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IEEE Std 1720™-2012

IEEE Recommended Practice for Near-Field Antenna Measurements Sponsor

Antenna Standards Committee of the

IEEE Antennas and Propagation Society

Approved 20 August 2012

IEEE-SA Standards Board


Abstract: Near-field test practices for the measurement of antenna properties are described in this document and near-field measurement practices for the three principal geometries: cylindrical, planar, and spherical are recommended. Measurement practices for the calibration of probes used as reference antennas in near-field measurements are also recommended. Keywords: antenna measurements, antenna near-field measurements, cylindrical near-field measurements, IEEE 1720, near-field measurements, planar near-field measurements, probe calibrations, spherical near-field measurements •

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Participants At the time this IEEE recommended practice was completed, the Near-Field Antenna Measurements Working Group had the following membership: Michael H. Francis, Chair Lars Jacob Foged, Secretary Donald Bodnar Martin Boettcher John Cable Francesco D’Agostino Justin Dobbins Jeffrey Fordham Dayel Garneski Claudio Gennarelli Jeffrey Guerrieri Doren Hess Kevin Higgins

Daniel Janse van Rensburg Frank Jensen Edward Joy Gerard Matyas Scott McBride Josef Migl Zachary Newbold Allen Newell Sergey Pivnenko Yahya Rahmat-Samii

Carlo Rizzo Luis Rolo Luca Salghetti-Drioli Manuel Sierra-Castañer Leili Shafai Hans Steiner Ivan Stonich Hulean Tyler Jeffrey Way Mark Winebrand Ronald Wittmann

During preparation of this recommended practice, the following people made substantial contributions: Aksel Frandsen

Shantnu Mishra

Giovanni Riccio

The following members of the individual balloting committee voted on this recommended practice. Balloters may have voted for approval, disapproval, or abstention.

William Byrd Keith Chow Justin Dobbins Carlo Donati Lars Foged Jeffrey Fordham Michael Francis Avraham Freedman Randall Groves Timothy Harrington

Doren Hess Werner Hoelzl Efthymios Karabetsos Greg Luri Ahmad Mahinfallah Wayne Manges Edward McCall Michael S. Newman Nick S. A. Nikjoo Satoshi Oyama

R. K. Rannow Robert Robinson Bartien Sayogo Gil Shultz Thomas Starai Walter Struppler John Vergis Jeffrey Way Mark Winebrand Ronald Wittmann

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When the IEEE-SA Standards Board approved this recommended practice on 20 August 2012, it had the following membership: Richard H. Hulett, Chair John Kulick , Vice Chair Robert M. Grow, Past Chair Konstantinos Karachalios, Secretary Satish Aggarwal Masayuki Ariyoshi Peter Balma William Bartley Ted Burse Clint Chaplin Wael Diab Jean-Philippe Faure

Alex Gelman Paul Houzé Jim Hughes Young Kyun Kim Joseph L. Koepfinger* David J. Law Thomas Lee Hung Ling

Oleg Logvinov Ted Olsen Gary Robinson Jon Rosdahl Mike Seavey Yatin Trivedi Phil Winston Yu Yuan

*Member Emeritus

Also included are the following nonvoting IEEE-SA Standards Board liaisons: Richard DeBlasio, DOE Representative Michael Janezic, NIST Representative Patrick Gibbons

IEEE Standards Program Manager, Document Development Michael Kipness

IEEE Standards Program Manager, Technical Program Development

vii



Introduction This introduction is not part of IEEE Std 1720 TM-2012, IEEE Recommended Practice for Near-Field Antenna Measurements. TM

When IEEE Std 149 -1979 (IEEE Standard Test Procedures for Antennas) was first developed, near-field antenna measurement was in its infancy. In the mid-1980s, the use of near-field methods for measuring antennas started becoming more widespread, especially for testing communication satellite antennas. Today, more than 200 facilities worldwide employ near-field methods for measuring antenna parameters. Many believe the time had come to develop a set of recommended practices for these measurements. This document lays out recommended practices for near-field measurements for the three principal geometries: cylindrical, planar, and spherical. It also indicates recommended measurement practices for the calibration of probes used as reference antennas in near-field measurements.

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Contents 1. Overview .................................................................................................................................................... 1 1.1 Scope ................................................................................................................................................... 1 1.2 Purpose ................................................................................................................................................ 1 2. Normative references.................................................................................................................................. 2 3. Background ................................................................................................................................................ 2 3.1 Antenna patterns .................................................................................................................................. 2 3.2 Basic near-field measurement theory .................................................................................................. 4 3.3 Far-field versus near-field measurements ............................................................................................ 6 3.4 Executive summary ............................................................................................................................. 6 4. Measurements systems ............................................................................................................................... 7 4.1 Mechanical scanning subsystems ........................................................................................................ 7 4.2 Typical RF subsystem.........................................................................................................................11 4.3 Typical data collection subsystem ......................................................................................................12 4.4 Data processing...................................................................................................................................14 4.5 Measurement accuracy .......................................................................................................................14 4.6 Correction schemes .............................................................................................................................17 5. Planar near-field scanning measurements .................................................................................................20 5.1 Introduction ........................................................................................................................................20 5.2 Summary of theory .............................................................................................................................22 5.3 Implementation ...................................................................................................................................24 6. Cylindrical near-field scanning measurements ..........................................................................................34 6.1 Introduction ........................................................................................................................................34 6.2 Summary of the basic theory ..............................................................................................................34 6.3 Implementation ...................................................................................................................................37 7. Spherical near-field scanning ....................................................................................................................40 7.1 Introduction ........................................................................................................................................40 7.2 Summary of spherical near-field theory .............................................................................................40 7.3 Implementation ...................................................................................................................................45 8. Probes ........................................................................................................................................................52 8.1 Probe properties ..................................................................................................................................53 8.2 Description and classification of probe antennas................................................................................55 8.3 Probe parameters ................................................................................................................................58 8.4 Probe characterization ........................................................................................................................58 8.5 Probe arrays ........................................................................................................................................59 9. Uncertainty analysis ..................................................................................................................................62 9.1 Introduction ........................................................................................................................................62 9.2 Initial system adjustment and tests .....................................................................................................65 9.3 Methods for estimating and expressing uncertainties of individual terms ..........................................65 9.4 Methods of evaluation of each term for planar, cylindrical, and spherical near-field measurements .66 9.5 Combining uncertainties .....................................................................................................................78 10. Special topics...........................................................................................................................................78 10.1 Effective isotropic radiated power ....................................................................................................78

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10.2 10.3 10.4 10.5 10.6 10.7 10.8

Saturating flux density ......................................................................................................................79 Pulsed-mode measurement techniques .............................................................................................79 Phase retrieval methods ....................................................................................................................80 Back projections ...............................................................................................................................80 Probe-position correction ..................................................................................................................81 Truncation mitigation .......................................................................................................................82 Time gating in near-field antenna measurements .............................................................................82

11. Summary .................................................................................................................................................82 Annex A (informative) Bibliography ............................................................................................................83

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IEEE Recommended Practice for Near-Field Antenna Measurements IMPORTANT NOTICE: IEEE Standards documents are not intended to ensure safety, health, or environmental protection, or ensure against interference with or from other devices or networks. Implementers of IEEE Standards documents are responsible for determining and complying with all appropriate safety, security, environmental, health, and interference protection practices and all applicable laws and regulations. This IEEE document is made available for use subject to important notices and legal disclaimers. These notices and disclaimers appear in all publications containing this document and may be found under the heading “Important Notice” or “Important Notices and Disclaimers Concerning IEEE Documents.” They can also be obtained on request from IEEE or viewed at http://standards.ieee.org/IPR/disclaimers.html .

1. Overview

1.1 Scope This document describes near-field test practices for the measurement of antenna properties. It provides information on developments in near-field measurements that have occurred since the writing of IEEE Std 149™-1979 (IEEE Standard Test Procedures for Antennas). This document recommends near-field measurement practices for the three principal geometries: cylindrical, planar, and spherical, and also recommends measurement practices for the calibration of probes used as reference antennas in near-field measurements.

1.2 Purpose The purpose of this recommended practice document is to provide practical guidance to those who are planning to do near-field measurements. This document also specifies capabilities required of a near-field measurement system.

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IEEE Std 1720-2012 IEEE Recommended Practice for Near-Field Antenna Measurements

2. Normative references The following referenced documents are indispensable for the application of this document (i.e., they must be understood and used, so each referenced document is cited in text and it s relationship to this document is explained). For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments or corrigenda) applies. IEEE Std 145™, IEEE Standard Definitions of Terms for Antennas.

1,2

IEEE Std 149, IEEE Standard Test Procedures for Antennas. IEEE Antennas and Propagation Society, “Special Issue on Near-Field Scanning Techniques,” IEEE Transactions on Antennas and Propagation, vol. 36, no. 6, pp. 727–901, 1988.

3. Background 3.1 Antenna patterns We consider an exp(− iω t ) time dependence with frequency f = ω /(2π ) , wave number k = 2π / λ , and wavelength λ . Note that modern receivers generally use the exp ( + jω t ) time dependence. However much of the early theory and current software uses the exp(− iω t ) convention. The practitioner needs to be aware of the potential conflict. A minus sign needs to be added to the phase of a receiver using the +jωt convention to get the proper result from software using the – iωt convention. Sufficiently distant from a radiating antenna, the electric field is transverse and is given by the expression

Et (r ) ~ t (rˆ ) r → ∞

exp (ikr ) ikr

a0

(1)

rˆ ⋅ t (rˆ ) = 0 .

(2)

In any direction, the transmitting function t (rˆ ) is characterized by amplitude and phase (or real and imaginary part) and complex polarization. Equation (1) embodies the linear relation between the radiated field and the excitation a0 . The power accepted by the transmitting antenna is

P0 = K1 (1− | Γ t |2 ) | a0 |2 ,

(3)

where

Γt

is the impedance reflection coefficient, looking into the transmitting antenna

K 1

is an arbitrary constant.

1

The IEEE standards or products referred to in this clause are trademarks of The Institute of Electric al and Electronics Engineers, Inc. IEEE publications are available from the Institute of Elect rical and Electronics Engineers (http://standards.ieee.org/).

2

2




Once K 1 is fixed, P 0 determines a0 , and hence t (rˆ ) , up to an arbitrary (and unimportant) overall phase factor. A common rule of thumb states that Equation (1) is valid in the far-field region r > r f (e.g., IEEE Std 145, IEEE Standard Definitions of Terms for Antennas) where

r f ~

2 D 2 λ

,10 D, or 10 λ ,

(4)

whichever is greatest. D is the diameter of the smallest sphere that encloses the radiating parts of the antenna. Larger values of r f may be needed depending on antenna type or accuracy requirements. Consider an incident plane wave

E0

Ei (r )

=

exp(ik ⋅ r)

(5)

k ⋅ E0

= 0 , k ⋅ k = k 2 = ω 2 / c2 .

(6)

2π

ˆ): The response of a receiving antenna is given in terms of the receiving function s(k

(1 − Γ Γ r ) b0 = s(kˆ ) ⋅ E0 .

(7)



The received power P r and the available power P a are

( Γ )|b | . P = K (1 − Γ ) | b | Pr = K 2 1 −

2

2

0



2

a

2

(8)

2

r

0

Here K 2 is an arbitrary constant,

Γ



and Γ r are the reflection coefficients looking into the load and

receiving antenna, respectively. To be definitive, we use the normalizations

K

= K1 = K 2 =

where

Z 0 =

1 2k 2 Z 0

,

(9)

µ 0 / ε 0 ≈ 377Ω is the impedance of free space. With this choice, a0 and b0 have the

dimensions of electric field [V/m] and the transmitting and receiving functions are dimensionless.

3




Following IEEE Std 145, the directional gain of the transmitting antenna and the effective area of the receiving antenna are given by

4π



G (r ) =

2

| t (rˆ ) |2

(10)

2

| s (rˆ ) |2 .

(11)

1− | Γt |

λ 2



σ (r ) =

1− | Γ r |

Also when Equation (9) is adopted, reciprocity implies that

s(rˆ ) = t (−rˆ )

(12)

or

λ 2

σ (rˆ ) =

4π

G ( −rˆ ) .

(13)

Throughout this document, we assume that the antenna under test (AUT) is a passive, linear, reciprocal device. Consequently, it can be measured in either the transmitting or receiving mode. However, many of the test practices can be adapted for measuring antennas with active, nonlinear, or nonreciprocal components. We also use the term pattern to refer to the transmitting or receiving function when a specific normalization is not implied. A pattern can be normalized easily to satisfy Equation (11), Equation (11), or Equation (12) if the gain or directivity is known in some direction.

3.2 Basic near-field measurement theory Near-field measurement methods require the development of transmission formulas that describe the coupling of two antennas in close proximity. First, expand the vector field of the test antenna in a complete set of modes u n (r )

u(r ) ≈

N

∑ t u (r ) a , n

n

(14)

0

n =1

where N is the total number of modes. It needs to be possible to represent u(r ) to acceptable accuracy using a finite summation. (In cases where modes are not discrete, the sum is replaced by an integral.) The expansion, Equation (14), needs to be valid where measurements are made and in the far-field region, as well, so that

t (rˆ ) ~

r →∞

ikr . a0 exp ( ikr )

u(r )

(15)

4




First consider an ideal probe that measures the actual field at a point. In principle, to determine the coefficients

t n , it suffices to make independent measurements at P many points r i ( 1 ≤ i ≤ P ≥ N ) and to

find the least-squares solution to the system of linear equations that results from Equation (14). This would require O( N 3 ) operations using, for example, Gaussian elimination. N will be specified for each of the three geometries in what follows. For many practical antenna problems 10 < N < 10 and computational efficiency is a major concern. For this reason, near-field measurements are made so that data points lie in regular grids on planar, cylindrical, or spherical surfaces. Separability of coordinates and modal orthogonality arising in these geometries allow significant reductions in processing time. The computational complexity is O ( N log N ) for planar and 4

6

cylindrical sampling, and O( N 3 / 2 ) for spherical sampling, where N is the total number of modes to be determined. Practical probes do not (or only approximately) measure the vector field at a point in space. This fact is especially important in close proximity to a source where fields may vary significantly over the volume of the probe. The probe converts the incident vector field to a complex voltage that is measured and recorded by the data collection system. This conversion can be mathematically represented by the generic transmission equation

w ( r , χ ,θ ,φ ) = [P • u ]( r , χ ,θ ,φ ) = a0

N

∑ t P • u n

n

( r ,χ ,θ ,φ ) ,

(16)

n =1

where P is an operator that depends on the properties of the probe. This transmission equation will be specialized to the three coordinate systems (planar, spherical, and cylindrical) in subsequent sections. To account for probe effects, it is necessary to catalog the response (via probe characterization) of a probe to each mode in Equation (14)

wn ( r, χ ,θ ,φ ) = [P • un ] ( r, χ ,θ ,φ ) .

(17)

Arguments give the probe position vector r and the Euler angles

( χ ,θ , ϕ ) describing probe orientation

3

(see section 19.2.4.2 in Francis and Wittmann [B37] ). Equation (16) assumes that the presence of the probe does not affect the test antenna field. (Discrepancies due to probe-test antenna interaction are often called multiple-reflection errors . None of the present nearfield-to-far-field transformations with probe correction accounts for the effect of multiple reflections, since this would require considering (generally unknown) scattering characteristics of antenna and probe. The approaches to compensate for the effect of multiple reflections, in those cases when this effect is not small, are described in 9.4.11.) The probe response

w(r, χ , θ , ϕ ) is typically normalized to correspond to unit

excitation ( a0 = 1 ) and reflectionless load ( Γ 

= 0 ).

Again, to determine t n , it suffices to make independent measurements at the points r i ( 1 ≤ i

≤ P ≥ N )

and to find the least-squares solution to the linear system that follows from the transmission equation, Equation (17). The need for numerical efficiency limits practical implementations to planar, cylindrical, or spherical scanning.

3

The numbers in brackets correspond to those of the bibliography in Annex A.

