NBSIR 74-380

PLANAR NEAR-FIELD MEASUREMENTS

ON HIGH PERFORMANCE ARRAY ANTENNAS

Allen C. Newell

Myron L. Crawford

Electromagneticis Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

July 1974

Prepared for

Air Force Avionics Laboratory

Wright Patterson Air Force Base, Ohio 45433

NBSIR 74-380

PLANilR NEAR-FIELD MEASUREMENTS

ON HIGH PERFORMANCE ARRAY ANTENNAS

Allen C. Newell

Myron L. Crawford

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

July 1974

Prepared for

Air Force Avionics Laboratory

Wright Patterson Air Force Base, Ohio 45433

u s. DEPART^IENT OF COMMERCE. Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS. Richard W Roberts. Director

CONTENTS

Page

1.0 Introduction 1

2.0 Concept Application Study - -Review of Plane Wave,

Scattering -Mat rix Theory of Antenna -Antenna

Interactions 4

3.0 Measurement Program 16

3.1 Test Antennas, Probe and Initial Alignment 16

3.2 Determining Scan Parameters and the Effects of

Multiple Reflections 24

3.2.1 Scan Area Determination 30

3.2.2 Data Point Spacing Determination-- 41

3.2.3 Scan Area and Data Point Spacing for Main

Beam Shifted Away from the Normal to the

Measurement Plane 47

3.2.4 Effects of Multiple Reflections 49

3.2.5 Detection of Faulty Array Elements and

Radome 54

3.2.6 Far-Field Patterns from Centerline Data-- 55

3.2.7 Summary of Conclusions from Tests Using

Centerline Data 66

3.3 Two -Dimens ional Measurements and Results 67

3.3.1 Measurement at Different z-Spacings for

Sum and Difference Antenna Modes on the

Test Antennas 67

3.3.2 Pattern Comparisons for the Constrained

Lens and Volphase Antenna 85

4.0 Conclusions 9 2 References 93

iii
LIST OF FIGURES

Page

Figure 1. Waveguide Junction 2 -Port Schematic 4

Figure 2. Antenna in Measurement Coordinate System 6

Figure 3. Relative Orientations o£ Orthogonal Unit Vector

triads; e^, e^, e ^

; £^ , e

^ ; e^ , e^ , 10

Figure 4. Relative Orientation of the Test Antenna and

Probe 13

Figure 5. Constrained Lens Antenna and Probe 17

Figure 6. Volphase Antenna and Probe 19

Figure 7. Scanner for Moving Probe in x-y Plane 21

Figure 8. Block Diagram of Automatic Position and Measurement System-- 22

Figure 9. Scanner Used for Volphase Antenna 23

Figure 10. Near-Field Measurement Setup for Electronically Steerable Phased Array Antenna 25

Figure 11. Near-Field Centerline Data, Constrained Lens

Antenna, z = 25 cm, Az = EL = 0° 31

Figure 12. Approximate Far-Field Pattern Computed from

Centerline Data Taken on Constrained Lens

Antenna. z = 25 cm, Az = EL = 0° 32

Figure 13. Change in Computed Far-Field Due to Decreasing

Scan Length 34

Figure 14. Change in Computed Gain Due to Decreasing Scan

Length 35

Figure 15. Change in Far-Field Pattern Due to Decreasing

Scan Length, L = 213 cm and L = 113 cm 36

Figure 16. Near-Field Centerline Data, Constrained Lens

Antenna, z = 254 cm, Az = EL = 0° 37

Figure 17. Approximate Far-Field Pattern Computed from

Centerline Data Taken on Constrained Lens

Antenna, z = 254 cm, Az = EL = 0° 39

iv
LIST OF FIGURES (continued)

Page

Figure 18. Schematic Relationship between Scan Length and

Maximum Angle to which Far-Field Pattern can

be Accurately Determined 40

Figure 19. Amplitude Spectrum for Both Propagating and

Evanescent Modes on Constrained Lens Antenna-- 43

Figure 20. Change in Far-Field Due to Increase of Data

Point Spacing 45

Figure 21. Comparison of Patterns Computed from NearField Data with 6 = .08A and 6 = 0.62X,

X X

* Constrained Lens Antenna 46

Figure 22. Near-Field Centerline Data, Constrained Lens

Antenna, z = 25 cm, Az = 20°, EL = 0° 48

Figure 23. Change in Computed Far-Field Due to Increased

Data Point Spacing. Volphase Antenna,

z = 38 cm. Az = 0% 30°, 45°, EL = 0° 50

Figure 24. Multipath Centerline Data for Volphase Antenna,

z = 38 cm 52

Figure 25. Far-Fields Computed from Data at Z-Distance

which Differ by A/4, Volphase Antenna 53

Figure 26. Near-Field Amplitude and Phase Centerline Data

on Constrained Lens Antenna With and Without

180° Simulated Phase Shifter Fault at x = 0--- 56

Figure 27. Change in Amplitude and Phase Due to 180°

Simulated Fault at x = 0 57

Figure 28. Change in Amplitude and Phase Due to 180°

Simulated Fault at x = 18 cm 58

Figure 29. Comparison Between Far-Field Patterns Computed

from Complete and Centerline Data. Constrained Lens Antenna, E-Plane Sum Pattern 60

Figure 30. Comparison Between Far-Field Patterns Computed

from Complete and Centerline Data. Constrained

Lens Antenna, H-Plane Sum Pattern 61

V
LIST OF FIGURES (continued)

Figure 31.

Figure 32.

Figure 33.

Figure 34.

Figure 35a.

Figure 35b.

Figure 36a.

Figure 36b.

Figure 37.

Figure 38.

Figure 39a.

Figure 39b .

Page

Comparison Between Far-Field Patterns Computed

from Complete and Centerline Data. Volpbase

Antenna, 0° Sum Pattern 62

Comparison Between Far-Field Patterns Computed

from Complete and Centerline Data. Volphase

Antenna, 30° Sum Pattern 63

Comparison Between Far-Field Patterns Computed

from Complete and Centerline Data. Volphase

Antenna, 0° Azimuth Difference Pattern 64

Comparison Between Far-Field Patterns Computed

from Complete and Centerline Data. Volphase

Antenna, 30° Azimuth Difference Pattern 65

Constrained Lens Sum Port Near-Field Log

Amplitude, f = 9.2 GHz, z = 2 5.0 cm. No Radome 71

Near-Field Phase, Constrained Lens Sum Port,

f = 9 .2 GHz, z = 25 cm 72

Constrained Lens Sum Port Near-Field Log

Amplitude, f = 9.2 GHz, z = 2 54 cm. No Radome- 73

Near-Field Phase, Constrained Lens Sum Port,

f = 9.2 GHz, z = 254 cm 74

Constrained Lens Sum Port Far-Field Log

Amplitude, f = 9.2 GHz, Computed from z = 25

cm Data, No Radome 75

Comparison Between Far-Field Patterns Computed

from Near-Field Data taken at Two Different

z-Distances. Constrained Lens Antenna. E-Plane

Sum Pattern 79

Constrained Lens Elevation Difference Port

Near-Field Log Amplitude, f = 9.2 GHz, z = 250

cm. No Radome 80

Near-Field Phase, Constrained Lens Elevation

Difference Port, f = 9.2 GHz, z = 250 cm 81

VI
LIST OF FIGURES (continued)

Page

Figure 40. Constrained Lens Elevation Difference Port Log

Amplitude, f = 9.2 GHz, Computed from z = 25

cm Data, No Radome 82

Figure 41. Comparison Between Far-Field Patterns Computed

from Near-Field Data taken at Two Different

z-Distances. Constrained Lens, E-Plane

Elevation Difference Pattern 83

Figure 42. Comparison Between Far-Field Patterns Computed

from Near-Field Data with Probe Transmitting

and Receiving. Constrained Lens Antenna, EPlane Elevation Difference Pattern 84

Figure 43. Comparison Between Far-Field Patterns Measured

on Far-Field Range and Computed from NearField Data. Constrained Lens, E-Plane Sum

Pattern 86

Figure 44. Comparison Between Far-Field Patterns Measured

on Far-Field Range and Computed from NearField Data. Constrained Lens, E-Plane Elevation Difference 87

Figure 45. Comparison Between Far-Field Patterns Measured

on Far-Field Range and Computed from NearField Data. Volphase Antenna, 0° Sum Pattern- 88

Figure 46. Comparison Between Far-Field Patterns Measured

on Far-Field Range and Computed from NearField Data. Volphase, 30° Sum Pattern 89

Figure 47. Comparison Between Far-Field Patterns Measured

on Far-Field Range and Computed from NearField Data. Volphase Antenna, 0° Azimuth

Difference Pattern 90

Figure 48. Comparison Between Far-Field Pattern Measured

on Far- Field Range and Computed from NearField Data. Volphase Antenna, 30° Azimuth

Difference Pattern 91

vii

PLANAR NEAR- FIELD MEASUREMENTS

ON HIGH PERFORMANCE ARRAY ANTENNAS

The results of measurements which apply the

planar near-field measurement technique to phased

array antennas are described. Fast and efficient

tests are used to determine the required scan area

and data point spacing. The use of these tests can

reduce the amount of data required for some antennas

without significantly increasing the errors in computed results.

Measurements were made at different distances

from the antennas, with the probe transmitting and

receiving, and for both sum and monopulse difference

patterns. Comparisons between the far-field patterns computed from the near-field data and those

measured on far-field ranges are presented.

Key words: T^tennas ; near-field measurements;

phased arrays.

1.0 Introduction

This program is concerned with determining the far-field

characteristics of phased array antennas from measured nearfield data. The required theory and basic measurement techniques have been developed in the past at the NBS Electromagnetics Division [1-4] and at other laboratories [5] and indicate

the usefulness of this approach. The purpose of this particular

program is to demonstrate that this measurement approach can

provide accurate results when applied to radar type arrays

which are mounted on an aircraft and contained within a radome

.

The details of this program are described in the Statement

of Work, and may be divided into three parts:
I -- Concept Application Study, which describes the planewave scattering matrix theory as it applies to the present

program. This is done in such a way that the antenna engineers,

who are potential users of this material, will appreciate the

value of the approach and be able to use the theoretical formulations and measurement procedures

.

