ. B(30,EL.) (AAZ^-AAZ.)

2 2

B(Tr,EL .) AAZ^'

+ 2 i

(4-32)

AELj cos ELj

Since B(30,ELj) and B(7T,ELj) are both about 50 dB below the

peak power, the only significant term in (4-32) is the one

92
involving B(0,ELj). This term is quite significant, however,

since for the principal polarization B(0,ELj) is the largest

point of each cut. The error for each cut can be estimated

by reading the value of B(0,ELj) from the analogue plots and

computing the error from (4-32). The total error for that

quadrant is the sum of the errors for each cut. For the

case of quadrant 2 for the vertical port, the reported results

of integration are

= 0.8373 (degrees)^

^2a " 0-04397 (degrees) 2

and the estimated error due to improper summation of the

first points is

5. „ 9o = 0.047 (degrees)^

sum 2 3

K b J

rr.

-y = 0.0004 (degrees)^

sum 2a & j

More will be said about this error in the section on error

analys is

.

4.3.4 Beam Efficiency Calculations

By the usual definition, the beam efficiency is the

ratio of the power in the main beam to the total radiated

power

,

P

e = —, (4-33)

Pt

where the main beam is defined as the region from boresight

to the first minimum of the principal polarization. The contractor has calculated as already described by trapezoidalrule integration of the measured patterns. They have not,

however, used the correct boundary to calculate P^. To obtain

a main beam power, they have performed a second integration

93
which employs a different set of angles than a and 3 of the

measurement system. The new angles are the usual spherical

angles 6 and (j). The z-axis is the 4)-axis with (j) measured from

X toward y and 0 measured from the z-axis as shown in figure

4-11. The measured data were then transformed from the a,

3

system to the e,c|) system. A Gaussian quadrature integration

was then used to compute the power as a function of the off-axis

angle 9, and it is this quantity which they have used to compute an approximate beam efficiency. However, this approach

gives the correct beam efficiency only if the main beam boundary

is at a constant angle from boresight. Figures 4-8 and 4-10

show that the minima are at about 2° in one plane and are

greater than 3° in the other. Because of this, a single number

has not been given as "the" beam effiency, but the contractor

provided the graph in figure 4-12 which he termed the beam

efficiency as a function of angle from boresight. For this

they have used the ratio of power in the main polarization to

total power in both polarizations.

For purposes of error analysis, we will use 2.5° off

axis as the "main beam" boundary to obtain a single number

representing the beam efficiency, and then estimate the error

due to the actual non-circular boundary.

4.3.5 Error Analysis

First, the results of the measurements and calculations

are summarized for ease of reference. The measurements were

made at a frequency of 13.9 GHz. Total powers were obtained

from pattern measurements and integration in quadrants 2 and

3 and the symmetry assumptions previously discussed. For the

vertical port the results of the pattern integrations are

summarized in Table 4.6.

94
Figure 4-11, Spherical Coordinate System Used in the Analysis

of the S-I93 Antenna

95
o

Ql.

t—o

tJLl o

LlJ CL<:

CO

_l

o

o

o

o

Q.

1 00

90

80

70

60

50

r: 40

30

20

10

0

I I CROSS POLARIZED POWER = 6.7%

VERTICAL PORT

0 1 2

ANGLE FROM BORESIGHT IN DEGREES

Figure 4-12. Contractor's "Beam Efficiency" vs Polar Angle

(see page 94)

96
Table 4.6 Results of Pattern Integration

for Power in Each Quadrant

Quadrant Component Power (degrees)^ Power (Steradians)

2 3(dominant) .8373 2.550 x lO"^

2 a(cross) .0440 0.134 x lO"^

3 6 .8038 2.448 x lO'^

3 a . 0756 0.230 x lo"^

P^, = 2(P^„+P__+P^ +P_ ) = 10 . 724 x 10 '"^ steradians

T ^ 23 33 2a 3a

From figure 4-12 and estimates of the cross polarized power

within 2.5° of boresight,

P„ = 0.845 P^ + P = 9.547 x lo"^ steradians.

m r ma

The beam efficiency is

P

e^, = — = 89.0%

P

for both polarizations, and

e = JUi = 84.5%

3

p^T

for the principal polarization.