5




A brief history of early near-field measurements can be found in the June 1988 issue of the IEEE Transactions on Antennas and Propagation Special Issue on Near-Field Scanning Techniques [B6], [B42], [B48], [B63]. During the 1940s and 1950s, near-field measurements of antennas were used primarily for diagnostic purposes (Gillespie [B42]). However, these measurements did not correct for probe-pattern effects. In the early 1960s, theories were developed by Kerns and Dayhoff [B72], Brown and Jull [B10], and Leach and Paris [B84] that accounted for these effects in planar and cylindrical geometries. These developments made it practical to determine the far-field properties of an antenna from measurements in the radiating near field.

3.3 Far-field versus near-field measurements The far-field pattern can be measured directly, direction by direction, if the probe-AUT separation can be made sufficiently large. (This may be impractical for some electrically large antennas.) Although near-field methods are more complicated physically and mathematically, the ability to use small separation distances means that it is possible to make many measurements in the climate- and electromagnetic-controlled environment of an antenna measurement facility (or range). Potentially, this fact can result in improvements in security, accuracy, and throughput. All near-field techniques require the acquisition and processing of two complex, (nearly) orthogonal polarization components (Yaghjian [B126]). Knowledge of this information helps ensure that both co-polar and cross-polar far-field radiation pattern information can be recovered. During the near-field acquisition, no reference needs to be made to the AUT polarization sense or the preferred definition of co-polarization or cross polarization. The near-field data set is converted to a far-field data set within a specific coordinate system, using a specific polarization definition (Ludwig [B85]). It is therefore possible to determine the AUT polarization sense during the processing phase of the measurement process. Since the two measured polarization components are orthogonal and therefore independent, it follows that circularly polarized (CP) AUTs can be measured using linearly polarized probes since any CP signal can be represented as the sum of two linearly polarized signals (Stutzman [B112]). However, in this case the CP component is the small difference between two large quantities and this tends to have a larger uncertainty than if measured with two orthogonal CP measurements.

3.4 Executive summary Clause 4 covers measurement systems. The geometries for the planar, cylindrical, and spherical near-field scanning methods necessitate data point acquisition on a plane, cylinder, and sphere respectively. For each of these near-field methods, there is a multitude of practical implementations of mechanical and electrical systems, depending on a particular need, suitability, or importance of one or the other factor. All scanning methods require a radio-frequency (RF) transmit and receive system with some type of computerized scanning, data acquisition, and analysis ability. A probe is selected depending on the geometry of the scan surface as well as to minimize its influence on the calculated far-field characteristics of the AUT. There are electrical requirements that need to be characterized and optimized when possible. Clause 4 discusses the various scanning subsystem configurations and their implementation and requirements. Clause 5 presents a brief summary of the planar near-field theory, followed by a discussion of the practical aspects of implementation. The planar near-field scanning method was the first geometry for which probecorrected theory was developed. This method is ideally suited for measuring moderately to highly directive antennas. The probe is scanned over a planar surface in front of the test antenna. In many instances, the near-to-far-field transform is accomplished with an FFT. Probe correction is performed direction by direction.

6




Clause 6 deals with the near-field-to-far-field transformation techniques using the cylindrical scanning. At the cost of a moderate increase in the analytical and computational complication with respect to the planar scanning, they allow reconstruction of the antenna complete radiation pattern except for the zones surrounding the + and – cylindrical axis. This method is ideally suited for fan-beam type antennas. In a cylindrical scanning facility, the AUT is mounted on a rotating table, whereas the probe moves along a line parallel to the rotation axis of the table. In such a way, the probe can measure the near-field data on a cylindrical grid for two different orientations of the probe. By taking into account the probe effects, it is possible to compute the far-field patter n. Clause 7 covers spherical scanning. A basic explanation of the theory is included. Descriptions of the geometry and implementation are provided and the benefits of the use of a probe with special symmetry properties (referred to as a μ = ±1 probe) are explained. Clause 8 discusses probe calibration and selection. To accurately determine the far field of a test antenna from near-field data, it is necessary to correct for the effects of the probe. This requires knowledge of the probe’s on-axis gain and polarization, as well as the probe’s co-polarization and cross-polarization p atterns. This section describes how to measure and determine these probe properties and provides guidance on selecting an appropriate probe. Clause 9 treats the analysis of measurement uncertainty. The sources of uncertainty will be delineated and methods of estimating the magnitudes of these uncertainties are discussed. Finally, Clause 10 deals with special topics. This section considers topics outside the routine near-field/farfield measurements of determining gain, polarization, and pattern. Some of the special topics include (but are not limited to) the description of how to determine effective isotropic radiated power (EIRP), saturated flux density, and array evaluation.

4. Measurements systems The geometries for the spherical, cylindrical, and planar near-field scanning methods necessitate data point acquisition on a sphere, cylinder, and plane, respectively. For each of these near-field methods, there is not one unique physical, mechanical, or electrical solution. All scanning methods require a radio-frequency (RF) transmit and receive system with some type of automated scanning, a data collection and control system (DCCS), and computerized analysis ability. A probe with known characteristics is selected to measure the AUT and minimize the distortion of its far-field characteristics. There are electrical and mechanical parameters that should be optimized. This section discusses the various scanning subsystem configurations and their implementation and requirements.

4.1 Mechanical scanning subsystems For any near-field measurement method, amplitude and phase data are acquired in an organized fashion on some specific surface. Given the surface geometry, data, and reference antenna (probe) properties, an efficient transform is preferably used to determine the far field of the AUT. The most common scanning techniques are planar near field (PNF), cylindrical near field (CNF), and spherical near field (SNF). Each of these typically requires a combination of translation and rotation to complete the scanning over the desired surface.

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4.1.1 Planar near-field (PNF) scanning PNF scanning requires a less-extensive anechoic surrounding and alignment technique, and a fairly simple mathematical analysis. This technique is best used for highly directive antennas such as a dish or phasedarray antennas where nearly all the received or transmitted energy passes through the planar scan area. Rectangular scanning is a common PNF technique where the data are gathered at specific x, y locations on a grid, illustrated in Figure 1. The probe is positioned along the y axis using a linear slide. The y axis slide is positioned along an x axis using a second slide. Details of rectangular PNF measurements are found in Newell, Ward, and McFarlane [B101]. Data sampling typically uses an increment of λ/2 or smaller. Other implementations of planar scanning are possible. Examples include plane-polar (Rahmat-Samii, GalindoIsrael, and Mittra [B102]), which uses a combination of translation and rotation to acquire data on a plane and plane bi-polar scanning (Williams, Rahmat-Samii, and Yaccarino [B118]), which uses two rotations to acquire data on a plane.

Figure 1 —Illustration of rectangular PNF scanning

8




4.1.2 Cylindrical near-field (CNF) scanning For CNF scanning the data are gathered on a cylindrical surface (Yaghjian [B128]). This technique is useful for fan-beam antennas where the energy is directional in one axis and broad in the orthogonal axis, such as cell phone base station antennas. Figure 2 illustrates the z and φ coordinate system typically used for CNF. Typically, the probe is positioned in the z coordinate using a linear slide. The AUT is typically mounted on a rotator that positions the AUT in the φ coordinate.

Figure 2 —Illustration of CNF scanning configuration

9




4.1.3 Spherical near-field (SNF) scanning In SNF scanning the data are gathered on a spherical surface that surrounds the AUT. This technique can be used to measure any antenna and is especially useful for isotropic or nearly isotropic antennas for which the planar and cylindrical methods are not suited. There are several scanning configurations that can be employed for SNF scanning (Hansen [B47], Wittmann and Stubenrauch [B123]). One configuration is to have the probe fixed, while the AUT is positioned to allow the probe to map out a sphere. The roll-overazimuth configuration is commonly used for this, where the data are gathered in the θ and φ coordinate system, as illustrated in Figure 3. The AUT is mounted on a rotator that positions the φ axis (roll). This rotator is mounted onto another rotator that positions the θ axis (azimuthal).

Figure 3 —Illustration of the roll-over-azimuth SNF scanning configuration

10




Another example of a spherical implementation is the combination consisting of an arch carrying a probe on a circular arc and an azimuth axis rotating the antenna. The plane of the circular arc might be vertical and the azimuth axis vertical and lying within the plane. An example is shown in Figure 4.

Figure 4 —Illustration of the azimuth/arch SNF scanning co nfiguration

4.2 Typical RF subsystem Figure 5 illustrates a typical RF system. The simplest RF subsystem consists of some type of source that supplies the AUT with RF power and a receiver that detects the signal received by the probe. To measure phase, a reference line is needed between the source and receiver. An attenuator used for RF leveling can be inserted between the source and AUT. It is also good practice to use isolators at the interface to t he AUT and probe to minimize any reflections due to the measurement system. For gain measurements, this is important to help ensure good matching to the source and receiver transmission lines and thus help avoid standing waves that introduce additional uncertainties. Some receivers have remote mixing capabilities to enhance system dynamic range. It is good practice to use attenuators of about 10 dB to protect the mixer. A vector network analyzer (VNA) is often used in near-field set-ups. In this case the VNA generates the source signal and also serves as the receiver. For frequencies above 20 GHz (in some instances up to 600 GHz) frequency extenders are frequently used. Cables are another component of the RF subsystem. The cable and connector type need to support the frequency range of the measurements. It is important that any moving cables remain amplitude and phase stable over the measurement surface. Rotary joints are necessary for any configurations where the AUT rotates and are sometimes used to minimize scanner cable motion. The user should evaluate the effects of phase and amplitude of the rotary joint with rot ation.

11




Figure 5 —Illustration of a typical RF system

4.3 Typical data collection subsystem The amplitude and phase data are collected at known locations on the measurement surface. This is achieved through knowledge of the location of the probe coordinate origin on the measurement surface and triggering the receiver to record data at the appropriate position. An illustration of a typical data acquisition system is shown in Figure 6.

12




Figure 6 —Illustration of typical data acquisition system The data collection and control system (DCCS) monitors and controls all the instruments and positioning systems in the set-up. Since this is a very complex system, an automated and fully computer-controlled DCCS is needed. It is necessary that the data-processing system be able to send and receive very large amounts of measured and processed data. For linear positioning equipment, a distance-measuring laser interferometer system can be used to measure location. If a stepper/servo motor is used to drive the linear position, the encoder feedback of the motor can be used to determine location. To save cost, a stepper motor can be used and position determined by counting the number of steps; however this method is not preferred where high accuracy is needed. For rotational positioning, a rotary encoder feedback from the drive motor usually determines the angular position. A laser tracker can also be used to monitor the probe aperture location. The laser tracks a target mirror affixed to the probe mount. The probe aperture location is referenced to the mirror location. This method provides real time location of the probe over a limited scanning area. It also needs integration of the laser tracker’s controller.

13




4.4 Data processing In the early years of near-field measurements, computer processing capabilities were limited. Much of the work was performed at government facilities, universities, or very large companies that had access to large main frame computers. Creative short cuts were used to minimize the amount of data needed. The data processing was performed offline. Today’s personal computers have more than enough power to process the large practical data sets and the computational intensive analysis routines.

4.5 Measurement accuracy It is important to choose the appropriate near-field method for the AUT measurement and to understand the correct technique to provide an accurate measurement. The probe should be carefully chosen to match the AUT and measurement method. The mechanical subsystem needs to meet the positioning and alignment tolerances needed for the measurement. The RF subsystem needs to be mechanically, temporally, and temperature stable to maintain the integrity of the amplitude and phase. Stability requirements depend on the desired accuracy. Better accuracy at lower side lobes generally implies greater phase and amplitude stability and better signal-to-noise ratio are needed.

4.5.1 Measurement environment Temperature, humidity, and vibration are environmental conditions that can effect measurements. The extent depends on sensitivity of components to these environmental conditions and the frequency of measurement. Temperature changes can cause thermal expansion in the mechanical subsystem components affecting the positioning accuracies. It can also cause amplitude and phase changes in RF subsystem components such as cables, couplers, and mixers and cause tracking laser beam scintillation. Temperature and humidity can interfere with stability of the receivers and sources in the RF subsystem. Humidity affects the performance and durability of the absorber. Poor humidity conditions affect the reflectivity of the absorber. Conditions that are too dry lead to a brittle absorber that breaks easily. Conditions that are too humid lead to water absorption, which deforms the absorber due to the added weight. Vibrations can have an effect on mechanical subsystem positioning accuracies and the stability of RF subsystem components. As the measurement frequency increases the sensitivity of the components to all of the environmental conditions increases primarily through phase stability.

4.5.2 Choice and use of near-field method The PNF method performs best for antennas with highly directional patterns. It can be used for gain measurements of directive antennas, but its limited area of pattern coverage can engender difficulty for directivity measurements. The CNF method is most useful for measuring antennas with fan-beam patterns like cell phone base station antennas, where the radiation pattern is largely restricted to a small range in elevations. In the SNF method a truncation of the measurement surface is not necessary and it can therefore be used for accurate determination of far-out side lobes for any antenna type. Because of the ability to cover a wide range of angles, it is especially useful in measuring nearly isotropic antennas, such as mobile phone handset antennas, and in measuring directivity.

14




4.5.3 Choice of probe antenna The choice of probe depends on the near-field technique. The best accuracy is achieved by using one probe that is polarization matched to the co-polarized component and a second probe that is matched to the cross polarized component. The second probe could be the first probe rotated 90° (for a linearly polarized probe) or the second port of a dual-polarized probe. A physically small probe will cause less disruption to the far field of the AUT. Details on the selection of a probe can be found in Clause 8.

4.5.4 Mechanical subsystem accuracies The needed probe-position accuracy for the mechanical subsystem is dependent on the measurement frequency and types of measurement parameters. For accurate side lobe measurements, a probe-position accuracy of a fraction of a wavelength is required, but it is not as crucial for gain measurements. The needed probe-position accuracy will depend on the accuracies needed for the far-field pattern. Periodic position errors will concentrate errors in specific directions, while random position errors will spread the errors out over many directions. A translational error within the scan plane for PNF measurements, shown as Δ x and Δ y in Figure 7, could result in a null or side lobe position uncertainty in the far-field results. Uncertainties in Δ z primarily affect uncertainties in the measured near-field phase. Also shown in Figure 7, Δazimuth and Δelevation uncertainties affect uncertainties in the pointing direction of the main beam. A constant translation offset in x and/or y of the probe will introduce a linear gradient in the far-field phase but will not result i n an amplitude change in the far field. For practical probes that have a very broad beam compared to the beam width of the AUT, the shift in the main beam pointing will be small due to azimuth or elevation uncertainties in the probe alignment. The azimuth and elevation misalignment will cause a small error in the magnitude of the probe correction in the side lobe region where the slope of the probe pattern is larger. The Δroll uncertainty affects uncertainty in the polarization measurements . These position errors cause similar effects in all near-field scanning geometries. See also Clause 9 for additional details.

Figure 7 —Probe-position uncertainties for PNF measurements

15




4.5.5 RF subsystem accuracies An unstable RF system has the potential of introducing uncertainties directly into the measured amplitude and phase. Some of the sources of uncertainty are illustrated in Figure 8. Interference signals from outside sources can be minimized in shielded chambers. Leakage can come from leaky sources, receivers, loose connections, coaxial and waveguide, and from damaged system components. Relocating equipment can reduce the effects of leakage and noise. It is important to keep RF and motor cabling separated to minimize motor noise on the RF cable. Noise is also caused by dynamic range limitations of the receiver at low amplitudes and thermal effects on RF cables. Multiple reflections between the AUT and probe can be reduced depending on separation distance. Proper absorber placement can reduce multipath and leakage.

Figure 8 —RF measurements sources of uncertainty

16




4.6 Correction schemes Many correction schemes have been developed to mitigate the effects of the non-ideal measurement systems. The more common ones are thermal drift correction, impedance mismatch correction, probe position correction, and cable variation correction.

4.6.1 Thermal drift correction As discussed in 4.5.1, temperature can cause changes in the amplitude and phase measurements. There are two methods of correcting for thermal drift. When the scanning and stepping axes are reversed, as shown in Figure 9, this is commonly referred to as a tie scan and is used to correct for thermal and power supply drift.

