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

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Allen C/Development of neer-flel h mm mn m mm* A Meet U56 NO 85-3031 V1985 C 1 NBS-PUB- II It L IVI fjL |\| F A N F S I ll

TEST PROCEDURES FOR

COMMUNICATION SATELLITE

ANTENNAS

Phase 1, Part 1

Reference

NBS

PUBLICATIONS

Allen C. Newell

Andrew G. Repjar

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado

September 1985

-QC

100

. U56

85-3031

1985

NBSIR 85-3031

NBS RESEARCH INTCRilATION CENTER $

DEVELOPMENT OF NEAR-FIELD

TEST PROCEDURES FOR

COMMUNICATION SATELLITE

ANTENNAS

PHASE I, Parti

Allen C. Newell

Andrew G. Repjar

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

September 1985

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

Page

1. Introduction 1

2. Definition of the Measurement Problem 2

3. Description of Near-Field and Compact Range Measurement Techniques

3.1 Planar Near-Field Measurements 8 3.2 Cylindrical Near-Field Measurements 26

3.3 Spherical Near-Field Measurements 32 3.4 Compact Ranges 34

4. Choice of the Optimum Measurement Technique for Directive Communications

Satellite Antenna Systems ' 43

References 45

Appendix A 46

Appendix B 71 Appendix C 75

i i i

DEVELOPMENT OF NEAR-FIELD TEST PROCEDURES

FOR COMMUNICATION SATELLITE ANTENNAS

PHASE I, PART 1

Allen C. Newell and Andrew G. Repjar

Electromagnetic Fields Division

National Bureau of Standards

Boulder, Colorado 80303

The purpose of this program is to define and further develop the capabilities of nearfield antenna test techniques, specifically for the requirements associated with the development and verification testing of reconf igurabl e, multibeam, frequency reuse, commercial satellite antennas. Phase I, Part 1 gives a general survey, definition, and

description of near-field and compact range measurement methods as they apply to satellite

antenna systems testing. Each of these methods is evaluated to determine how well they

meet the measurement requirements. Included for each technique is a summary of the mea- surement method, discussions on probe correction and data processing, measurement hardware

considerations, a results available section, and measurement accuracy and range certification considerations. The basis for the choice of the best measurement technique is established with the planar near-field measurement method receiving the best score for the directive antennas considered. As a result, further study will focus on this technique and

will be reported on subsequently. A detailed presentation of planar near-field measurements theory is presented in Appendix A.

Key words: antennas; antenna measurements; compact range; cylindrical near-field

scanning; near-field measurements; near-field testing; planar near-field scanning;

satellite antennas; spherical near-field scanning.

1.0 Introduction

The purpose of this program is to define and further develop the capabilities of near-field

antenna test techniques, specifically for the requirements associated with the development and verification testing of reconfigurable, multibeam, frequency reuse, commercial satellite antennas. The

program includes two phases. Phase I is a study program that will include the following tasks as outlined in the statement of work:

Task I/A & I/I General survey, definition, and description of near-field and compact range configurations including a description of their comparative advantages. These tasks will be

discussed in two parts:

1. A clear and concise description of the antenna and satellite systems to be measured, and the

associated measurement problems.

2. A description of the three near-field measurement techniques being studied along with the

compact range approach. Each of these will be evaluated to determine how well they meet the

requirement defined in Part 1 above.

Task I/H Selection of the optimum measurement technique from the above study.

Once the optimum technique has been chosen, the remainder of the study will focus on that tec h - nique only. Items to be covered in the remainder of Phase I are:

Task I/B Determination of sampling criteria and scan limits.

1
Task I/D Development of beam alignment techniques.

Task I/F Specification of hardware requirements for the measurement system.

Task I/C Development of diagnostic and design-assist methods.

Task I/E Development of swept frequency equivalent tests.

Task I/G Outline available computer programs and make them available.

Task I/J Develop the test plan for Phase II.

In the following report. Tasks I/A and I/I will be reported on, covering the research during the

first 6 months of the contract.

Phase II is a measurement program that will demonstrate the results of Phase I.

2.0 Definition of the Measurement Problem

The first major goal of this research program, as outlined in Task I/H, is to choose an "optimum"

measurement technique for the communication antenna system. To make that choice as objective as possible and to clearly document the reasons for the final choice, we have developed a three-step

evaluation process which compares the relative merits of various measurement approaches for a particular application.

The first step in the process, as developed in this section of the report, is a clear description

of the antenna system to be measured and the evaluation factors which are determined by the antenna.

These evaluation factors are statements of the important measurement results or test requirements that

are defined by the antenna rather than the measurement system. For instance, the size of the required

test zone, the susceptibility of the antenna to adverse environments, etc., are antenna evaluation

factors since the antenna and not the measurement system defines the requirements and their relative

importance.

The second step in the evaluation process, to be detailed in Section 3, is a description of the

essential features of the measurement techniques under consideration and a definition of the measurement system evaluation factors. Examples of such factors are measurement time for a given result,

data processing complexity, diagnostic capability, etc.

In the third step, relative weights are assigned to each of the factors (the subscript denotes

the factor index) representing the relative importance of the factor for the particular application

being studied. These weights vary from two for critical requirements to one half for factors with

minor importance. In a similar way, each measurement technique denoted by a subscript j is rated by

assigning values R^j to represent how well that technique satisfies the requirements of each evaluation factor. The overall score for a given technique is then the sum of the products of the ratings

and the weights

= Z ukR

i=l,n 1 ij* ( 1 )

2
In addition to the weighted sum of all factors, the weighted sum of just the critical factors is also

important to ensure that the sum of highly rated minor factors does not have undue influence on the

final evaluation.

Using the above process, the details and the assumptions leading to a final decision are clearly

presented. If there are questions about the final decision, these details and assumptions can be re- viewed to verify a correct statement of the problem and justifiable rating of each alternative.

With the evaluation process outlined, let us now turn our attention to the specification of the

measurement problem and the identification of the antenna evaluation factors. The type of antenna

system being considered is represented by the Intelsat VI satellite shown in figure 1 composed of a number of complex antennas mounted in close proximity to each other on the spacecraft. Because of

this close proximity, there will be scattering and interaction between the various feeds, reflectors,

and the support structure. The measurement system must accurately account for this interaction so the

results will represent the composite antenna/structure effect.

Since the satellite will operate in a zero gravity environment, and total satellite weight is reduced wherever possible, some of the antennas and their support structures are not rigid in Earth's

gravity. Because of this, auxiliary support structures are often necessary to hold reflectors in

their deployed shape and position. Even with these support structures, it is very difficult to either

translate or rotate the satellite in azimuth and elevation and maintain the antenna alignment. It is

therefore highly desirable to eliminate or minimize any movement of the antennas during testing.

The size of the antennas affects the measurement system in two ways. First, the large antennas

with the large offset distances require a test volume with dimensions of at least 5 meters along each

side. The smaller antennas require a measurement technique that is flexible to a wide range in an- tenna sizes.

Because the satellite is intended for synchronous orbit use, and the Earth subtends an angle of

less than 20 degrees at that altitude, all of the antenna beams are relatively narrow. The beamwidths

vary from the Earth coverage beams of approximately 20 degrees to the spot beams of approximately 2 degrees. The most difficult requirements are presented by the antennas which are capable of producing

a number of different beams, each of which is shaped to match an irregular land mass and steered to a different direction off axis, as shown in figure 2. It has been shown in past studies [1] that farfield measurements on these antennas require ranges on the order of 10 D

2 /A rather than the typical

2 D

2/A for less complex antennas. This implies that the test zone of a compact range must have more

uniform fields than for testing simple antennas. In the case of near-field measurements, the phase

will not be constant over the measurement plane as would be the case for a more simple antenna.

Because of the multiple complex beams, the patterns must be measured at closely spaced intervals

on the order of 0.25 to 0.5 degree increments over the +10 degree region in azimuth and elevation.

Typically, contour patterns such as figure 3 are required to completely define the pattern shape over the intended coverage region and to ensure noninterference with other beams. The measurement

technique must be capable of producing the complete detailed patterns.

Because orthogonal polarizations are used to improve beam isolation, it is important to determine

the cross polarized patterns at levels of -30 to -50 dB below the main beam peak and to quantify the

accuracy of such measurements.

3
At present the required measurement frequencies are between 4 and 30 GHz, and the measurement

system must have the capability of changing easily from one band to another. The detailed contour

patterns shown in figure 3 are obtained at representative fixed frequencies within the operating band

of each antenna system. In addition to these fixed frequency patterns, continuous swept frequency

measurements are also taken at a few angular positions in the patterns. In a typical requirement, six

angular positions are chosen for each hemi-or zone-beam (one at center and five at points along the

edge of coverage). At each of these points, swept measurements are made across the operating frequency band for main and cross polarized response. These tests include not only the antenna but the

transmission lines and electronic components associated with the satellite transmitter and/or

receiver. These tests are important to detect resonant responses which might not show up in fixed

frequency pattern measurements.

The pattern measurements are important for diagnostic use as well as verifying specified performance. To do this, measurement technique should have the ability to determine the presence of

a) STOWED M DEPLOYED

Figure 1. INTELSAT VI satellite illustrating the type of antenna systems under consideration.

4
elevation,

degrees

10

8 —

- 10 -8 -6-4 -2 0 2 4 6 8 10 AZIMUTH DEGREES

ATLANTIC OCEAN COVERAGE

-10 -3 -6 -4 -2 0 2 4 6 8 10 AZIMUTH. DEGREES

INDIAN OCEAN COVERAGE

AZIMUTH, DEGREES

PACIFIC OCEAN COVERAGE

Figure 2. Examples of shaped beams achievable from one system using beam switching.

5
abnormal or undesirable antenna system performance as well as their cause. From either the directly

measured data or from some manipulation of the data, such problems as feed element excitation errors, reflector deformations, or alignment problems should be easily identified.

The precise angular location of each beam relative to a coordinate system fixed to the spacecraft

must be determined as a routine part of the measurement procedure. Beam alignment accuracies on the

order of 0.01 degree are required.

In addition to the antenna parameters of gain, pattern and polarization already discussed, the

measurement system must be capable of measuring the total system parameters such as effective isotropic radiated power (EIRP) and the incident flux density required to saturate the receiver.

To summarize the above discussion, table 1 lists the antenna evaluation factors which have been

identified along with their assigned weights. (The index refers to the subscript i in eq (1).)

O

o

Figure 3. Example of detailed contour patterns required for antenna measurements

to ensure noninterference with other beams.

6
Table 1. Antenna Evaluation Factors

Index Antenna Evaluation Factors Wei ght

1. Characterize antenna farm interactions 1 2. Require minimum motion of antenna during measurement 2 3. Provide required test zone for:

a. Individual antennas 2 b. Antenna and interactions 1 4. Output detailed patterns for shaped beams 1.5

5. Give accurate gain, pattern, and cross-polarization

results 2 6. Ease of changing frequency range 0.5

7. Provide swept frequency results 2 8. Provide diagnostic information 1.5

9. Beam alignment accuracies of 0.01 degree 1.5

10. Provide system parameters of EIRP and saturating

flux density 1

3.0 Description of Near-Field and Compact Range Measurement Techniques

Before beginning a discussion of the individual techniques, the measurement system evaluation

factors will be identified and listed in table 2. These are largely determined by the measurement

system and in some cases are independent of the antenna being measured.

In the following sections, each of the measurement techniques under consideration will be described and the evaluation factors considered. Brief discussions of the theory and basic equations

for the planar, cylindrical, and spherical techniques are contained respectively in appendices A, B,

and C. These will be referred to as necessary in the following sections which will concentrate on analyzing each measurement technique with respect to the satellite measurement problem. Sufficient

information will be presented or referenced to serve as the basis for assigning a rating to each of

the evaluation factors for each measurement technique.

Table 2. Measurement System Evaluation Factors

Index Measurement System Evaluation Factors Wei ght

11. Need for probe correction 0.5

12. Software is efficient and fast 0.5

13. Hardware is practical for:

a. Antenna size test zone 2

b. Antenna and interaction size test zone 1 14. Commercial availability 0.5

15. Practical implementation 2 16. Flexibility to antenna size 1 17. Measurement time 1.5

18. Demonstrated results and users experience available 1.5

19. Achievable accuracy and methods of facility certification 1.5

7
3.1 Planar Near-Field Measurements

3.1.1

Measurement Summary

Before actually making near-field measurements on the antenna under test (AUT), a probe must be

chosen and calibrated. Generally, the probe is one whose main polarization is the same as that of the

AUT. The calibration involves on-axis measurement of gain and polarization parameters along with farfield pattern measurements. The pattern measurements include both amplitude and phase patterns for

the probe's main and cross polarized responses. With these data and the appropriate computer program,

the probes' plane wave receiving characteri sti c, So 2 (K) is obtained. (See section A-4 of Appendix A for the definition of the probe, AUT, and data quantities referred to below.) The above process is repeated for a "second" probe whose polarization is nominally orthogonal to the first. The second

probe may be a separate antenna, a second output port on a dual polarized probe, or the first probe

rotated by 90 degrees in the case of linear polarization. If the latter is used, repeat measurements

are not required since the original data may be rotated by the computer. In any case, the second

probe characteristic s'q 2 (K) is likewise obtained.