II -- A Measurement Program, which consisted of nearfield measurements on two test antennas. The test antennas

were chosen with characteristics representative of high performance radars. These included narrow beamwidths, side lobes

below 30 dB , monopulse difference minima of at least 30 dB

,

beam steering to ± 45°, and operation frequencies in the x- band range. Neither test antenna had all these features, but

all were realized in at least one of the antennas. Some of

the goals of the measurement program are summarized below.

a. Data Minimization. Since a large amount of near-field

data is generally required, large computer storage is needed

for data processing. If the amount of measured data could be

reduced without a significant sacrifice in the accuracy of

computed results, a large savings could be realized in both

measurement and computation time. Tests were therefore made

to determine the optimum spacing of data points and the size of

the scan area for a given test antenna and probe combination.

b. Measurements on Radome Enclosed Antennas. In the

past, all of our measurements have been done within 10-50 wavelengths of the test antenna. If a long radome encloses the

antenna, the measurement plane must be moved farther from the

antenna. Tests were performed to determine what effect this

would have on the scan parameters (spacing and area) and the

accuracy of computed results.

2
c. Transmitting From Probe. In previous measurements,

the test antenna was transmitting and the probe receiving. For

test antennas which are non-reciprocal or which do not operate

in the transmit modes , the probe would have to be used as the

transmitter. The theory indicated that this should not present

any difficulties, and measurements were performed to determine

if there were any unforeseen experimental problems

.

d. Locating Faults in the Array and/or Radome . Tests

were performed to see how effective the near-field technique

would be in detecting and locating failures in the array, and

if possible, also in the radome.

e. Demonstration of Agreement with Far-Field Measurements.

Since this measurement approach is new to most antenna engineers,

and involves the use of fairly sophisticated theory and computations, it does not enjoy the confidence placed in conventional

far- field measurements. Questions are frequently asked if the

results from near-field measurements agree with "actual" (farfield) measurements. While such comparisons are helpful, and

have been performed in the past, it must be realized that errors

and approximations exist in both measurements. In some cases,

the far- field measurements are less accurate than the nearfield measurement, and they cannot serve as a suitable standard

to judge the accuracy of this new method.

Comparing the results of both measurements will demonstrate

that there are no gross errors in either approach, and will help

to build confidence in the near- field approach. A more complete

and valid approach to proving accuracy, however, is to study how

the approximations to the theory, and measurement errors in the

near-field data affect the accuracy of the computed far-field

parameters . This approach is being pursued as a part of a thorough error analysis of the near-field techniques.

Ill -- The third part of the program involves a System

Design Study to specify the hardware and software necessary to

implement the planar near-field measurement technique.

3
2.0 Concept Application Study -- Review of the Plane Wave,

Scattering-Matrix Theory of Antenna -Antenna Interactions

Frequent use is made in this report of the quantities used

in a plane wave scattering matrix theory of antennas (more

completely covered in references [1-4]). A brief discussion

is given here to acquaint the reader with the basic quantities

and their meaning and to give the results of the theory that

are required in a treatment of near- field measurements. The

intent of the following discussion is to describe the concepts

used in this new approach to antenna theory in terms of quantities which should be familiar to the microwave and antenna

engineer

.

SOURCE

WAVEGUIDE

<— JUNCTION —

bo —

b)

^1 — LOAD

Figure 1. Waveguide Junction 2 -Port Schematic.

The theoretical formulation and notation employed here are,

in many respects, similar to those found in the familiar scattering matrix description of waveguide junctions. Therefore,

we begin by referring to a waveguide two-port, shown schematically

in figure 1 as it is described by the S (scattering) parameters.

The incident and emergent wave amplitudes a^ , a^ , b^, b-j^ , on

two terminal surfaces, 0 and 1, at the ends of the two-port

4
are related by the equations [6]

^0 = ^00^0 ^ ^01^1 ^^^^

^1 " ^10^0 ^11^1' ^^^^

where S^^ and S^-j^ are the reflection coefficients of the twoport and Sq^ and S-^^ are the transmission coefficients. These

S parameters are complex scalar quantities which specify the

response of the two-port transducer at a given frequency and

for one waveguide mode. Once these quantities have been obtained from measurements, they can be used to determine how

this device will interact with others in a composite system.

Although an antenna is more complicated than a simple

waveguide two-port, it can still be described by the same sort

of formal representation. The antenna is viewed as a multiport transducer (one input port and an output port for each

polarization and direction in space) , which transforms wave

amplitudes in a closed transmission line system to an angular

spectrum of plane waves in the space system and vice versa.

The plane-wave S parameters provide a powerful description of

an antenna from this transducer point of view. As with the

two-port, once these S parameters have been determined, they

may be used to evaluate the antenna performance in a larger,

more complicated system. Familiar quantities such as power

gain and axial ratio are easily derived from the S parameters,

but the S-parameters are not limited to use in the far-field

plane wave situations which are usually assumed. One of their

main advantages is that they give a means of formulating nearfield antenna interaction problems in a way which gives new

insight into the problems and which allows practical solutions.

5
Figure 2. Antenna in Measurement Coordinate System.

To further define these parameters, consider the antenna

shown in figure 2 oriented in the coordinate system Oxyz with

unit vectors e^, e^, e^ in the space to the right of the antenna,

and let k be the propagation vector for plane waves in this

space. Since k'k is fixed by the relation, k'k = k^ = co^ye,

we can consider k and k to be functions of K, the transverse

z — —

part of k. That is,K = ke + ke and k = ± y* where ^ — ' — X—X y—y z

*

Y = A K' (2)

K will be the independent variable in most of what follows,

and defines directions in the space to the right of the antenna. For example K = 0 defines the reference boresight

direction; K = k e + 0 e defines the E-plane for an antenna ' — y —y —X

^ with linear polarization in the y-direction; and K = 0 £ + k e defines the H-plane for the same antenna.

6
Two additional transverse unit vectors which are used in

the formulation are defined as

= K/|K| , £2 = e^ X K-^. (3)

These vectors are respectively in and perpendicular to the

plane of k and e_^ and are used to specify the independent

polarizations of the electric field associated with any given

k. This choice of polarization is the one used in electromagnetic theory in deriving the Fresnel equations and also

corresponds to TE and TM modes of waveguide theory.

In figure 2 , a^ and bg are incident and emergent wave

amplitudes at the surface just as in the waveguide junction

formulation. ^^i^K) and b^CK) are spectral density functions

for incoming and outgoing plane waves and are analogous to a^

and b^ in figure 1 in that each represents the complex amplitude

of a plane wave traveling in the K direction. This decomposition of the transverse electric field into a continuous angular

spectrum of plane waves is analogous to the familiar practice

of analyzing a complicated time function in terms of its frequency components. (Indeed there are many concepts from time

and frequency domain analysis which can be carried over to

the antenna problem and which give new insight to the processes

involved.) These ideas are formalized by the following equations which define the S parameter functions that characterize

the antenna

^0 = ^00^0 " ! 5: SQ^Cm,K) a^(K) dK (4a)

m

b^(K) = S^Q(m,K) aQ + / I S^^(m,K;n,L) a^(L) dL, (4b)

n

where the summation is over the two values of the polarization

index, m or n, and integration is over all values of

K, dK E dk dk .

7
The significance of each parameter can best be seen by

considering two special cases. First assume that the antenna

is transmitting into free space, and therefore there are no

waves incident from the right, a (K) =0. We then have ° m —

^0 " ^00^0' ^^^^ b^CK) = S^Q(m,K) a^. (5b)

Sqq is thus a simple input reflection coefficient term, and

S^Q(m,K) defines the transmitting characteristic since it

describes how the input wave amplitude a^ is transformed by

the antenna into an angular pattern of plane waves b^(K)

.

Next assume that the antenna is being used as a receiver

and is terminated in a reflect ionless load. In this case

a^ = 0 and

=

J ^ SQ^(m,K) a^(K) dK, C6a)

m

b^(K) =

/ I S^^(m,K;n,L) a^(L) dL. C6b)

m

SQ^(m,K) is called the receiving characteristic since it describes how the antenna responds to an incident spectrum of

plane waves a^(K) . S-^^ (m, K ;n , L) is called the scattering

characteristic as it describes how waves incident from the

right are scattered back into the same space.

If the antenna is reciprocal, then S-j^Q(m,K) and SQ^(m,K)

are related by the reciprocity relation [1]

-ng SQ^(m,K) = n^m S^Q(m,-K), (m = 1,2) (7)

where Hi = — and - t- \f^i and are referred to as wave

1 y^y Y

" y 2z k^u* K ' y

tances

line

.

admittances, and Hq is the wave admittance of the transmission

8
It should be noted that the formulation is expressed in

terms of transverse components, where transverse as used here

means transverse to z. We will most generally be working with

X- and y-components or and K2 -components (which are in the

x-y plane) rather than the spherical components which are

employed in far-field measurements. The spherical components

may of course be obtained by the appropriate coordinate transformation, but they will not generally appear in the formulation.

To obtain spherical components of the transmitting characteristic

for instance, the z-component is first obtained from the

transversality relation

SiqCK) • k = 0, (8)

which may be written

k^s,^^(K) - k^^s^^^^CK)

10 z^-^ ~

~ Y

In these and following equations, the small "s" will denote

the complete vector, and the capital "S" will denote its

transverse components. This may be expressed by the equation,

Sio(K) = S^qCK) + s^Q^e^(K) (10)

The spherical components for the usual spherical coordinate

system shown in figure 3 are then obtained from the relations

e_Q = cos 9 ic

-j^ - s in 0 e_^ , (llaO

£<f = £2- (lib)

Additional insight into the character of S2^q(K) and S^q^C^)

may be obtained by comparing them to familiar quantities such

as the far electric field and a measured antenna pattern. If

the magnitude of one component of either S-|^q(K) or Sq-j^(K) is

plotted as a function k and k , the plot closely resembles X y

9
10
a 3 -dimensional antenna pattern. There is a simple relationship between S-j^q(K) and the far-electric field which is obtained

from the asymptotic value of the integral relation between

Sto(K) and the electric field at arbitrary distance [1]. In

k

the direction specified by the unit vector — and at a large

distance p from the antenna, the electric field is given by

-iys, f.(K)af.e^^P

E(p) = " " , (12)

P k

where £ = p . If this equation is inverted to give s,^(K)

|k| "^^ ~

in terms of E the relation is more apparent,

^10^^^ = 4- i^^^^P e-i^P]. (13) —±u — yag 1^— J

Since in the far- field the magnitude of varies as 1/p and

i k D its phase change is given by e , the quantity in the brackets

is a far-field distance-invariant quantity referred to as the

radiation vector which expresses the vector pattern of the

antenna as a function of direction. The transmitting characteristic s_^q(K) also contains this information, but it is

modified by the factor l/y which varies with direction, where

Y = kcos e, andeis the angle between k and e_^.