Figure 9 —Illustration of tie scans During the time difference between the first and last regular scans, the amplitude and phase reference value can experience a drift. The tie scan gathers the data at the same row position for each regular scan in a short amount of time greatly reducing the risk for drift. Using this information, a correction can be applied to the data set. Another technique of correcting for thermal drift is known as return-to-point (Hess et al. [B52], Melson, Hess, and Jones [B87]). In this method, a point that has a high signal level is selected from the scan; this point is designated as the selected point . The technique consists of measuring and recording this selected

17




point repeatedly during the scanning process and thereby monitoring the thermal and power supply drift that occurs. For completeness, the time of measurement may also be recorded. To accomplish this, the scanning process is interrupted periodically to return the probe to this point of the scan. After the scan is finished the phase/amplitude data from each scan line is corrected by the amount of thermal drift that was seen in the selected point. The advantage of this technique over the tie scan technique is that it overcomes the difficulty of the position offsets across the sampling interval for highly multiplexed data sets and a continuously moving probe.

4.6.2 Impedance mismatch correction To obtain the correct gain, a mismatch correction needs to be included. The impedance mismatch correction applies to the gain measurements. It accounts for the small portion of the signal that is reflected at the measurement ports. These reflection terms are represented as Γa for the AUT, Γ g for the generator, Γ p for the probe, and Γ l for the load as shown in Figure 10. When an insertion loss method with the probe as the gain standard is used then the uncorrected (for mismatch) gain needs to be multiplied by the correction factor M c (Kummer and Gillespie [B75])

2

M c =

1 − Γ p Γ  1 − Γ a Γ g

2

(1 − Γ ) (1 − Γ ) 1 − Γ Γ 2

p

2

2

a

g

.

(18)



Figure 10 —Impedance mismatch

18




When the gain transfer standard method is used, the uncorrected gain needs to be multiplied by

M c′ =

1 − Γ g Γ a

2

1 − Γ g Γ s

2

(1 − Γ ) , (1 − Γ ) 2

s

(19)

2

a

where Γ s is the reflection coefficient of the gain standard.

4.6.3 Probe-position correction If actual measurement points are recorded (rather than assumed ideal), then it is possible to correct for nonideal probe positioning. For example, the simple k -correction method (Francis [B34]) will approximately correct the pattern. More rigorous approaches are described by Corey [B23] and Wittmann, Alpert, and Francis [B121], [B122]. The latter method can correct position errors to a level characteristic of the position-measuring device. Probe-position correction is discussed in 10.6.

4.6.4 Cable variation correction All measurement set-ups for near-field scanning necessarily have at least one RF path that undergoes motion. The purpose of the moving path is to transfer a continuous wave analog signal, characterized by its phase and amplitude, from the port of an antenna undergoing relative rotary or translational motion, to a stationary point in the laboratory. This signal is commonly the received signal at the port of the moving probe; however in some set-ups it may be a reference signal used for phase measurement. The per turbation of this analog signal by the flexure of the moving path can often be a significant contributor to RF measurement uncertainty. Usually one addresses this problem by choice of a sufficiently good cable, designed to minimize the variation in phase due to cable flexure. Where rotary positioners are utilized, RF rotary joints are alternately employed that are designed to minimize the phase (and amplitude) variation as a function of rotation. Various approaches to correction for the effects of cable variation have been suggested and implemented. Choice of a particular scheme depends upon whether the system employs remote mixers and whether it is to operate at microwave or at millimeter wave frequencies. A method utilizing analog signals has been suggested by Newell [B94]. However, most approaches in current use entail digitally recording auxiliary measurements of the cable path, simultaneously with the near-field scanning measurement, then applying a correction to the acquired near-field data by post processing. For operation in the microwave regime, a three-cable measurement approach has been devised by Hess [B49]. The changes in the primary cable—which carries the signal from the moving probe to the stationary receiver—are monitored by the receiving subsystem, assisted by a thermally stabilized switching network (Caldwell [B20], Hess [B50]). The scheme may be understood by analogy to the three-antenna technique. The primary cable is measured in transmission as a member of a pair; its transmission characteristic is determined from a set of three pair-wise measurements among a set of three similarly positioned cables, as illustrated in the Figure 11. Along with the received signal from the probe, these auxiliary data are acquired at each grid point. Each of the three cables can vary in its own way. The only assumption regarding stability is that no changes occur during the fraction of a second when the three pairs are measured and the probe’s signal is sampled. In a post-processing step, the received signal at each grid point is modified by the observed change in the transmission characteristic of the primary cable.

19




Figure 11 —Schematic of hardware layout for implementing the three-cable technique to correct for cable variations

Janse van Rensburg [B58] has reported on a method in which the cable variation, as a function of position, is recorded once prior to making near-field antenna measurements. The cable characteristic is thus correlated to the position of the scanner. Then for each ensuing near-field scan the acquired data are corrected in a post-processing step, with the assumption of an unchanging cable characteristic. There is furthermore a class of cable correction methods devised and implemented for millimeter-wave frequencies and higher devised by Tuovinen, Lehto, and Raisanen [B114]. They have demonstrated a scheme that entails measurement of the phase of a signal reflected by a short-circuit element at the moving end of the cable that is switched in a multiplex arrangement. Saily, Eskelinen, and Raisanen [B108] have employed a pilot signal approach that measures the cable in two-way reflection at a neighboring frequency and infers a post-processing correction factor from a calibration. These methods are limited by the attenuation of the cable. When modern cables do not give the needed phase stability, then correction methods should be employed.

5. Planar near-field scanning measurements

5.1 Introduction In this section, a brief summary of the planar near-field theory is presented, followed by a discussion of aspects of practical implementation. Planar near-field scanning was the first geometry for which probecorrected theory was developed. This method is ideally suited for measuring moderately to highly directive (greater than about 15 dBi) antennas. The probe is scanned over a planar surface in front of the test antenna. The near-to-far-field transform is accomplished with an FFT. Probe correction is performed direction by direction.

20




5.1.1 Plane rectangular method The usual measurement grid is rectangular with regular spacing in x and y (see Figure 1). Scanning is usually accomplished by continuously moving the probe in x (or y) and stepping in y (or x). An example planar near-field range is shown in Figure 12.

Figure 12 —Example of a planar near-field range (photo courtesy of IMST [Institute of Mobile and Satellite Communication Technology])

5.1.2 Plane-polar and bi-polar methods There are other methods that have been used for scanning over a plane—the plane-polar and the bi-polar methods. The advantage of these methods is that the probe transport mechanism is simpler. They are discussed in more detail in Tuovinen, Lehto, and Raisanen [B14], [B15], Rahmat-Samii, Galindo-Israel, and Mittra, [B102], Rahmat-Samii, Williams, and Yaccarino [B103], and Williams, Rahmat-Samii, and Yaccarino [B118]. Plane-polar method scanning is implemented by scanning the probe in y and rotating the test antenna about its z axis. The AUT is mounted on a rotary positioner, such that the AUT can be rotated about its axis, which is perpendicular to the probe translation axis. In the plane bi-polar technique, the AUT also is mounted on a rotary positioner, such that the AUT can be rotated about its axis. The second mechanical degree of freedom is provided by a mechanical arm, which rotates about a second axis. A measurement probe is attached to the end of this arm, to sample the near field at locations which are displaced from and perpendicular to the AUT-rotation axis as the arm-rotation angle is increased.

21




5.2 Summary of theory 5.2.1 Plane-wave expansions for planar systems The electric field of the test antenna can be expanded in plane waves (Kerns [B74]):

E(r ) =

a0 2π

∞ ∞

∫∫

t (kˆ )exp ( ik ⋅ r )

−∞ −∞

dk xdk y , γ k

(20)

( )

ˆ is the transmitting function and where t k

γ = k z

=

k 2 − k x2

− k y2

ˆ ) = 0. k ⋅ t (k γ is positive real or positive imaginary, k x and k y are the x and y components of the propagation vector k . When γ is imaginary, the plane-wave contribution is termed evanescent . All sources are required to be in the region z < 0; then, Equation (20) is valid for z > 0. For r large, the asymptotic formula [see Equation (1)] applies

E(r ) ~ a0t ( rˆ )

exp ( ikr )

.

(21)

ikr

5.2.2 Transmitting and receiving functions The transmitting and receiving functions are described in Clause 3, Equation (7) and Equation (12).

5.2.3 Kerns transmission formula The Kern’s transmission formula (Kerns [B74]) describes the relation between the transmitting function of the AUT, the receiving function of the probe, and the measured output signal w ' at the probe

w′ ( r ) a0

∞ ∞

=

∫−∞ −∞∫ ( ) ⋅ t ( kˆ ) exp ( ik ⋅ r ) s kˆ

dkxdk y

,

(22)

γ k

( )

ˆ is the receiving function and where s k

w ' ( r ) = (1 − Γr Γ ) b0′ ; that is, w ' is the amplitude of the emergent waveguide mode, were the load non-reflecting.

22




Equation (22) is a superposition of the response of the probe to each plane-wave component that can be inverted (by Fourier transformation) to give

( ) ⋅ t ( kˆ ) =

s kˆ

γ k 4π 2

∞ ∞

w '(r ) exp ( − ik ⋅ r ) dx dy . −∞ −∞ a0

∫∫

(23)

5.2.4 Probe correction The solution for t(k ) in Equation (23) requires measurements using two probes with approximately orthogonal polarizations. Two equations are obtained of the form

( ) ( ) ( ) ( ) ( ) ( ) T ′′ ( kˆ ) = s (kˆ ) ⋅ t ( kˆ ) = s ( kˆ ) t ( kˆ ) + s (kˆ ) t (kˆ ) T ′ kˆ = s1 (kˆ ) ⋅ t kˆ = s1i kˆ ti kˆ + s1 j kˆ t j kˆ 2

2i

i

2j

(24)

j

where T ' and T " are coupling products. If the probe properties s1 and s2 are known, then Equation (24) can be solved for both polarizations of the test antenna t i and t j. Note that Equation (24) implies that for planar near-field measurements the probe correction is done direction by direction. That is, the test antenna far field depends only on the coupling product in that direction and the probe’s far-field properties in that direction.

5.2.5 Discretization and sampling criteria In practice, the probe response w ' will be measured at discrete points. The integral in Equation (23), once it is restricted to a finite portion of k-space, can be discretized and evaluated provided the sampling criterion has been met. This requires a minimum of two data points for the fastest varying period. Thus,

∆ x, ∆y ≤ λ / 2,

(25)

where Δx Δy λ

is the sample spacings in x is the sample spacings in y is the wavelength.

When the separation between the probe and AUT is less than about 5 λ, sample spacings of less than λ/2 may be necessary due to evanescent components.

5.2.6 Data processing In practice, Equation (23) is discretized consistent with the sampling theorem and evaluated using a twodimensional FFT. The results from the FFTs (for both polarizations) are then used in Equation (24) to solve for the properties of the test antenna.

23




5.3 Implementation 5.3.1 Measurement set-up A planar near-field measurement requires a signal source, receive system, scanner, and known reference antenna (the probe). See Clause 4 for more details, especially Figure 1 and Figure 5.

5.3.1.1 Alignment of the scanner A planar near-field scanner consists of a pair of translation stages, stacked orthogonally, one above the other, to provide an uppermost carriage that supports a probe to be scanned over a planar surface. This “scan plane” is nominally parallel to the aperture of the AUT. The scanner needs to be aligned so that the x and y axes are perpendicular. Furthermore, the plane over which the probe moves needs to be flat to within a small fraction of a wavelength (typically 0.01 λ to 0.02 λ) depending on the desired accuracy (see Newell [B93] and Clause 9). Periodic position errors produce larger errors in the far-field pattern; these errors are concentrated in specific directions. Thus, it is desirable to minimize periodic position errors by aligning the scanner and reducing periodic deformations in the scanner. An efficient way of aligning a planar scanner is to use a laser tracker. Instead of a laser tracker, another alignment procedure can be used involving mirrors, a theodolite, and an electronic level, but this takes considerably more time. Often, a mirror is positioned parallel to the scanner and used as a reference when using a theodolite in the alignment of the probe and AUT. Figure 13 illustrates the use of a laser tracker. The laser tracker is used to determine the actual locations of the probe as it is scanned. This information can be used to determine the best fit plane and the deviations from that plane. The scan plane flatness can also be measured via optical methods. A theodolite and probe-mounted target is one such example. Another method that is extremely useful for very large scanners is the use of a spinning plane laser in combination with a lateral photodetector mounted to the probe. As the probe is moved to various scanner locations, the spinning plane laser will illuminate various parts of the photodetector that measures the out-of-plane movement. This arrangement can also be utilized for quick verification of scan plane flatness. Using similar methods, an optical skeleton can be assembled that will also measure the straightness of the x and y rails as the probe travels. Of course these monitoring methods will add cost and complexity to the system.

24




Figure 13 —Laser tracker set-up for recording position 5.3.1.2 Alignment of test antenna and probe The x and y axes of the range coordinate system can be defined as being parallel to the orthogonal lines of travel of the origin of the probe coordinate system as it executes single axis linear travel. The probe z axis needs to be aligned perpendicular to the scan plane. The probe x and y axes needs to be aligned parallel to the scanner x and y axes. The test antenna needs to be aligned so that its coordinate system is parallel to the scan plane coordinate system. The alignment of the probe may be accomplished by aligning a theodolite to the reference mirror mentioned above and using auto-collimation of the theodolite. Mirrors used for alignment should be of high quality with good optical surfaces and parallel front and back surfaces. The quality of available optical mirrors generally exceeds the RF requirements. Alternatively, this alignment may be performed with a tracking laser by placing its retro-reflector on the probe and moving the probe about the scan axis. The test antenna is usually aligned mechanically relative to the scan plane. However, the test antenna is sometimes aligned electrically to minimize the phase gradient in the scan plane (in this case beam pointing and polarization accuracy will be forfeited). In some applications, the AUT alignment may be measured relative to the scan plane and recorded. In order to reduce the amount of time to align the AUT to the scanner, the AUT would be measured as is, without performing an alignment. The angular bias can be removed during post-processing of the pointing data.

5.3.1.3 Positioning tolerances The standard FFT, which provides an efficient near-field-to-far-field transform for the planar geometry, requires measurement points to be located on the plane z = d in a regular grid, equispaced in x and equispaced in y. Errors can occur in the z coordinate (perpendicular to the scan plane) due to imperfections in the scanner (see Figure 14). Errors can occur in the step coordinate due to inertia in the scanner and errors in the y rails,

25




which limit the step resolution (see Figure 15). Lastly, errors can occur in the scan coordinate due to errors in the x rails, the position encoders, the trigger timing accuracy, and the time to acquire a measurement. Newell [B93] and Yaghjian [B129] provide estimates of the errors in the far-field pattern due to position errors. Alternatively, a laser tracker can be used to determine the actual positions where the data are acquired and a position-correction method can be used such as that developed by Wittmann, Alpert, and Francis [B121] to perform an efficient near-field-to-far-field transform. As a rule of thumb, determining position to an accuracy of 0.01 λ to 0.02 λ is suggested. Actual position accuracies depend on desired accuracies for the far field and the nature of the position error. Position correction software offers the potential to evaluate or greatly reduce position error uncertainties so that they are unimportant.

Figure 14 —Illustration of z errors due to imperfections in the y -rails (Reprinted with permission from Balanis, C. A., Modern Antenna Handbook . New York, NY: John Wiley & Sons, 2008. © 2008 John Wiley & Sons.)

26




Figure 15 —Illustration of step-position error (Reprinted with permission from Balanis, C. A., Modern Antenna Handbook . New York, NY: John Wiley & Sons, 2008. © 2008 John Wiley & Sons.)