As noted in Appendix A, the AUT and probe coordinate systems are defined with reference mirrors,

boresight scopes, or fiducial marks, and the antenna and probe are aligned in a known orientation with

respect to the planar measurement surface. The first probe is moved over the measurement plane and

relative near-field data Bq(P) are obtained at equally spaced points of a rectangular lattice. Bq(P)

represents the amplitude and phase output of the probe. Similar data are obtained with the second

probe and denoted B q( P )In addition to these relative data, insertion loss normalization constants

are measured for each set of data (see eq (A53)).

The Fast Fourier Transform algorithm is used to calculate the angular spectra of the two sets of

data (see eqs (A54) and (A56)) and the probe correction is applied to obtain the plane wave spectra

for the AUT, t 10 (K). From t 10 (K) the usual parameters of gain, pattern, and polarization are easily

obtained (see eqs (A68) - (A70)).

3.1.2

Probe Correction

As evidenced by eq (A57) and eqs (A60) - (A61), the probes act as both polarization and angular

filters on the AUT spectrum producing the measured spectra D'(_K) and D"(J£). The probe correction

removes that filtering effect to give the desired result, t 10 (K). In many cases the effect of the

probe correction is small and may be neglected, and by using the basic equations and some knowledge

about the probe the necessary conditions are easily defined.

If we assume that the first probe is polarization matched to the AUT, eq (A60) reduces to

t D'(K)

02m -

( 2 )

where the m subscript denotes the main component of the AUT. Since I s 02m ^ K ^ I P ro P ort i° na ^ to the

relative far-field pattern of the probe, the directivity of the probe and the angular region over

which results are desired determine the need for a probe correction. For instance, figure 4 shows a plot of the far-field pattern for two typical probes along the k x =0 plane. The maximum errors due to neglecting probe correction for these probes and various angles off-axis are shown in table 3.

8
Far-Field

Amplitude

mdB

Table 3. Maximum Errors due to Neglect of Probe Correction

Probe Off-Axis Angle (deg) Error in ( dB )

Waveguide 18 0.25

Waveguide 54 1.75

Horn 18 4.0

Horn 54 16.5

Azimuthal Angle in Degrees

Figure 4. Two typical probe patterns with different directive patterns.

9
The relative polarization ratios of the AUT and the "second" probe, the one used to measure the cross polarization, also affect the need for a probe correction. If the second probe is better

polarized than the AUT, eq (A61) reduces to

D" ( K)

t 10c ( ^ ) = s" 2c

(K)* ( 3 )

where c denotes the cross polarization of the AUT, and only the directivity of the second probe has an influence on the effect or lack of a probe correction. If the second probe is not as well polarized

as the AUT, both the patterns and polarization of the second probe must be considered. Every situation cannot be discussed in detail, but given the parameters of a measurement situation, the effect of

probe correction can be easily determined.

The probe is usually chosen to enhance/improve the accuracy of the most important information in

a given measurement. Very small probes, such as open-ended waveguides, are used when wide angle pattern results are desired. More directive probes such as horns are used when the important information

is within a limited angular region centered on the z-axis. The more directive probes filter out the more rapid variations in the near-field data associated with wide-angle sidelobes allowing larger data

point spacings. The accuracy in the gain of the AUT is also alightly improved due to better signalto-noise ratio and better accuracy in both the probe gain and the normalization constant A

1 (see eq (A53)). The improved value of A

1 is due to the fact that A1 is approximately equal to the ratio of

AUT and probe gains (difference of gains in dB). As the gain of the probe increases, the dB value of

A' decreases and it can be measured with better accuracy.

3.1.3 Data Processing

The data processing can be divided into three categories: 1) editing and normalization of mea- sured data, 2) calculation of antenna parameters, and 3) graphical representation of results. The

times required for categories 1 and 3 are largely independent of the measurement approach, whether it

is near-field, far-field, or compact range. In category 2, the planar technique uses the Fast Fourier

Transform (FFT) to evaluate the integral in eqs (A52) and (A56) and complex arithmetic for the probe

correction and pattern calculations. It is the most efficient of the three near-field techniques in

terms of data processing. Figure 5 shows the relative times for planar, cylindrical and spherical for one specific computer. (In the figure, the parameter n indicates the effect of increasing the theoretical data point spacing in <f> by a factor n. It has been demonstrated that this can be accomplished

without loss of accuracy for certain antennas.)

3.1.4 Measurement Systems Hardware Considerations

The hardware for any of the measurement approaches is composed of the electronic system, the an- tenna positioner, and the scanner, or reflector, in the case of the compact range. The electronic

system for all three near-field techniques and also the compact range are basically the same and will

not be considered in detail in this section. We will consider the antenna positioner and scanner and

point out how they impact the measurement.

In the planar measurements, the scanner is a mechanical structure which moves the probe over a plane area along a rectangular lattice where measurements are obtained. Examples of two types of scanner are shown in figures 6 and 7.

10
COMPUTER

RUN

TIME

HR MIN SEC

SPHERICAL, n =1 2 5 TO (see text)

D/A FOR PLANAR, DQ /X FOR SPHERICAL

Figure 5. Comparison of computer CPU times for three near-field techniques.

11
Figure 6. Box frame planar scanner.

12
POSITIONER TOWER

COVERAGE:

6.1M X

5.5M Y

13

SCHEMATIC

OF

TRACK/TOWER

PLANAR

SCANNER
The size of the scanner determines the sizes of antennas that can be measured, the angular region over which results are valid, and the magnitude of errors due to scan area truncation. The theory

requires data over an infinite plane, and truncation of the measurement plane produces errors in the

measured results. It has been shown [2,3] both theoretically and experimentally that the truncation

causes two effects. First, the pattern results of the measurements are valid only for angles smaller

than 0

$ shown in figure 8. Secondly, the abrupt truncation of the measured data causes a "ringing" on the far-field pattern producing some errors for angles less than 0

S

. The characters of the amplitude

and phase at the edge of the scan area determine the magnitude of these errors. Generally, if the

amplitude at the boundary of the scan area is 30-40 dB below the peak amplitude and the phase varies

rapidly around the boundary, the ringing effects are small.

Referring to figure 8, the size of the scanner is chosen to cover the antenna area plus the

additional area required to ensure valid results over the specified angle 0

$

. In the case of the

Measurement

Plane

Lx

9C - Tan 1

TRUNCATION OF MEASUREMENT AREA

Figure 8. Schematic relationship between scan length and maximum angle

to which far-field patterns can be accurately computed.

14
Intelsat satellite shown schematically in figure 9, the offset configuration of the reflectors and the

diameter of the satellite body supporting the feeds requires a large separation distance between the

Hectors and the scan plane. For the transmit reflector the minimum separation distance is 6.0 m. For the Earth coverage requirement, 0

$ is ten degrees and therefore the scan length must be at least

2.12 m longer than the antenna. If the complete antenna farm interactions with all multiple scattering effects are to be included in the measurement, the "antenna" dimension must include all the feeds,

reflectors, and supports on the spacecraft. As shown in figure 10, this requires scan lengths of 10.4 m in the x-direction and 6.6 m in the y-direction. Every near-field measurement on the satellite will

not require this complete area, however. Preliminary scans may indicate that for a given feed there

is negligible scattering or radiation from some parts of the structure, and the scan area may then be

limited to the region where there is significant energy contributing to the angular region of interest

defined by 0

$

. In another case it may be desirable to reduce the scan area to purposely exclude the

effects of scattering and concentrate the measurement on one reflector and its feed, as shown in

figure 11. This would be the case in diagnostic measurements when checking feed alignment, reflector

shape, or feed illumination errors. In these cases, scattering from other objects could tend to obscure the desired results and by limiting the scan area these extraneous effects are excluded. The

maximum required scan area of 10.4 m x 6.6 m is feasible with existing technology. Using the design

shown in figure 7, x- and y-scan lengths of 6.7 m are currently being achieved. It is relatively easy

to increase the scan length in the x-direction by increasing the length of the horizontal rails, and

the 10.4 m length should be easily achieved. One of the main advantages of the planar technique for

spacecraft testing is that the antennas do not have to move during measurement. The antennas may then

be supported in a fixed position to overcome the distorting effects of Earth's gravity.

Currently there are at least 20 planar near-field measurement systems in operation at various

commercial and government laboratories around the world. These include a variety of mechanical designs similar to those shown in figures 6 and 7, as well as some which employ horizontal scan

planes. Commercial companies do not sell these as standard product items, partly because each user

has fairly unique requi rements . The experience and expertise does exist, and some companies have ex- pressed an interest in designing and constructing planar scanners to meet user specifications.

With the planar measurements it is relatively easy to change from one frequency band to another

since only the probe has to be changed. This will require calibration of the probe or calculation of

its gain, pattern, and polarization, depending on the accuracy requi rements

Due to the large scan areas, the planar measurements may require a number of hours to complete.

For a scan area with dimensions of LAyand L , data point spacing in the x-direction 6 , and probe scan

x speed v, the measurement time is approximately

L L T

=

6 v x y

(4)

Since the probe speed is limited to about 10 cm/sec due to mechanical vibrations, and the scan area

and data point spacings are fixed by the antenna being measured, little can be done to reduce the

total measurement time. The measurement efficiency can be greatly improved, however, by obtain^;

multiple patterns during one traverse of the measurement area. This is accomplished by swi f ’ - between different frequencies, beams, polarizations, etc., between each data point in the . - direction. (It is assumed for this discussion that the probe moves continuously in the / - ' i ^ • '

15
8.3m I E

r^- *r

16

Figure

9.

Schematic

of

satellite

with

offset

antennas

and

resulting

scan

plane.
10.4

m

17

measure

all

antennas.
Reflector

And

Feed

Reflector

only

E

CM

LO *

18

interaction

coverage.
i-teasuring data at intervals of and stepping in the x-direction at the end of each y-scan.) The

total number of patterns obtainable during one scan is

N < V T y

( 5 )

where t is the time required to accomplish the switching. The various time intervals comprising t, along with some representative times available with current equipment, are shown in table 4. Using

the multiplexing scheme, it is possible to obtain many patterns during one scan of the plane area.

Table 4. Representative Switching Times

Acti on Time (msec)

Beam or polarization switch

Frequency switching

Receiver settling (after frequency change)

Receiver analog to digital conversion

*Computer command time

0.5 - 2.0

10.0 - 20.0

10.0 - 100.0

0.5 - 10.0

0.5 - 50.0

*The computer time is dependent on how many different patterns are switched

3.1.5 Results Available

The required detailed far-field patterns for both main and cross polarization are readily available from the planar technique. There is no difficulty in obtaining the high resolution contour patterns, such as shown in figure 3. The accuracies of these results are dependent on the accuracy of

the measurement systems, and this will be discussed in more detail in the following section.

Absolute gain values are obtained as a natural result of the data processing. In addition, it is possible to obtain system parameters such as EIRP and saturating flux density, as illustrated in

figures 12 and 13. The relative near-field data used to obtain patterns and gain, Bg(P), are also em- ployed here. In addition, the probe is placed at the reference point, P 0 , and either the received

power (for EIRP) or transmitted power (for saturating flux density) are also measured. These techniques are relatively new developments, and will require some refinement in the measurement details,

but they should be strai ghtforward and very reliable.

Beam alignment is a topic which will be covered in more detail in a future report. We assert

here that it is possible to achieve beam alignment with errors of ± 0.01 degrees or less.

The near-field data before transformati on can be used very effectively for antenna diagnostics.

Figures 14 and 15 show the measured phase data as contour plots superimposed on the reflector i -v* -

being measured. The regions of reflector surface i regularities are easily identified. There are existing techniques for transforming measured data back to a plane closer to the reflector or ar r i .

This additional processing can enhance the diagnostic capability of the planar near-field me,r, jr.«- ments. No other technique offers the present capabilities and future possibilities in the area if diagnostics. This is related to the fact that for the directive antennas being considered here, t’-- desired field on a plane is generally the known quantity and especially the phase data are i vr,

sensitive measure of performance.

19
Near-Field

Measurement

of

EIRP

20

Figure

12.

Schematic

of

EIRP

planar

near-field

measurement.
Near-Field

Measurement

of

Saturating

Flux

Density

21

Figure

13.

Schematic

of

planar

near-field

saturating

flux

density

measurement
-90

Probe

y-position

in

inches

+90

-90

Near field phase 30 degree contours on 3m Parabolic dish antenna at f = 14.5 GHz

Probe x-position in inches

Figure 14. Measured near-field phase contours for 3 m parabolic reflector.

+90

22
The one area where all three near-field techniques are lacking in development when compared to

'hr measurement requirements is in obtaining swept frequency results. In far-field tests, a few

spe lfic directions are chosen, and continuous swept frequency gain, side lobe level, and crosspolarized isolation are measured. The combination of far-field pattern measurements at fixed

frequencies combined with the swept data is illustrated graphically in figure 16. The solid cube

represents the "volume" describing the complete antenna performance at any azimuthal and elevation

angle (horizontal coordinates) and frequency (the vertical coordinate). At any frequency the antenna

pattern is represented by a contour plot, and the cube is composed of a continuous layer of these

plots, of which three representative ones are shown. The swept frequency measurements are taken at specific fixed azimuthal and elevation coordinates and are represented by the vertical lines.