Far-field quantities may therefore be obtained quite

easily in terms of s_^q(K) but in addition, it can be used to

formulate near- field antenna measurement situations more compactly than E or the radiation vector. For instance the power

gain and effective area functions are given by

4TrY k2[|S,.(l,K)|2 + |S (2,K)Y/k|M

G(K) = — = — = (14)

no(i-ISool^)

11
nQ[|SQ^Ci,K)Y/kr + |Sq^C2,k)|2]

-L1 - I s P Poo"

a(K) = (15)

where is the value of /e/y for the transmission medium.

The goal of near-field measurements is then to determine

§-10^—-^ ^l^^ -^^^ values of K which are of interest. One

of the key equations in the near field measurement approach is

referred to as the transmission integral. It relates the transmission and receiving characteristics of the test and probe

antennas to the observed data. This equation will now be

discussed for the case where the test antenna is used as the

transmitter.

Suppose that the transmission characteristic of the test

antenna is given by S^-j^q(K) when it is placed in a specific

orientation in the reference coordinate system. It should be

noted that the S-parameters do depend in part on the orientation of the antenna. A convenient arrangement is to define

a set of antenna coordinates fixed to the antenna and orient

the antenna in the reference measurement system of figure 2 such that the two coordinate systems are coincident. In this

way the measured parameters will be defined with respect to the

antenna coordinate system. The x- and y-axes of the antenna

are defined by reference marks on the antenna structure. The

z-axis is chosen in some clearly defined direction, such as perpendicular to the aperture.

Now suppose that the probe antenna has a receiving characteristic Rq-|^(K) when it is placed in the prescribed orientation

in the reference system. Let the probe be placed in the receiving orientation by a 180° rotation about the y-axis and

a translation along the z-axis to z = d. In its new orientation, the probe receiving characteristic will be denoted by

12
Rq^CK)* The rectangular components in the two orientations

are related by the equations

^Olx^^x^V = -^Olx^-^x'V

^Oly^^x'V = ^Oly^-^x'V-

(16a)

(16b)

Radiating

System

Si-

(z-0)

t b,(K)

Hz

arr(K)

(z = d)

Receiving

Systenn

Figure 4. Relative Orientations of the Test Antenna

and Probe.

Let the receiving probe be moved in the plane z = d by a transverse displacement P = x e + y e . The two antennas are shown ^ — —X —

y

schematically in figure 4. If we now assume that the multiple

reflections between the antennas are small enough to neglect,

the transmission equation is given by

^0 !

iyd iK'P

e dK. (17)

13
I It should be pointed out at this point that b^CP) is the actual

observed quantity, and that the product in the brackets, and

more specifically Sj^q(K) , is the desired result. Since eq. (17)

is a Fourier integral transformation, we may write

/ D'(K) = R^^(K) • S^o(K), (18)

where D' (K) denotes the determinate function of K given by

D'(K) = / b„(P)e - dP. (19]

Equation (18) gives one equation for the two transverse components of S^^q(K) in terms of the function determined from the

measurements, D' (K) , and the probe receiving characteristic,

t Rq-^ (K) . A second equation is required and is obtained by repeating the measurement with a second "independent" probe.

This second probe may be obtained in effect by simply rotating

the original probe about its axis by 90° unless the probe is

circularly polarized. The second equation is then

D"(K) = Roi(K) • Siq(K) , (20)

where

D"(K) = -— L-}^ j b.(P) e ^- - dP (21)

4.^ao

II II and bQ(P) and Rq-j^(K) are respectively the received signal and

probe receiving characteristic for the second orientation.

An alternative form of eqs. (18) and (20) employs the

complete vectors rather than the transverse parts and may

be of more use in many applications than the original form.

14
It can be shown [7] that

D'(K) = RqiW-S^qCK) = I^iW-s^qCK) = rQ^Q(K)s^QQ(K) +

" ^Olc^m^lO^W, (22)

where again the small r and s denote the complete vectors. If

eq. (13) is now used to substitute E for s^q* the coupling

product can be expressed in terms of the spherical components

of the far-electric field.

D'(K) = iP£-^ [loi®*^s^^^ • ^^^^ YaQ

It can also be shown that the reciprocity relationship between

the complete spectral vectors is given by

Y Y

If the probe is reciprocal, then eqs. (24) and (13) may be used

to express s_q-]^(K) in terms of the far-electric field which the

probe would produce at a distance p' with input amplitude aQ.

The coupling product may then be expressed completely in terms

of familiar electric field quantities,

Y.pp'e-i^^P^P'^

, D'CK) = --^ [Er(p') • Es(P)]» C25)

ngkYaQaJ

where E and E denote the electric fields of the probe and —r —s ^ test antennas respectively. Equation (22) is more useful than

eq. (18) when the probe correction is given in spherical components and one desires the spherical components of either s_^q

or E as the field results. When this form is used, it is not

necessary to transform from the rectangular to the spherical

components, and the number of calculations is therefore reduced.

15
The steps in the measurement and computation may be summarized as follows.

1. Define the coordinate axes of the reference measurement

system, the test antenna, and the probe.

2. Measure or calculate from theory the probe receiving

characteristic for all values of K for which the test antenna

characteristics are to be determined.

3. Place the test antenna and probe in the measurement

system in the prescribed orientation and verify that multiple

reflections are small enough to neglect.

! tf 4. Measure b^CP) and b^CP) over a sufficient area and at

adequate spacing in x and y. (Defining the scan parameters

is one of the main tasks of this program.)

5. Evaluate the integrals in eqs. (19) and (21) and

solve eqs. (18) and (20) for the two transverse components

of S^q(K).

6. Compute power gain, spherical components, polarization

ratios or other desired quantities, or use S^^q(K) to obtain

the field in any other transverse plane to evaluate antenna

performance.

Each of these topics will be discussed in more detail in

the following sections, with special reference to the application of this project.

3.0 Measurement Program

3.1 Test Antennas, Probe, and Initial Alignment

Two test antennas were used during the first series of

tests. The first is shown in figure 5 and is called a constrained lens array. It is a fixed-beam array composed of

1788 elements which are space fed from an eight-horn feed.

16
Figure 5. Constrained Lens Antenna and Probe

17
The principal features of this antenna are that it has sidelobes

of about-30 dB over a fairly large frequency range, and operates

in a sum and two difference modes. Since there are no ferrite

devices in the array, it is a reciprocal antenna.

The second test antenna is shown in figure 6, and is referred to as the Volphase [Volumetric Phase Scanning) array.

It is a corporate fed phased array composed of 1600 elements.

The array is steerable to ± 45° in both azimuth and elevation

and also operates in both sum and monopulse difference modes.

The probe which was used for most of these measurements

is also shown in both of the figures . It was an open-ended

section of WR90 waveguide. The waveguide provides a simple

probe which possesses a number of advantages when patterns are

to be determined out to fairly wide angles . Its pattern is

smoothly varying without nulls , and the magnitude of the relative

probe correction is fairly uniform over a large angular region.

Its axial ratio is approximately 40 dB ; it provides a small

scattering cross section; and its gain can be measured to high

accuracy.

The probe receiving characteristic is obtained by measuring its relative far-field patterns for both polarizations

and its gain in the boresight direction. If the probe is placed

on a rotator which is in the far-field of a source antenna,

and rotated through the angles 6 and (}) , then from the asymptotic

(large d) form of eq. (17) expressed in terms of spherical

components

,

b^ce^t) r;^(-6,-j,)-E^(p3

= -—, . (26)

bQ(0,0) 1^^(0,0) •E^(p)

If the polarization characteristics of the source antenna are

known, then the measured patterns (both amplitude and phase

for two polarizations of the source) give the relative probe

18

correction data for the two spherical components o£ rQ-|^CK) . These relative values are sufficient if only relative patterns

of the test anenna are required. If absolute power gain is

required, then the power gain of the probe must also be measured.

In all of this and past work, the necessary data have been obtained to give the absolute as well as relative patterns.

The reference coordinate system for measurements made on

each test antenna is defined with the x-axis horizontal, the

y-axis vertical, and the z-axis in the center of, and normal

to the plane of the scanner.

The scanner used to make measurements with the constrained

lens antenna is a large mechanical structure which moves the

probe over the required area and is shown in figure 7. A

variety of tests were carried out initially to align the

scanner so that its measurement plane was vertical, and the

probe motions orthogonal. Reference lines were scribed on the

antennas and probe to define their x- and y-axes, and then

precision transits and autocollimators were used to place the

test antenna's axes coincident with the reference coordinate

system.

The measurement system is shown schematically in figure

8. This system provides the programming control to the positioner to move the probe in a raster-type scan. During the

scan, the phase and amplitude of the probe output signal are

automatically recorded at preset intervals in x and y.

Measurements with the Volphase antenna were made at a different site than those on the constrained lens, and the

large scanner was not available. They demonstrate quite

dramatically that good results are possible using the nearfield scanning technique without ideal measurement conditions.

The measurement setup in figure 9 shows the smaller scanner

20
Figure 7. Scanner for Moving Probe in x-y Plane.

21
AL

.

AhPLITuDE PHASE

SE?<SITIVE

RECEIVER SIGNAL FROM

PROBE

.'J M

CC V)

» *

Q

-H M

9

O D- ^ DIGITAL DATA

COUPLER PHASEDIGITIZER o o

JOS •< M g E-i E-i << M M CtJ WMOOS2 5.t Q CU Qi

-a: n <«lE-1 E- >

h-i (—t a. < O to CO -

1-1 O i-l>- Q a. Q —

T

o o

£8

O 02 E-<

l-l M

E-" 2 3

M O 3 CO

O

JO >-i to

•< M <C M

HE-. X MM CL, <

OCO CO I MO M X

ao, o

to o

O CL. w o

ij§

E-" 2:o

aio

Figure 8. Block Diagram o£ Automatic Position and Measurement

System

.