Using the computed total power and (4-6), the directivity

obtained from pattern integration is

Dp = — = 40.69 dB.

P^T

Using the measured gain of 41.1 dB ±0.37 dB and the efficiency

of -0.32 dB t*25 ' directivity is

= - = 41.42 dB""^*^?^ dB.

G ri -0.51

The errors which will be considered are due to pattern

non - symme try , non-linear polarization of source antenna,

97
receiver system non-linearity, multipath interference, integration errors, incorrect main beam boundary, and reorientation

of the antenna.

To estimate these errors we will use a slightly different

approximate formula for the integral in (4-18) which employs

the spherical angles 6 and previously discussed. Let us denote the solid angle between the circular boundaries

e = a and 6 = b by , , which is given by

2Tr b n . = f f sin e de d(j) = 2tt[cos a - cos b] . (4-34)

* o a

The total power for one component is then given by

where B , is the average value of the relative power pattern

within the solid angle Q, , , and the summation is taken over

the full 47T steradians. The values of B , can be estimated

a , b

from the analogue patterns and from the Gaussian quadrature

integration results. The results of this integration are

shown in figure 4-12 which is a plot of the function

PrO)

y(e) E ^ . (4-36)

^T

By using the total power obtained from the first integration

and the plot of the y (Q) function, the average power/solid

angle for one component is given by

(Y(b) - yW]V^

F_ . = (4-37)

a,b

For angles greater than 3° and for the cross component,

^a b estimated from the analogue plots.

Table 4.7 gives the pertinent data for the vertical port.

With the values of B. , determined, we can now estimate how

a . D

98
various sources of error could change the B , 's and therefore

a J D the calculation of beam efficiency and directivity.

Table 4.7. Estimates of Average Power Per Unit Solid Angle

Within Solid Angle n^^^.

Average

'olar Angles Solid Power Per

a ,b

Power in

in Degrees Angle Solid Angle in Solid Angle

a b

a ,b

dB

-4

^ of

Principal Component

0 1 9.5x10"^ .6434 -1.91 6 .113 57 . 0

1 2 28.7x10"^ . 0953 -10.21 2 .735 25.5

2 3 47.8x10"^ .0079 -21 . 0 0.375 3 . 5

3 4 66.9x10'^ . 0021 -26.8 0.139 1.3

4 5 86 . OxlO"^ .0010 -30 .0 0 .086 0.8

5 6 105 .1x10'^ .0005 -32 . 9 0 .054 0.5

6 30 0 .807 42 . 5x10"^ -43.7 n 1 A t U . o 4 o

7. 9 30 90 5 .44 4. 7x10'^ -53. 2 0.257 2 .

4

90 180 6.28 l.OxlO"^ -60.0 0 064 0 .

6

Cross Component

0 2 38 . 3x10"^ .0081 -20.9 0 .311 2.9

2 4 114 .8x10"'^ .001 -30 0 .118 1.1

4 180 12 .55 IxlO"^ -60 0.129 1 . 2 TOTALS 10.724 100 .0

1 . Pattern Non-Symmetry

One of the largest sources of error is due to the significant non -symmetry between quadrants 2 and 1 or 3 and 4.

The magnitude of this error is estimated by a close examination of the analogue plots like those in figure 4-10. From

99
these plots we can estimate the ratio of B , in quadrant 2 a , D to the same quantity in quadrant 1, denoted by B , , and therefore estimate the resulting change in the partial and total

powers from (4 -35) . The results of this comparison are summarized in the

table 4.8.

Table 4 .8. Change in Power Due to Non -Symmetry.

Polar Angle Power in

Polar izat ion in Degrees Estimated Solid Angle

TTl n pi r~i "t" aa hu

1 B /B

a ,b a ,b

pr 1 Ay1J. U a ,b

Principal 0 1 . 98 6.051

1 2 . 63 2.229

1 f 2 3 .79 0 .336

t» 3 4 . 79 0 .125

II 4 180 1.00 0 .804

Cross 0 2 1.9 0.451

ri 2 4 .8 0.106

II 4 180 1.0 0.129

10 . 245

This indicates that the beam efficiency would be in error

by +2% and the directivity in error by -0.2 dB due to the

lack of symmetry in the 2-1 and 3-4 quadrant pairs.