Currently it is not feasible to obtain continuous results along the vertical lines with nearfield techniques in the same way as far-field tests. Fixed frequency measurements could be obtained

at a large number of fixed frequencies, but this would be very time consuming. Preliminary research

has indicated that it may be possible to develop near-field measurements that would give swept frequency information equivalent to the far-field results. The proposed approach is to place the nearfield probe at representati ve points in the x-y plane and obtain near field swept frequency amplitude

Panel - support screws -

120 cm —1)

Figure 15. Measured near-field phase contours for hexagonal panel reflector

showing effect of one support screw maladjustment.

23
and phase data. By appropriate analysis, which is currently under development as a part of this con- tract, the frequency intervals required to completely specify the antenna system frequency response

would be determined. This would guarantee that if fixed-frequency near-field measurements were obtained at these intervals, the continuous response could be reliably interpolated. In addition, techniques to reduce the amount of near-field data required to obtain the frequency response patterns are to be investigated. At present these methods are not fully developed. They show promise and, if

developed, could provide swept frequency results equivalent to far-field techniques.

3.1.6 Measurement Accuracy and Range Certification

For any measurement technique, accuracy is one of the primary concerns, and this is especially

true of a new method involving a significant level of mathematical analysis such as the near-field

technique. The determination of error bounds for any given antenna/probe/near-field measurement

system combination is a difficult and demanding task, and the mathematical complexity is a major

reason for the difficulty. There is a temptation to bypass the mathematics and attempt to establish error bounds for the general measurement technique by a comparison measurement on a specific

Figure 16. Schematic representation of fixed and swept frequency

results as part of data volume.

24
antenna. In this approach, the results of near-field measurements on a given antenna are compared

with far-field measurements, and differences between the two are taken as a measure of the errors in tne near-field technique. The limitations of such an approach are obvious. 1) The observed differences are due in part, and could be primarily due, to errors in the far-field measurement. 2) It

is difficult to generalize one result to other antennas and measurement systems. 3) There is no indication of which measurement parameters are the most critical or the contribution from each error

source.

This does not mean that comparisons are not valuable exercises. They demonstrate reliability,

help to establish confidence without detailed mathematical study, and indicate possible areas where

more detailed study should be done. They are one piece in the error analysis puzzle, but certainly

not the whole picture.

A second useful approach is computer simulation of various types of errors. Either actual or hypothetical near-field data are assumed to represent perfect, error-free measurements. These data

are then modified with errors of various types and magnitudes. Differences between far-field parameters computed from the error-free and modified data sets are a direct measure of the effect of each error source. This approach also has limitations. 1) The error types considered (i.e., linear, quadratic, random) may not represent actual or worst-case types of errors. 2) The assumed effect of a given error may not be correct. For instance, assumptions must be made about how probe position

errors or multiple reflections effect the data, and those assumptions may not be completely valid. 3) The results may not be general unless the simulation is performed for a wide variety of antenna types.

A third method of error analysis can result in a direct measurement of the effect of some error

sources for a specific measurement. This is essentially a self-comparison technique where measurements on a given AUT are repeated after making a specific known change in the system. The change is

made to produce a sign reversal in the effect of some particular error, and the difference between two results is then a direct measure of that error. For instance, measurements made at z-separation distances differing by A/4 will show the effect of multiple reflections. Other examples include translation of the antenna between measurement sets in x or y to identify probe position error or room scattering effects and sequentially reducing the data area size or data point density to produce

changes in the errors due to truncation and aliasing. The combination of all these tests is involved,

time consuming, and generally will not be performed on every antenna; but they are valuable in initially certifying a measurement facility or studying the details of a particular error source. Along

with the other approaches, they can be used when appropriate, and provide part of a complete method of error analysis.

The fourth method of error analysis is the most detailed and generally the most useful. This

method is based on a study of the mathematical relations between near-field data and far-field

results. The results of this study are general error equations which define the error in various farfield parameters as a function of essential antenna parameters and the magnitudes of individual nearfield errors. The equations are quite general, can easily be applied to different antennas, and can

be used either to estimate final error bounds or to design a measurement system capable of achieving • given level of accuracy.

The mathematical error analysis begins from the point of view that the basic equations are i *,

without approximation, and, therefore, include no built-in limit on attainable accuracy. Thesp

include the transmission integral, eq (A50); the calculation of the angular spectra, eqs (A54 in)

25
(A56) ; the probe correction, eqs (A60) and (A61); and the evaluation of far-field parameters in eqs

(A68) - (A70). The generality and rigor of these equations, although not obvious in the development

in Appendix A are established by a more detailed analysis [4], There are, indeed, some assumptions

made in the derivation of these equations concerning ideal measurement conditions (such as a planar

surface, rectangular measurement lattice, absence of multiple reflections, etc.), and if these

conditions are not realized, errors will result. These errors are simply included with others that

arise from the nonideal character of the measurement system. By adopting the above point of view, the

focus of the error analysis is on the nonideal character of the measurement system, not the

mathematics

All four of the above approaches have been used extensively to test and verify the accuracy of

the planar near-field measurement techniques. Comparisons with far-field measurements were some of

the earliest [5] and continue to be used as each new facility is first used. Extensive computer simulations of various errors were done by Joy [6] and were used to verify and assist in the mathematical error analyses [7,8]. The net result of these studies has been the identification of a number of error sources in the near-field measurement system and equations to specify bounds on the magnitude of

the resulting far-field error. The details of these equations can be obtained from the supplied ref- erences, and the various error sources are listed in Table 5. These error sources can be classified

under two categories. Namely, uncertainties in probe parameters Sq 2 (K) and s'o 2 (K) arising from the

gain, pattern, and polarization measurements on the probe; and errors in the calculated spectra

D'(K) and D"(K) arising from the measured data Bq(P) and Bq(P). All of the error sources in Table 5,

except number 15, are systematic errors. That is, the effect of the error is not reduced by repeating

the measurement a number of times under the same conditions.

Reliable and realistic error bounds will be predicted if the following assumptions are true: 1) The equations used to calculate the far-field parameters are exact. This can be shown from a careful

study of the theory. 2) All known sources of error have been included in the list of Table 5. 3) The

magnitudes of the near-field errors have been reliably measured. This requires, for instance, the use

of laser optical systems to measure the x-, y-, and z-position errors; calibration techniques to measure receiver linearity; and system tests to determine the effect of reflection, area truncation, and

aliasing. 4) The error equations correctly predict the far-field error. This is verified by the

mathematical analysis, the computer simulation, and self-comparison tests. 5) The individual error components are correctly combined to give a realistic estimate of total resultant error.

3.2 Cylindrical Near-Field Measurements

3.2.1 Measurement Summary

It should be evident from a comparison of appendices A and B as well as more complete and

detailed derivations [4,8] that there are many parallels between the planar and cylindrical theories,

basic equations, and, as a result, the measurement techniques. These similarities include: 1) transmission equations written in terms of AUT transmitting coefficients and probe receiving coefficients;

2) the general requirement to measure near-field data with two independent probes; 3) solution of the

transmission equation by using the FFT and probe correction; and 4) virtually identical electronic

measurement systems.

Because of these similarities, this section will only cover in detail the areas where there are distinct differences that have an impact on the measurement problem under consideration.

26
Table 5 Error Sources in Planar Near-Field Measurements

Source of Error

Primary Method of Evaluating

Computer Test on Meas. Error

Si mul ati on System Equati ons

1. Probe gain measurement

2. Probe relative pattern

3. Probe polarization ratio

4. Normalization constant

5. Probe alignment error

6. Antenna alignment error

7. Measurement area truncation x 8. Data point spacing (aliasing)

9. Multiple reflections (probe/AUT)

10. Room scattering

11. Probe x-y position errors x 12. Probe z-position errors x 13. Receiver amplitude nonlinearity

14. System phase error due to: Recei ver Flexing cables/rotary joints

Temperature effects

15. Impedance mismatch factor

16. Random errors in amplitude/phase

17. Leakage and crosstalk

x

x

x

x

x

x

x

x

x

xx

x

x

x

x

x

x

x

x

x

x

x

xx

NOTE: The above errors are all associated with the measurement system and do not include such things

as changes in the antenna during measurement due to environmental factors.

3.2.2 Probe Correction

In the planar technique there are measurement situations where the probe correction can be ignored completely, and reliable results may still be obtained. In contrast, the probe correction or

its equivalent is always required in cylindrical measurements. If the probe is small compared to the

measurement wavelength, and/or the diameter of the measurement cylinder is large enough, an "ideal"

probe may be assumed. The probe receiving coefficients are then given analytically as proportional to Hankel functions. An alternative point of view is to consider the near-field data as a direct measure

of the electric field components. From this point of view, the resulting equations do not involve an explicit probe correction, but they do include the Hankel functions representing the ideal probe

effect. If the probe correction is required, the probe calibration process used for the planar method

also applies here. Part of the data processing is also employed, but in addition the probe

coefficients must be transformed from the probe's coordinates to that of the AUT (see eq (37) in reference [8]).

3.2.3 Data Processing

Since the FFT is used extensively for the planar and cylindrical methods, the computation

for these methods are similar. One additional step is required here in the calculation of thn f i r - field since the AUT coefficients must be summed (see eqs (Bl) and (B2)). But since this is a om»- dimensional sum, and again the FFT is used, the additional computer time is fairly minor.

27
3.2.4 Measurement System Hardware Considerations

The usual configuration for a cylindrical near-field scanner is shown in figure 17. The AUT is mounted on an azimuth rotator whose axis of rotation is parallel to the axis of the one-dimensioned

probe transport. This generally means that the scanner is less expensive than for planar. More com- plete pattern coverage is also achieved since results can be obtained over 360 degrees in $ (azimuth), even though the size of the probe transport limits the elevation coverage in the same way it did with

planar measurements.

The main disadvantage of the cylindrical scanning for the satellite problem is the required

satellite rotation during measurement. This produces stability problems for the fragile antennas and

support structures. The amount of rotation required depends on the dimensions of the "antenna" being

measured, the radius of the "minimum cylinder" and the angular region over which patterns are re- quired. As previously mentioned, the "antenna" dimensions should include the reflector and any other

objects which could radiate or scatter energy. The minimum cylinder is defined as one centered on the

azimuth axis of rotation which will completely enclose the antenna as above defined. Given a radius

of R for the minimum cylinder, an antenna dimension a, and requirement for results over azimuthal

angles bounded by 4> , the ^-rotation required is as illustrated in figure 18. For the Intelsat

satellite dimensions, and including all structures as potential scattering sources, the ^-rotation

angles required for +10 degree coverage on the transmit reflector and feed are from -72 degrees to 11.5 degrees as shown in figure 19.

The size of the minimum cylinder also determines the data point spacing in <j>, and therefore influences the measurement and calculation times. To satisfy the sampling criteria and therefore avoid

aliasing errors, the angular data point spacing must satisfy the criteria

and the number of data points is

with the additional requirement that

N, A<j> = 2n = 360°.

( 6 )

(7)

( 8 )

Since all of the antennas are located away from the center of rotation of the satellite, the minimum

cylinders in every case are larger than the reflector dimensions and relatively fine spacing are required. Table 6 lists the estimated scan parameters for each of the Intelsat VI antennas, assuming

that the minimum cylinders include the reflector and feed for each antenna, but may exclude some

potential scatterers.

Table 6. Cylindrical Scan Parameters

Antenna Frequency (GHz) R(meters) A<(> (degrees)

Transmit 4.0 5.4 0.40 900

Recei ve 6.0 4.5 0.36 1000

Spot Beam 14.0 2.5 0.25 1440

28
Figure 17. Cylindrical near-field schematic for satellite antennas.

29
<j> c =ANGULAR BOUNDRY OF COLLIMATED REGION

<J> b =ANGULAR BOUNDRY OF MEASURED REGION

<J> S =ANGULAR BOUNDRY OF RELIABLE RESULTS region

i=ARCSIN ^

(j) s =ARCTAN l

Sm ^b ~ 2R \

\ Cos 4> b -1 + d/R /

Figure 18. Relationship between antenna dimensions, its location in measurement cylinder , angular coverage, and angular scan region.

30
Figure 19. Angular scan sector for transmit antenna and feed giving +10 degrees iver.i resultant patterns.

31
3.2.5 Results Available

The pattern, gain, and polarization results obtainable from cylindrical measurements are very

similar to those for planar. The measurement details have not been developed to provide the system

parameters of EIRP and saturating flux density; however, it should be straightforward and could be

achieved with appropriate research. The same is true of beam alignment techniques. Little has been

done to develop these techniques, test them on sample antenna systems and document the results, but

there is no fundamental reason why they could not be perfected.

The cylindrical approach does not offer either the same current state of development or the potential of the planar method in the area of antenna diagnostics. Very little has been reported in

this area. The best possibility appears to be in processing the measured data to obtain far-field

amplitude and phase patterns, and then using these results to calculate reflector or feed illumination

patterns. This requires more processing than using the planar data directly, but is comparable to the

steps required when using planar data to obtain illumination on other planes.

3.2.6 Measurement Accuracy and Range Certification

Of the four methods for evaluating measurement errors discussed in section 3.1.6, only two have

been employed to a significant extent for cylindrical near-field measurements. These are comparison

with other methods and computer simulation. The comparisons have been encouraging and indicate that

the cylindrical method has a potential for accuracy similar to the planar technique. Computer simulation has provided some guidelines for predicting errors, but there is a need for the analytical error analysis to serve as the basis for designing measurement systems and reliably estimating the errors in each measurement.