22
,1:
used and the limited amount o£ absorbing material necessary.

Figure 10 shows the room in which the measurements were made.

In this environment, larger multiple reflections would be

expected, and yet as the tests described in section 3.2.4

verify, their effect was quite small.

Near- field measurements were made on these two test antennas under a wide variety of conditions in order to meet the

objectives outlined in section 1. These included, for instance,

different beam steering direction, different scan lengths and

point spacings, the presence or absence of a radome , simulated

antenna faults, and use of the test antenna as a transmitter

and as a receiver. Only part of the voluminous amount of data

obtained from these measurements has been completely analyzed

at this time, and this report will deal primarily with that

data which has been analyzed and the conclusions which were

derived from the completed tests. Tables 1-4 summarize the

various measurements which were performed under the headings

of centerline data and two-dimensional data. The centerline

data were obtained by moving the probe along the lines x=0

and/or y=0 and recording the probe output amplitude and phase.

These data were used in preliminary type tests to be discussed

in the next section. The complete two-dimensional data were

used to obtain complete and detailed far-field parameters, and

the results of these tests will be discussed in a later section.

3 . 2 Determining Scan Parameters and the

Effects of Multiple Reflections

The parameters to be determined were the scan lengths L

and L^, and the spacings between data points 6^ and 6^. To

determine these, and to estimate the effects of multiple

reflections, a series of tests were performed using centerline

data.

24
25
to

+->p

c: o •H •H cl> •H

<l> ci

T 1 U

uU

C!

w

w

+-*

O o I—1

tH

Pi *H

H >> t

+-* +-> +-* •p £ g3 rH +J +-* t—I P

0) ci 3 CD <D 3 - 0)

J-t •H o3 t/1 t/) 03 t/l 3 E tin Mh M-i MH

t/i f-l s s Jh '4H '4H nj <1> o Cl> o d) O O <U o o o o

<D +-1 •H 1—1

•H 4-> r-H •H • H •H

(U 4-» & 4-» d) >^ P<

p P p

Q cd •r-t o3 oj •H 03 o3 o3 oS

m 3 +-> 3 P 3 S-i 3 3 o Sh 1—t I—1 1—1

Jh Sh rH 1—1

Jh 1—1

iH

<u 05 3 OS <^ 3 <l> o3 OS

<u !-> > > »-» > 6 > >

pM CD

U o PJ >v s 4-> tj P

-d Mh M-l - o3 rd

o3 1 1

•H 'H •H o3 4_> Pi 'H

03 Oj 03 OS OS a, & (D p. CO CO 0) P. to Pu

•H 1—1

•H r-1

•H P •H •H

!=:

M

M

M e 6 W) P rH e P P

tH 1—1OS OS 03 OS T—1 3 03 iH iH o 3 •H u 0) 0 •H 3 03 3 3

CO S CO

m 2 S S

•H

tH (=:

p 00 o oq o O oo

Si OS 6

<D o c o tn o o r-. 00

rr : t- ~ 00 P CO 0) w tH (Nl iH Ln iH LO CM LO <X1 C rH (Nl tH iH iH (V! tH (Nl o2 p

p; •H e u

OS (D

C

in tH 03 P 3 P o

I/l (/) (/) LO

03 -H (XI o (U Q S

of

>,u (=1 03 •H o e S-t • 00 (VI e ttJ rH 3 o

CO P

CO

PN pU Pl^ Pl^ + ^

(U 00

tH tn to.. rP OS • M o o o

03 !-i

N CU o (NJ o (Nl (Nl

(Nl o : (NJ Z < ^ o o o o ' o

(U

p

•H o e 2 u

PC

<u P

(h3 O

(/I P-i 03 e3

CO

U

a: x; o

(U Pi

26
X >< • c

c •H •H 3

<u g

e n 6 'H d

<u 0 4J 0 0 0 N 0

u 3 -H •H 3 N .H 6 +J P 1-H +-> to X t-~ .H rt (4

1:3 tvl N N •H N

<a 4-> tlj .H r •H : •4-> -H

<D U H (DO >H (/ICO) 03 (/) 0 CO 00 m -H r-( rH M-l tNl iH O U-l 0 0 •4-1 0

1 00 Bi 0 Dh

(U 0 0) ft w >N-l-> (« a" nj t/i w CO ca u) H !h 13 0 : 0 = H 4-> 0

u u u 0 U u < 0; u

X 0)

.-I o

n! CO O2 :

U5

0) o2 : o2 : o2

00 00 2 2=22

(/J

i-H 0) 3 e

(0 0) Ph >-I w

^ u p ^

W) >> C J

e

c o

CO ^

U X W -J

e

o

CO

in <n in l/i 0 (U 0 0 (U 0 a) 0 0 0 0 0 0 <D 0 0 0 0 2 >- 2 2 >- 2 >H 2 2 2 = 2 2 : 2 r >- 2 : 2 2 r 2 2

0 0 0 CNl 0 vO 00 \o vO 0 vD vO 0 tn

csi (Nl 00 CNl 00 - : 00 00 r~ t 00 : 00 r-~ 00 00 : in (Ni un (SI LO (Nl (Nl 0 (NJ (NJ r- CNl CNl (NJ CNl (NJ CNl LO

1—1 t—

1

i-H I-H (NJ I-H (Nl (Nl (Nj ,—1 (NJ (Nl CNl (NJ (Nl rH rH 0 0 (NJ 0 0 0 vD 0 vO

tvi t-- r~- (Nl 00 (Nl 00 : : 00 00 ^- : t-- 00 : r- 00

LO CNI (Nl LO (Nl CNl 0 (Nl (NJ 0 CNl CNl CNl (Nl CNJ CNl

i-H i-t tH (Nl t-H fNJ (Nl CNl ^ CNl i-H rH iH rH CNl rH

(/I IT) tn in m in in in 0 0 0 (D 0 0 0) (D 0 0 (U 0 (D (U (D CD 2 : 2 2 2 2 >H >^ 2 : 2 >- 2 >H >H r

c

(D ID £ O

(D d '-^

!-i CO S

3 -M o

in in ^

CO -H

(D Q

(D t-j +-> M p p p p p p p H H •H •H • H u H U H • H u •H 0 e (D 6 6 : = S e

(D e <D 6 = 0

s: X X X X X X Oi X X OS X

e EG

3 - 3 3:

to CO CO e3 : LO 6

3

CO

IP Mh m <P m MH

Mh m m m tp m • H H •H •H H •H Q = 0 r r Q : 0 Q : : Q

rH rH rH rH N M

PJ PJ W w < <

27
Table 3. Summary of Volphase Array Centerline Data

Azimuth Beam Measurement

Radome Type of Measurement

Measurement

Port

Sum

Az

.

Dif f

.

Position Distance

Ccm)

0, 30 ,45

0,10 ,30

0,30

0,5

0, 30

0,5

38.1

38.1 -

38.1

304 .8

304.8 - ^

304.8

It

304.8 - ^

304.8

38.1

304 .8

38.1

304 .8

304.8 - ^

304 .8

304.8 -

304.8

nX

No Scan Parameter Tests

" Multipath Eval.

" Cross Polarization

" Scan Parameter Tests

Multipath Eval.

" Cross Polarization

Yes Beam Shift

" Multipath Eval.

" Cross Polarization

No Faulty Elements

If M II

Yes

No Beam Shift

II n It

" Multipath Eval.

Yes Beam Shift

" Multipath Eval.

" Cross Polarization

28
Table 4. Summary of Volphase Array Two Dimensional Data

Measurement Azimuth Beam Measurement

Port Position (deg) Distance Radome

Sum 0 38.1 cm No

" 5 " "

" 30 " "

II 45 tf ti

" 0 304.8 cm

" 5 " "

0 " Yes

" 5 " "

Az. Di££ 0 38.1 cm No

" 5 "

" 30

0 304.8 cm

If 5 .1 „

0 " Yes

5 " "

29
A typical set of data for the constrained lens antenna

along the centerline y=0, z=25 cm, is shown in figure 11. The

first step in the processing is to compute the Fourier transform

of these data in order to implement eq. (19) to obtain an approximate far-field pattern as shown in figure 12. This is an

approximate pattern because only centerline data have been used

and probe correction is ignored. For this to give correct results, the measured response must be expressible as a product

function, i.e., bQ(x,y) = bQ(0,y) b^CxjO). To the degree that

this is valid, figure 12 is a plot of the relative magnitude of

D' (k ,0) plotted as a function of the azimuthal angle A, which

is related to k along the principal planes by

k = —T- sm A.

X X Although this is not the actual far-field pattern, it is very

useful for making these preliminary tests. One of the main

advantages of these tests is that actual data for the particular

antenna-probe pair serve as the basis upon which the scan

parameters are determined.

3.2.1 Scan Area Determination

In principle, eqs. and (21) must be integrated over an

infinite plane. This of course is not possible, and so we

must determine what errors are introduced by using a finite

areas, and the size of the area required for good accuracy.

The use of a finite area is one of two approximations to the

theory which must be evaluated. Since the scan area was very

limited for measurements made with the Volphase antenna, these

tests were performed primarily with the constrained lens

antenna and its measurement system.

30

'-'S'J.OC -72.00 -54.00 -36.00 -18.00 0.00 18.00 36.00 54.00 72.00 50.

Azimuthal Angle in Degrees

Figure 12. Approximate Far-Field Pattern Computed from

Centerline Data Taken on Constrained Lens Antenna

z = 25 cm, Az = EL = 0°.

32
To determine the required scan length, data were taken

over the maximum extent of the scanner. The transform is

computed for the complete data set, and for subsets obtained

by deleting points from each edge. The change in the transform

was measured by computing the RMS and maximum differences in

percent of the on -axis value, and the change in the on-axis

gain. These quantities are shown plotted as a function of

distance deleted from each edge and the ratio of scan length

to antenna diameter a, in figures 13 and 14. It is evident

from these curves that a scan length which is only slightly

larger than the width of the antenna is sufficient for good

accuracy at the indicated z-separation distance of 25 cm.

Figure 15 is a plot of the far-field pattern obtained

from the complete centerline data and a plot of the difference

between this pattern and the pattern obtained after deleting

50 cm from both edges of the near-field data shown in figure 11

This shows that the changes due to reducing the scan length

occur primarily in the nulls, at wide angles, and where the

pattern is below about 40 dB . This is generally true when the

deleted data are in the region of rapidly increasing phase

similar to the region bounded by |x| > 40 cm in figure 11.