There will be an additional error due to the non-symmetry

between quadrants 1 and 4. The apparent 1-4 symmetry is

probably about the same as the 2-3 symmetry, and therefore

this error would be about equal to the measured difference

between quadrants 2 and 3. Since AP^ was 0.102 and AP was

0.096, the worst case estimate for the difference would be

APrp = ± 0.198. This would result in a change in e of ± 0.81,

100
and a change in D of ± 0.08 dB.

2 . Non-Linear Polarization of Source Antenna

This error is due to the polarization factors in (4-16)

and [4-17). Since the phases of the polarization ratios are

not known, we will assume a worst case phase. The magnitude

of pg will be taken as 0.02 which corresponds to an axial

ratio of 34 dB. The magnitude of will be estimated from

the relative amplitudes of the principal and cross polarized

patterns

p^Ca,3) 2 _ E2C-cx,-6)

B^C-a,-3)

C4-38)

From these estimates of p^^ and Pg, and the polarization

factors I 1 - Pgp^ (a , 3 ) I ^ and 1 1 + pg/ p-p (a , 3) | ^

, the changes in

B , are estimated. These are tabulated with the error

a , b

due to receiver non-linearity in Table 4.9.

3 . Receiver Non-Linearity

If we assume a systematic error in the measured power

patterns due to a receiver calibration error equal to

0.02 dB/dB, then the error in B , can easily be estimated.

3. y 0

Although an estimate of the receiver linearity is not given

in test reports, the error assumed here is reasonable for

the type of receiver used.

101
Table 4.9. Errors due to receiver non-linearity

and polarization mismatch.

Principal Polarization

Polariza

Pol ar Angle Error in Rece iver t ion

in Degrees a,b Error Error

a b dB APxlO 1 Drr. 1

j 1 1 - DmD<- 1 ^ APxlO"

0 1 0 . 04 0 .05 0.1 1 .004 0 . 02

1 2 0.2 0.10 0 .3 to 10 .0 1 . 08 0.18

2 .5 0.4 0 .03 0 .2 to 5.0 1 . 08 0. 03

3 4 0.5 0 .01 0 .1 to 2.0 1.1 0 . 01

4 - 5 0.6 0 .01 1 1.04 0 . 003

5 6 0.7 0 .007 1

30 0.9 0 .04 1

30^ 90 1.1 0 .04 1

90 180 1.2 0 .01 1

Cross Polarization

APxlO 1+Ps/Pxl^ APxlO

0 2 0.4 0 .04 0 .1 to 10 1

.

10 0 .04

2 4 0.6 0 .01 0 .1 to 5.0 1. 04 0 . 004

4 180 1.2 0 .03 1

TOTALS ± 0 .38 ± 0 .29

The receiver error changes e by ± 1.3% and D by ± 0.15 dB,

while the polarization factors change e by ± 0.03% and D

by ± 0.12 dB. The error due to the polarization factor

might be reduced if data were taken in all four quadrants.

The phase of prp(a,3) would probably differ by 180° between

each quadrant due to the phase change of the cross component

102
at its minimum point. This would make the polarization

factor, |l-prpPg|^, greater than unity in one quadrant, and

less than unity in the other, thereby reducing the total

effect of the polarization factor.

4 . Multipath Interference

To estimate the effect of multipath, patterns were taken

with the antenna in its original orientation and then rotated

about its axis by 180°. Differences of 0.1 to 0.4 dB were

observed over the main beam, and between 0.4 and 1.5 dB over

the remainder of the pattern. With the small amount of

information available, it is difficult to estimate the effect

of these errors on the computed parameters. The character

of the error will be similar to the receiver error, in that

it should be small over the main beam and become larger at

low signal levels. There will also be some periodic effect

as the main and multipath signals go in and out of phase,

which will reduce the total effect when integrated. A

reasonable estimate is that the effect of multipath on the

present measurements should be somewhat smaller than the

error due to receiver non-linearity. We will use a Ae

of ± 1.0% and AD of ± 0.10 dB.