3.3 Spherical Near-Field Measurements

3.3.1 Measurement Summary

The spherical technique shows the same similarities with the planar and cylindrical techniques

that were outlined in section 3.2.1, and again only the differences will be discussed in detail. The

theory for this technique is more complex, and this leads to more involved computer programs and some increase in the difficulty of implementing practical measurements. The measurement procedures that

have been developed and verified, however, are very similar to those for planar and cylindrical.

3.3.2 Probe Correction

In the two previous near-field techniques, there were no theoretical limitations on the probe

characteristics other than requiring the two probes to produce independent data. This requirement

meant that the two probes could not have identical polarization ratios for any combination of the independent variables, namely _K_ for planar and y»n for cylindrical (see Appendices A and B for definitions). The patterns could be essentially arbitrary and in principle the two probes could have distinctly different patterns.

The probe used for spherical near-field measurements does have restrictions, however. The pattern of the probe must have rotational symmetry about its z-axis, and therefore the 4> dependence of

the pattern must be given in terms of sin<j> and cos <f> . This restriction is necessary to allow both an inversion of the coupling equation (eq (C3)) and practical limits on the amount of near-field data

32
required. If the probe did not have this symmetry, prohibitively large amounts of data would be re- quired as a function of three variables, 0, <}> and x> where x is the rotation of the probe about its

axis. In addition to the ^-pattern restriction and when the probe is nominally linearly polarized,

the "second" probe must be the first probe rotated about its axis by 90 degrees. In principle, two circularly polarized probes with opposite senses of polarization can be used, but they must be

perfectly polarized on-axis.

These restrictions are not too difficult to realize, for with careful design and fabrication the

required pattern can be achieved to high accuracy. Circular waveguide or conical horns can be

machined or el ectroformed to produce the pattern symmetry.

As with cylindrical measurements, the probe correction or its equivalent is always required.

There are many cases where the probe is small or the measurement sphere is fairly large and under

these conditions, the probe can be assumed to be an ideal dipole. Some of the details of a general

probe correction are then eliminated, but others involving the analytical probe coefficients still

remai n.

3.3.3 Data Processing

A practical data processing approach was developed by Wacker [9] and is the basis for all spherical near-field programs. It utilizes the special symmetrical probe concept to invert the transmission equation and employs a combination of FFT and matrix multiplication to accomplish the

numerical integration. It is a highly efficient method but not as efficient as planar or cylindrical

calculations as evidenced by figure 5. The spherical processing time is proportional to (where N

is the number of data points) as compared to for the others.

3.3.4 Measurement System Hardware

In the usual implementation of spherical measurements, the probe remains fixed and the antenna is rotated about two axes. The rotator/antenna configuration may be as shown in figure A4 where the

boresight direction is along the z axis, the main beam is near the pole of the sphere, and the antenna

is rotated in <j> by 180 or 360 degrees during measurements. This is completely impractical for the

satellite system due to the nonrigid character of the antennas. Alternatively, the antenna can be

mounted on either of the rotators shown in figures A5 and A6 with the beam along the equator. In these situations, reduced angular rotations are possible, but due to the large offset distances, the

antenna must still be rotated over much larger angles than the +10 degree far-field coverage obtained.

From figure 20, and for measurements on the Intelsat VI transmit reflector,

R = measurement sphere radius = 6.0 m, a/2 = x-distance from rotation center to antenna edge = 4.7 m,

d = z- distance from antenna to sphere surface = 9.7 m, and

0

$ = angular boundary of reliable results region = 10 degrees.

This leads to the requirement that the antenna must be rotated in azimuth by 0 b

= 72 degrees, similar

to the requirement for cylindrical measurements shown in figure 19. Similar rotations in elevation

would also be required for this reflector, and though smaller rotations would be sufficient for **.. other smaller antennas, this makes the spherical measurements very undesirable for these satellite

appl i cati ons.

33
Smaller rotation angles could be achieved by increasing the size of the measurement sphere. For instance, if R = 18 m, 0^ - 30 degrees for the above case, but this would require a much larger room

with increased amounts of microwave absorber.

3.3.5 & 3.3.6 Results Available and Accuracy

The spherical and cylindrical techniques are essentially the same in the area of results

available and predicted accuracy. More work needs to be done in developing system measurement

techniques as well as analytical error analyses.

3.4 Compact Ranges

The far-field testing of microwave antennas requires that the test antenna be illuminated by a uniform plane wave. Approximating this condition for adequate far-field range operation requires that

the distance between the transmitter and receiver be between 2 D

2 /X to 10 D2 /A, where D is the diameter of the test antenna including significant scattering/reflecting surfaces, and X is the wavelength

[10]. For electrically large antennas, this distance can be several kilometers, requiring that the

test antenna be measured outdoors. In compact ranges, the uniform plane wave can be approximated

close to the antenna by illuminating either a single parabolic reflector [11,12] or two parabolic

Figure 20. Relationship between antenna dimensions, its location in measurement sphere , angular coverage, and angular scan region.

34
ylinders that are positioned perpendicular to one another [13] with a spherical source feed. Simply

stated, the rays from the feed are collimated by the reflector(s) , resulting in an approximate plane

wave illumination over a measurement zone where the test antenna is to be placed (figure 21). Such a facility can be placed indoors, thereby avoiding ground reflections, adverse weather conditions, and

high towers--features associated with outdoor ranges (figure 22). Compact ranges offer the advantage

of the direct measurement of far-field antenna patterns when compared to near-field methods which

require the measured near-field data to be processed using FFTs and other mathematics. Hence, there

are no software requirements other than those routinely used with far-field ranges. Compact ranges

are widely used for both antenna and radar cross section measurements and, as a result, much

experience has been obtained in their use.

As with any measurement facility, however, compact ranges have problem areas which must be addressed. Of primary importance is the certification of the measurement zone (also known as test zone, quiet zone, sweet spot, plane wave zone, etc.) where the antenna under test is positioned. Ideally,

the measurement zone without antenna is illuminated by a uniform plane wave; that is, the amplitude

and phase are constant over any plane transverse to the range axis in the test zone, and the phase

progresses linearly along the axis through the test zone. Practically, however, the plane wave illumination is approximate and a typical specification for antennas with D _<_ 1 . 2 m requires the measurement zone to be 1.2 m high by 1.2 m wide by 1.2 m deep; to have less than a 0.5 dB amplitude variation, and less than a 10 degree phase variation at any operating frequency that may extend from 1 to

100 GHz (figures 23-25). (This compares to a far-field range where typically a 0.25-0.50 dB amplitude

taper and 22.5 degree phase variation is assumed over the test aperture at a range distance of

Compact Range

Re f lector

Ampli tude

Variation

Antenna or Target

Under Test

Phase Fronts

Figure 21. Compact range schematic

35
36

Figure

22.

Indoor

compact

antenna

range

(15).
2 D^/A. For a distance of 4 D^/A, one assumes an 11.25 degree phase variation over the test aperture.) To verify the adherence to such specifications at each frequency band requires a planar nearfield scanner (figure 26) or at least a field probe mechanism (figure 27).

The sources of error that contribute to the nonuniform plane wave in the test zone must be con- sidered in the design of a compact range. They include space attenuation from the feed, diffraction

from the reflector edges, reflector surface tolerances, and depolarizations. Also important are the

adverse effects due to the direct radiation from the feed, diffraction from the feed and its supporting structure, stray radiation in the room, and reflections between the test antenna and compact

range [11].

In the light of the above discussion, the important question to be resolved is how well the

compact range facility applies to spacecraft antenna testing problems. First, where antenna patterns

Figure 23. Compact range main component, 1 dB amplitude contours, f = 18 GHz, horn pr<; , .

37
over ±10 degrees are required in azimuth and elevation, the spacecraft antennas must be positioned on

a rotator capable of these motions (figure 22). For systems whose antennas are fragile and are meant

to operate in a zero gravity environment, one must ensure that the "antenna configuration" does not change during the required rotations. This is a disadvantage for the compact range system, especially

when compared to the planar near-field method which does not require antenna rotations. Second, the

size of the test zone for the compact range must be sufficiently large not only to accommodate tipping

the antennas in elevation and rotating them in azimuth, but also to house the entire satellite (not

including perhaps the solar drum) if one is to measure the effects of antenna-antenna and antennastructure interactions on the antenna parameters. To satisfy these requirements for the Intelsat VI satellite would require a test zone approximately 9.8 m wide, 6.1 m high, and 6.1 m deep! Since

Figure 24. Compact range main component, 10° phase contours, f = 18 GHz, horn probe.

38
CCO

4->aaX

0) XIou

Cu

39

Figure

25.

Compact

range

main

component,

amplitude

and

phase,

before

and

after

feed

translation

in

x

scan, 7=

335

cm

(upper

portion), f=

18.0

GHz.
40

Figure

26.

Measurement

facility

schematic

and

coordinate

system,

compact

range,

NBS

Boulder,

Colorado.
single reflector compact ranges require reflector heights approximately two to four times the height

of the test zone, a 6.1 m high quiet zone would require the reflector's radius to be in the order of

12 m or more, which is roughly twice the linear size of a compatible planar near-field scanner. Compact ranges of this size are neither available nor anticipated in the near future. Currently, compact ranges with quiet zones 7.3 m wide by 4.5 m high with no depth specified are available and are presently expected to cost between $ 1 . 5M and $3.0M dollars. This estimate does not include test

equipment, and does not include the housing facility itself. For comparison, a compact range with a 1.5 m quiet zones cost in the order of $0.3M. Third, the measurement accuracies using a compact

range need to be addressed. For the measurement of the main polarization component of test antennas,

error bounds have been obtained for a compact zange whose quiet zone is 1.2 m wide by 1.2 m high with

an amplitude taper of 0.5 dB and phase variations less than 10 degrees [14]. Typically, errors on the

order of 0.05 dB and 1.0 dB occur respectively at the 0 dB and -40 dB power levels, as can be seen in

figure 28. Such results are also comparable to those obtained on a far-field range with a 0.5 dB

Figure 27. Schematic diagram of field probe mechanism (15).

41
4-> O

03CLEO

o

CDO

L_3

O

CO

4-> Co

CL

COco

~ac

03

a)CDc

03

t_co •

+-> CO

CL)

-t-> L_ M 3

03 OO

a)

<4- CD o o

C T—

o

CO +-> •r- 03

c.03 <1) Cl CD E C

O 03 O C00

OJ

CDD

CD

SP H2rt0a aAlIVTIE

42

AZIMUTH

ANGTJ5

DEGREES
amplitude taper [15]. For the measurement of the cross polarized component, however, one must realize

that the cross polarization of the field in the test zone is typically in the order of -30 dB. As a result, accurate measurements of the cross polarized component of the antenna under test below -30 dB

is presently questionable using the compact range. This is a serious drawback where frequency reuse

is utilized and polarization isolations need to be established.

As mentioned earlier, the certification of a compact range at each frequency band requires using

either a planar near-field scanner or at least a field probe mechanism to assure that the specification in the quiet zone is attained. When changing frequency bands on the compact range, one must change the feed to accommodate the measurement. (Four feed changes would be required to cover the 4-

14 GHz frequency range.) This necessitates realigning the compact range for each feed to ensure both

acceptable amplitude taper and phase uniformity in the quiet zone. This can be quite time consuming

but is very important for proper beam alignments, boresighting of the antenna under test, gain comparison measurements, effective isotropic radiated power (EIRP) measurements, and flux density measurements used for determining receiver saturation levels. These items are discussed in the next paragraph.

Of particular importance in antenna measurements using a compact range is the assumed uniformity

of the plane wave field in the quiet zone. For example, when one utilizes a standard gain horn in the

quiet zone as a reference standard, its receiving response should be independent of its location (not

orientation, obviously) within the zone. This, of course, should also be true for the antenna under

test, thereby assuring that accurate gain transfer measurements are made. This planarity of the field

also is a factor in EIRP and flux density measurements. In the former case, the accuracy of the EIRP

measurement is dependent on the accuracy of the gain transfer measurement. In the latter case, the

accuracy of the flux density (to saturate the receiver) measurement depends on the uniformity of the

flux density in the test zone. What is to be inferred here is that care should be taken, particularly

in the use of a new compact range, to verify or establish the error bounds for antenna parameter measurements. In addition, with the compact range and for determining beam alignments or boresighting of

the antenna under test, one is presently required to rotate the antenna 180 degrees about the range

axis using a polarization positioner [16], Since the size of the satellite antenna farm prohibits its

placement on a polarization positioner, one must devise and evaluate alternate schemes to boresight

these antennas using compact ranges. Where polarization positioners have been utilized for antennas

under test, typical boresight alignment accuracies of 0.25 to 0.5 mrad (0.014 - 0.028 degrees) are cited [14].

Swept frequency measurement methods across a frequency band using compact ranges can result in the same advantages given by the far-field range. Specifically, the methods can provide diagnostic

tools that are useful in identifying frequency sensitive beam squint, antenna resonances, and unwanted

scattering sources of error. However, as in the far-field method, the compact range method does not yield the near-field data whose contour plots are often used to diagnose local anomalies in an ante'' • under test [13].

4.0 Choice of the Optimum Measurement Technique for Directive Communications

Satellite Antenna Systems.