It is evident that the data in this region are primarily due

to the field diffracted around the edges of the antenna and

contribute mainly to the wide-angle regions of the far-field.

The near-field for a well collimated antenna is conveniently

divided into two regions. The area of relatively constant

phase may be referred to as the collimated region, and the

remaining region as the diffracted region. It is the collimated region which determines the primary structure of the

far- field pattern and which must be retained in the measurement

This is further illustrated by figure 16 which shows the y=0

centerline data for z = 254 cm. The collimated region has

33
S.SS I II I I I I I I I I 0.00 1.10 16.2! 24.3: 32.41 40.51 41.(2 SS. 72 64. 12 72.92 11.33

Distance Deleted From Each Edge in CM

2.6 2.2 1.8 1.3 0.9

Ratio of Scan Length to Antenna Diameter

Figure 13. Change in Computed Far-Field Due to Decreasing

Scan Length.

34
;.25C0

:.2::3

:. :500

• • o »

n

:.05flo

•HV

Distance Deleted From Each Edge in cm. 2.6 2.2 l.fl 1.4 l-.O 0.6

Ratio of Scan Length to Antenna Dieuneter

Figure 14. Change in Computed Gain Due to Decreasing Scan

Length.

35
Figure 15. Change in Far-Field Pattern Due to Decreasing

Scan Length, L = 213 cm and L = 113 cm.

36
37
increased somewhat to about |x| < 60 cm, and the scan length

tests indicate that measurements over this interval will give

good results for the principal part of the far field. There

is, however, some loss of information at this distance if

measurements are made over only the collimated region.

I f we compare the far-field computed from the z = 254 cm

data shown in figure 17 with that obtained from z = 25 cm data

shown in figure 12, a significant change is apparent. Since

only centerline data have been used, detailed agreement would

not be expected, but the reduction of the sidelobes for angles

greater than about 18 degrees is significant. Both patterns

have been computed for scan lengths of 213 cm, and the decreased

sidelobes in figure 17 are due to a spacial filtering resulting

from increasing the z-distance while maintaining the same scan

length. To a first approximation, this means that the portions

of the transmitted spectrum which do not cross the measurement

area are essentially filtered out of the measured data. From

the tests which have been made, it appears that the far-field

cutoff angle which results from this filtering can be estimated as equal to the angle between a normal to the measurement

plane and a line from the edge of the antenna to the edge of

the measurement plane as illustrated in figure 18. In terms

of the scan length L , the distance between the two antennas

d, and the antenna diameter a, the cutoff angle is given

approximately by

JL -al

) - tan"-"" (27)

c

fL -a

X

From tests on two-dimensional data, it appears that the

cutoff angle is actually larger than this, but eq. (27) is

useful in estimating the required size of the measurement

area.

38
-5.::

-•.5.::

94.00 72.00 90.00

Azlmuthal Angle In Degrees

Figure 17. Approximate Far-Field Pattern Computed from Centerline Data Taken on' Coils tfdined Lens Antenna,

z » 254 cm. As - EL • 0^'.

3.9
Measurement

Plane

Test Antenna

Maximum Angle for Accurate Far Field =ft

9r- Tan

-1 U-a

TRUNCATION OF MEASUREMENT AREA

Figure 18. Schematic Relationship between Scan Length and

Maximum Angle to which Far-Field Pattern can be

Accurately Determined.

40
There are times when this filtering effect, due to increasing the separation distance, will cause errors in an

important angular region. The area must therefore be increased,

or the separation distance decreased. There are times however

when it has a beneficial effect. When high accuracy is required

over a limited angular region, the spatial filtering reduces

the complexity of the near-field and fewer data points are

required. More will be said about this in the following

section

.

3.2.2 Data Point Spacing Determination

The choice of an adequate spacing of data points is obtained by use of a two-dimensional form of the sampling theorem.

t This theorem states that if bQCP) is the Fourier transform of

a band limited function of I( with band limits

k-L = and = j^, (28)

X y

then the required spacings are 6^ and 6^. Furthermore, the integrals in eqs . (19) and (21) may be replaced by a summation,

without approximation. The problem is then to determine the

band limit of the transform of bQ(P). The transform whose band

limit we seek is the quantity within the brackets of eq. (17)

given by

D'(K)e^'^^ = R^^(K) • S^o(K)e^'^^. (29)

In the strictest sense, band limiting would require eq . (29)

to be zero for |K^| greater than some value K^^ . Although it

may not be zero, an arbitrarily small value of eq. (29) may

be attained by choosing the band limit in the evanescent mode

region where [IC] > k. In this region, y is purely imaginary,

41
and the attenuation due to the e factor insures cutoff

for |K| only slightly greater than k. This was pointed out

originally by Kerns [2] , and later discussed in more detail

by Joy and Paris [5]

.

The high degree of cutoff is illustrated by the data for one

of the test antennas. Figure 19 is a plot of the relative

magnitude of D' (k ,0) plotted as a function of k /k. This was

computed from the near- field data shown in figure 11 where

d - 8X and 6 = O.IOA. The region where k /k is greater than

unity represents evanescent modes which are all at least 50 dB

below the main beam. If we choose a band limit of k^ = 1.05 k

which corresponds to a data point spacing of 0.476X, an additional attenuation of 140 dB results from the factor e"""^^.

It is clear that the band limit need be only slightly greater

than k, and therefore that the minimum required spacing for

this antenna at this distance is only slightly less than A/2.

i Y d The factor of e is not the only term which can produce

a band limit however. Band limiting can also occur in the

t region where y is real. If either Rq^^—^ §.io^—^ their

product is small enough for all K greater than some value,

this will produce a practical cutoff. The question as to how

small they must be, or equivalently how large 6 and 6 may be,

X y

is answered in terms of the effect produced on the important

part of the far-field for a given cutoff level or data point

spacing. To answer this question, the centerline data are

again used in a test similar to the one described in the last

section. The original data were taken at a closely spaced

interval, 6 - X/10. The spectrum D'(k ,0) is computed from

this closely spaced data and stored in the computer. The

spectrum is then computed using only every other data point

and the results compared with the stored values . This is

repeated for increased intervals and the change in the spectrum

42
C. 0300

0000

-2C. 0000

o ^ ^ r * ^

-5.:: -4.00 -3.00 -2.c: -i.oo o.oo t.oo 2.00 300 4.00 5.0:

Figure 19. Amplitude Spectrum for Both Propagating and

Evanescent Modes on Constrained Lens Antenna.

43
is measured by computing the RMS and peak difference in the

pattern over all real angles and the change in the on-axis

gain. These quantities are shown plotted in figure 20 for

the centerline data in figure 11. A comparison of patterns

for cases where the RMS and peak differences are less than 1%

shows that the major changes are at nulls. The positions of

nulls and sidelobes are not changed, and the maximum change in

sidelobe magnitude is less than 2 dB as shown in figure 21.

If this is an acceptable level of accuracy, then for this

antenna pair, a spacing of about 0.8 X can be used. This

results in a reduction of over 60% in the number of points

required when compared to A/2 spacing. This is very significant when applied to antennas with aperture dimensions of

100 A or more.

From tests on a number of antennas whose near-field is

well collimated it is apparent that spacings greater than A/2

can frequently be used. For narrow beam antennas, a spacing

of slightly less than A/2 can therefore be considered as a lower limit rather than A/2 being an upper bound as previously

had been reported [5]

.

It must be remembered that when a band limit of K^^ is

used, and measurements are made at the corresponding spacing,

no pattern information is available for |K| > K^* The maximum

angle to which patterns are calculable is given by

e = sin"-^ • (30) max 2o ^ If information is desired over a limited angular region,

then certain things can be done to produce spatial filterings

in the measured data, reduce the band limits, and therefore

increase 6 and 6 . We have already seen how increasing the

X y

separation distance accomplishes this, and a similar effect

can be achieved by using a probe with a more directive receiving

pattern

.

44
:. ::co

;.c5oo

a

(0 x:u

c

•H

• O

(U

o

c

0)u

i-l a> cuc

•H

i-lQ)

Q)Cu

E3

e

•rHX

T3

CSCO

;500

:30

0.90

ceo

0.70

o.so

0.50

0.40

0.30

0.20

!0

;.oo

/— RMS I

Maxii

i f f ere

I urn '.:if

ice

Eerenc( /

/ L

A

/

/

1

/ tT'

^

1

1 /

1

\

\

/

/ —/- i

/

/

V?V

<< y

0.00 O.IO 0.20 0.30 O.iO 0.50 O.SO 0.70 0.80 0. 90 1. 00

Distance Between Data Points in Wavelengths

Figure 20. Change in Far-Field Due to Increase of Data Point

Spacing

.

45
0.0000

!0. 0000

-20. 0000

90. o:3o

9C.0fl -72.00 -54.00 -36.00 -IS. 0 0 0.00 1 8.00 3S. 00 54.00 '^2. 09 »5. 00 Azirauthal Angle in Degrees.

10

- 20

30

- 40

50

60

Figure 21. Comparison of Patterns Computed from Near-Field

Data with 6 = .08X and 6 = 0.62X, Constrained

X X

Lens Antenna.

46
3.2.3 Scan Area and Data Point Spacing for Main Beam Shifted

Away from the Normal to the Measurement Plane

When the planar near-field technique is used on an electronically steerable array, there are times when the main beam

is steered to directions other than normal to the measurement

plane. Under these conditions, the required scan parameters

may change with steering angles, and tests were therefore performed to determine the nature of those changes for scan angles

of 45° or less. On the constrained lens antenna, the beam was

shifted by mechanically rotating the antenna in its mount, and

near-field centerline patterns were measured for azimuth rotations of 0°, 20°, and 38° and elevation rotations of 0°, 10°,

and 20°. The data for the 20° azimuth rotation is shown in

figure 22 and should be compared to figure 11 which is the

comparable data for 0° rotation. The major changes in the data

are the translation of the amplitude by the distance,

Ax = d tan 6, and the change of the phase in the collimated

region from a fairly uniform function to a rapidly increasing

function with a slope of = sin 20°. The scan area which

is required for a given angular region about the main beam is

approximately the same as for normal incidence, but it has been

shifted in space. The maximum scan area for all beam positions

can therefore be determined from a knowledge of the maximum

scan angles, the angular region about the main beam, and the

relationship given in eq. (27). For example, if the beam is

to be steered to ± 45°, and patterns computed ± 10° about the

main beam, then the scan length must be L = 2d tan 55° + a. The distance d between test antenna and the probe must be

kept small to maintain a reasonable scan area under these

circumstances

.