5 . Integration Error

The largest integration error is due to the improper

summation of the initial point of each azimuth cut. It was

previously estimated that this error resulted in the power

in one quadrant being 0.144x10 ^ steradians too high. The

total power will therefore be 0.576x10 ^ steradians too

high, resulting in an error in D of -0.24 dB.

There is not enough information about the Gaussian

quadrature integration to determine if a similar or additional

error exists there for the beam efficiency calculation. If

it was done correctly, and does not contain integration

errors, then this above change in would result in an

error in beam efficiency of -5%.

103
Additional integration errors due to the size of the azimuth and elevation increments and the numerical summation should

be on the order of ± 0.10 dB for D and ± 1.0% for e.

6 . Incorrect Main Beam Boundary

This error results from using a circular boundary

(9 = constant) for the main beam when the actual boundary

is not circular. This causes no error in the total power

calculation, and therefore no error in directivity, but it

does cause an error in the computed beam efficiency. It is

apparent from figures 4-8 through 4-10 that the main beam

boundary is between 1.8 and 3 degrees from boresight, and we

have chosen 2.5 degrees to use as the approximate boundary.

The resulting error in P^^ by this approximate boundary can be

estimated by the change in the curve of figure 4-12 between 1.8

and 3 degrees. There is a change of 5.5% over this range.

Since a circular boundary which contains the same power as the actual boundary is between 2.25 and 2.75 degrees, the

error in e due to using the approximate boundary is ± II.

7 . Reorientation of Antenna

A description of how the reorientation of the antenna

changed the measured components was given previously. This

does not produce errors in the total power calculation or the

total power in the main beam. It does produce a slight change

in the power assigned to each component within the main

beam. But since the main beam is so narrow, the change is

very small and can be neglected.

Error Summary

The various sources of error are summarized in the

following table.

104
Table 4.10. Summary of Errors in

Beam Efficiency and Directivity .

Source of Error

N on -Symmetry

Polarization Factor

Receiver Non-Linearity

Multipath Signals

Integration Error

Main Beam Boundary

TOTALS

Error in Calculated

Parameters

±0 .03

±1.3

±1.0

-5±2.0

±1 . 0

-3±2 . 8

AD(dB)

+2±0.13 -0.20±0.13

±0.12

±0.15

±0.10

-0. 24±0.18

0.0

-0.44±0.

3

The final results are then:

Total Beam Efficiency = = 89.0% + 3 ± 2.8%

Principal Beam Efficiency = = 84.5% + 3 ± 2.

Directivity = D = 40.69 dB + 0.44 ± 0.3 dB

4.3.6 Recommendations

The integration error could be reduced a great deal by

correcting the summation of the end points. The program

could be corrected and the data rerun, or the correction

could be computed from the listing of the measured data

and (4-32). If this is done, the results would be about

= 94.0% - 2 ± 2.8%

= 89.5% - 2 ± 2.8%

pD = 40.93 dB + 0.2 ± 0.3 dB.

105
This would make the calculated directivity closer to the

41.42 dB obtained from gain and efficiency measurements.

It would certainly be desirable to obtain data in

quadrants 1 and/or 4 to reduce the error due to non - symmetry

.

It might be possible to read the data from the original plots

like those of figures 4-8 to 4-10, which covered some of the

area in quadrant 1, and thereby obtain data out to at least

5° in azimuth and 6° in elevation. This would give data for

the most significant non-symmetrical region of quadrant 1,

and would reduce the required symmetry assumptions and the

associated error.

Of course the best solution would be to actually make

measurements in quadrants 1 and 4 over the full area and

eliminate any symmetry assumptions.

If the symmetry assumptions could be eliminated, along

with the integration errors, the results would be about

e,p = 92.0% ± 2.8°6

Cq = 87.5% ± 2.8%

pD = 41.13 dB ± 0.3 dB.

4.3.7 Comparison of Gain, Efficiency and Directivity

Due to the errors in the measured gain and in the directivity computed from pattern data, a more accurate efficiency

cannot be obtained from the ratio of gain to directivity.

However, the gain and efficiency can be used to compute a directivity which can be compared with the pattern directivity.