The basis for the choice of the best measurement technique has been established in thp pr<wi , sections. Using this information, ratings were assigned to each evaluation factor for ea ’ • •• ment approach. The results are tabulated in table 7. The planar near-field measurement :

43
the best score for both the critical factors and all the factors. In addition, it has the potential

to improve its rating by further development of swept frequency and beam alignment techniques.

Because of this, the planar technique will be the focus of the research effort for the remainder of this study.

Table 7 Comparative Rating of Measurement Techniques

Ratings of Measurement Techniques

Evaluation Factor Weight Planar Cylindrical Spherical Compact Range

1 . Characterize Interactions 1 10 10 10 2

2. Minimum Antenna Motion 2 10 5 2 2

3. Test Zone Size Acheivable

a. Individual Antennas 2 10 10 10 10

b. Antennas and Interactions 1 10 10 10 2

4. Detailed Pattern Results 1.5 10 10 10 10

5. Accurate Results 2 10 8 8 8

6. Frequency Change Ease 0.5 8 8 8 8

7. Swept Frequency Results 2 4 2 2 10

8. Diagnostic Information 1.5 10 6 5 4

9. Bean Alignment Accuracy 1.5 8 7 7 8

10. System Parameter Results 1 10 7 7 7 11. Ease of or Need for Probe

Correction 0.5 7 6 6 10

12. Software Complexity and Speed 0.5 8 7 6 10

13. Hardware Practical

a. Antenna Size Test Zone 2 9 9 10 8

b. Interaction Size Test Zone 1 9 9 10 2 14. Hardware Commercially Available 0.5 8 9 10 10

15. Practical to Implement 2 10 5 5 5 16. Flexible to Antenna Size 1 8 8 8 8

17. Measurement Time 1.5 7 6 5 10

18. Demonstrated Results 1.5 10 7 5 10

19. Accuracy Demonstratable 1.5 10 7 6 8

Total Weighted Sum 280 251 201.5 191 199

90% 72% 68% 71%

Critical Factors Weighted Sum 120 106 78 74 86

(Those with Weight = 2) 88% 65% 62% 72%

44
References

[1] DiFonso, D.F.; English, W.J. Far-field criteria for reflectors with phased array feeds.

IEEE/AP-S International Symposium Digest; 1974. p. 54-56.

[2] Yaghjian, A.D. Upper-bound errors in far-field antenna parameters determined from planar nearfield measurements. Part 1: Analysis. Nat. Bur. Stand. (U.S.) Tech. Note 667; 1975.

[3] Newell, A.C.; Crawford, M.L. Planar near-field measurements on high performance array an- tennas. Nat. Bur. Stand. (U.S.) NBSIR 74-380; 1974 July.

[4] Kerns. D.M. Plane-wave scattering-matrix theory of antennas and antenna-antenna interactions.

Nat. Bur. Stand. (U.S.) Monograph 162; 1981 June.

[5] Rodrigue, G.P.; Joy, E.B.; Huddleston, G.K.; Burns, C.P.; Burdette, E.C. A study of phased array

antenna patterns determined by measurements on a near-field range. U.S. Army Missile Command,

Redstone Arsenal, Alabama, Internal Report; 1975 March.

[6] Rodrigue, G.P.; Joy, E.B.; Burns, C.P. An investigation of the accuracy of far-field radiation

patterns determined from near-field measurements. U.S. Army Missile Command, Redstone Arsenal,

Alabama, Internal Report; 1973 August.

[7] Newell, A.C. Upper bound errors in far-field antenna parameters determined from planar nearfield measurements. Part 2: analysis and computer simulation. Lecture notes for NBS short

course. Antenna parameter measurements by near-field techniques. 1975 July 7-11.

[8] Yaghjian, A.D. Near-field measurements on a cylindrical surface: A source scattering-matrix

formulation. Nat. Bur. Stand. (U.S.) Tech. Note 696; 1977 June.

[9] Wacker, P.F. Non-planar near-field measurements: Spherical scanning. Nat. Bur. Stand. (U.S.)

NBSIR 75-809; 1975 June.

[10] Hacker, P.S.; Schrank, H.E. Range distance requirements for measuring low and ultralow sidelobe

antenna patterns. IEEE Trans. AP-S, AP-30(5); 1982 September.

[11] Vokurka, V.J. Seeing double improves indoor range. Design feature. Microwaves and RF. 24(2):

71-76; 1985 February.

[12] Johnson, R.C.; Ecker, H.A., Hollis, J.S. Determination of far-field antenna patterns from nearfield measurements. Proc. IEEE 61(12); 1973 December.

[13] Repjar, A.G.; Kremer, D.P. Accurate evaluation of a millimeter wave compact range using planar

near-field scanning. IEEE Trans, on Ant. and Prop. AP-30(3); 1982 May.

[14] Scientific Atlanta 1984/85 Instrumentation Products Catalog. Atlanta, GA: Scientific-Atlanta,

Inc. 103-104.

[15] Hollis, J.S.; Lyon, T.J., Clayton, L., Jr. Microwave antenna measurements. Atlanta, GA: Scientific-Atlanta, Inc.: 1970 July. p. 14-14.

[16] Hess, P. Boresighting antennas. Atlanta, GA, Scientific-Atlanta Inc.: 1978 February.

[17] Johnson, R.C.; Poinsett, R.J. Compact antenna range techniques. Technical Report. RADC-TR-66-

15; 1966 April

45
APPENDIX A Planar Near-Field Measurements Theory

A-l. Introduction

The planar near-field (PNF) measurement technique was the first of the near-field techniques to

be developed, verified, and implemented as an operational method of obtaining antenna parameters. It represented a major departure from previous methods where the attempt had been to observe the farfield parameters of the antenna under test (AUT) directly and where very little mathematical theory or data processing was required between measured data and final results. A need for an alternative mea- surement technique, serious enough to justify the additional complexity, has been generated by the

development of increasingly complex antennas such as phased-arrays and shaped-beam communication an- tennas. These antennas, and their associated electronic systems, have presented measurement problems

which were impractical or impossible to meet with far-field ranges or anechoic chambers.

The success of this measurement technique has depended upon advances in three diverse areas.

First, there has been the development of a rigorous, and yet easily applied, plane-wave scattering

matrix theory which can be applied to arbitrary antennas and includes the mechanism to correct for the

non-ideal characteristics of the probe. Secondly, the rapid growth of high-speed digital computers

has made practical both the automatic control of the measurement process as well as accurate and efficient means of mathematical calculation. Finally, electronic receiving equipment is readily available which will accurately measure the amplitude and phase of microwave signals over large dynamic

ranges.

The material which follows will be presented primarily from an experimental or applied point of view. It is oriented towards the engineer who must use the theory, computer programs, and instrumentation in the measurement of antennas.

A-2. Planar Near-Field Theory from a Measurement Point of View

The mathematical formulation used in this summary follows very closely, and is based entirely

upon, the pioneering work of D. M. Kerns in his development of plane-wave scattering matrix theory.

This work began in the late 1950' s , was presented and used in various measurements during the 1960's,

and has recently been published in a very complete and extensive monograph [Al] Although there have

been other approaches to the theory and, as summarized both by Kerns and in a review paper [A2], there were a number of earlier developments; none have received the widespread acceptance and success that

Kerns's work has. This is due to a combination of rigor, completeness, and practicality which has

made the transition from mathematical theory to actual implementation much easier. In the present

theory, it is not necessary to make simplifying assumptions related to the symmetry, separability of

fields, polarization, or reciprocal nature of the AUT. Neither must the probe have similar or additional ideal properties. Yet in spite of, or perhaps because of, the rigorous nature of the theory,

the final working equations and mathematical operations used in the implementations of the theory are surprisingly concise and easy to understand and use.

The following discussion of the theory will focus on these final working equations and their

use. No attempt will be made to present a complete and rigorous derivation such as presented by

Kerns, or to trace the development of near-field measurements as done by Johnson et al. in their

review paper. We will, instead, present a development of the basic working equations from an intuitive or measurement point of view, then relate the near-field parameters and equations to more

46
i onventional far-field quantities, finally pointing out some subtle aspects of the plane-wave scattering matrix theory which may be overlooked and can lead to confusion if not handled correctly.

A-3. Definition of Antenna Coordinate System, Vector Components, and

Direction Parameters

The results of either near- or far-field measurements are generally given in terms of the vector

components of the radiated electric field as a function of direction or position. Both the vector

components and the direction parameters must be defined with respect to some coordinate system and,

for maximum utility, the coordinate system should be fixed to the antenna. With such a coordinate

system, the measured parameters are independent of the mounting or orientation of the antenna and, if

required, can be easily transformed from the antenna coordinate system to another measurement or operation system if their relative orientation and position are given.

The antenna coordinate system used throughout this discussion will be one with the plus or minus

z-axis in the nominal boresight direction and the major polarization axis in the x- or y-direction for

linearly polarized antennas. For other polarizations, the locations of the x- and y-axes are defined

by either the geometrical structure of the antenna or the location of fiducial marks.

One example of an array antenna with its coordinate system defined as above is shown in figure

A1 . In this case, the beam may be electronically steered in many directions, so the z-axis is defined

as normal to the plane of the array with the y-axis parallel to the narrow walls of the radiating

horns and, therefore, in the direction of the main component of the aperture electric field.

Once the coordinate system is defined, we must also define vectors and/or angles to specify directions relative to the antenna, as well as unit vectors to be used in describing the vector components of the field. There are a number of possible choices for these direction and component parameters. As each of the possible choices is used at some point in the analysis, they will now be discussed.

The components of the electric field, _V_, can be described in terms of rectangular components and

as functions of a position vector _r.

V (r ) — —

= V (r ) e + V (r ) e + V (r ) e (Al) ' x

' — ; —x y — —y z

' — ' —

where

r = xe + ye + ze , (A2)

and the e/s are unit vectors along the three axes. An alternative position or direction vector used

extensively in the planar analysis is the propagation vector k_ whi ch specifies the direction of propagation and phase constant of a plane wave. The three rectangular components are denoted k , k , and

x y

k

z = +y . Since the magnitude of k_ is fixed by the relation _k • _k = k 2 = a) 2 ue, only two of the com- ponents are required to specify the complete vector and, therefore, a given direction in space.

Generally, the two components used are those transverse to the z-direction and the transverse vector

is denoted by the symbol K.

K = k e — x-x

+ k e y-y

I A'

47
y ( A4) = /k 2 -k 2 - k

2 = /k 2 - K

2 x y

Since k and k vary independently between -» and +® and are chosen as real quantities, y is taken as

x y positive for K < k and positive imaginary for K > k. Real values of y correspond to real space, real

angles, and propagating plane waves. Imaginary values of y correspond to imaginary space and evanescent waves.

While the above parameters are useful in many applications, spherical angles and spherical vector

components are more widely used for describing far-field parameters where the field is perpendicular

to the radial direction, and, therefore, to k_. Figure A1 shows the spherical angles 0, <|>, and the

unit vectors e_g

, _e^ which are widely used and very appropriate in many cases. If the main beam of the

antenna is along the z-axis, as specified in the definition of the coordinates, and the antenna is linearly polarized, the 6- and ^-components are not the most appropriate for specifying the field vec- tors. In the region of the main beam, the unit vectors —e. and e ± change direction relative to the —(J) antenna as a function of <t>. We could change the definition of the antenna coordinates so that the

polar axis (the z-axis) was not in the vicinity of the main beam; however, this would make the refer- ence to existing planar analysis more difficult, and there are times when the 0 -

4>-coordi nates and

components are required. For these, and other reasons which will become apparent, the defined antenna

coordinates and 0- 4> definitions should be retained.

To obtain an alternate set of spherical angles and components, the x-, y-, z-axes are left fixed

in the same position relative to the antenna, and the y-axis is chosen as a new polar axis for the

definition of the angles E, A, and the unit vectors _e£, _e^, shown in figure A2. These components have

the advantage that, for a linearly polarized antenna appropriately rotated about the z-axis, the field

is primarily either E- or A-polarized.

A third set of spherical angles is shown in figure A3 where the x-axis is the polar axis and the

angles and unit vectors are denoted respectively by a, e, e^, e^. This set is useful for specifying

a linearly polarized field, as is the A-E set.

All three of the spherical angle sets are useful in certain instances, and are each closely as- sociated with one of the three types of rotator mounts used in measuring antenna patterns. Figures

A4, A5, and A6 show how the 0-$, A-E, and a-e angles and components are respectively appropriate for

the model, az over el, and el over az mounts. In each case, the upper rotator of the mount produces a rotation about an axis fixed to the antenna and is, therefore, the polar axis of the rotator. The

spheres shown in the figures are fixed to the antennas and represent their spherical coordinates.

When the mount rotates, the sphere moves with the antenna, and the source antenna, or probe, traces

out the longitude and latitude lines on the sphere. The relative motion between the AUT and the

source, or probe, is equivalent to their moving on the surface of the sphere and measuring the field

along lines of longitude or latitude.

One of the primary motivations in maintaining a coordinate system fixed to the antenna, and in

defining three different sets of spherical angles, is to facilitate the reference to each different

set and to avoid confusion in the transformation equations between different sets. If all three were referred to as 0-<f> sets with the coordinate system reoriented relative to the antenna each time, the

notation, references, and transformations would be quite confusing.

48
Yn

X

Figure A-l. Antenna coordinate system using 0 and $ spherical angles with z as the polar a« • .