5.3.1.4 Choosing a separation distance To help ensure that evanescent (non-propagating) modes do not contribute significantly to the measured near-field data, a minimum separation of 3 λ to 5 λ is recommended. A second consideration is that, as the separation distance increases, the valid region of the pattern decreases for a given scan area [see Equation (27)]. Thus, a separation distance should be chosen that allows adequate pattern coverage. A third consideration is that of probe-AUT multiple reflections. Some of the signal incident on the receive antenna from the transmit antenna is scattered back to the transmit antenna and re-reflected to the receive antenna. These reflections are not included in the practical implementation of the theory. Multiple reflection errors generally increase with decreasing separation distance. It is preferable to choose a separation distance where the amplitude of the variation is smaller and where the field gradient is small. The multiple reflection effect can be estimated by taking measurements on two planes separated by λ/4, calculating the far field for each measurement, and computing the difference, direction by direction. In choosing a separation distance, the need of smaller separation distances to increase pattern coverage needs to be counterbalanced with the need to increase separation distance to decrease the effects of multiple reflections and evanescent modes.

27




5.3.1.5 Sampling Sampling considerations require that two data points be acquired for the shortest period in the measured data. Provided the measurements are acquired in a region where the evanescent (non-propagating modes) are unimportant, increments of less than λ/2 in both x and y will generally satisfy the sampling criteria. If the AUT pattern is only desired over a small angular region ± θ ν (where θ ν is less than 90°) then the sampling requirement can usually be relaxed{Francis [B35], see Equation (7)}.

∆ x, ∆ y

λ

(26)

1 sin θ v

However, there may also be error mechanisms present that have periods that are less than a wavelength. In these cases, a sample spacing of less than λ/2 is needed to help prevent such errors from being aliased into the pattern (e.g., Francis et al. [B36]). If measurements are made at separation distances of less than 3 λ to 5 λ, then smaller sample sizes will be required (Joy and Paris [B67]).

5.3.1.6 Scan area truncation The theory assumes an infinite scan plane and this is obviously not practical. Acquiring data over a finite area has two effects. First, the pattern beyond about θ ± is invalid (see Newell [B93]), where

 L − a   ± 2 θ ± = arctan  , d    

(27)

where

L± a d

is the length of that portion of the scan above (below) the z axis is the test antenna diameter is the separation distance between the AUT aperture and the scan plane (see Figure 16).

θ ± may vary with the principal plane and in between the principal planes. Second, there are errors in the valid region due to ringing caused by the truncation at the edge of the scan plane. Yaghjian [B129] showed that this truncation error can be estimated from knowledge of the measured data on the perimeter of the scan area. To practically determine whether the scan area is large enough, one sets the data in the outer perimeter of the scan area to zero and observes how much the computed far-field changes. (See 9.4.9 for details.) As a rule of thumb, the scan area should be large enough so that amplitude measurements, at the edges, are at least 30 dB below (and preferably 40 dB or more below) the near-field peak.

28




Figure 16 —Schematic indicating the geometry for determining the angle of validity beyond which there is no valid far-field data

5.3.1.7 Other considerations Leakage and crosstalk, noise and dynamic range, nonlinearity, phase errors due to cable flexing, and room scattering are potential sources of measurement error and should be minimized. Their estimation and mitigation are discussed in Clause 9.

5.3.1.8 Absorber placement The use of good quality microwave absorber helps to reduce the effects of stray signals and leakage. The planar technique is best used for moderately to highly directive antennas. Since the test antenna is fixed in the range, it is usually sufficient to place absorber in front of the test antenna (such that the main beam radiation is maximally absorbed) and the mounting structure in the immediate vicinity of the test antenna. The mounting structure behind the probe is especially critical. Absorber placed to shield the RF source can greatly reduce leakage from the source. More absorber coverage is needed for nondirective test antennas. Typically, pyramidal absorber is used. The optimal size of the pyramids depends on the operational frequency range.

5.3.2 Probe correction To correct for the effects of the measurement probes, s1 and s2 in Equation (24), the relative phase between them needs to be known. Methods for determining these are described in Clause 8 and in Repjar, Newell, and Francis [B104].

29




5.3.2.1 Choice of probe The choice of probe(s) depends on several factors. Two of the more important factors are a) b)

whether gain is to be measured which portion of the AUT far-field pattern is desired.

In either case, the effects of multiple reflections between the probe and AUT should be minimized. Ideally, this means decreasing the radar cross section (RCS) of the probe. However, decreasing the RCS of the probe usually results in a reduction of the probe’s effective area and hence its gain. Experience shows that the larger the difference in gain between the probe and test antenna, the less will be the effect of multiple reflections between the probe and test antenna. However, too large a difference in gain can result in a loss of dynamic range and will result in a less-accurate measure of the test antenna gain and pattern. Often a probe with a gain of 20 to 30 dB less than the test antenna is a good compromise. In any direction in which we want to know the test antenna’s far-field pattern accurately, the probe should not have a null since this implies dividing by zero (or at least a very small number) when solving Equation (24) for the test antenna transmit function t k ˆ . The return loss of the probe should be at least 10 dB

( )

(preferably 20 dB or more) in order to minimize impedance mismatch and reduce multiple reflections. The probe should be physically stable and easy to mechanically align.

5.3.2.1.1 Single-port probes Another factor to consider is whether to use a dual-port or single-port probe. If the probe is linearly polarized, then the ort hogonal polarization (s2) can be obtained by rotating the first probe (s1) by 90°. It has the advantage that the properties of only one probe needs to be measured as the properties of the “second probe” can be obtained by rotating the probe pattern in software. It has the disadvantage of requiring a second alignment and second near-field scan since multiplexing the two polarizations is not possible. A single-port circularly polarized (CP) probe is not recommended for accurately measuring the cross polarization of a CP test antenna. This probe does not produce an orthogonal polarization when rotated by 90° so it cannot be used to obtain the cross polarization of a CP test antenna. A single-port linearly polarized probe can be used to obtain the two linear polarizations of the CP test antenna. These needs to then be combined to obtain the two CP polarizations by

t R = t L =

t x − it y 2 t x + it y

(28)

2

where the subscripts R and L refer to the right and left polarization, and the subscripts x and y refer to the x and y (linear) polarization. For a test antenna that has good circular polarization, the y component will lead or lag the x component by 90° in phase. From Equation (28), this results in the main circular polarization being approximately the sum of the magnitudes of the x and y components. The cross-component is approximately the small difference in the large magnitudes of the x and y components. Computationally, this can have a large relative uncertainty. Thus, the use of a dual-port CP probe is recommended for measuring a CP AUT.

30




5.3.2.1.2 Dual-port probes The use of a dual-port probe, with two nominally orthogonal polarizations, has the advantage that the scan corresponding to the second polarization can be obtained without an additional probe alignment. By multiplexing between the two ports to obtain both polarizations with one physical scan, the time otherwise needed for a second scan can be saved. The disadvantage is that both ports need to have their main and cross-components measured and the relative amplitude and phase between the two port responses need to be determined at each frequency of interest. The use of a dual-port CP probe is recommended for achieving high accuracy in the cross polarization of a CP test antenna.

5.3.3 Normalization The normalization can be divided into two parts: a) b)

An overall normalization relative to some reference such as a throughput connection or a reference horn A relative normalization between the two nominally orthogonal polarizations.

5.3.3.1 Overall normalization (insertion loss, mismatch) There are several methods for determining the overall normalization: a)

Insertion loss measurement

b)

Substitution method

c)

Absolute power measurement.

The insertion-loss method is a measurement of the power and phase with the probe antenna and test antenna inserted in the circuit relative to the amplitude and power with the generator and load connected directly together without the antennas) at a near-field reference point, as illustrated in Figure 17. The insertion-loss measurement needs multiple connections and disconnections, so a connector of high quality should be used. For details see Newell, Ward, and McFarlane [B101]. For the substitution method, a known reference antenna is scanned to calibrate the measurement system. In the absolute power method, the power is measured using a power meter.

31




Figure 17 —Schematic of insertion-loss measurement 5.3.3.2 Relative normalization of components In order to solve Equation (24) correctly, the relative normalization of T " with respect to T ' needs to be known. This can be accomplished by measuring the relative ratio (including phase and amplitude) of the two polarizations at some point in the near field. T " is then normalized relative to T ' using this information. This ratio can also be measured indirectly by using the throughput connection (generator-toload connection in Figure 17) as the amplitude and phase reference in measuring T ' and T " at a reference point in the near field.

5.3.4 Gain determination Gain may be determined in several ways: a)

By determining the directivity and ohmic loss in the antenna

b)

By performing a near-field scan and using the probe as the gain standard

c)

By performing two near-field scans (one of the AUT and one of a transfer standard).

If the gain is determined from the directivity (see Chapter 5 in Hansen [B47]), then the directivity is just determined from the test antenna pattern t ( rˆ ) using

32




Da ( rˆ ) =

2

4π t ( rˆ ) 2π π

∫∫

.

(29)

2

t ( rˆ ) sin θ dθ d ϕ

0 0

The gain is then determined from the directivity using

Ga ( rˆ ) = Da ( rˆ )

P T , P 0

(30)

where Ga is the gain, P 0 is the power accepted by the test antenna, and P T is the total radiated power. The difference between the two powers is the ohmic loss. If the gain is determined from the directivity, t ( rˆ ) appears in both the numerator and denominator of Equation (29) so the absolute normalization is unimportant. For the planar scanning method, it is not possible to determine the pattern over the full sphere, so we can only approximately determine the integral in the denominator of Equation (29). This can cause large errors in the determination of the AUT gain, especially for test antennas with significant amounts of radiation not intercepted by the scan plane. If the AUT gain Ga is determined using the probe as the gain standard, then the gain in the direction K 0 is Equation (17b) in Newell, Ward, and McFarlane [B101]:

 4π  Ga ( K 0 ) =  2   λ 

1 − Γ  Γ p

2

1 − Γ g Γ 

2

2

1 − Γ g Γa

δ xδ y

2

i

i

i

(1 − Γ ) (1 − Γ ) 2

2

a

∑ w ′ ( P )e

2

− iK 0 • Pi

p

2

an′ G p ( K 0 )

,

(31)

where Г K 0 Pi

defined as in Figure 10 is the transverse component of the propagation vector is the vector location of the ith point within the scan plane

wi′

is the probe response at the ith point

an′

is the insertion loss measured at the near-field reference point.

Equation (31) assumes the probe and AUT are polarization matched. If Ga is determined using the transfer standard method, then the gain is given by Equation 24 in Newell, Ward, and McFarlane [B101]:

(1 − Γ ) (1 − Γ ) δ ′δ ′ ∑ w ′ ( P )e 2

Ga ( K 0 ) =

∑ w ′ ( P )e

2

− iK 0 • Pi

s

δ xδ y

ai

i

i

2

2

a

x

y

si

i

− iK 0 •Pi

wai′ ( P0 a )

2

w si′ ( P0s )

2

Gs ( K 0 ) ,

(32)

i

where the subscripts s refer to the transfer standard and P0 are the normalization points for each scan. The two points do not have to be the same, but the relative ratio between them needs to be measured accurately.

33




The gain of the transfer standard needs to be known, either from theory (for example a horn built using the NRL model) or from prior measurement. The principal disadvantage of this method is that the transfer standard is often a standard gain horn with a relatively broad pattern. This results in much of the horn’s radiation not being intercepted within the scan area, which is potentially a source of significant errors.

6. Cylindrical near-field scanning measurements

6.1 Introduction In this section a brief summary of the cylindrical near-field theory is presented, followed by a discussion of aspects of practical implementation. The probe-corrected cylindrical near-field theory was developed using reciprocity by Leach and Paris [B84] at the Georgia Institute of Technology. A few years later, Yaghjian [B128] developed the cylindrical transformation using a scattering-matrix approach. Other approaches and improvements have been made by others (Appel-Hansen [B4], Borgiotti [B9], Bucci and Gennarelli [B13], Bucci et al. [B16], D’Agostino et al. [B24], Gennarelli et al. [B39], Joy et al. [B65], and Yaghjian [B128]). This method is ideally suited for measuring fan-beam antennas that concentrate the radiation in one plane. In a typical cylindrical near-field scanning facility (see Figure 2), the AUT is mounted on a rotating table, and the probe moves along a line parallel to the rotation axis of the table. By properly matching these movements, the probe can acquire the near-field amplitude and phase data on the desired cylindrical grid. From these data, measured using two orthogonal orientations of the probe about its longitudinal axis (or two different probes with approximately orthogonal polarization), the probe effects can be taken into account in the computed far-field pattern (Leach and Paris [B84], Yaghjian [B128]).

6.2 Summary of the basic theory 6.2.1 Cylindrical-wave expansion Commonly, the measured near-field data are transformed into far-field patterns by using an expansion of the AUT field in terms of modes, i.e., a complete set of solutions of the vector wave equation in the region outside the antenna. In a cylindrical-wave expansion, the field is represented as a superposition of transverse electric (TE) and transverse magnetic (TM) modes, which are elementary solutions of the Helmholtz equation in the cylindrical coordinates ( ρ , φ, z). By assuming and suppressing a time dependence exp( j ω t ), in a linear, source-free, isotropic region, the electric and magnetic fields can be expressed (Balanis [B7], Stratton [B111]) as linear combinations of the vectors M and N related to the TE and TM cylindrical solutions, respectively. The desired solution needs to be valid in the region external to the smallest cylinder enclosing the AUT. Thus, only outgoing cylindrical waves have to be contemplated in order to satisfy the radiation conditions at infinity. These vectors are given by (Leach and Paris [B84]):

 jn

M nγ ( ρ , ϕ , z ) = 

 ρ

H n(2) ( Λρ ) ρˆ −

 ∂ H n(2) ( Λ ρ ) ) ϕˆ  exp ( jnϕ ) exp ( − j γ z ) ( ∂ρ 

nγ (2)  jγ ∂  (2)  − k ∂ ρ ( H n ( Λ ρ ) ) ρˆ + k ρ H n (Λ ρ )ϕ ˆ   exp ( jnϕ ) exp ( − jγ z ) , N nγ ( ρ , ϕ , z ) =   ∆ 2 (2 )   + H n ( Λ ρ ) z ˆ   k 

(33)

(34)

34




where

k n

= 2π/λ

γ

is an integer is a real number

Λ

= ( k − γ 2

2

)

1 2

H n(2 ) is the Hankel function of the second kind. Its large argument form is 2 j

lim H n(2) ( x ) =

x →∞

π x

j n exp ( − jx ) .

(35)

Therefore, the electric field E radiated by an antenna can be represented as a superposition of elementary outgoing cylindrical waves, namely, a linear combination of vectors M and N involving an integral over all γ, and a sum over all n. Accordingly,

E ( ρ ,ϕ , z ) =

∞

∞

∑ ∫ a (γ ) M n

nγ

n =−∞ −∞

( ρ ,ϕ , z ) + bn (γ ) Nnγ ( ρ ,ϕ , z )  d γ ,

where the complex weighting functions an ( γ ) and

(36)

bn (γ ) are the modal expansion coefficients.

In light of the above considerations, the expansion Equation (36) is valid in a source-free region outside the minimum cylinder. In general, its evaluation is quite onerous, but becomes very simple when only the knowledge of the AUT far field is desired. By replacing the Hankel function and its first derivative by their asymptotic expansions and evaluating the resulting integral by means of the steepest descent method, results in (Leach and Paris [B84]):

E ( R, Θ, Φ ) = − 2k

exp(− jkR) R

sin Θ

∞

∑ j ( a ( k cosΘ )Φˆ + jb ( k cosΘ )Θˆ ) exp( jnΦ ) , n

n

n

(37)

n =−∞

where ( R,Θ ,Φ) are the spherical coordinates usually adopted for describing the AUT far field. As can be seen from Equation (37), since |cos Θ| ≤ 1, the wave components in Equation (36) for which |γ | > k do not contribute to the antenna far field. These are called evanescent waves and do not influence the far field. The highest angular harmonic n in the far-field expansion is usually given by nmax = ka / 2 (Leach and Paris [B84]), where a is the diameter of the smallest cylinder enclosing the AUT.

6.2.2 Classical probe-compensated near-field-to-far-field transformation The probe sees the AUT center under different directions when moving on the scanning cylinder. In addition, at a fixed position, the probe sees each portion of the AUT from a different direction. As a consequence, the antenna far field cannot be accurately recovered from the measured near-field data by employing the uncompensated (for the probe) near-field-to-far-field transformation. The basic theory of probe-compensated near-field measurements over a cylinder was developed by Leach and Paris [B84] and is based on an application of the Lorentz reciprocity theorem. They demonstrated rigorously that the modal coefficients an and bn of the cylindrical wave expansion of the field radiated by the AUT are related to:

35




a) b)

The two-dimensional Fourier transform of the output voltage of the probe for two independent sets of measurements (the probe is often rotated 90° about its longitudinal axis in the second set) The coefficients of the cylindrical wave expansion of the field radiated by the probe and the rotated probe, when used as transmitting antennas.