This comparison indicates the consistency of measured data and

error estimates. The directivity obtained from the gain/

efficiency ratio is 41.42 dB, which is within the estimates

of error for the directivity computed by pattern integration.

The best agreement is with the value which has been corrected

for non-symmetry and integration errors. This indicates that

the corrections are fairly close.

106
Another approach to improving the beam efficiency measurements might be to use the gain and efficiency results to

compute the total power. If the gain results were improved

as suggested in section 2.4, this would yield a total power

value with an error of about ± 0.7%. Integration of existing

or new pattern measurements over the main beam would then

provide the main beam power, which would not be affected as

much by sources of error as measurements over the complete

angular range

.

4 . 4 S-195 Radiometer Receiver Error Analysis

The radiometric portion of the S-193 Microwave Radiometer/

Scatterome ter Altimeter System is analyzed in this section.

This analysis includes: (1) a derivation of the noise output

equation based on the radiometer model described in PIR No.

U-1K00-S193-706, and in Specification No. SVS 7846, Revision C,

27 April 1972 , p. 2 -282 ; and (2) an analysis of this model via

the output equation for error in the value of antenna temperature determined. This analysis is not intended to supplant

the contractor's analysis, but is performed as a check on the

previous loss measurements and calculations. An estimate of

the system resolution is given at the end of this section and

should be considered as a limitation to the accuracy of the

antenna temperature determined.

A simplified version of figure 2.7.3.2 of page 2-282 of

the specifications is shown in Figure 4-13 for the mode in

which the receiver is measuring the horizontal antenna output

temperature TH. The symbols in the figure are defined as follows

TH(TV) = antenna temperature as seen at input port H(V)

.

TRF = temperature of the "termination" on the isolated port

circulator D.

Tl , T2 = noise temperatures of references 1 and 2, respectively.

107
UJ

LU (_3 UJ Z z

<c UJ 1—(

1— z ct:

—i

_J UJ UJ UJ o 1— u. > z UJ <

«=c en CQ 1— 1 1 1 D_1— o ca

ZD o o o

CD UJ UJ UJ
TD, TE, TF, TG = temperature of the switching circulators D,

E, F, G respectively.

TN = effective input noise temperature of the TDA.

d,e,f,g represent available power ratios (see section 2) in the

directions indicated for all equations through (4-43)

and represent attenuations (see section 2) for all

equations after (4-43) for circulators D, E, F, G respectively of the thru paths - 0.96.

D,E,F,G represent available power ratios in the directions indicated through equation (4-43), and thereafter attenuations of the isolation paths - 0.001.

G = system gain as an available power ratio.

M = mismatch factor at radiometer processor output which

converts available power output to delivered or net

power output.

EOA = output voltage when system is measuring antenna temperature TH.

EOB = zero offset or baseline voltage.

EOC = output voltage when system is measuring the difference

noise temperature Tl - T2

.

A number of reasonable assumptions which do not significantly

affect the results have been made to ease the calculations.

These assumptions are:

1. TN is the same for each mode of operation of the

receiver (this should be a good assumption since the

antenna and reference sources have comparable reflection

coefficients)

.

2. The mismatch factor M is independent of operational

mode, allowing available powers (rather than net or

delivered powers) to be used at the radiometer processor

output port (rigorously true).

3. The measured values of d, D, e, E etc., remain unchanged from laboratory measurement to final use.

109
4. The gain G remains constant during the measurement.

5. When the circulators are switched, d and D, etc.,

change position. Although this assumption is not strictly

valid, it is sufficiently true for the following analysis.

6. In the numerical estimates, d = e = f=g, D = E =

F = G, and TD = TE = TF = TG are assumed.

Therefore, using the theory presented in section 2.1 of

this report it can be seen that the output noise temperature

PH at the TDA input when the system is in the horizontal mode is

PH=TH'g»d-e+TV«G'd«e+ TG(1 - g

- G)d • e

+ TRF . D • e + TD(1 - d - D) e + TE (1 - e - E)

+ (Tl • f + T2 • F + Tl • F + T2 • f)E/2

+ TFCl - f - F)E + TN (4-39)

Equations can be written in a similar manner when the system is measuring the output noise temperatures PI, P2 , and PR

at the TDA resulting from viewing Tl , T2 , and TR, respectively.