47
Near-Field Centerline Data, Constrained Lens

Antenna, z = 25 cm, Az = 20°, EL = 0°.

48
The data point spacing is affected by a shift of the beam

in two ways. First the main beam and sidelobes are shifted

to wider angles, and band limiting in the real angle region

will therefore occur at larger angles, which results in a smaller data point spacing. The magnitude of the sidelobes

may also increase as the beam is steered, and this will also

result in a wider band limit and still smaller data point

spacing. Second, there may be an increase in the evanescent

modes at the wide steering angles, which would extend the

practical cutoff into the imaginary angle region and therefore

require a data point spacing of less than X/2. This latter

effect was not observed for the Volphase antenna for steering

angles of 45° or less. The tests on centerline data for

various steering angles did show a slight decrease in required

spacing for off axis angles, but as figure 23 shows, they were

all close to A/2.

3.2.4 Effect of Multiple Reflections

It was previously mentioned that multiple reflections between the antennas are assumed to be small enough to neglect.

Since this is an approximation, it must be determined how low

the reflections actually are, and what their effect is on the

computed parameters.

To accomplish this, centerline data were employed in

a slightly different way. A series of scans which differed

in the z-separation by intervals of A/4 were taken along a centerline, and the far- fields were computed for each scan

and compared with each other. The multipath signals will have

different phase relations at each z-position, and some of the

changes in the computed far-fields will be due to the multiple

reflections. If the near-field is not a product pattern, some

49
50
change will occur in the patterns computed from centerline

data at different z-distances even if there is no multipath

interference. This will probably make the apparent effect

of multipath larger than it actually is, and the tests therefore set a probable upper bound to the error.

A typical set of data is illustrated in figure 24. Two

scans at z distances which differ by X/4 are plotted. These

particular data are for the Volphase antenna operating in the

sum mode with the beam steered to zero degrees in both azimuth

and elevation. Measurements at one distance are shown as continuous curves, and at the second distance as individual

points. The far-fields computed from these two sets of data

are shown in figure 25, with similar plotting of the two results.

It is apparent that the multiple reflections will not cause any

serious error in the far- field parameters for this antenna and

probe pair.

The magnitude of the multipath can also be estimated by

measuring the amplitude of the near-field as a function of

separation distance at various points near the center of the

collimated region. Periodic variations with a period of A/2

are due to multiple reflections, and the magnitude of the

interference signal can be determined from the peak-to-peak

amplitude of the variations by the expressions,

\ = 20 log (^), p = log"\M/20), (31)

where M is the measured variation in dB , and A is the ratio

m

of the true field to the multipath interference signal. Typical measurements of M between 0.1 to 0.2 dB indicate interference levels of approximately 40 dB below the true signal.

If the relative phase between the true and interference field

did not change over the area of the collimated region, the

multipath would increase or decrease all measured amplitudes

51
0. 0090

•iO.OO -40.00 -50.06 -20. OC -lO.O; : 00 10 00 20. CO 30.00 40.00 50.00

X-Position of Probe in cm. Figure 24. Multipath Centerline Data for Volphase Antenna,

z = 38 cm.

52.
0.0000

-5.0000

1 0. 0000

'90.00 -72.00 -54.00 -3C. 00 - 16.00 0.00 18.00 3C. 00 54.00 72.00 90.00

Azimuthal Angle in Degrees.

Figure 25. Far-Fields Computed from Data at z-Distance which

Differ by X/4, Volphase Antenna.

53
by a constant amount. The maximum error in the on -axis gain

would therefore be ± M/2 dB , and since all o£ the pattern would

be changed by the same amount, there would be no error in the

relative pattern.

The more typical situation is where the multipath goes in

and out of phase with the true field across the collimated

area, which results in a small periodic variation in the amplitude and phase as a function of x and y. This reduces the

error in the on-axis gain, but causes some error in the relative far-field pattern.

In some cases, the multiple reflections may be too large

to neglect for a given probe and z - separation . They can be

reduced by reducing the size of the probe or increasing the

distance between the antennas. Since the mounting structures,

the floor and walls, and the scanner do in fact contribute to

the scattering characteristics of the total system, the reflections can also be reduced by the appropriate placement of

microwave absorbers. For antennas with well collimated beams,

and fairly small z-distances, a large amount of absorbing

material is not required. It is generally not necessary that

the room be completely covered with absorbing material.

3.2.5 Detection of Faulty Array Elements and Radome

One very useful side benefit of the near-field scanning

techniques is the possibility of detecting and identifying

faults associated with the test antenna. Ideally one would

like to differentiate between array faults and radome faults

and locate the position of faulty elements and/or radome

anomalies. To investigate possible means of using the nearfield data to accomplish this fault detection/location,

numerous scans were taken with and without real or simulated

faults. The general approach was to record a set of data with

54
the array and/or radome operating properly, introduce a real

or simulated fault, and record data at the same positions as the first case. The raw data were compared, or the data after

identical processing were compared, to evaluate the sensitivity

to various faults. Most of the data involving fault location

are still to be processed and only preliminary results are

available at this time.

Some of the data which have been processed involves

simulated phase shifter faults on the constrained lens antenna.

Aluminum oxide disks were cut to fit over a single radiating

element. Various thicknesses were used to produce phase shifts

of 45°, 90°, and 180°. Figure 26 shows the superimposed plots

of the amplitude and phase along the near-field centerline y=0

,

z=25 cm with and without a 180° dielectric disk at x=0 , y=0

.

The effect of the simulated fault is more clearly seen in

figure 2 7 where the changes in amplitude and phase due to the

simulated fault are plotted. Figure 28 is a similar difference

plot for the case when the dielectric disk had been moved to

the position x=25, y=0 . In both cases, the changes in phase

and amplitude are a good indication of the general locations

of the faulty element. Further data processing is being done

on this and similar two-dimensional data to try to improve

the indication and location of faulty array elements.

3.2.6 Far-Field Patterns from Centerline Data

In the previous sections , the centerline data have been

used to determine scan parameters and estimate errors. The

far- field patterns and gains derived from the one dimensional

scans have not been examined in detail. Only their changes due

to changes in the amount or character of the data have been

examined. It is also of interest to determine the accuracy of

the far-field parameters which have been determined from centerline data and therefore to discuss the possibility of using

centerline scans in other types of tests.

55
( vo. vw

72.00

0)0)u 36.00

(U Q

0.00

1 i-.-niT,,— . —

No Fault

•

• ^—

•

t V

^^^^^

« \

• 1•1

iVO.OO

90.00

% 80.00 uM

(U Pi

.S 70.00

0) a

3

•H CO. 00 I

50.00

40.00

30.00

20.00

10.00

oje

Probe X-Position in CM

Figure 26. Near-Field Amplitude and Phase Centerline Data on

Constrained Lens Antenna With and Without 180°

Simulated Phase Shifter Fault at x = 0

.

56
1.00

4.00

0.00

-i.OO

-I.OI

e.oo

4.00

0.00

-4.00

-8.00

-!2.00

IC.OO

-2ojie

A

LX f

A —/

/

A

j A

J

00 0.00 coo 12.00 11.00 24.00 50. 00

Probe X-Position in CM

Figure 27. Change in Amplitude and Phase Due to 180

Simulated Fault at x = 0

.

57
m

0)(Uu

Q) Q

C

•H

(UO

C

0)

0)

(0

-Pc

0)o

^^

0) Pyc

•H

<0u

c

0)

<u

14-1 Q

<U •O3

•4-1 •H

iH

e.oo

4.00

0.00

-4.00

-e.oo

e.oo

4.00

0.00-

-4.00

-e.oo

12.00

IS. 00

«4>

A

r f

t

A

Probe X-Position in CM

Figure 28. Change in Amplitude and Phase Due to 180

Simulated Fault at x = 18 cm.

58
The validity of using this approach rests upon the assumption that the measured complete data are expressible as a rectangular product function. That is that

bQ(x,y) = bQ(0,y) bQ(x,0).

If this is true for a given antenna, then the centerline data

will give accurate results. If it is not true, then the results will only be an approximation to the actual far-field

parameters. The design and construction of the antennas usually

will give some indication as to whether or not the rectangular

separability will be a good approximation. Because of the

circular aperture on the constrained lens, the centerline

data would not be expected to give very accurate results.

Figures 29 and 30 show the comparison between far-field patterns

for the constrained lens antenna which were computed from

complete two-dimensional data and only centerline scans.

As expected, there is qualitative agreement but a significant

difference in the detail of the sidelobes.

For the Volphase antenna with a rectangular aperture and

a design which fits the rectangular separability assumption,

the centerline data should give much better results . This is

verified by reference to figures 31-34, which also compare

results from complete and centerline data for this antenna for

both sum and azimuth difference modes.

Certainly for an antenna like the Volphase, and even to

some degree for the constrained lens type, the results of

one-dimensional scans would be helpful during the initial

construction and testing of an antenna. The approximate

results could be computed quickly and used in the adjustment

of feeds, phase shifters, or other elements to optimize

antenna performance. The final configuration could then be

tested using more complete data.

59
i

•lb. BO -24.90 -le. 00 -12. CO -5.30 o.o: s. oe !2.oo 18.00 24.00 so. 00 Elevation Anglo In D«gr«es

Figure 29. Comparison Between Far-Field Patterns Computed

from Complete and Centerline Data. Constrained

Lens Antenna, E- Plane Sum Pattern.

60
Azimiithal Angle in Degrees

F^-gure 30. Comparison Between Far-Field Patterns Computed

from Complete and Centerline Data. Constrained

Lens Antenna, H-Plane Sum Pattern.

61
Figure 31. Comparison Between Far-Field Patterns Computed

from Complete and Centerline Data. Volphase

Antenna, 0° Sum Pattern.