49
Y

Figure A-2. Antenna coordinate system using A and E spherical angles with y as the polar axis.

50
YA

Figure A-3. Antenna coordinate system using a and e spherical angles with x as the polar t .-

51
ya

Figure A-4. Model tower used to measure 0-<t> and h-v vector components.

52
Figure A-5. Azimuth over elevation rotator used to measure A-E vector components.

53
ya

Figure A-6. Elevation over azimuth rotator used to measure a-e vector components.

54
As already noted, a direction in real space can be defined by specifying either the components of

the propagation vector or one of the sets of spherical angles. Transformation between different parameters is accomplished by the following equations:

k = sine cos <f> = cosE sinA = sina , (A5)

k = sine sin<|> = sinE = cosa sine , (A6)

k = cose = cosE cosA = cosa cose . (A7)

The transformations are one-to-one for all directions except at the poles of each set where am- biguities do exist. The problem is in determining the azimuthal angles (those which are a rotation

about the polar axes, namely <t>, A, and e) at the poles of the corresponding coordinate system. For example, from eqs (A5), (A6), and (A7), the transformation equations from the (A, E) to (0, <)>) coor- dinates are

cos0 = cosA cosE, (A8)

tan<j> = tanE/si nA ,

( A9)

and when A=E=0, <j> is indeterminate. In such cases, it is necessary to choose a specific value for

<j>, and, depending upon the application, it is usually set to either tt/2 or zero. Similar situations

arise in determining A and e when at the poles of those coordinates, but values can be assigned which

will give consistent and correct results.

The transformations between the vector components are also required and are derived from expressions for the spherical unit vectors in terms of the rectangular unit vectors.

(AlOa)

(AlOb)

(Alla)

( Allb)

( A12a)

( A12b)

(A13a)

( A13b)

e. = cos0 cos<j> e + cos0 sin* e - sin0 e —0 T —x

T -y —

e = - si n<i> e + cos<j> e

-4> -x y -y

e . = cosA e - si nA e —x —

e c = -sinA sinE e + cosE e - cosA sinE e -E -x -y -z

e = cosa e - sina sine e - sina cose e -a -x -y -z

cose e - sine e - y -z

From these expressions, the vector component transformations are: VA - E > = IMf V6 ’ ) - —00^^ V8 ' > ' and

v

e (A, E) - c088s

s

E in ^ v8 (e, ) + |2f|v (9, ) ,

where cosE = /I - (sin0 s i

4>

2

, and the angles 0 and $ are given by eq (A8);

55
where

w / \ cose cos* „ , a , x sin* „ > v (<*> £ ) = —ttt

r V Q ( 0 > 4>) - - --t* \Me, $) a COSa 0 Y/ COSa <(> T

11/ \ 0 ^o*.i/ Q cose cos*.. /. \ V (a, e) = —31 v.(e, *) + 31 v (e, *)

e COSa 0 COSa <f> T/

(A14a)

(A14b)

cosa = /I - (sine cos 4>

2

, and

cose = cosa cose ,

tan<(> = cosa si ne ;

V (a, e) = v (A, E) - SinA SinEV

C (A, E) a COSa A

v ’ ' COSa E

V (a, e) = SinA S1nEV.(A, E) +

COSA_

v (A, E)

e

v ’ ' COSa Av ’

' cosa E

v * '

cosa = /I - (sinA cosE) 2

sinE = cosa sine , tanA = tana/cose

(A15)

(A16)

(A17)

(A18a)

(A18b)

(A19)

( A20)

There is a fourth set of linear components which are sometimes measured, and arise from a different

use of the model mount shown in figure A4. If the source antenna is linearly polarized and stays

fixed as the antenna is rotated on the mount, the 0-<t> components are obtained. In some cases, the source antenna is rotated about its axis by the same 4>-angl e as the AUT. The vector components obtained and denoted e

h and e

y are those shown in figure A7, which is a projection of the 0-<j> coordinates on the x-y plane. The transformation between these components and the 0-<t> components are:

e

h = cos<f> e0 - s i n<t> e^ (A21a)

e = sin* e Q + cos* e A (A21b)

-v -o -<p

V

h

(e,<|>) = V

Q

( 6 ,<}>) cos <(> - V (0,4*) sin* (A22a)

V

v (e , 4>) = VQ (0 ,4») si n<j> + V (0,4*) cos<j> (A22b)

It should be noted that with the above definition of components and angles and along the x-z plane

where ky=0

V A(A ’ 0) = V a(ct ’ 0) = V6 ’ 0 or tt) = ± V

0

( 0 , 0 or n) (A23a)

V c (A,0) = V (a,0) = V (0, 0 or tt) = ± V A (0, 0 or tt). (A23b)

t e V <p

Similarly, along the y-z plane where k x =0

V a

( 0,E) = V a (0,e) = V

h (0, ±tt/2) = + V^(0, ±tt/2) (A24a)

V

e

( 0,E) = V

e (0,e) = Vv (0, ± tt/ 2 ) = ± V

0 (0, ±tt/2). (A24b)

56
With the aid of the above transformations and their inverses, any of the vector components can be obtained from any other set.

A-4. The Transmission Integral and Associated Parameters

Consider now the two-antenna system shown schematically in figure A8. The antenna on the left,

referred to as the antenna under test (AUT), is oriented with its coordinate system coincident with

what may be called the reference coordinate system OXYZ. The generator connected to this antenna produces an incident wave amplitude ag at the terminal surface Sg. As a starting point, assume that the

antenna radiates a single y-polarized, plane wave propagating along the z-axis which is proportional

to the input amplitude. The complex proportionality constant, T 10 (K_= 0) is referred to as the plane wave transmitting coefficient and the subscript "10" denotes that it applies to the transmission from

Figure A-7. Relationship between h-v and e= 4

> vector components.

57
Scan

Plane

<L> >

03£

QJC

03Q.

TD

O)NE

<1) _c

o

oo

00I <c

58

Single,

Linearly

Polarized

Plane

Wave
terminal surface So to Sx at the origin of the coordinate system. The independent vari abl e

_K def i nes the direction of propagation of the plane wave and is zero along the z-axis. The plane wave propagating from Sx to S 2 will be modified by the phase factor e

1 kd and received by the "probe" antenna on the right. It will produce an output wave amplitude at the terminal surface Sq denoted by b q

The

probe's receiving coefficient for this incident plane wave is denoted by Sq 2 (J< = 0). If we assume

that multiple reflections are negligible, the transmission equation for this highly simplified condition is then

bo = F'a 0Tio(K = 0) e lkd

S(, 2 (K = 0), (A25)

where F' = 1/(1- r

£

rp

)» and r

x> and r

p are reflection coefficients for the load and probe respectively.

(It should be noted that the time factor assumed here is e"

lajt

. While this is the opposite of most

electrical engineering formulations, it is consistent with the original derivation of the plane wave

theory and will be used herein.) In general, a plane wave will have some cross component, as shown in

figure A9, and the transmitting and receiving coefficients are generalized from complex scalars to

complex two-component vectors, namely.

Il0<* - °> T 10x ( i

* °> 5* + T lo/— -

°> %

• (A26 >

S^{K - 0) = S^

2x

(K - 0) e

x + SJ 2y

(K - 0) , (A27)

and the transmission equation becomes

b

0

- F VT 10x<i - °> °> + T 10y<* °> Wi - °» e1M

(A28)

= F'a 0 (T 10 (K = 0) • S_q 2

( K_ = 0))e

lkd

.

To further generalize the equation, the transmitting coefficient is extended from a complex vector

describing a single plane wave to a complex vector function describing a continuous spectrum of plane

waves, as shown in figure A10, and will hereafter be referred to as the plane wave transmitting characteristic (PWTC). For each value of _K, a 0 Txo(K) completely specifies the amplitude, phase, and

polarization of the plane wave propagating in that direction. In a similar way, S_q 2 (K) defines the

probe's response to incident plane waves and this parameter will be referred to as the plane wave re- ceiving characteristic (PWRC). The total output signal is now the combination of responses to each

plane wave and is expressed mathematically by integrating over all values of k

x and k

y

. Hence,

bo = F'a 0 JjTio(K) • Sj) 2 (K)e

lYd

dk

x dk y

.

Note that the exponential now contains the factor y rather than k since the phase change will vary

with K_ and, although not generally noted explicitly, y is a function of _K (see eq A4). If the prose

is now translated in the plane z = d to the position P = xe + ye , as shown in figure All, an a

•-

i K -P -y

ditional phase factor e will result and the final form for the transmission integral is

bo(P) = F'a 0 //Txo(K) • S[)2 (K)e 1Yde'

, ^kx dk y

;

59
Scan

Plane

60

Single

Plane

Wave

with

Two

Polarization

Components
Scan

Plane

61

Angular

Spectrum

of

Plane

Waves

with

Different

Polarization
or, written in the shorthand notation.

t>o( P.) = F'ao/T 10 (K) • S|)2 (K)e

lYd

e

1 ^K . (A31)

Although this equation has been developed here by using a specific highly idealized situation, the

results are much more general. The only approximation actually required in the derivation is the as- sumption that multiple reflections between the two antennas are negligible. When this assumption is

satisfied, the transmission integral is valid for any antennas with arbitrary pattern and polarization

properties and for arbitrary separation distance. It is the basic equation upon which the PNF mea- surements are based.

In keeping with the development by Kerns, the transmitting and receiving functions T 10 (J<) and S^OO

used here are the “transverse" vectors; they include only the components transverse to the z-axis.

The z-component of the complete transmitting vector, t_ 10 (J<), can be found from the requirement that

the complete vector must be orthogonal to the direction of propagation

Since the z-component is redundant, and the theory is used to analyze measurements made in the x-y plane, there is a logical justification, and in some cases a convenience and economy, in developing

the theory in terms of the transverse rather than the complete vectors. Kerns uses the transverse

vectors almost exclusively in his work and when individual components are specified, they are the xt 10 (K) • k = 0 . (A32)

PnHintinn

P

Receiving

System

(z = 0) (z = d)

Figure A-ll. Translation of probe in measurement plane.

62
,uM y-components or j^- and < 2

- components. The latter unit vectors are, respectively, in and perpendicular to the plane of k_ and where

£i = K/K ,

( A33)

<2 = ? z x je lt ( A34)

and the notations for the and <2 components of T_io(JS) are > respectively, T 10 ( 1 ,J<), T 1 0

(

,J£) - Where necessary or convenient, Kerns does introduce the complete vectors and uses a notation, also

employed here, for denoting the transverse vectors by capital letters and the complete vectors by

lower case letters. The use of the transverse vectors has continued in other analyses, but the con- vention to differentiate between the two has not always been followed; therefore, care must be taken

to determine which one is actually being used.

While the transverse vectors are convenient in the development of the theory, it is often preferable to use the complete vectors for practical implementation of the theory, and the latter approach

will be used almost exclusively in the following presentation. This choice is made because the desired final result of either near- or far-field measurements is generally the complete electric (or

magnetic) field vector or the components orthogonal to k_ rather than the components orthogonal to e^

If TioOO 1S determined from the near-field measurements and calculations, additional steps are re- quired to calculate its z-component and then obtain either circular or linear components corresponding

to main and cross polarizations. These extra steps can be eliminated by employing the complete vectors in the working equations. In addition, there is occasionally a simplification and clarity in the

equations which improves understanding.

In order to define the relationship between the complete and transverse vectors we define the

unit vectors

\ = k/k , (A35)

e|

| e £2 x e^ , (A36)

III (A37)

and note, that for the propagating region where K < k

* ie «i

= V ( A38)

For the propagati ng region, the relationships between the complete vectors and the transverse components are

Ll

(JO = 7

Tiod.K) Iq + T 10 (2,K) e^ , (A39a)

t2o(K) =

" 7

T 20 ( 1 ,K) + T 20 ( 2 ,K) e^ , (A39b)

I01OO =- 7

Soi(l.K) eg + S 02 ( 2 ,K) , (A40a)

63
i02 (K) = ( A40b) {

Sozd.K) eg + S 02 (2,K) e

(The subscripts "10" and "20" are discussed following eq (A48).) For the evanescent region where

e_Q and e_^ are not defined, the unit vectors e_|

| and e

± should be substituted, respectively, in eqs

(A39) - (A40) for e. and e A

. —t) —<p

A number of interesting and important facts related to eqs (A39) and (A40) should be noted. For the transmitting characteristics, the complete vector is transverse to k_.

k • t_ 10 (K) = 0, ( A41

k • t 20 ( K) = 0, ( A42)

the on-axis values of complete and transverse vectors are equal

t 10 (0) = T 10 (0), (A43)

t 2o( 0) =

l2(}( 0) ,

and lio(K) is the projection of t_i o (JS) on the x-y plane.

The complete and transverse receiving characteristics are related in a much different way which,

at first, may seem unreasonable. Due to the factor y/k in eq (A40), the magnitude of the complete

vector is less than the magnitude of the transverse vector, i.e.

lioiOOl < |S 01 (K)| , (A45)

or, equivalently,

Sjdi(K) * loiOO <S01 (K) • So dK) (A46)

(the asterisk denotes the complex conjugate).