Quite analogous results have been obtained (Rudge et al. [B107], Yaghjian [B128]) by using the scatteringmatrix formulation. In fact, as explicitly shown in Appel-Hansen [B4], this last formulation leads, except for a normalization constant, to the same expressions obtained when using the reciprocity theorem. The key relations (Leach and Paris [B84]) are:

∞ ∞   (2) ′ ′ − Λ − I γ d γ H d I γ dm ( −γ ) H n(2) ( ) ( ) ( ) ( ) ∑ ∑ +m ( Λd )  , n m n +m n  2 Λ ∆ n ( γ )  m =−∞ m =−∞ 

k 2

an ( γ ) =

(38)

∞ ∞  ′  (2) bn ( γ ) = 2 I n (γ ) ∑ cm ( −γ ) H n +m ( Λd ) − I n (γ ) ∑ cm′ ( −γ ) Hn(2)+m ( Λd ) ,  Λ ∆ n ( γ )  m =−∞ m =−∞ 

k 2

(39)

where

∞ π

I n ( γ ) =

∫ ∫ V (ϕ , z)exp ( − jnϕ ) exp( jγ z) dϕ dz;

∞ π

∫ ∫ V ′(ϕ, z) exp( − jnϕ) exp( jγ z) d ϕ dz ;

I n′ ( γ ) =

−∞ −π

−∞ − π

∆n (γ ) =

(40)

∞

∑c

m

( −γ ) H

∞

(2) n +m

m =−∞

−

( Λ d ) ∑ dm′ ( −γ ) H n(2)+m ( Λ d )

∞

∑ c′ ( −γ ) H m

m =−∞

m =−∞

(2) n+m

( Λd )

∞

∑d

m

( −γ ) H

(2) n +m

( Λd )

(41)

m =−∞

(

)

and where V and V ' are the complex output voltages of the probe and the rotated probe at the point d, φ , z . In the classical approach (Leach and Paris [B84]), the Fourier transform integrals I n and I n ' are efficiently evaluated via the FFT and the near-field data are again equally spaced according to the sampling theorem. The modal coefficients associated to the probe ( cm, d m) and rotated probe ( cm′ , d m′ ) can be evaluated from the measured amplitude and phase of the far-field components radiated by them. Once an and bn have been determined, the far-field components of the electric field can be evaluated via Equation (37).

6.2.3 Other approaches for the near-field-to-far-field transformation Alternative approaches have been developed for sampling and scanning in cylindrical near-field measurements. One approach exploits the spatial band limits of electromagnetic fields to reduce the number of samples as one moves from the central rings to the peripheral ones. Details can be found in the references Bucci and Franceschetti [B12], Bucci, Gennarelli, and Savarese [B15], Bucci, et al. [B16], Bucci, et al. [B18], D’Agostino [B24], Gennarelli et al. [B39]. Another approach allows helicoidal scanning (in z and φ simultaneously) (Bucci et al. [B17], D’Agostino et al. [B25], Gennarelli et al. [B40], Yaccarino, Williams, and Rahmat-Samii [B125]).

36




6.3 Implementation

6.3.1 Measurement set-up A cylindrical near-field measurement set-up is similar to that of the planar and spherical scanning set-ups in that it contains an RF system, mechanical positioning system, data collection and control system, and analysis system. The RF system is discussed in Clause 4 (see Figure 5). The only difference is the movement of the AUT and/or the reference antenna.

6.3.1.1 Scanner geometry The scanner system for the cylindrical scanning is typically based on a vertical linear axis for the probe antenna and an azimuth turntable for the AUT. An example of a cylindrical scanner system is depicted in Figure 18. The probe antenna is moved up and down using a linear scanning axis, and the AUT is moved in a circle on top of the azimuth turntable. The combination of both movements allows the measurement of the grid points on a cylindrical surface in dependency of z and φ.

Figure 18 —Example of a cylindrical scanner system with probe (left) and AUT (right) 6.3.1.2 Alignment of the test facility The alignment of the test facility requires the alignment of the scanner axes to each other and optionally to gravity or the facility system. The linear scanner axis ( z´) of the probe movement has to be aligned parallel to the rotation axis of the azimuth turntable ( z) and perpendicular in the facility. The circular movement of the azimuth turntable has to be verified along the selected scan range to keep the turntable axis stable and

37




therefore parallel to the probe scanner axis. The accuracy of the alignment has to be on the order of 0.01 λ for the radius of measurement versus z and φ. Figure 19 shows the corresponding coordinate systems. The typical tools for the alignment are theodolites or a laser tracker. The advantage of the laser tracker is that the complete movement of the scanner axes can be controlled semi-automatically and needs only one operator. Thus, alignment with a laser tracker can usually be accomplished in less time compared to the alignment with theodolites.

z’

z

d

x

ϕ y y’

x’

Figure 19 —Coordinate systems in the reference position when the probe and AUT are looking at each other Typically, the complete alignment of the scanner axes is referenced to the facility reference, e.g., a special positioned mirror cube in the facility or a reference theodolite in order to set the scanner system perpendicular. Facilit y references can also be targets that are attached permanently to a “solid” point, such as the floor. Attachment can be made with embedded target holders that can hold tooling balls, mirrors, or accommodate retro-reflectors for laser trackers.

6.3.1.3 Alignment of test antenna and probe After setting up the scanner system, alignment of both antennas is needed. The y´ axis of the probe antenna has to be set perpendicular to the x´ z´ plane of the linear scanner axis. In the case of a linearly polarized probe antenna the electrical polarization axis has to be aligned to the x´ or z´ axis, respectively. The AUT is typically aligned in the first step by geometrical means using mirror cubes and/or tooling balls with respect to the probe antenna, i.e., the z coordinate of the AUT has to be parallel to the rotation axis of the azimuth turntable.

38




6.3.1.4 Requirements on positioning accuracy For the determination of the far-field pattern from the near-field data, the geometrical relation between the probe and the AUT is essential. Any positioning errors will affect the final test results. The major errors that contribute to this item can be summarized as: a)

Mechanical positioning of the scanner: The z′ -axis scanner carries the probe to the expected relative z grid point. The analysis of Newell [B93], [B95], and Yaghjian [B129] can be used to estimate the errors in the far field due to errors in z′ .

b)

Mechanical positioning of the turntable: The turntable carries the AUT to the expected relative φ grid point. For the ρ and φ positioning errors simulations should be used to estimate the effect on the far field.

If not corrected by post-processing similar to that described in Wittmann, Alpert, and Francis [B121], the positioning accuracy should be on the order of λ/50 to achieve ±1 dB accuracy for a −35 dB side lobe. Farfield errors due to probe-position errors depend on the nature of the position errors (whether they are periodic, random, or some other form).

6.3.1.5 Other considerations for RF measurement accuracy Minimizing and mitigating errors due to nonlinearity, noise and dynamic range, drift, impedance mismatch, leakage and crosstalk, and random errors are discussed in Hess [B49], Newell [B93], [B95], Wittmann, Alpert, and Francis [B121], Yaghjian [B129] and in Clause 9.

6.3.1.6 Choice of probe antenna The selection of a probe is discussed in Clause 8.

6.3.1.7 Sampling According to the well-known Nyquist criteria, the sampling step between two adjacent data points should be no more than half of the wavelength ( λu/2) of the highest frequency for which there is a significant component in the spectrum (including undesirable and evanescent components). Taking into account the special geometry of the cylindrical surface, the sampling in the azimuth direction is given by ∆ φ = λu /a and in the z direction simply by λu/2, with a representing the diameter of the minimum cylinder. The minimum cylinder is the smallest cylinder that is centered on the axis of the φ rotator that encloses the test antenna.

6.3.1.8 Scan area In the case of possible scattering effects from the AUT itself (e.g., ground plane) or surrounding structures (e.g., mock-up structures at spacecraft antenna testing facilities), the effective diameter of the AUT has to be taken into account. The effective diameter can be larger than the physical AUT diameter. Given the near-field scanning range in the z direction, the corresponding far-field range of validity is similar to that in planar scanning (Equation [26]) and is given by the following equations:

  a Θ FF ± = arctan  Lz ± −  d  , 2  

(42)

39




where

a L z+ L z / d

is the effective diameter of the AUT is the upward vertical scan distance is the downward vertical scan distance is the distance of AUT to probe. L z+ and L z- are not necessarily equal.

Given the near-field azimuthal scanning range in the φ direction, the corresponding far-field range of validity

Φ FF ± is similar to that found in spherical scanning (see section B6.6 in Hansen [B47],) and is

given by

 ρ  Φ FF ± = Φ NF ± − arcsin  0  ,  ρ m 

(43)

where

ρ 0

is the radius of the minimum cylinder

ρ m

is the radius of the measurement cylinder

Φ NF ± is the range of angles over which the near-field scan is performed. 7. Spherical near-field scanning

7.1 Introduction This clause presents a summary of the concepts of spherical near-field antenna testing. In 7.2, the theoretical foundations are outlined. The description of antenna radiation in terms of a spherical wave expansion is introduced and the equation for describing the coupling between two antennas, the transmission formula, is stated. General issues related to practical implementations are discussed in 7.3.

7.2 Summary of spherical near-field theory The theoretical basis for all antenna testing techniques is a transmission formula, which expresses the signal received by an antenna when another antenna is transmitting. The receiving characteristics of the first antenna, as well as the transmitting characteristics of the second antenna, enter into the transmission equation. Assuming reciprocity, it does not matter which of the two antennas transmits and which receives. In practice, however, restrictions may be imposed on the antenna to be tested, e.g., it may only operate in receive mode. In spherical near-field antenna testing one utilizes the fact that each of the two antennas involved in the measurement, the AUT and the reference antenna (the probe), can be characterized by a finite, discrete set of coefficients, which expresses the radiation, and—due to reciprocity—the receiving properties of the antenna. These coefficients are the weight factors in a truncated expansion of the antenna radiation in spherical vector waves. This expansion satisfies Maxwell’s equations.

40




7.2.1 Basic theory A complete and thorough exposition of spherical near-field antenna testing can be found in Hansen’s authoritative book [B47] on the subject. This section is restricted to what is most essential and many details are omitted.

7.2.1.1 Spherical wave expansion A spherical wave expansion (SWE) of the electric field radiated by an antenna into free space may be defined as a weighted sum of spherical vector wave functions

 E (r , , ) 

k



 Qsmn Fsmn (r, , ) ,

(44)

 smn

where

Q smn k η

are the complex expansion coefficients is the wave number, k = 2π / λ , λ being the wavelength is the free-space admittance

(r,θ,φ) are the usual spherical coordinates. In Equation (44) the triple summation is understood as





smn

2

N

m n

 

2



s 1 n 1 m n

m N



N



s 1 m N n max(1, m )

.

(45)

 The spherical vector wave functions Fsmn (r , , ) are defined as follows:  m  m  1  F1mn r , ,      m  2   

  m m       cos  cos imP P     1 1   1     im  ˆ im  ˆ n n   h n (kr )   e e h n kr   sin      n n  1     

(46)

and

 m  m  1  F2mn r , ,      m  2   

n n  1 1 m im   h n kr  Pn  cos e rˆ  kr n n  1   1

 m m      cos cos P imP         1 1 1    1    im ˆ im ˆ n n      e e   krhn kr  krhn kr      kr  kr   kr  kr    sin     

(47)

41




i t where we have assumed—and suppressed—a time dependence of e . In Equation (46) and Equation

1

(47), h n

kr  is

the spherical Hankel function of the first kind, corresponding to outward wave

propagation, while P n m cos   is the normalized associated Legendre function (Appendix A1 of Hansen [B47]). In this notation any single radiated spherical wave with unit amplitude will radiate a power of ½ watt. Therefore the expansion above is denoted a power-normalized spherical wave expansion, where the



wave functions Fsmn (r , , ) are dimensionless, and the dimension of the expansion coefficients Q smn ½ becomes [watt] . The total power radiated from the test antenna then becomes

Prad 

1 2 Q smn watt.  2 smn

(48)

7.2.1.2 Minimum sphere and mode truncation The expansion in Equation (44) is valid in a source-free region outside the minimum sphere , which is defined as the smallest spherical surface with its center in the origin of the coordinate system that completely encloses the antenna. It needs to be emphasized that the minimum sphere needs to include any portions of the support structure that can affect the radiation pattern. Traditionally the radius of this sphere is denoted r o . Note that the AUT does not necessarily need to be centered in the spherical coordinate system, although this position will result in the smallest minimum sphere. The determination of the upper truncation limit, N  max(n ) , in the SWE in Equation (44) and Equation (45) is closely related to the size of the minimum sphere and the cut-off properties of the spherical Hankel 1 functions hn kr  . Leaving out the details, the maximum summation index in given by the empirical rule

N  kro   n 1 ,

n , N , is customarily

(49)

where kr o represents the integer closest to kr o, and n1 is an integer which depends on the positions of the sources within the minimum sphere, the distance from the minimum sphere at which the field is evaluated, as well as on the accuracy needs. If the evaluation distance is more than a few wavelengths from the minimum sphere, early numerical studies have shown that a value of n1 = 10 would be adequate for most practical purposes. However, with increasing antenna sizes, tighter accuracy specifications, and the vast speed and capacity increase of computers, a need for a revision of the truncation limit has emerged. Recently, a more elaborate estimate for the truncation limit N has been devised by Jensen and Frandsen [B60]. This revised truncation criterion is





N  kro  n 2 ,

(50)

where n2 is given by





n 2  max A  3 kro  ,10



(51)

42




and A is an empirically determined factor which depends on the desired accuracy. The minimum value of 10 for n2 applies to small antennas, in accordance with Equation (49). For a relative accuracy level of −80 dB, A = 3.6, while A = 5.0 for a −100 dB relative accuracy. Previously, only the truncation of the expansion imposed by the size of the minimum sphere was treated, i.e., truncation in the polar index n. However, in certain cases the expansion can also be truncated in the azimuthal index m, at some m  M , where M < N . This will be considered later in 7.3.1. In the case of antennas smaller than λ, the needed number of spherical modes can be much less than indicated by the formula with n1, n2 = 10. It is recommended that the user examine the mode spectrum to determine a proper limit for the truncation.

7.2.1.3 Transmission formula The transmission formula is the fundamental basis for spherical near-field antenna testing. As in planar near-field scanning, the interaction between a test antenna and the probe in the near field may conveniently be analyzed using the scattering-matrix theory of antennas (Kerns [B73], Larsen [B83], and Wacker [B117]). The formula expresses the complex signal received by a probe with known receiving characteristics as a function of the probe coordinates ( A, θ, φ) and the probe rotation angle χ , when a test antenna with unknown radiation characteristics transmits. A here represents the radial location of the probe origin in the laboratory coordinate system (see Figure 20). Figure 20 shows schematically the AUT and the probe minimum spheres and their associated coordinate systems. The derivation of the transmission formula involves fairly complex mathematical operations with spherical vector waves under rotation and translation of coordinate systems, and will not be detailed here. Interested readers are referred to Chapter 3 of Hansen [B47].

43




Figure 20 —Test antenna and probe with minimum spheres (Reprinted with permission from Hansen, J. E., ed., Spherical Near-Field Antenna Measurements, London, UK: Peter Peregrinus, Ltd., Figure 3.1, 1988. © 1988 The Institute of Engineering and Technology.) The signal w A, , ,  received by the probe antenna may be written in the form

w A, , ,   v



Tsmne

im n d m

 e

i 

Ps n kA 

(52)

smn 

where

Ps n kA 

1 sn p C  kA R  2 

(53)

44




p have been are the probe response constants, which are known once the probe-receiving coefficients R

determined. The Greek indices , ,   in the above summations relate to the probe, in the same manner as sn n the Latin indices s, m, n  relate to the test antenna. The d  m   and C  kA are well-defined rotation and translation coefficients, respectively (Appendices A2 and A3 in Hansen [B47]). The T smn are the sought-for quantities for the AUT, while v represents the complex excitation of the AUT [Equation (54). The relation between the Q smn in Equation (44) and the T smn in Equation (52) is (Chapter 3 in Hansen [B47])

Qsmn  vT smn .