62
CQ

C

•H

-a

00

-5. 00

-10.00

15. 00

-20.00

-25.00

9' -30.00

35,00

iO.OO

-45.00

•50.00

Complete Data

4-

/

• 9

•

1

0.00 S.OO 12.00 16.00 24.00 32. OC 3G. 00 42.00 41.00 $4.00 CO.OO Azimuthal Angle in Degrees

Figure 32. Comparison Between Far-Field Patterns Computed

from Complete and Centerline Data. Volphase

Antenna, 30° Sum Pattern.

63
Figure 33. Comparison Between Far-Field Patterns Computed

from Complete and Centerline Data. Volphase

Antenna, 0° Azimuth Difference Pattern.

64
Figure 34. Comparison Between Far-Field Patterns Computed

from Complete and Centerline Data. Volphase

Antenna, 30° Azimuth Difference Pattern.

65
"S.l.l Summary of Conclusions from Tests Using Centerline Data

Tests have been described which are very helpful, and in

some instances required, to determine the scan parameters and

the effects of multiple reflections . Additional tests were

also made indicating the feasibility of using this technique

to detect antenna element and/or radome faults. Since an

assumption of product pattern separability is implicit in these

preliminary tests, the results will in general indicate a worst case error due to area truncation, data point spacing

increase, and multipath. This is because the effect of the

three things being tested will not have the same character

along every scan. The variations will tend to have more of a random effect when complete two-dimensional data are used,

which reduces the actual error in far-field parameters.

Each given test antenna and test program will have a particular set of desired results. One may require pattern information over a large angular region on a fairly broad beam

antenna while another seeks for high accuracy in on-axis gain

plus pattern information over a limited angular region. The

scan parameters and the type of probe should be chosen to

achieve the measurement goals in each situation. The guidelines discussed here and the tests which were described are

very helpful in choosing the optimum scan parameters.

It has been shown that for directional antennas, the

effects of actual evanescent modes are usually very small,

and therefore the minimum required data point spacings are

only slightly less than A/2.

Spatial filtering can be accomplished by using a directive

probe or increasing the distance between the test antenna and

probe. This spatial filtering reduces the number of data

points required by reducing the scan area and/or increasing

the data point spacing. Such filtering will however decrease

the angular region over which far-field results are obtainable.

The desirability of such filtering will depend on the individual

applicat ion

.

66
If the antenna design is such that the measured nearfield can be approximated by a separable product pattern, the

far-field patterns computed from centerline data will be fairly

accurate. Centerline data for this type of antenna may be

sufficient for many purposes and would be very useful, for

instance, during the design and construction of the array.

Pattern and gain measurements could be obtained quickly and

the effects of modification could be determined.

3.3 Two- Dimensional Measurements and Results

In the present program, complete two-dimensional data

have been obtained for the two test antennas under a number of

different conditions . The test parameters which have been

varied include the use or absence of a radome , z -distance

between the probe and test antenna, sum or difference mode,

transmitting or receiving from the probe, beam steering direction, and simulation of antenna and radome faults. In total

over forty complete near-field scans were recorded (tables 2 and 4) , but only part have been completely processed. Those

that have been processed will be discussed here to illustrate

the measurement technique and demonstrate the results which

have been obtained.

3.3.1 Measurements at Different z-Spacings for Sum and

Difference Antenna Modes on the Test Antennas

Once the scan parameters are determined, the antennas

aligned, and the source and receiver systems checked for

stability, a complete scan can be taken. With an automated

system, the scan parameters are entered into the position

programmer and the measurement from that point on is completely

automatic. The probe is moved continuously in the chosen scan

67
direction (y in our case) and at the preset intervals the position programmer triggers the data system to record the amplitude

and phase of the probe output. When the scan length has been

covered, the programmer either steps the positioner the prescribed amount in the x-direction or retraces and then steps,

and repeats the scan. This process may take from two to eight

hours depending on the size of the scan area and the travel

speed of the positioner.

Since the relatively long measurement times are required,

the receiver system may drift, and some correction for this

drift is desirable. The system is very stable during one scan,

but the drift between the first and latter scans can be significant. To correct for this, normalization scans are taken at

the original measurement points over a small area through the

center of the scan area. These normalization scans are taken

in the direction perpendicular to the original scans, and used

to obtain correction coefficients for all the data in each

linear scan. As an additional step in this calculation of the

normalization coefficients, the amplitudes and phases of all

the data are also normalized with respect to one point in the

measurement matrix. The particular point is arbitrary, but it

is convenient to choose it close to the center and near the

peak amplitude point. If we denote the reference point by , then the normalized data are given by

B (P) = -? . (32)

b (P ) o ^—o^

To obtain the second complete set of data (which is necessary to solve for the two components of S-|^q(K))» the probe is

rotated about its z-axis by 90° and the scanning procedure is

repeated. For a test antenna and probe which are nearly linearly

polarized, the amplitude of this second set of data may be very

68
small. In some cases it may even be neglected. It must be

measured however if spherical components of the far-field are

to be determined along non-principal planes or if polarization

ratios are desired. The normalization point for these data

need not be the same as for the first set. In fact it is

usually" different, since the cross component is usually

smallest in the center where the principal component is

largest. If we denote the normalization point for these data

by P , then the normalized data are given by

b^(P)

B (P) = ^ . (33)

The two sets of data, B^(P) and (P) , must now be referenced

to the input signal, a^ , so that they will have a common phase

and amplitude reference. This can be accomplished by first

placing the probe at P^, and orienting it for response to the

first measured component. The transmission lines connected to

the two antennas are removed and connected directly together.

The normalization factor

b' (P )

1 %

'

is then determined from the measured change in the received

signal and the appropriate impedance mismatch factors. The

second factor,

T

2

can be measured in a similar manner, or it can be obtained

from and a measurement of the ratio = (P_^) /b^ (P^) . If the latter approach is used, only the magnitude of is

required, but both phase and amplitude of x^ are necessary.

69
For a test antenna which is approximately linearly polarized in the y- direct ion, and a probe with similar polarization,

B^(P) is termed the y- or principal -component data, and (P)

the X- or cross component-data. These terms are not completely

accurate, since the probe will generally respond to both x and

y components even if it transmits only a y-component, but they

are descriptive and useful.

Figures 35a and 35b are three-dimensional plots of the

amplitude and phase of (P) resulting from measurements at

z = 25 cm on the sum port of the constrained lens antenna.

Figures 36a and 36b show the data for the same antenna and

probe for a z-spacing of 250 cm. The spatial filtering due

to the increased separation distance is very apparent in the

smoothness of figure 36a. Figure 36b also illustrates an

alternate way of plotting the phase data, where only half of

the data are plotted and viewed from a lower observation point.

The phase plot in figure 36b shows more detail of the important

center section.

The far- field patterns were computed for both of these

sets of data, and the result for the data in figure 35 is

shown in figure 37. The first step in this computation is

the evaluation of the integrals of eqs. (19) and (21) by the

Fast Fourier Transform. This routine is extremely efficient,

requiring about 30 seconds to transform an array of 128 x 128

complex near-field points to an equal number of far-field values.

It is most efficient when the array size is a power of two,

and so the data arrays are often padded with zeroes to increase

their dimensions to powers of two.

After both sets of data have been transformed, the probe

correction is applied to obtain the two rectangular or spherical

components of s_^q(K). This probe correction consists of using

the previously measured receiving characteristic of the probe.

70
Fipure 35a. Constrained Lens Sum Port Near-Field Log Anplitude, f = 9.2 CHz, z = 2 5.0 cm. No Radome

.

71
72
73
74
Figure 37. Constrained Lens Sum Port Far-Field Log Amplitude, £ = 9.2 GHz, Computed from z = 25 cm Data,

No Radome

.

75
t Rq^(K), and solving the simultaneous equations (18) and (20).

The probe correction equations in terms of linear components

are

^lOx® = D'mRQ^^(K) - D"(K)Rq^^(K)/A^^ (34a)

S^Q^(K) = D"(K)Rq^^(K) - D'(K)Rq\^(K)/A^^ (34b)

where

= •^Olx^'^OlyW - Roi^mR^l/K). (35)

The single primed quantities are the components for the probe

in the first orientation and the results from the data measured

in that orientation. The double primed quantities are similar

quantities after rotating the probe by 90° about its axis, or

using a second independent probe, as the case may be. The

nature of the probe correction may be seen more clearly by

looking at a special case. Let us assume that the probe

responds to only one rectangular component of the incident

t ft spectrum, and therefore ^qj^-j^CK) = ^^giy^— ~ ^* Equations (34)

then reduce to

S,„^CK) = ?, , and (36a) -

Roi,(K)

f

It is apparent from eq. (36) why the probe may be viewed as

a spatial filter, and the probe correction as the adjustment

to the computed spectrum for this filtering. Equations (36)

also illustrate another important feature of the probe correction, namely that the probe characteristic Rq^C^) is

required only for those directions (K values) for which S^-j^Q (K)

76
is desired. This means that the probe correction is a simple

algebraic calculation rather than an integration over an angular

region. The probe receiving pattern is therefore required only

within the same angular region over which S^j^q(K) is to be

determined.

The probe correction equations in terms of spherical

components of s_(K) and r(K) are very similar, and they illustrate that the various components of s_(K) are easily obtainable

by using the corresponding components of r' (K) in the probe

correction equations. They are

= 109 = 0'®^014,W - D"(K)r;^^(K)/Ag^

^10* = D"CK)r;^g(K) - D'CK)ro„(K)/Ag^

whe re

^ec^

= ^OieWroi^m - rQ^gWrQ^^CK)

Similar equations in terms of i<_-|^ and on left and right

circular components are easily obtained by using these components

in the expansions of eqs. (18), (20) or (22).

The perspective or "three-dimensional" plots such as those

in figures 35-37 are very helpful in obtaining an overall view

of the measured data and results . Prolems in the data which

may not be apparent in the digital printouts are easily detected in this type of presentation. Figure 37 also illustrates

the detail and resolution available from the near-field technique.

This is one of the distinct advantages of this approach, because the antenna characteristics are obtained over a complete

angular region and not just along the principal planes. When

it is desirable to look at individual pattern cuts , these

are easily obtained from the complete results. Figure 38

(37a)

(37b)

(38)

77
shows the patterns in the plane defined by k =0 (E-plane for

this antenna) for the two sets of data having different separation distances. Over this angular region they are very similar,

which illustrates that within the region specified by eq. (27)

,

accurate pattern information can be obtained at fairly large

z distances.