This is due to the fact that the receiving characteristic does not represent an actual vector

field quantity. It represents the antenna's response to two orthogonal polarizations of incident

plane waves. The two components of that response, corresponding to the two polarizations, are com- bined into a "vector" for convenience and conciseness in writing equations. But, as illustrated by eq (A45), it has this non-vector property which must be noted in the transformation between complete and

transverse vectors. And, although the terms "complete" and "transverse" are used, Sj)i(jO is not the

projection of s_oi(_K) on the x-y plane. However, the relations

s_oi(0) = Sqi(0) , (A47)

k • s 0 i(0) = 0, ( A48)

do hold and the same is true for s_02*

64
Some comments are advisable at this point to explain the reason for the use of both "1" and "2"

in the subscripts for the spectral coefficients, such as iio* y.o> ioi > and s_02 . This notation is

used to distinguish between the plane wave characteristics of the antenna in the right (subscripts 01,

10) and left (subscripts 02, 20) half spaces corresponding respectively to plane waves with

k = +y and = -y. For instance, in the configuration shown in figure All, the characteristic of

the AUT being measured and appearing in eqs (A25) - (A31) is T_io(j£)» and > correspondingly, the pertinent probe receiving characteristic is Sq 2 {K) • This is also the case in almost all planar measurements. We are generally not concerned with the back lobes of the AUT, described by X2

( JS.)

- The

right-side receiving characteri sti c of the probe, Xoi(M> does not appear in the transmission integral

and, therefore, cannot affect the measurement. In cases where the back lobes are of interest, the AUT

can be reoriented and the transmission equation written in terms of XoOO* A concise notation, to be

used at appropriate times hereafter, is the subscript "q" in place of the "1" or "2" where equations

apply to either value. Table A1 contains a summary of the notation denoting the meaning of the

various symbols and subscripts.

Table A1 Notation Summary

Subscripts denote

Transmitting 10,20

Receiving -*- 01,02

Right Side * 10,01

Left Side + 20,02

Vector Component

Tl0x(—) = x-comP oner| t

tiQR(_K) = right circular component

t

1 qa(—

= az1 muthal -component

Capital letters denote transverse vector (x- and y-components or x\ and X 2

) IloCO = T

1 0x + T 10y

= T1q (1 +

Tiq(2,J<)_X2

Small letters denote complete vectors (linear spherical such as 0 and ^-components

A and E-components or circular R and L-components)

-Lio^—

CD *1 0

r—

II -4-> + t 10^(Ji)l4

- hoA^^A + 1

1 0E

= hoR^-SR + t 10L^lL

Different letters or primes are used to denote plane-wave parameters for different

antennas

jL02^’ JL." 02^)

"t" is typically used for the antenna under test, and "s" for the probe

65
Returning to the transmission integral, and noting from eqs (A39) and (A40) that

t_io(]0 * .Lo 2

( K.) = Iio(K) • S_02 (Ji)» (A49)

we see that eq (A31) can be written in terms of the complete vectors as

bJj(P) = F

1 a 0 /tio(K) • s_o 2 ( j<) e lYd

e

1 ^-

dK , (A50)

and this becomes the final form for the transmission integral. Since the object of the measurements

is the properties of the AUT, a solution of eq (A50) is required in terms of the measured data

b o( P_) and the probe's PWRC s_q 2 (J<). The first step in this solution uses the fact that ea (A50) is a Fourier transform relation. If we denote the coupling product as

D'(K) = t 10 (K) • !q 2 (K) , (A51)

the Fourier inverse is

ei,cl

, W -ik-P jn (A52)

In actual measurements, the ratio bo(P)/a 0 is generally obtained in two steps. First, a reference

point P 0 is chosen which is at or near the maximum amplitude of bg ( P ) . Relative near-field data are then obtained with respect to the probe output at this point and denoted by

t>o(P)

B o(p) = (A53)

A normalization constant A' is then measured, which is the ratio of the AUT input to the probe output

with the probe at P 0

. In terms of these parameters eq (A52) becomes

-iyd -i K-P D'(K) = 47W ^ B

o

( -

} 6

"

" d

-

’ (A54)

a o where

A' = WT * (A55)

Equation (A51) provides one equation for the two unknown components of t 10 (K). A second equation is

obtained by using another probe with a suitable PWRC Sq 2 (K) which produces measured data

Bq(P), normalization constant A", and calculated plane wave spectrum

-iyd -i K -P

= WF 1 B

»

( ^

8

"

"d ?‘ (fl56)

The two equations to be solved for t_i o (Jl) are > therefore,

D'(K) = t 10 (K) • s_g 2( K. ) ,

D"(K) = t 10 (K) • sS 2 (K) .

(A57a)

( A57b)

An explicit solution of eq (A57) requires a choice of orthogonal unit vectors such as e^, e^.; e^, e^; etc. to be used in the expansion of the dot product in eq (A57). Rather than choose a specific set at

66
this time, let us denote two general orthogonal unit vectors by e and e_, which have the connotation

of representing the main and cross-component fields of the AUT. Expanding eq (A57) in terms of these

components, and solving for t 10m

(_K) and t 1Qc (J<), gives

t

t

D

1 s'

s ' s

m c D"s

1 m

m c

D"s

1c

s ' s"

c m

D

1 s"m TrT

ir c m

(A58a)

( A58b)

-here the abbreviations tm

= t JOm

(K), t(. = t 10c(K>, sj, = s^K), s“ - sJ 2m

(K), etc. have been

employed for brevity. As a general rule the probes are chosen such that the first one couples primarily to the main component and the second couples primarily to the cross component. An exception to

this is when linear probes are used to measure a circularly polarized antenna, or vice versa. However, in either case.

( A59)

and the solution is then written

D"

D"sT

p'/p" H

s H

s

D'

*c

=

S p m

H

s

1 ri 7 IT 1 - P

s /Ps

where the receiving polarization ratios are

( A60)

(A61)

p s^-^

s 02c^ /s 02m^ ’

Ps(D = S 02 C (—)/ S 02m(—) *

( A62

( A63)

It is apparent that the PWRC's of the two probes must be linearly independent to give independent

equations in (A57). From eqs (A60) and (A61), the essential requirement is that

p;(K) * Pg(K) ,

( A64)

where the dependence upon _K has been made explicit to emphasize that this condition must hold for

every direction where t_ 10 (_K) is desired. The linear independence requirement does not demand that the

probes be orthogonally polarized in every direction, although this would be the best arrangement. Nor does it prohibit the use of circularly polarized probes; for if the first probe is nominally righthand circular, and the second nominally left-hand circular, or vise versa, eq (A64) is satisfied.

In many cases, instead of using two distinct probes, a single probe with nominal linear polar’

zation is used. The "second" one is obtained by rotating the probe about its z-axis by 90°. This

approach has the advantages that only one probe measurement is required; s_02 (jO and sjj 2 (J<) are obtained from the same measured data, and certain normalizations and phase measurements are simph‘:»*d.

The transmission equation and probe correction have been obtained for the case of a *rans ’•• •

test antenna and receiving probe. The inverse arrangement is also possible where the probe i

67
transmitting and the receiving characteristics of the AUT are obtained. In this case, the transmission equation becomes

where

b 0 (P) = F a l) J toi(K) • s^ 0 (K) e"

1 Yd

e

-1 dK (A65)

F = 1/(1 - r

] ra

)

(A66)

r is the reflection coefficient of the AUT and aj is the input amplitude to the probe. The measurea ments and calculations follow in a parallel way to the case of a transmitting test antenna.

Now that the PWTC has been obtained, equations are desirable to relate it both to receiving properties and to more conventional antenna parameters. If the antenna is reciprocal, t^

Q and are related by the reciprocity equation

t (K) = —oq —

yJ y t ( o —go

K)

%

k (A67)

The total power gain, receiving effective area, and asymptotic far-electric field are, respectively.

G

q

(K) >

4 iw2 lL o(k) -q u -

Hot 1 rJ

2

! a

(A68)

4Tt 2n It ( K) 1 2 o|—oq — |

E (r) ~ iy t (Rk/r)a e ikr/r —

q

v —

' -qo — ' o

( A69)

( A70)

In the above relations, y 0 = /e/p is the plane wave admittance in the transmission medium, n

0 is the

characteristic admittance for propagated waves in the transmission line connected to the antennas, r a is the antennas' reflection coefficient, and ^is the position vector with transverse part R_,

r_ = R_ + ze_z

. (A71)

In measurement-related calculations, it is seldom, if ever, necessary to utilize the admittance factors no and y 0 , explicitly. They generally cancel out in final results; and, since a flexible nor- malization is employed (Kerns, 1981, p. 52), it is also possible to arbitrarily choose no = Yo* The

only situation where explicit values must be used is when the transmission lines on the AUT and probe

are different.

The above relations in eqs (A67) - (A70) are written for the test antennas coefficients t 10 (K),

but the same equations are true for the probe and are valid if "t" is replaced by "s". When writing

general relations such as eqs (A67) - (A70) and (A78) - (A92) that are true for any antenna, the "t" will be used but the equations are valid for any antenna and the symbol denoting that antenna can be

substituted for the "t" where appropriate.

We conclude this section with a discussion of circularly-polarized parameters, which are often

useful alternatives to the linear components. The circular basis vectors are defined in terms of the

general linear unit vectors (e_ ls e_2 ). In this use, (e ls e 2 ) are any pair of unit vectors orthogonal

to k_ such that (e^, £2 , e^) are a right-handed triad. In particular,

68
(A72)

and the circular basis vectors are

Then

and

-1 -6’ ^A’ -h’

®e» §£» ev

;

= (e x + ie_2)//2 ,

e

L = (e L + e 2 )//2 ,

i ( k r - ait

( A7 3

-R Sr e

v-l

= e

- L e

i ( kr - ut)

(A74)

(A75)

(A76)

( A77

represent, respectively, right and left ci rcul arly-pol ari zed plane waves traveling in the outward

radial direction and the complete PWTC in terms of circular components is

t (K) = t d (K) e„ + t . (K) e, . -^0 — qoR — -R qoL —

—

The transformati ons between linear and circular components are then,

(K)

(A78)

t W = (t qoR 1 qOl

it11 (!S))//2

q02

;/vV

'qoL

. (t Q01

W

'q02

Vi'’’ = (t qoR

( -’ + Vl( - ))//J'

t W=Ut W

q02

1 qoR qoL

( A79

( A80)

(A81)

(A82)

where the third subscript denotes the component. Transmitting polarization ratios are defined for

linear and circular components, respectively, as

1 + P*„(K)

P t£^ = t q01^- )/t q02^-^

“ _1

^1 - P^K))’

n m

P t^ ( ^

+1 tC - \oR (K) _i

‘

( A83)

( A84)

While these complex polarization ratios are very useful in calculations involving polarization mismatch, more conventional parameters, such as axial ratio and tilt angle, are also required. In terns

of the polarization ratios, these are

AR (K)

t qoR^- ) + V(KJ 1 + »tc ( «

t qoR ( -

) V( -

K) 1 - [Off (A85)

t(K) = 1/2 arg (P

tc

(K)

69
The circular polarization components of the PWTC are defined to correspond to the polarization of the

transmitted waves, in accordance with the IEEE definitions [A3], The receiving parameters, s/ , however, are defined in terms of the antennas response to incident plane waves. s^

R should, therefore,

couple only to an incident right circularly-polarized wave and, similarly, s^

^ should couple only to

one of left circular polarization. This implies that the coupling product, eq (A51), should be

wri tten

D‘(K) =

^OR (—) s 02R (—} + 1 10L ( —)s 02L^—^ * (A87)

This consistent choice for the coupling product requires that

s ;q R<«

= (S oq

l

( -’ + iS

iq 2<^ )/Z > (A88)

V(!!) * < s ;q i<« - is

;q2 (0)/^

( A89)

s ;q i(5>

*

< S iqR<« * • ( A90)

- i(s iqR ( ^

- s

;qL (5»/^ • (A91)

The resulting differences between eqs (A79) - (A82) and eqs (A88) - (A91) imply that the receiving

basis vectors are complex conjugates of the transmitting ones, i.e..

s' (K) = s d -oq — oqR

(K) —' -R^

*

e n + s oqlW (A92)

The only assumptions involved in the development of the equations in this section other than the usual ones of linearity, superposition, etc., are:

1. There is no scattering from the probe, the scanner, or the room to produce extraneous signals

at the probe.

2. Measurements extend over an infinite area.

3. The measured spectrum is band limited and data are measured at increments equal to or smaller

than specified by the sampling theorem.

Since each of the above three assumptions are evaluated and considered in the error analysis, the

working equations can be considered to be exact and the sources of error are then due to uncertainties

in measured data.

References

[Al] Kerns, D.M. Plane-wave scattering-matrix theory of antennas and antenna-antenna interactions.

Nat. Bur. Stand. (U.S.) Monograph 162; 1981 June.

[A2] Johnson, R.C.; Ecker, H.A.; Hollis, J.S. Determination of far-field antenna patterns from near- field measurements. Proc., IEEE 61; 1973 December, p. 1668-1694.

[A3] IEEE Standard 145-1983 Definitions of Terms for Antennas. The Institute of Electrical and Electronics Engineers, Inc. New York.