(54)

As is common practice in derivations leading to the transmission formulas, multiple reflections (interactions) between the AUT and probe are assumed to be negligible, and are therefore considered an error. Their inclusion in the formulation would require a complete knowledge of the AUT and probescattering matrices, not only their transmitting and receiving parts.

7.3 Implementation The main problem in spherical near-field antenna testing is the determination of the AUT transmitting (or receiving) coefficients from measurements carried out in its near field, i.e., from the measured probe signal

w A, , ,  , the transmission formula [Equation (52)] needs to be “inverted” to find the T smn. In solving for the T smn, the influence of the probe is accounted for through a probe correction . With a knowledge of the T smn the field radiated from the AUT may be evaluated anywhere outside the minimum sphere, in particular in the far field, which is typically what is needed in most applications. Since the measured signal w A, , ,  on the left-hand side of Equation (52) for practical and obvious reasons is not a continuous function, but merely consists of a discrete set of recorded data, the inversion of the transmission formula in a computer requires discretization as well. Counting the number of terms in the summation Equation (45) one finds that there are 2 N ( N + 2) unknown T smn coefficients, and hence at least the same number of discrete measurement samples needs to be present in order to solve for the AUT transmitting coefficients. The transmission formula may of course be solved numerically by brute force , simply by forming a system of linear equations by inserting at least 2 N ( N + 2) discrete samples of w A, , ,  in Equation (52), but this is cumbersome, time-consuming, and not very efficient for practical AUTs, where the maximum index N [Equation (49) and Equation (50)] can easily be considerably larger than 100, thus putting severe demands on computer memory. This approach may possibly also lead to ill-conditioned systems. An efficient algorithm to solve the transmission formula has been proposed (Jensen [B59], Wacker [B116], [B117]), and improved and implemented by Larsen [B83]. The algorithm employs advanced data-reduction techniques in combination with FFTS, and is thus very efficient. The detailed derivations and steps in the algorithm may be found in Hansen [B47].

45




7.3.1 Probe As formulated, the algorithm does not impose restrictions on the probe in terms of its content of spherical harmonics. In each for as many

A, ,  sample point on the measurement sphere, the near-field needs to be measured

 positions (see Figure 20) of the probe as there are significant, azimuthal  harmonics in

the probe-radiation pattern. However, as pointed out by Wacker [B117], if the probe is restricted to only possess two harmonics in its azimuthal pattern, namely harmonics with    1 , corresponding to a cos  and sin  azimuthal variation, the algorithm becomes extremely efficient even for very large AUTs. The    1 restriction on the probe does not present a severe limitation, since such a probe can easily be constructed. A circular waveguide, smooth-walled or corrugated conical horn excited with the fundamental TE11 cylindrical waveguide mode fulfills this condition. An additional advantage for such a probe is the ability to make it dual-polarized, which reduces the measurement time by a factor of about 2, since both the  and the  component of the field can be measured simultaneously, e.g., by using a switch between the two probe ports. Two different ways of applying the Wacker/Jensen/Larsen technique based on the use of all three orthogonalities of the spherical rotation functions have been suggested by Laitinen and Breinbjerg [B78] allowing partial or full probe correction for modes µ = ±1 and µ = ±3. Importantly, many practical probes have a rectangular aperture and approximate this class of first-third-order probes. The technique presented by Laitinen and Breinbjerg [B78] proposes to apply three probe orientation angles i nstead of two, showing that this gives a possibility for a full probe correction for modes µ = ±1 and µ = ±3. In Laitinen [B77] a θ scanning scheme has been proposed based on performing the measurement for χ = 0°/90° for every second φ angle and for χ = 45°/135° for the other φ angles. Methods for probes with all higher-order µ modes (including µ = 0) have also been suggested (Laitinen [B76], Laitinen and Pivnenko [B79], Laitinen, Pivnenko, and Breinbjerg [B80], [B81], Laitinen et al. [B82], Schmidt, Leibfritz, and Eibert [B109], Schmidt and Eibert [B110]).

7.3.2 Measurement set-up The actual implementation of the mechanical system can be achieved in a multitude of ways. It needs to provide for the three axes of rotation corresponding to the three angular variables , ,  in Equation (52). Figure 21 illustrates the general spherical near-field set-up.

46




Figure 21 —Geometry of general spherical near-field s et-up. (Reprinted with permission from Hansen, J. E., ed., Spherical Near-Field Antenna Measurements, London, UK: Peter Peregrinus, Ltd., Figure 5.7, 1988. © 1988 The Institute of Engineering and Technology.) At any point on the spherical measurement surface ( A, θ , φ) the probe needs to point to the center of the sphere and sample two orthogonal polarizations, corresponding to two values of χ . In principle, it does not matter which of the two antennas moves relative to the other: The AUT may be fixed, with all rotations being done by the probe, the AUT may rotate around two axes with the probe rotating around the χ axis, or the AUT may rotate around one axis with the probe rotating around two axes. If the probe is dual-polarized, there is no need for rotating the probe in χ . However, the pattern of the second port needs to equal that of the first port rotated by 90° about the probe z axis. The actual implementation of the mechanical system can be achieved in a multitude of ways, with varying degrees of mechanical complexity, ranging from a fairly simple roll-over-azimuth set-up to complex double-gantry arm systems. Systems employing probes on telescopic and/or robotic arms have also been implemented. The advantage of such systems is their flexibility and the ability to accommodate the planar and cylindrical scanning geometries. High-speed measurement systems employing only one mechanical axis of rotation in φ, and a circular arch with a series of dual-polarized probes providing electrical “rotation” in θ and χ are also feasible set-ups for spherical near-field antenna testing (see 8.5 for more details on probe arrays). The mounting of the AUT in the set-up is usually dictated by mechanical considerations, either enforced by the mechanical system per se and/or by the AUT mechanical interface. Restrictions on how the AUT may be moved and rotated may also influence the choice of mounting. Traditionally the orientation of the AUT is either pole pointing or equator pointing as illustrated in Figure 22, where the AUT is depicted as a circular aperture antenna. Parts of the measurement grid are also shown.

47




Figure 22 —Orientation of AUT in measurement coordinate system. (a) polar pointing, (b) equator pointing. (Reprinted with permission from Hansen, J. E., ed., Spherical Near-Field Antenna Measurements, London, UK: Peter Peregrinus, Ltd., Figure 5.8, 1988. © 1988 The Institute of Engineering and Technology.) The RF subsystem comprises the signal source, a receiver which can measure both amplitude and phase, the probe, and cables and circuitry to connect the various parts. Both short- and long-term stability of the RF system during scanning of the AUT is very critical for the accuracy of the measurements.

7.3.3 Sampling criteria The number of significant spherical modes present in the field radiated from the AUT depends on the size of the antenna, as stated in 7.2.1.2. The algorithm for inversion of the transmission formula [Equation (52)] defines the sampling scheme to be used during the scanning of the AUT near field. The sampling is uniform in  and uniform in  , which is a prerequisite for using the FFT techniques. The FFT in turn helps ensure a very efficient algorithm. NOTE—There are recent methods developed for using non-uniform sampling that are described in 10.6. 4

When the expansion of the field radiated from the AUT can be truncated at    is e iN , and hence a sampling interval of

 

180 N

N , then the fastest variation in



(55)

4

Notes in text, tables, and figures of a standard are given for information only and do not contain requirements needed to implement this standard.

48




or less will be sufficient. Furthermore, since max  m   N , the maximum sampling interval in

 is the

same, i.e.,

   .

(56)

However, in many cases a larger value of

 may be used, if e.g., the AUT possesses some degree of

symmetry. Assuming, e.g., that the antenna can be enclosed by a minimum cylinder with its axis coincident with the z axis and with a radius Ro  r o  , then the upper limit on m is close to kRo  10 . Further reduction in the upper limit on m is possible if one is only interested in the field within a certain angular 

region around the pole at   0 . The latter is a consequence of the cut-off properties of the associated Legendre functions. Examples are rotational symmetric antennas with their axis of rotation coinciding with im  the z axis, and where the antenna excitation contains azimuthal harmonics e , m  0, 1, ..., M only. 

For a directive antenna pointing toward the equator plane of the measurement grid (i.e., at   90 ), one needs to choose    . When projected on the minimum sphere, r  r o , the sampling density in Equation (55), as derived from the truncation criterion in Equation (49), yields a distance of roughly λ/2 between the (projected) sample points, in agreement with t he Nyquist sampling criterion. In addition to the angular sampling criteria, it needs to also be observed that the minimum sphere for the AUT and the minimum sphere for the probe do not intersect each other (see Figure 20), since this situation would violate the transmission formula. This restriction can be expressed through the relation

max ( n ) AUT + max (ν ) probe < kA .

(57)

7.3.4 Probe correction Realistic probes do not detect the field at a single point, but rather some weighted average over the probe aperture. If the probe cannot be assumed to behave very much like a Hertzian dipole, its influence needs to be properly accounted for. This is referred to as probe correction. If the probe has low directivity and the measurement distance to the AUT is more than a few wavelengths, then the probe may often be assumed to perform like a Hertzian dipole, and probe correction can be ignored, since the received signal will be proportional to the electric field parallel to the polarization of the probe. The effects of not performing a probe pattern correction should be examined as part of the uncertainty analysis (Section 6.5 of Hansen [B47]). A necessary prerequisite for this probe correction is a knowledge of the probe-receiving characteristics as p , cf. 7.2.1.3. These need to be determined from a separate expressed through its coefficients R measurement of the probe or, alternatively, from a numerical model of the probe. If the Wacker/Jensen/Larsen transformation algorithm is employed in the data-processing scheme, then certain restrictions on the probe needs to be observed. As described earlier, it is required that the probe azimuthal pattern contains only the two harmonics with    1 , corresponding to a cos  and sin  variation. This does not in any way limit the directivity of the probe, since this is related to the maximum

49




value of the polar index  . This type of probe can easily be manufactured (e.g., as a circular waveguide or conical horn excited in the fundamental TE11 waveguide mode). The structure has the added advantage that it lends itself to dual-polarized operation, where the on-axis polarization ratios of the two ports are allowed to be inverses of each other, but where the relative patterns radiated by the two ports are the same.

7.3.5 Alignment requirements To achieve high accuracy in spherical near-field antenna testing one needs to pay careful attention to the alignment of the system. As described in 7.3.2, the mechanical set-up should provide for the three axes of rotation to comply with the geometrical requirements of spherical near-field antenna testing. Before initiating any measurement task, the system needs to be precisely aligned, therefore it needs to have built-in adjustment possibilities, and tools that facilitate the alignment, e.g., levelers, theodolites, mirrors, laser-tracking interferometers, optical targets, etc. Mounting and dismounting of the AUT and probe needs to be precise and reproducible, and the mechanical parts need to be sufficiently stable and rigid to help ensure that the alignment is not altered significantly when probe and/or AUT is rotated during the measurements. The effects of alignment imperfections should be analyzed as part of the uncertainty analysis. Several different types of mechanical set-ups can be envisioned, many are already in use (for example, see 7.3.2), and each one will typically need its own alignment procedures specially tailored to it. An example of a spherical near-field range is shown in Figure 23. In general, and only to be considered as a guideline, the axes should intersect each other to within about 0.02 λ, and at right angles typically on the order of hundredths of a degree. Hence at very high frequencies (sub-millimeter range) it becomes much more involved to reach an acceptable accuracy. Special consideration should be taken into account to remove any deviations that translation stages impart to the AUT as it travels back and forth along the transmit axis. This can result in pointing error. In addition, any gravity droop of the antenna should be compensated for as well.

50




Figure 23 —An example of a spherical near-field s ystem at the Technical University of Denmark (DTU-ESA Spherical Near-Field Antenna Test Facility) with a central part of the space-borne radiometer during on-ground calibration 7.3.6 Scan truncation Unlike planar and cylindrical scanning, if scanning is performed over a full sphere there will not be truncation error. However, on occasion it may not be possible to scan over a complete 4π steradians of the sphere. In this case there will be truncation error and only some angles of the far field will be valid (see Ssection 6.6 and Equation 6.7 in Hansen [B47]). The range of validity θ FF ± is given by

θ FF ±

 r  = θ NF ± − arcsin  0  ,  R 

(58)

where is the radius of the minimum sphere r 0 is the radius of the measurement sphere R θ NF ± is the range of angles over which the near-field scan is performed.

51




8. Probes This section contains general requirements for the probe (usually the reference antenna) used in near-field antenna measurements. We discuss the advantages and disadvantages of typical antennas that are used as probes for near-field antenna measurements. In near-field antenna measurements, the measured signal is the coupling product between the probe and an AUT. The coupling product is measured at a number of points on a surface located in the near field of the AUT. The measurements are used to calculate the far-field characteristics of the AUT. Conventional nearto-far-field transformation algorithms require that two complex (amplitude and phase) measurements be made at each point on the surface. Probes are oriented using a reference or fiducial coordinate system embedded in the probe so that the probe can be easily aligned to the scanning mechanism. Often the probe is scribed so as to define a coordinate system. The coordinate system defined for the probe should be a right-handed coordinate system. The xy plane is usually chosen to be parallel to the probe aperture. The origin of the probe coordinate system defines the mathematical and physical location of the probe. See Figure 24 for an example. The radiation characteristics of the probe are determined in the probe coordinate system, as discussed in 8.4.

Figure 24 —This probe coordinate system has been chosen so that the origin is at the center of the circular aperture, the z axis is perpendicular to the aperture, and the y axis is perpendicular to the broad side of the rectangular waveguide section. (Reprinted with permission from Balanis, C. A., Modern Antenna Handbook . New York, NY: John Wiley & Sons, Figure 19.18, 2008. © 2008 John Wiley & Sons.)

52




8.1 Probe properties The desirable properties for near-field antenna measurement probes are often contradictory and cannot be fulfilled completely. The selection of the most suitable measurement probe is therefore often a compromise. There are, however, some general rules applicable to all probes for near-field antenna measurements (listed here in no particular order):



The probe characteristics need to be stable with time, environmental conditions, and in different orientations with respect to gravity.



The probe needs to have a suitable mechanical interface defining a probe coordinate system (see Figure 24) that can accurately be reproduced and it should have means for mechanical and/or optical alignment.



The mounting structure supporting the probe, including its feed line, should be well covered with absorbers, or constructed in such a way that it helps ensure minimum scattering toward the AUT.



The probe should introduce minimum disturbance into the field being measured. The probe should present a low structural scattering in the angular region toward the AUT and it should be well matched to its feed line.

Other useful, but less important, features are:



Wide bandwidth, (preferably a waveguide band or more)



Light weight and easy to handle



Low cost



Easy to calibrate



A standard probe interface to facilitate interchange with another probe



A dual-polarized probe with two ports—one for each orthogonal polarization. This halves overall measurement time and also reduces influence of system drift on the measurement results. If a single linearly polarized probe is used, the orthogonal polarization component can be measured by rotating the probe 90° about its z axis. Ideally, one probe (or port) should be most sensitive to the co-polarized component of the AUT and much less sensitive to the cross-polarized component while the second probe (or port) should be most sensitive to the cross-polarized component and much less sensitive to the co-polarized component.

It is sometimes beneficial to use a directive probe to suppress undesired signals scattered from the environment. In any near-field measurement configuration, the probe directivity should be chosen to help avoid nulls or low field levels within the field of view (FOV, see Figure 25). The probe directivity should also be chosen depending on the measurement technique. For example, the more directive the probe, the worse the probe-AUT multiple reflection problem tends to be. In planar and cylindrical configurations, the probe pattern should be nearly uniform over a hemispherical solid angle toward the AUT as shown in Figure 25a. To achieve this, the probe should have low directivity. However, a higher directivity probe can be used in the case when only a limited angular region of the AUT far field is desired. In spherical near-field measurement configurations, the probe is always pointing toward the center of rotation of the AUT and the FOV is often smaller, thus a quasi-uniform pattern is desired over a solid angle, which is essentially less than hemispherical, as shown in Figure 25b.