Similar near-field data is shown in figures 39a and 39b

for the antenna operating in the elevation difference mode,

with complete and principal plane patterns in figures 40 and 41

respectively. The two patterns in figure 41 are again for data

taken at z = 25 and z = 254 cm.

The data and results in all the previous figures have

been for the usual case where the test antenna was transmitting

and the probe receiving. For some tests, the mode of operation

was changed, and the probe was used in the transmitting mode.

The test antenna remained in the elevation difference mode

since this more complex pattern should provide a more difficult

test. Since both antennas in this case are reciprocal, the

results of the test should be identical with those obtained

with the probe receiving. The patterns are essentially identical as can be seen from figure 42. This confirms that measurements can be made with either a transmitting or receiving

probe. This is required if the antenna is not reciprocal, and

was in fact the case for the Volphase antenna.

Measurements with the Volphase antenna were not as fully

automated using the small scanner system as were those with

the constrained lens using the large scanner system. The small

scanner consisted of a modified lathe bed driven by a constantspeed synchronous motor combined with a digital clock and

optical position indicator and trigger mechanism. The scanner

had to be manually reset in y after each scan for the desired

step interval. The scan direction for this case was x. The

measurement process is somewhat slower than the fully automated

78
Elevation Angle in Degrees

Figure 38. Comparison Between Far-Field Patterns Computed

from Near-Field Data taken at Two Different

z-Distances. Constrained Lens Antenna, E-Plane

Sum Pattern.

79
Figure 39a. Constrained Lens Elevation Difference Port NearField Log Amplitude, f = 9.2 GHz, z = 250 cm.

No Radome

.

80
y Distance in cm

Figure 39b. Near-Field Phase, Constrained Lens Elevation

Difference Port, f = 9.2 GHz, z = 250 cm.

81
-16 0 16

ELEVATION ANGLE IN DEGREES

Figure 40. Constrained Lens Elevation Difference Port Log Amplitude, f = 9.2 GHz, Computed from z = 25 cm

Data, No Radome

.

82
0.00 Z = 25 cm Data

Z = 254 cm Data

Elevation Angle in Degrees

Figure 41. Comparison Between Far-Field Patterns Computed

from Near-Field Data taken at Two Different

z-Distances. Constrained Lens, E-Plane Elevation

Difference Pattern.

83
s.oo

m

c

0) -aP

-20.00

25.00

Figure 42. Comparison Between Far-Field Patterns Computed

from Near-Field Data with Probe Transmitting and

Receiving. Constrained Lens Antenna, E-Plane

Elevation Difference Pattern.

84
system used with the constrained lens but did allow limited

sized, two dimensional scans that took approximately four hours

to complete. Because movement in the y direction was manual

only, it was not practical to take normalization scans as was

done with the large scanner with the constrained lens antenna.

Therefore, the measurements with the Volphase antenna system

were checked periodically and corrected for drift. The technique otherwise is the same for the two systems and utilizes

the same equations for computing the far field patterns. A

number of two-dimensional scans were made with the Volphase

antenna (table 4). The same data processing was carried out

on this data, and the results for some measurement cases will

be described in the following section.

3.3.2 Pattern Comparisons for the Constrained Lens

and Volphase Antenna

Pattern measurements were made on the antennas on conventional far-field ranges both before and after the near-field

measurements. These patterns were compared with those computed

from near- field data to demonstrate the agreement between these

two methods. The results of some of these comparisons are

shown in figures 43-48. The comparisons for the constrained

lens are certainly within the limits of accuracy of the farfield measurements where ground reflections cause significant

errors when the pattern is below about 30 dB.

On the Volphase comparisons, there is a definite degradation in accuracy in the near-field results for positive angles

when the beam was steered to +30° off boresight. This is due

to the limited scan area available with the small portable

scanner. With the beam steered to +30°, the amplitude at the

+x edge of the scan area was only 15-20 dB below the near-field

85
-12.:: -s.:: s ;: ;2.::

Elevation Angle in Degrees

24. O: 33. 3J

Figure 43. Comparison Between Far-Field Patterns Measured on

Far-Field Range and Computed from Near-Field Data

Constrained Lens, E-Plane Sum Pattern.

86
-5C JO f i -1 I t I I t

* ' '90.00 -2i. 00 -18.00 -!2.00 -6.00 0.00 6.00 12.00 18.00 24.00 50.00

Elevation Angle in Degrees

ure 44. Comparison Between Far-Field Patterns Measured on

Far-Field Range and Computed from Near-Field Data

Constrained Lens, E-Plane Elevation Difference.

87
0.0000

•5. 0000

-10.0000

-15. 0000

^ -20.0000

•H^ -25.0000 3

P

•H

-30. 0000

35. 0000

40. :;co

45. ::::

i: ::::

Far-Field Range

^

*

24 C : •!2.:: -6.: &. c :2. c : !9.:: 24.:: 3c.::

Azimuthal Angle in Degrees

FJ-gure 45. Comparison Between Far-Field Patterns Measured on

Far-Field Range and Computed from Near-Field Data

Volphase Antenna, 0° Sum Pattern.

88
n

-a

4J

I

0.0000

-5.0000

•10.0000

15.0000

-20.0000

-25.0000

30.0000

-35.0000

40.0000

45.0C00

5C.C909

Far-Field Range —f

4-

\^ • \

* t

0.00 e.OO 12.00 le.OO 24. OO 30.C9 3S.00 42.00 48.00 54.00 SO. 00

Azimuth Angle 5" '^•arees

Figure 46. Comparison Between Far-Field Patterns Measured on

Far-Field Range and Computed from Near-Field Data

Volphase, 30° Sum Pattern.

89
V

0.0000

-5.0000

-10.0000

-15.0000

-20.0000

-25.0000

50.0000

-55.0000

40.0000

45. 0009

5C. 0500 -30.00 -24.00 -18.00 -12.00 -6.00 0.00 6.00 12.00 18.00 24.00 30.00 Azimuthal Angle in Degrees

Figure 47. Comparison Between Far-Field Patterns Measured on

Far-Field Range and Computed from Near-Field Data

Volphase Antenna, 0° Azimuth Difference Pattern.

90
3.0000

-5. 0000

10.0000

•15. 0000

-20.0000

-25.0000

tarsG

-HV

A

a -30.0000

55. 0000

iO.. 0000

45. 0500

50. C5;0

J. CO 6.00 12.00 18.00 24.00 30.00 3S. OC 42.00 48.00 54.00 60.00

Azimuthal Angle in Degrees

Figure 48. Comparison Between Far-Field Pattern Measured on

Far-Field Range and Computed from Near-Field Data.

Volphase Antenna, S0° Azimuth Difference Pattern.

91
maximum and the truncation of significant data caused the

larger errors on this side of the pattern. Considering the

small scan area, the small amount of absorbing material used,

and the very unconventional "range," these comparisons are

quite remarkable. They illustrate quite graphically that the

planar near-field technique can be used very successfully in

many antenna measurement situations.

4.0 Conclusions

The planar near- field measurement technique can be applied

very successfully to high performance phased array antennas.

In some cases, the amount of required data can be reduced by

using data-point spacings of greater than X/2, reducing the

measurement area, or both. Even when the beam is steered to

45 degrees off axis, the required spacing is still only slightly

less than X/2

.

Fast and efficient tests using centerline data can be performed to determine the required scan area, data point spacings,

the effect of multiple reflections, and possibly the location

of faults in the test antenna and/or radome

.

The pattern comparisons indicate that the results computed

from near- field data are in good agreement with those measured

on far-field ranges.

92
References

[1] D.M. Kerns and E.S. Dayhoff, "Theory of diffraction in

microwave inter fe rome t ry Jj_ Res . Nat . Bur Stand

.

, Vol.

64B, pp. 1-13, Jan. -Mar. 1960.

[2] D.M. Kerns, "Correction of near-field antenna measurements

made with an arbitrary but known measuring antenna,"

Electron. Lett. , Vol. 6, pp. 346-347, May 1970.

[3] D.M. Kerns, "New method of gain measurement using two

identical antennas," Electron . Lett

.

, Vol. 6, pp. 347 , 349 , May 19 70.

[4] R.C. Baird, A.C. Newell, P.P. Wacker, and D.M. Kerns,

"Recent experimental results in near-field antenna measurements," Electron. Lett. , Vol. 6_, pp. 349-351 , May 1970.

[5] E.B. Joy and D.T. Paris, "Spatial sampling and filtering in

near-field measurements," IEEE Trans . Antennas Propagat

.

, Vol. AP-20, pp. 253-261, May 1972.

[6] D.M. Kerns and R.W. Beatty, Basic Theory of Waveguide

Junctions and Introductory Microwave Network Analysis

[Pergamon Press, Oxford, 1967).

[7] D.M. Kerns, "Plane-wave scattering matrix and generalized

reciprocity relations for antennas and scatters," NBS

Report Cunpublished) , June 1972.

93
NBS.n4A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 74-3802. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Planar Near-Field Measurements on High Performance

Array Antennas

5. Publication Date

6. Performing Organization Code

7. AUTHOR(S)

All on P Nowfkl 1 £ Mvfon T. PfawFoi**^

8. Performing Organ. Report No. NBSIR 74-380

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

Boulder, Colorado 80302

10. Project/Task/Work Unit No. 2727454

11. Contract/Grant No. F33615-73-M-6001

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

Air Force Avionics Laboratory

Wright-Patterson Air Force Base

Ohio 45433

13. Type of Report & Period Covered

Final Report FY 73

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

U.S. Air Force Technical Report

16. ABSTRACT (A 200-word or leaa {mctual summary of most si^idcant information. U document includes a significant

bibliography or literature survey, mention it here.) The results of measurements which apply the planar near-field measurement technique to phased array antennas are described. Fast and eff icien

tests are used to determine the required scan area and data point spacing. The use of these tests can reduce the amount of data required for

some antennas without significantly increasing the errors in computed

results.

Measurements were made at different distances frcan the antennas, with the

probe transmitting and receiving, and for both sum and monopulse difference patterns. Comparisons between the far-field patterns computed

from the near-field data and those measured on far-field ranges are presented .

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

Antennas; near-field measurements; phased arrays.

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