70
APPENDIX B Cylindrical Near-Field Theory Summary

Just as in the planar theory, we begin here by defining reference and probe coordinates. In this

case, there are actually three coordinate systems, as shown in figure Bl. The reference system C

Q

is

fixed relative to the test antenna, with its origin at the center of the measurement cylinder [Bl] and

the coordinates and components of the results will be defined with respect to this coordinate system. The probe cylindrical system is fixed to the probe with its origin at the end of the probe

and the z^-axis parallel to z Q

. The auxiliary probe coordinates are also fixed to the probe, but the

origin of the system is along the z Q -axis, as shown in figure Bl, displaced a distance z Q along

this axis and rotated by the angle <t> Q about the z Q

-axis. The transmitting properties of the test an- tenna, relative to C

Q

, for the given orientation, is denoted by T^(y). The polarization index "s" takes on the values 1 and 2 which corresponds respectively to <t> Q

- and 0 Q -components. For each component, the complex value of T (y) defines the amplitude and phase of the cylindrical wave with z- component of k_ equal to y and mode index n. Once T^(y) has been determined, the far-field parameters

are easily obtained from the relations.

Wv j> , 0 J

= -2k sin 0 o o

a o

e

i kr

l n=-®

(-D" CTj(r) <4

- iT^(r) <4 ] Y 0 0

in<t> (Bl)

G (0 , $ ) o o

16 irk 2 sin 2 0 Z n (1 - |r I 2

) oo a

r , . , n 1 . . i n <j> l (-i) T

n (y) e l (- 1 )" T*(y) e

in *

VJ...O 1 1

<- i)nT

J w

^ la x \

«1) 0 0

p( “•o’ - Vg(e°^

0

) - -

l e

1 "*

(B 2 )

(B3)

respectively for electric field, power gain, and polarization ratio, when y

= k cos0.

In a similar way, the cyl i ndri cal -mode receiving coefficients of the probe relative to C' are

1 s ^ denoted by R

n (y), where s, n, and y are the same as for the test antenna transmitting coefficients

T^(y). The prime on the R denotes that these are coefficients with respect to the auxiliary probe

coordinates. The transmission formula is then given by the equation.

B' ( <t> , o VTo’

z o

}

b

1 (d> , z ) 0

v Y0 ’ o'

b ' ( <}> , z ) o

Tm m

b

1 ( <±> ,z ) o

vm’ m

i 1 • r *V

oo 00 2 = l I Cl

n=-» -» s=l

R

S (y)

n

v ' 1 s in * 0 T*(y)] e dy (

4 )

As in the planar case, two independent measurements with different probes are, in general, required to obtain the two polarization components of T (y). The second probe's coefficients are denoted by

m 5n R

n (y) and the second transmission equation is

bo

( V z o

} B <V z o> b° u°, ,°)

r\ ' Y n 9 n ' (B 5 )

b"(d>,z)(l-rr) ^ ^ o

' v

n n' v a p

' n=-« -<*>

2 „ i n<(> iyz

C l rS (y) T^(y)] e

0 e0 dy . s=l

n n

71
o

Figure B-l. Three coordinate systems referred to in cylindrical measurements.

72
In eqs (40) and (41) the two normalization points are ( , z m

) and (<f> n

, z^) and the measurements

include the relative data B^, B^, and the normalization constants

Am

=

b‘ ( <j> , z ) o

Ym * m

A

n = b“ ( 4> , z o

y n* n'

The first step in the solution for the T's is to invert the transmission equations by noting that

eqs (40) and (41) involve a Fourier series in <|> and Fourier integral in z Q

. The inverse is easily

obtained to give the coupling products within the brackets

I'M

Ji

r'„ s M t*M

(1 - r r ) A “ 2 tt -i n<|> -iyz

l p m , r _ . . . o Oj — II B'OOO<f> , z ) e e d<f> dz , 00 -00 0

4tt 2 (B6)

V'M - I R>) T

s

n M

(1 - r r ) A » 2 tt -ind -iyz Up fir r r, I, , \ 0 0 , f I

B (<p , z ) e e d<j> dz 1 1 0 0 0 0 0

-CO 0

4tt 2 (B7

* C Assuming that the receiving parameters (R , R

n

) are known, eqs (42) and (43) can be solved from the

transmitting functions T^(y) of the test antenna:

tJ(y) - [R^

2 (y) V

n M - R*M l"( y) D/a„

(

r

)

T

2 (r) - [R^(ir) I“(t) - r“'{y) i;(Y)]/i

n (Y),

(B8a

(B8b)

where

A

n (y) = R^

2 (t) Rp 1(T) " R

n 2(Y) (B9)

'2 “1 Dividing numerators and denominators of eq (B7) by the product (-R (y) R

p (y)) puts the above probe

correction equations in a form more parallel to those for planar measurements (see eqs (A60) and

( A61)

I n (Y) I ' (if) n

T>>

"1

R

n M Rn 2(Y) P

n (y)

1 - P'

n (y)/p"(y)

n

1 * ( Y

I (y)

n n , (y) '2 R (y)

111 P

_ x < » n R Y

n n T (y) =

n m 1 - p

' (y )/ p"

y

(BlOa)

(BlOb)

73
In the above equations, the p's are cylindrical mode polarization ratios.

(Bll)

p"M (B12)

The steps in the cylindrical near-field measurements and calculations are then:

1. Measure the far-field pattern, polarization and gain of the probe relative to its own coordinate

system.

3. Place the antenna in a known orientation in the reference coordinate system C

Q

.

4. Measure the relative near-field data and normalization constants B'(<j> , z ), B"(d> , z ), o o o o o o A

n

(<t> n

, z

n ), Am

(<}>m

, z ) with two independent probes or two orientations of a linearly polarized

probe.

5. Calculate the coupling product coefficients for the measured data, P(y) and I “ ( y) and apply the

6. From the cylindrical modes, calculate the far-field parameters.

References

[Bl] Yaghjian, A.D. Near-field measurements on a cylindrical surface: A source scattering-matrix

formulation. Nat. Bur. Stand. (U.S.) Tech. Note 696; 1977 September.

1 c 2. For the specified orientation in the coordinate system calculate the probe parameters R

n (y) andn

74
APPENDIX C Spherical Near-Field Theory Summary

For spherical near-field measurements, a probe is used whose pattern is symmetrical about its

axis (z-axis). Far-field pattern measurements are obtained for the probe, and the data are fitted

with a spherical mode expansion.

W(e,4>) = 2 Q° MV

F oyv(e, 4,) a,u,v 1 '

where W ( 0 , <(>) is the complex vector far-field pattern, F auv

(0,<|>) are vector spherical wave functions,

and Q° wv is the spherical mode expansion for the probe. The polarization index a assumes the values 1 and 2 corresponding to TE and TM modes; the p index expresses the dependence on the azimuthal angle Q;

and the v index refers to the 0 or polar angle dependence. When the Q's for the probe have been obtained, reciprocity is generally employed to find the spherical mode receiving coefficients denoted

as g° MV

. Both the £'s and Q's for the probe at this point are defined with respect to the coordinate

system of the probe. For probes with the assumed <j>-symmetry , only those modes for which p

= +1 are nonzero. Furthermore, when the probe is small it will have relatively few v values that are nonzero. An ideal dipole, for instance, would have only v = 1 as a nonzero £

or Q.

The next step in the data processing is referred to as the translation of centers. In this procedure, the probe coefficients are determined with respect to the coordinate system of the AUT at a radius A from the origin by the relation

spnA

o,v

CSn

(A)

apv £*-opv

(C2)

In the above, p SunA denotes the translated coefficients; s and n relate respectively for polarization

and 0 just as o and v did; and the translation coefficients C^^(A) are obtained by complex involved

recursion relations [1],

The spherical coupling equation for the measurement shown schematically in figure Cl and corre- sponding to similar expressions for planar and cylindrical methods (see eqs (A50) and ( B4) ) is then

given by [C2,C3]

B A (xo»®o»4> o) = £ Qsmn

Z p

s ** n V1B*o d^(0„) e lyXo (C3) s,m,n p

The Q's in eq (C3) are the spherical mode coefficients for the AUT and correspond to the planar

t 10 (l<) and cylindrical T^(v) coefficients. The Q's are similarly the objective of the measurement

process.

Equation (3) can be inverted by using the orthogonality relation

1

2tt it 2tt ^

, , o_2 J J 1 & (<t>o> 0 o» x o) D (

<f

> 0’ 9 0» x o) S1 n ®0$0®0*0 on o 0 0 m w

,_.lm'n lp'n'A rt 2m'n' 2p'n'A. </ „ ,,

= (Q P + Q P )/(2n + 1).

(C4)

75
wV.M) = £(pSynA

m,n,y,s\

PROBE RECEIVING

COEFFICIENTS WITH

RESPECT TO oxyz

Q

smn

) e

1 m

+d

(n)

(e) e iyX

. v mu- ,

1 FACTORS DUE TO PROBE

MOTION ON SURFACE OF , SPHERE

ANT TRANSMITTING COEFFICIENTS

WITH RESPECT TO oxyz

A = RADIUS OF SPHERE s = POLARIZATION INDEX

Figure C-l. Spherical scanning schematic.

76
Equation (C4) implies the need for numerical integration of the measured data in xo ,<J>o, and 0 O

. The

integration in xo is reduced to a sum of two data sets by the properties of the symmetrical probe.

Since all of the p's are zero except for those with p = ±1, data are obtained for xo

= 0 denoted

A A

B (0,e 0 ,<t>o) and X

= tt/2 denoted B ( -rr/ 2 ,

0 4>o ) • Combining these data sets accomplishes the integration

in xo* Integration in <j> 0 is accomplished with the FFT making that process accurate and efficient.

Numerical integration in 6 would be time consuming and possibly subject to errors. Wacker, who

also proposed the use of the symmetric probe to accomplish the x integration, developed an efficient

algorithm for accomplishing the 6-integration as well. This involves a combination of FFTs and matrix

multiplication which give accurate results and good efficiency [ C 3] . This algorithm was further

implemented, developed and improved [C4,C5], and is the basis for all spherical near-field data processing.

Once the model coefficients are determined, the far-field pattern is computed by using eq (C3) in

a novel way that takes advantage of the above algorithm and eliminates the need for evaluating any of

the vector basis function, the F's of eq (Cl). It uses the concept that an ideal dipole at infinity

would measure the electric field. So the ideal dipole coefficient is used in eq (C2) to obtain the

translated coefficients for an ideal dipole at A = ®. These coefficients are then used in eq (C3)

along with the Q's of the AUT obtained from the near-field measurement and calculations. The calculated B°°( xo

= 0 , 0q

4>o) and B”(xo = it/2, Sq ,<t>o) are the far electric field components. The evaluation

of the summation in eq (C3) employs the efficient Wacker algorithm process for speed and accuracy.

Once the far-field has been obtained, gain, pattern, and polarization parameters are easily obtained.

References

[Cl] Bruning, J.H.; Lo, Y.T. Multiple scattering of EM waves by spheres. IEEE Trans. Ant. Propagat.

AP-19; 1971 May. p. 378-390.

[C2] Jensen, F. Electromagnetic near-field far-field correlations. LD- 15. Technical University of

Denmark, Lyngby; 1970.

[C3] Wacker, P.F. Non-planar near-field measurements: Spherical scanning. Nat. Bur. Stand. (U.S.)

NBSIR 75-809; 1975 June. 69 p.

[C4] Lewis, R.L. The use of three-term recursion relations for numerical computations as applied to near-field spherical scanning. URSI Symposium on Electromagnetic Wave Theory, Stanford,

California; 1977. p. 224-226.

[C5] Holm Larsen, F. Improved algorithm for probe-corrected spherical near field far field transformation. Electronic Letters. 15; 1979 September 13. p. 588-589.

77
NBS-1I4A nev. i-aci u.l. OCPT. OF COMM. 1. PUBLICATION OR

REPORT NO.

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

SHEET (See instruction s) NBSIR 85-3031 September 1985

4. TITLE AND SUBTITLE

Development of Near-Field Test Procedures for Communication Satellite Antennas

Phase I , Part 1

5. AUTHOR(S)

Alien C. Newell and Andrew G. Repjar

6. PERFORMING ORGANIZATION (If / oint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, O.C, 20234

7. Contract/Grant No.

• . Type of Report & Period Covered

9.

SPONSORING ORGANIZATION NAME AND COMPLETE AOORESS (Street. City. State. ZIP)

10.

SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-IB5, FlPS Software Summary, is attached.

11.

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 purpose of this program is to define and further develop the capabilities of nearfield antenna test techniques, specifically for the requirements associated with the

development and verification testing of reconfigurable, multi beam, frequency reuse,

commercial satellite antennas. Phase I, Part 1 gives a general survey, definition, and

description of near-field and compact range measurement methods as they apply to

satellite antenna systems testing. Each of these methods is evaluated to determine

how well they meet the measurement requirements. Included for each technique is a summary of the measurement method, discussions on probe correction and data processing,

measurement hardware considerations, a results available section, and measurement

accuracy and range certification considerations. The basis for the choice of the best

measurement technique is established with the planar near-field measurement method re- ceiving the best score for the directive antennas considered. As a result, further

study will focus on this technique and will be reported on subsequently. A detailed

presentation of planar near-field measurements theory is presented in Appendix A.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) antennas; antenna measurements; compact range; cylindrical near-field scanning; near- field measurements; near-field testing; planar near-field scanning; satellite antennas;

13.i£herjcai near-field scan n i ng*. ,. — — availability

I | Unlimited

I j For Official Distribution. Do Not Release to NTIS

I | Order From Superintendent of Documents, U.S. Government Printing Office, Washington, O.C.

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

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15. Price

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