In the antenna mode the output voltage EOA is given by

(EOA - EOB)/G = PR - PH

= TR • f • e + TF(1 - f)e - TH • g • d • e - TG(l-g)d • e

- TD • (1 - d) • e

+ ((TH - TG) • g + (TV - TG) • G + TG) • d • E

+ ((TRF - TD) • D + TD(1 - d)) • E - TE • E

+ (TR - TF) • F • e

- (TV - TG) • G • d • e - (TRF - TD) • D • e

- (TR - TF) . (f + F) • E - (TF - TE) • E, (4-40)

which should be compared with equation (5) in the PIR.

In the calibration mode, the output voltage EOC is given by

K • (EOC - EOB) = PI - P2

(4-41)

= (T1-T2) f (e'G) + (T2-Tl)F(e'G)

,

which compares with equation (6) in the PIR, and K is a gating

constant described therein, G and e are grouped together

110
because they appear naturally together in the analysis. Equation (4-41) is rearranged to obtain eG which is used in equation (4-40).

The isolation terms (those terms involving one or more of

the capital letters D, E, F, or G) in equations (4-40) and

(4-41) are discarded in the contractor's analysis given in the

PIR. By equating the small letters (d , e, £, and g) to their

approximate value of 0.96, the capital letters to the approximate value of 0.001, and the switch temperatures (TD, TE , TF,

and TG) and TRF to their approximate value of 298K, the error

introduced into TH (in kelvins) by discarding these isolation

terms is

9.3 X 10"^(TH - TV) + (0.31, 0.01). (4-42)

The first term in (4-42) results from a cell (a cell on the

earth's surface) polarization and should be negligible. The

first and second values in the last term result from viewing

a 50K and 350K cell, respectively.

Another source of error in determining TH from equations

(4-40) and (4-41) comes from replacing the remaining available

power ratios (d , e, f, g) by attenuations (see section 2.1 for

the definition of attenuation). An estimate of the size of

this error can be obtained by examining the relationship

between the available power ratio and the attenuation of the

three port switching circulators. IVhen this is done the resulting maximum errors in TH are, respectively, 0.02 and 0,

which are seen to be quite negligible.

After removing the isolation terms and replacing the

remaining available power ratios by attenuations (from now on

d, e, f, and g refer to attenuations) the equations given then

reduce to

K(EOC - EOB) = f(Tl - T2)(eG) (4-44)

and

ill
TH = f . TR/d/g +(!-£)• TF/d/g

- (1 - g) . TG/g - (1 - d) . TD/d/g

+ (EOB - EOA) /d/g/(eG) . (4-45)

After these equations are analyzed for errors in TH due to the

various parameters, the following table of errors results:

Parameter Resulting

Parameters Uncertainty Error in TH

TR 0.25K 0 , 26K

TD, TF, TG 0.5K 0.02K

EOB - EOA 0.001 relative error (0.31, 0.01)K

eG 0.0026 (0.80, 0.02)K

d,f,g 0.0023 (1.15, 0.23)K

Probable Error (1.5, 0.3)K

(Quadrature Sum)

(4-46)

The parametric uncertainties leading to the uncertainty

in eG quoted in the above table are tabulated below.

Parameter Resulting UncerParameter Uncertainty tainty in eG

Tl - T2 0.039K 0.00067

K 9.8 X lO"'' 10"^

f 0.0022 0.0023

EOC - EOB 0.001 relative error 0.001

Probable error 0.0026

(4-47)

The analysis of the separate uncertainties in these two

tables is straightforward, and since they do not indicate

results significantly different from the contractor's values,

the analysis is not included here.