53




Figure 25 —Illustration of the requirements to the probe pattern in (a) planar and (b) spherical near-field measurements. The probe characteristics are typically determined from a separate far-field measurement. In spherical nearfield measurement configurations, probe compensation is less important when using a low-directivity probe. Work on the determination of planar near-field correction parameters for linearly polarized probes has been done by Repjar, Newell, and Francis [B104] and for circularly polarized probes by Newell, Francis, and Kremer [B97] and Newell, Kremer, and Guerrieri [B99]. The cylindrical near-field correction technique has been treated by Leach and Paris [B84] and Hansen [B47] for spherical near-field measurement configurations. Spherical scanning is simplified by the use of special symmetric probes. A circularly symmetric horn fed with the fundamental mode from a circular waveguide has sinχ/cosχ probe response when the probe is rotated about its z axis. For this type of probe, the pattern is fully specified from knowledge of the E- and H-plane patterns only. Probes with this property are often referred to as μ = ±1, or first-order, probes (Hansen [B47]). Most conventional near-field-to-far-field transformation software in spherical geometry requires this property. If the measurement distance is large enough, any practical probe will behave as a μ = ±1 probe (Francis and Wittmann [B37]). The usefulness of this assumption depends on the size of the antenna, the separation

54




distance, and the desired far-field accuracy. The possible errors associated with this assumption need to be evaluated as part of the uncertainty analysis. Absorbers covering the probe interface may have a significant effect on both pattern and on-axis gain of a probe. This is particularly the case for small aperture probes with low front-to-back ratios. Even minor changes in the absorber layout may lead to noticeable changes in the radiation pattern. To minimize the effect of the absorber on the probe performance, experience shows that the angle between the end of the probe and the edge of the absorber should be at least 120° (Newell et al. [B98]) and the distance between the aperture and absorber tips should be greater than 5 λ at the lower operating frequency of the probe. The probe absorber configuration should not be significantly changed after characterization. Care should be taken when handling probes and their absorbers. Absorbers can be easily deformed or broken, affecting the probe characteristics. A dual-port circularly polarized (CP) probe is often useful in the measurement of circularly polarized AUTs since it is difficult to accurately measure the cross polarization using a linearly polarized (LP) probe. In the case of the LP probe, the probe-corrected cross-polarization tends to be a small difference between two large terms. Unlike LP probes which can be rotated 90° to obtain the cross polarization, rotating a CP probe provides no additional useful information. A CP probe of the opposite sense is required. It is difficult to construct a broadband dual-port CP probe (Foged et al. [B31]). A common probe for planar near-field scanning is the rectangular, open-ended waveguide (RWG). This probe is single port and linearly polarized. The second component requires an additional scan with an independent probe that could be the first probe rotated 90° about its z axis. One probe often used for spherical near-field scanning is the dual-polarized conically flared horn with a directivity chosen based on the application. An example of a simple μ = ±1 single port probe is described by Francis and Wittmann [B37]. Another probe often used for spherical near-field scanning is the dual-ported open-ended round waveguide horn whose aperture is treated to minimize probe-AUT reflections or to minimize back lobes [B26], [B61].

8.2 Description and classification of probe antennas We discuss the types of antennas that are used for probes. We assume these probes are single moded. Some sample probes are shown in Figure 26, Figure 27, and Figure 28. Figure 26 is a photo of a linearly polarized open-ended waveguide probe that could be used for PNF or CNF measurements on a linearly polarized AUT. Figure 27 is a photograph of a dual-port circularly polarized probe that provides both right and left components. A circular aperture probe with μ = ±1 symmetry, like the one shown in Figure 28, is for SNF measurements made at close distances. Bandwidth of the probe and its cross-polarization performance are important when measuring antennas with significant bandwidth and stringent axial ratio or cross polarization specifications.

55




Figure 26 —Open-ended waveguide probe

Figure 27 —Dual-port circularly polarized probe

Figure 28 —Circular aperture probe used especially for SNF measurements

56




8.2.1 Small dipoles and loops Small dipoles and small loops are sometimes used as probes in near-field antenna measurements. Their main advantages are that they introduce very small disturbances into the measured field and that their patterns are close to that of an ideal p oint source and thus pattern correction has a small eff ect and can often be ignored. A major disadvantage is the small radiation resistance, which makes it difficult to match to practical feed networks. Wideband small dipoles and loops with resistive loading have been described by Kanda [B71].

8.2.2 Open-ended waveguide probes Open-ended waveguides, either rectangular waveguide (RWG) or circular waveguide (CWG), are often used as probes in near-field antenna measurements. Any open-ended waveguide probe for measurement applications should have tapered edges to reduce the on-axis scattering cross section. a)

An RWG probe excited with the fundamental TE 10 mode is particularly attractive because it is relatively wideband ( f max /f min ≈ 1.5), inexpensive, and yet has very good pattern characteristics. Another advantage is that simple, approximate formulas for the co-polarization radiation pattern are available for use with general probe-compensation software (Yaghjian [B127]). Disadvantages of an RWG probe include: it cannot practically be made dual polarized [unless the cross section is square [see c) below] and its front-to-back ratio i s low.

b)

A CWG probe is also widely used. This probe has essential advantages: it is a μ = ±1 probe if properly constructed, it can be made dual-polar ized and is relatively wideband ( f max /f min ~ 1.5 to 1.8) (Foged, Giacomini, and Morbidini [B30]). Feeding a CWG probe is more complicated. Another disadvantage is the low front-to-back ratio.

c)

An open-ended square waveguide probe has features and characteristics similar to the CWG probe and can be made dual-polarized. However, although it comes close, it is not a μ = ±1 probe. The bandwidth is about the same as for the RWG pr obe.

The bandwidth of an open-ended waveguide can be increased by the addition of ridges. On the other hand, it degrades the μ = ±1 properties of the circular waveguide probes. Also, cross-polarization levels are relatively high The high level of backward radiation from any waveguide type probe can be reduced by adding one or more corrugations (chokes) around the aperture. This is usually limited to CWG apertures. With a welldesigned corrugation the radiation pattern can become highly symmetric and, although the directivity increases, both the cross-polar radiation within the main beam and the level of backward radiation is significantly reduced. A single choke probe can be relatively wideband ( f max /f min ~ 1.5) (Foged et al. [B28]) while a multi corrugated structure can cover an even larger bandwidth ( f max /f min ~ 1.8/2.0) (Foged, Giacomini, and Morbidini [B29], Foged, Giacomini, and Pivnenko [B32]). Chokes, however, increase multiple scattering.

8.2.3 Conical and pyramidal horns It is tempting to use a directive probe to suppress undesired signals scattered from the environment (but practical experience has shown there are pitfalls for the unwary). In spherical near-field measurement configurations, the FOV is often less than a hemisphere and more directive antennas, such as small horns, can be used as probes. Design formulas can be found in many antenna handbooks. A conical horn fed by a circular waveguide excited with the fundamental mode preserves the μ = ±1 properties, and when implemented as a dual-polarized probe represents one of the best probes for spherical near-field measurement configurations (Hansen [B47]).

57




Pyramidal horns with apertures larger than about 1.25 λ by 1.25 λ are infrequently used as probes for nearfield antenna measurements. The fact that they have nulls in the forward hemisphere limits their use in planar and cylindrical scanning. However, they can be used i n planar and cylindrical scanning if knowledge of only a limited angular region near boresight is needed. The fact that they do not possess the μ = ±1 symmetry limits their use for spherical scanning.

8.2.4 Log-periodic antennas In spite of their large bandwidths, log-periodic antennas are usually considered to be poorly suited as nearfield probes because of high cross-polarization levels and poor mechanical stability.

8.3 Probe parameters To fully probe correct typical near-field antenna measurements, the gain, reflection coefficient, polarization, and relative pattern of the probe are required for all frequencies. This generally requires a measurement of the probe in a reference facility. If only the AUT radiation pattern is desired, then gain and reflection coefficient are not needed. If two probes are used (either two separate probes or two ports of a dual-port probe), the complex port-to-port ratio is also required.

8.4 Probe characterization 8.4.1 Gain A measurement of gain can be done by several methods, such as a three-antenna far-field gain method (IEEE Std 149, Clause 12.2.2), gain-transfer (substitution) far-field technique (IEEE Std 149, 12.3.1), gaintransfer (substitution) near-field technique (Hansen [B47], pp. 210–214), or the three-antenna near-field extrapolation technique described by Newell, Baird, and Wacker [B96].

8.4.2 Polarization The polarization characteristics can be determined by the three-antenna method described in IEEE Std 149, Clause 11.2 and Hansen ([B47] pp. 160–161). Alternatively, these characteristics can be determined from a polarization measurement made with a polarization-characterized antenna (Hansen [B47] pp. 157–160). The probe characterization should be performed in the far field. The polarization characteristics should be determined for each port of the probe.

8.4.3 Amplitude and phase port-to-port ratio When two probes (two separate probes or two ports of a dual-port probe) are used, the port-to-port ratio needs to be determined. This ratio can be determined using the measurement method described in Hansen ([B47] pp. 161–163) for linearly polarized probes and using the method described by Newell, Kremer, and Guerrieri [B99] for circularly polarized probes. The far-field conditions should apply during the measurement. A simplified example follows. Probe 1 is nominally y-polarized and Probe 2 is nominally x polarized. The probes are illuminated wit h a y-polarized plane wave. Next, Probe 1 is aligned so its y axis is parallel to the field (the measurement range y axis) and the complex signal M 1 is recorded. The process is repeated with Probe 2 but its x axis is aligned parallel to the measurement range y axis and the complex signal M 2 is measured. The port-to-port ratio (Probe 2 to Probe 1) is

58




M 2 M 1

=

s2 x s1 y

,

(59)

where s1 and s2 are described following Equation (24).

8.4.4 Pattern The probe relative pattern is determined using a standard far-field method, for linearly polarized probes described in Wacker [B117], while for circularly polarized probes described in Newell, Francis, and Kremer [B97] and Newell, Kremer, and Guerrieri [B99]. For PNF and CNF probes, complex pattern knowledge in the forward hemisphere is usually needed with a high density of the measurement points, for example ∆θ = 1° and ∆φ = 3° . For the first-order ( µ = ±1 ) probes, only E- and H-plane co-polar pattern cuts are needed. The complete pattern can then be reconstructed fr om these two cuts (Hansen [B47] p. 150). The E-plane and H-plane co polar pattern cuts are measured under far-field conditions by a polarization matched linearly polarized antenna. Alternatively, an iterative procedure described in Hansen (pp. 71–73) [B47] can be applied. The spacing between the polar pattern samples is chosen to satisfy the sampling criterion:

∆θ , ∆φ ≤

360° 2 N + 1

,

(60)

where

N r 0

= (2π r 0 / λ ) + 10 is the radius of the minimum sphere enclosing the probe.

8.4.5 Reflection coefficient and port-to-port isolation The reflection coefficient of each probe or port should be measured with a calibrated network analyzer or reflectometer in an anechoic environment with the second port appropriately terminated. In principle, it is possible to measure and correct for port-to-port isolation. However, it is preferable to mitigate the problem by using quality probes with negligible crosstalk between ports.

8.5 Probe arrays Probe arrays systems with up to hundreds of elements are commonly used in near-field antenna measurement systems (Duchesne et al. [B27], Gennarelli et al. [B38], Iversen et al. [B57], Newell, Baird, and Wacker [B96]). In all near-field measurement geometries (spherical, planar, cylindrical, etc.) the time needed to physically move the measurement probe for each sampling step is the main contributor to the overall measurement time. With a probe array system, one or more mechanical axes of the near-field scanning is substituted with fast electronic scanning which provides a significant improvement in measurement speed for typical antenna measurement applications. The pertinent probe array layouts are illustrated in Figure 29 for the main three near-field scan geometries: spherical, planar, and cylindrical.

59




a) Spherical scan geometry

b) Planar scan geometry

c) Cylindrical scan geometry

Figure 29 —Illustration of probe array geometries for different near-field measurement configurations: a) spherical geometry (probes are inserted in the arch surrounding the AUT, thus eliminating the elevation scan axis), b) planar geometry (a linear array is moved in front of the AUT), and c) cylindrical geometry (the AUT is rotated in front of a fixed linear array) The conventional single-probe approach and the probe array system both perform a measurement of the near-field on a surface surrounding the antenna and both methods employ standard near-field-to-far-field transformation techniques to determine the far-field pattern radiated by the AUT (Yaghjian [B129]). If the embedded pattern of each individual array element is available, the probe array system may use full probe correction. Typical probe array implementations apply probe correction based on the assumption of a common identical embedded probe pattern. In spherical geometry a low-directivity probe and the distance between probe and AUT often contain the assumption of the probe behaving like a Hertzian dipole. When this assumption is valid, probe correction can be ignored (see 7.3.4).

8.5.1 Array implementation In order to receive amplitude and phase information from each individual probe port in the probe array, a high-frequency multiplexing network is needed. The simplest form is a switching network connecting each probe port with a single common output of the array. Another way to proceed is the modulated scattering technique described by Bolomey and Gardiol [B8] or the enhanced implementation advanced modulated scattering technique (A-MST) (Duchesne et al. [B27], Garreau et al. [B38], Iversen et al. [B57]). It should be noted that probe array systems i ntroduce additional contributions into the overall uncertainty budget for the measurement. Uncertainties due to mutual coupling between the probes, difference in probe-to-probe electrical characteristics (amplitude, phase, and polarization), and uncertainty on the exact probe positions need to be quantified and taken into account in the uncertainty budget. The above uncertainty terms, specific to probe array systems, substitute uncertainty terms linked to a conventional single probe system in the overall budget for measurement uncertainty. For the remaining items the measurement uncertainty budget of a probe array system is similar to conventional systems and need to be evaluated following standard techniques (see Clause 9 on uncertainty).

8.5.2 Probe array characterization The individual probes in a probe array system are often mass produced to limit the overall cost of the system. Although good mechanical accuracies can be achieved in high reliability production series, some imperfections in the polarization alignment and the low frequency modulation components of an A-MST system, or in the switching network of a switched array system, are to be expected. The probe array characterization serves to compensate such imperfections in the manufacturing and mounting of each

60




individual dual-polarized probe. Although the single uncharacterized probe’s performance is often acceptable, a significant improvement of the probe array performance can be obtained from the proper characterization scheme. An example of a characterization procedure for an array of dual-linearly polarized probes is illustrated in Figure 30. A linearly polarized reference antenna with high polarization purity is rotated in front of each probe changing the incident field polarization with the rotation angle. Amplitude and phase measurements are taken at each probe port as a function of the rotation angle. By applying a Fourier transform to the measured data, polarization correction coefficients can be accurately determined for each probe port. The same data are also used to properly align the amplitude and phase response of each probe in the array. A calibration matrix (Y ) is generated, linking the H and V (horizontal and vertical) field components with the obtained signals M1, M2 measured at the probe ports. Additional details of the calibration procedure are given in Bolomey and Gardiol [B8], Duchesne et al. [B27], Garreau et al. [B38], and Iversen et al. [B57]. This calibration of the array probes does not include mutual coupling or multiple scattering among the array probes. If the probe array is based on circularly polarized probes, the calibration procedures can be further improved if a dual circularly polarized reference antenna with high polarization purity is used. As in the linear polarization case, the resulting ( Y ) coefficient matrix compensates for differences among probes, aligns the phase reference axes, and reduces the cross-polarization components based on the purity of the reference antenna.

Figure 30 —Illustration of the probe array calibration procedure. Amplitude and phase measurements are recorded while rotating a reference horn in front of each probe of the probe array. A calibration matrix (Y) is generated, linking the H and V (horizontal and vertical) field components of the electric field with the obtained from signals M1, M2 measured at the probe ports.