The total probable error, DTH , in calculating TH from

equations (4-44) and (4-45) is then the linear sum of the

values given in (4-42), (4-43), and (4-46). This total is

DTH = 1.5K for a 50K cell r. .r.. 0.3K for a 350K cell. ^ ^

112
The theoretical one-sigma resolution, DT , of the S-193

radiometric receiver system (assuming no gain instability) is

approximately [1]

DT = 2-CTH»TH/2 + TR'TR/2 + TN«TN + TH-TN + TR-TN) ^/ (B'T) ^,

(4-49)

where B is the limiting bandwidth (190 MHz) of the system and

T is the integration time constant. The other symbols are

defined in the figure. In this case TN is referred to the

switch input and is taken to be lOOOK instead of 830K as shown

in the figure. For a one-second time constant DT for both a 50K and 350K cell turns out to be approximately 0,2K. This

value indicates that, assuming a Gaussian distributed output

and no gain fluctuations, the output TH lies within ± 0.2K of

the true averaged output with 681 probability. This 0.2 value

is a lower limit to the system and it has been our experience

that the actual value is at least a factor of 5 greater.

Therefore, it seems reasonable to assume that the S-193 system

resolution is around

DT = IK. (4-50)

References

[1] D.F. Wait, "Thermal Noise From a Passive Linear Multiport," IEEE Trans. Microwave Theory and Techniques,

Vol. A4TT-16, No. 9, pp. 687-691 , Sept. 1968 . [2] Glenn F. Engen, An Introduction to the Description an d

Evaluation of Microwave Systems Using Terminal Invariant

Parameters, NBS Monograph 112 (Supt. Doc, Washington, D.C.,

Oct. 1969) pp. 14, 56.

[3] D.M. Kerns and R.W. Beatty, Basic Theory of Waveguide

Junctions and Introductory Microwave Network Analysis

(Pergamon Press, Oxford, 1967).

[4] M. Hamermesh, Group Theory and its Application to Physical

Problems (Addison -Wesley Publ. Co., Inc., Reading, Mass.,

1962).

113
D.M. Kerns, "Analysis of symmetrical waveguide junctions,"

J. Res. Nat. Bur. Stand. (U.S.), 46^, No. 4 , 267-282 , (April 1951) . Theodore Moreno, Microwave Transmission Data (McGraw-Hill,

New York, 1948) p. 132.

Ibid. , pp . 138-139

.

114
FORM NBS-114A (1-71) U.S. DEPT. OF COMM. 1. PUBLICATION OR REPORT NO. 2. Gov't Accession

BIBLIOGRAPHIC DATA „^ SHEET NBSIR 73-314

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Evaluation of Antenna Loss and Beam Efficiency Measurements and Radiometer L-aiibrations lor tne o-i-y~> ana 0-174

Skylab Systems

5. Publication Date May 1973

6. Perfonning Organization Code

7. AUTHOR(s) A.C. Newell, P.F. Wacker, D.F. Wait

W„C. naywitt. R. C. R^ird

8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS, BoulderLabs.

DEPARTMENT OF COMMERCE

Boulder, Colorado 80302

10. Project/Task/Work Unit No. 2727436

11. Contract/Grant No.

12, Sponsoring Organization Name and Address National Aeronautics and Space Administration

Manned Spacecraft Center

J: at-iiiuy ctnu j_(aucjrai.ory Dupport ijrancn

Houston, Texas

13. Type of Report & Period Covered

NBS Interagency Report

5/1-12/31 1972

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.) The program represents an effort to determine the most appropriate techniques for

measuring the critical parameters of the radiometer -antenna systems used in the NASA.

Earth Resources and Skylab programs. For this first phase, the contractors' measurements on the S-I93 and S — 194 Skylab systems were studied in detail. The measurec

quantities included antenna loss, antenna power gain, antenna patterns (which yield directivity and beam efficiency), and radiometric noise temperatures.

From the analysis of the contractors' data and aioxiliary information, best values

and their estimated errors were determined for each of the parameters. In addition,

specific recommendations were made for easy upgrading of individual measurements,

and the errors thus reduced were estimated. For some of the parameters, errors

attainable with the current state-of-the-art were estimated.

In the measurements of antenna "loss", both contractors determined insertion loss

rather than the ratio of output available power to input available power, required for

radiometric determinations. For systems with significant reflections, these two

qxxantities may be rather different, and the available power ratio should always be

specified.

Antenna measurements made in an anechoic chamber showed surprisingly large wall

reflections, suggesting that such, chambers should be used for cross polarization measurements only with great caution.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Antenna; Antenna Loss; Beam Efficiency; Calibration and Measurement;

Radiometer

18. AVAILABILITY STATEMENT

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