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9. Uncertainty analysis A general discussion of the expression of uncertainty in measurements can be found in ISO/IEC Guide 983:2008(E) [B56]. Following the ISO, we distinguish between the terms error and uncertainty. The error is defined as the difference between the true value (which is unknowable) and the measurement result (Annex D in [B56]). It is possible to estimate the range over which the error likely lies and that estimate will be referred to as the uncertainty. Without a statement of uncertainty, measurement results cannot be compared ([B56], p. vii]. Thus, a measurement is not truly complete without a statement of uncertainty.

9.1 Introduction The procedures for estimating uncertainties in the results of near-field antenna measurements are largely based on the U.S. National Institute of Standards and Technology (NIST) 18-term uncertainty analysis (Newell [B93]) which has become an industry standard for evaluating near-field antenna measurement facilities. It is based on the following assumptions and procedures. a)

The theory on which the near-field measurements are based is exact and introduces no uncertainties in the calculated antenna parameters due to inherent approximations such as assuming ideal probe properties, separability, or symmetry of the near or far field of the AUT, small angle approximations, etc. Only two approximations are needed in the planar and cylindrical theories and one in the spherical theory. Practically, a finite scan area is used rather than an infinite scan plane or cylinder. In addition, multiple reflections between the AUT and the probe are not included in the transmission equations. Both of these approximations are treated as sources of uncertainty in the measured data.

b)

The numerical techniques that are used to calculate the planar, cylindrical, or spherical spectrum of the measured data and followed by the application of the probe correction are also exact except for round-off errors, which are usually small compared to other measurement errors. These techniques include the calculation of the plane-wave angular spectrum or modal expansion of the measured data using the FFT and other numerical calculations, and the probe correction which corrects for the properties of the probe. The FFT and other algorithms are valid if the sampling criteria are satisfied, which is confirmed during the uncertainty analysis where measurements are performed to determine the needed data point spacing. The probe correction is derived from the theory, and the uncertainties in the receiving properties of the probe are included as one of the uncertainty terms.

c)

The measured near-field data and the probe pattern, polarization, impedance, and gain data are the only sources of uncertainty in the final antenna parameters that are calculated by processing the measured data through the near-field-to-far-field software. It is also assumed that all significant sources of uncertainty are accounted for in the 18-term process and that the effect of each term on AUT parameters can be estimated using theoretical analysis, measurements, or simulation.

d)

When near-field measurements on a test antenna are used to estimate the uncertainty, the tests use a self-comparison approach which does not depend on knowing the true antenna parameters or even assuming that the results of a given measurement are free from other sources of error. The tests are designed to be sensitive primarily to only a single uncertainty source, and ideally the difference between two or more measurements will estimate the uncertainty for a single term. For instance, when the z distance between the AUT and probe is changed in small increments over a halfwavelength interval, the changes in the far-field results are primarily due to the multiple reflection and this term can be estimated even though there is a non-repeatable random error due to electronic and mechanical noise in the measurements. The random error term sets a lower limit for all of the terms that are determined by the self-comparison measurements, and in some cases this may be true for other terms.

e)

For the terms that use theoretical analysis to estimate uncertainty, the equations are derived from the basic theory using approximations where necessary to simplify the expressions and highlight the essential factors in the expressions. For instance, in the case of planar direct gain measurements 62




where the polarization of the probe is approximately the same as the AUT, the gain equation can be simplified (Newell, Ward, and McFarlane [B101]) to show that the uncertainty in the gain of the probe produces the same uncertainty in the gain of the AUT. It is also apparent that uncertainties in the mismatch factor and the input amplitude produce the same effect. A similar equation can be derived for the case of comparison gain measurements which shows that the mismatch factor, the gain of the standard and the far-field peak obtained from the near-field measurements on the gain standard have similar effects. f)

For planar measurements, the equations derived for estimating the effects of probe pattern and polarization are derived from the probe-correction equations. Approximations are used that are appropriate to the properties of the AUT and probe polarizations to obtain simplified expressions. This is also true for the term related to planar probe-position uncertainty. In all cases, the approximations have been tested by applying known perturbations to measured data and comparing the resulting changes in calculated AUT parameters with the changes predicted by the analysis.

g)

Each error term is assumed to be independent and uncorrelated with all other terms, and the total uncertainty is estimated with a root sum square (RSS) combination.

h)

Each of the sources listed in Table 1 produces an error in far-field parameters resulting from the measurement and data analysis process. It is never possible to determine the actual error for any of the sources. Since the results of our analysis are estimates, they are dependent on some judgment and interpretation by the user. Other users could interpret the tests differently and arrive at a slightly different estimate. The results are most useful therefore when the uncertainty process is described clearly, the data used is presented, and the resulting value for each uncertainty source is itemized.

Table 1 (Table I in Newell [B93]) summarizes the 18-term uncertainty model and the methods used to evaluate each term. These will be described more fully in the following discussion, especially in 9.4. While Table 1 is general, its specific application will vary depending on the practical implementation (for example, the geometry).

63




Table 1 —NIST 18-term uncertainty model summary Source of uncertainty

Measurement notes

Input data for analysis

1. Probe relative pattern

Probe pattern uncertainty

2. Probe po larization ratio

Probe polarization uncertainty

3. Gain standard

Standard gain uncertainty

4. Probe alignment

Alignment uncertainty

5. Normalization constant or gain standard farfield peak

Insertion loss/gain standard peak far-field

6. Impedance mismatch factor

Reflection coefficients

7. AUT alignment

AUT alignment uncertainty

8. Data point spacing (aliasing)

Over-sample near-field data

9. Measurement area truncation

Use larger scan area and truncate

10. Probe transverse position errors (errors within scan surface)

Mechanical alignment and position encoder uncertainty

11. Probe orthogonal position errors (errors orthogonal to scan surface)

Scanner planarity data

12. Multiple reflections (probe/AUT)

Multiple z data set

13. Receiver amplitude non linearity

Change input power level and averaging for constant S/N (signal-to-noise ratio)

14. System amplitude and phase errors due to : Flexing cables/rotary joints

Use loopback cable or rotary joints in series

Temperature effects

Long term stability test

Receiver errors

Simulation using near-field data

15. Receiver dynamic range

Change S/N by changing averaging with constant input power

16. Room scattering

Move AUT and probe together

17. Leakage and crosstalk

Terminate AUT or probe

18. Miscellaneous random errors in amplitude/phase

Run multiple measurements with no changes

64




9.2 Initial system adjustment and tests The efficiency and sensitivity of the uncertainty process can be improved by first making adjustments to the measurement system and then performing some tests to ensure that some controllable error sources do not limit the sensitivity of future tests. The transmitted signal level and the receiver averaging should be set to achieve the highest practical signal-to-noise ratio of the RF signal. A signal-to-noise ratio of at least 40 dB is needed (60 dB is preferred) for reliable results. This will help ensure that the contribution to the random error term due to electronic noise in the receiver will not unduly limit the sensitivity of the tests. The maximum signal level is limited by the compression level of the receiver. All transmission line connectors should be examined and properly tightened to help avoid leakage from cables, connectors, and waveguide joints. The first measurement test should then be to verify that the leakage from all components within the measurement chamber is as low as possible. See 9.4.16 for details of this test.

9.3 Methods for estimating and expressing uncertainties of individual terms Each of the terms listed in Table 1 is independently evaluated using mathematical analysis, self-comparison measurements, or computer simulation. The analysis begins with the equations relating the measured nearfield data to the far-field antenna parameters. It is then possible for some of the measurement geometries and some of the uncertainty terms to derive approximate relations that predict the uncertainty in terms of parameters such as mechanical or electrical tolerances of the measurement system. This approach is most successful for the planar geometry. The self-comparison tests compare the far-field results obtained from two or more different near-field measurements. Specific controlled changes are made between each measurement that ideally will change the effect of a single uncertainty term. The resulting changes in the far-field parameters are then used to estimate the uncertainty due to that single term. The computer simulation method begins with a typical near-field measurement on the actual AUT. It is then assumed that this data represents an error-free measurement for a hypothetical antenna and the resulting far field is also free from any errors due to measurements or processing. The near-field data, the probe-correction parameters, or the data processing can then be modified to produce results that are compared to the original far field. For instance, random amplitude or phase variations can be applied to the data, the probe pattern can be changed, or interpolation can be used to calculate some of the far-field pattern points. The methods used for each term have been selected as a result of extensive testing on many different systems and these will be described in detail in the following sections. The estimated uncertainty from each analysis, measurement, or simulation is generally expressed in one of two ways. The uncertainty can be given in terms of the change in the far-field parameter in dB or percent. For instance, the gain uncertainty determined from two self-comparison tests is represented as

G

G1

G2 ,

(61)

where the gain ( G) is in dBi. Similar expressions apply for other parameters such as side lobe level, cross polarization, etc. It can also be represented as an interference signal relative to the far-field parameter that would produce the observed change in dB. The interference signal is expressed as the ratio of an equivalent stray signal ( ESS ) to the signal ( S ) of the far-field parameter.

ESS / S

dB

20*log ESS / S ,

(62)

where ESS and the S are measured in voltage. To compare and combine the individual terms, it is useful to convert from one representation to the other using the following expressions.

65




ESS / S

Uncertainty in dB

∆

dB

20 * log 1 10

20

dB

.

(63)

9.4 Methods of evaluation of each term for planar, cylindrical, and spherical nearfield measurements In the following sections, descriptions and examples will be presented for each of the terms in Table 1. In most cases, the terms listed in Table 1 will produce uncertainties in all far-field parameters and the evaluation method is the same for all three measurement geometries. For simplicity, we assume that one probe is approximately polarization matched to the AUT and the second probe has a polarization that is approximately orthogonal to the first probe.

9.4.1 Probe relative pattern The full probe-corrected far field requires that the properties of two independent probes be known. This includes knowing the relative amplitude and phase of some point in the far field of the two probes. Usually this is determined at the far-field peak of the two probe patterns. In the special case where the second probe is the first probe rotated 90°, the relative amplitude is 1.0 and the relative phase is 0°. In the case of a dual port probe the relative amplitude and phase are given by the port-to-port ratio (port-to-port channel balance). The uncertainty in the relative amplitude of the second probe with respect to the first can affect the probe-corrected relative far-field pattern.

9.4.1.1 Planar The probe correction of near-field measured data can be considered as being composed of two parts. The first part, discussed in this section, is a pattern correction that corrects for the effects of the aperture size and shape of the probe and can be analyzed in terms of the far-field main component pattern of the probe. The second part is due to the non-ideal polarization properties of the probe and will be covered in 9.4.2. For planar measurements, the probe-correction equations can be used to show that the uncertainty in the farfield pattern in any direction due to the probe’s pattern is equal to the uncertainty in the pattern of the probe in that same direction.

9.4.1.2 Spherical The complexity of the spherical transformation prevents the derivation of a simple relation similar to the planar case. The primary effect of t he probe pattern correction in a spherical measurement is a small change in the beam width of the AUT main beam. Computer simulation is the best method for estimating the effect of spherical probe pattern uncertainties (Chapter 6 in Hansen [B47]). The far-field pattern of the AUT is calculated using the best available pattern data for the probe used in the measurement. The AUT pattern is then recalculated using a slightly modified probe pattern where the modifications are typical or larger than the estimated uncertainties in the probe data. Probe patterns for a slightly different frequency or an adjacent waveguide band are most convenient, or the probe data can be modified with specific uncertainty models. For spherical measurements, in the most frequent implementation the same probe is used to measure the second component but it is rotated by 90°.

66




9.4.1.3 Cylindrical The pattern correction effect and analysis for cylindrical measurements is a combination of the planar and spherical cases. Along cuts parallel to the axis, it is similar to planar and the planar analysis can be used. Along the φ cuts it is similar to spherical and simulation is used.

9.4.2 Probe polarization ratio If the probe responded to only one vector component of the incident field in all directions and were perfectly aligned to that component, the polarization correction would be unnecessary. Since all probes have some response to each of two orthogonal components, the polarization correction needs to be included and uncertainties in the probe polarization will produce an uncertainty in the far-field results. The planar probe-correction equations can be used to derive relations (Newell [B93], p. 757) to estimate the effect of uncertainties in the polarization properties of the probe. For example, if the AUT is x-polarized and a probe with approximately linearly polarization and aligned perfectly to the x axis is used to obtain main and cross component near-field data, the uncertainty in the cross polarization of the AUT is approximately

p(θ , φ ) pε (θ , φ )

≅ 1 + p(θ ,ϕ )ρ ′′(θ ,φ ) − p (θ ,φ )ρ ε ′′

For x -polarized AUT

(64)

where

p (θ , φ ) = AUT polarization ratio =

E x E y

ρ ′′(θ , φ ) = y -Polarized probe's polarization ratio =

E PX E PY

ρε ′′(θ , φ ) = Polarization ratio including uncertainty. It can also be shown that the uncertainty in the main component of the AUT due to uncertainty in the cross polarization of the probe is negligible. The analysis used to derive Equation (64) has been extended (Newell [B92]) to include both linear and circular polarized AUTs and probes for planar measurements and also to treat spherical measurements with linearly polarized probes. The resulting equations cover all the typical cases and polarization uncertainty can be easily estimated.

9.4.3 Gain standard This term will only affect the gain results. The gain of the AUT can be determined by using either a direct gain technique where the probe is the gain standard or a comparison technique using another antenna such as a standard gain horn as the standard. Both analysis and computer simulation verify that the uncertainty in the AUT gain due to the gain standard is identical to the uncertainty in the gain of the standard. The gain standard uncertainty is generally obtained from calibration documents or estimates of uncertainty in the method used to determine the gain of the standard.

9.4.4 Probe alignment Ideally, the pattern of the probe is measured with respect to a well-defined and reproducible coordinate system defined with fiducial references, alignment mirrors, or leveling devices. The probe is then aligned in the near-field measurement system with its coordinate system parallel to the reference coordinates. If there

67




is an angular misalignment of the probe, the measured pattern used in the probe correction is different than the pattern of the actual misaligned probe. The effect on the far-field results of the AUT is equivalent to an uncertainty in the probe pattern as discussed in 9.4.1. In this case, the probe pattern uncertainty is estimated using the slope of the probe pattern in the direction under consideration along with the estimated angular misalignments.

9.4.5 Normalization constant or gain standard far-field peak This term affects the gain. In direct gain measurements, a normalization constant, sometimes referred to as an insertion loss (Newell, Ward, and McFarlane [B101] p. 794), is determined by measuring the change in signal level when the AUT input and probe output transmission lines are connected directly together as illustrated in Figure 17. In comparison gain measurements, this measurement is not necessary, but a quantity referred to as the far-field peak (FFP) needs to be determined from the near-field data for both the AUT and the gain standard. The far-field peak for planar measurements is given by

 − iK • P FFP = 10log  δ xδ y ∑ B0' ( P j ) e  j 0

2 j

 , 

(65)

where

K 0

is the direction of the far-field peak

P j

is the vector location of the jth point within the scan plane.

Analysis and simulation show that the uncertainty in the far-field gain of the AUT is identical to the uncertainty in either the normalization constant or the FFP . The uncertainty in the normalization constant is estimated by combining the effects of connector repeatability and loss, receiver linearity, amplitude variations due to drift or cable flexing, and the insertion loss of attenuators or substitution cables. The uncertainty in the FFP for the gain standard is estimated by performing a limited uncertainty analysis on the near-field measurement of the gain standard. Only those terms in Table 1 that affect the relative nearfield data in a way that would change the FFP are considered in this analysis. The primary contributors are multiple reflections, truncation, leakage, and room scattering. The practitioner needs to be aware that the full probe-corrected far-field pattern, including both polarization components, requires that the relative amplitude and phase be known at some point in the near field. Uncertainties in this value can lead to uncertainties in the probe-corrected far field.

9.4.6 Impedance mismatch factor If the second probe is just the first probe rotated by 90° then this term will affect only the gain results. For either the direct or comparison gain measurements at least one transmission line connection is changed or a switch is changed. This results in a signal level change due to the different impedance mismatch interactions and produces an error in the calculated gain. A correction can be applied to reduce the error by measuring the complex reflection coefficients of the antennas and transmission line components and deriving a mismatch correction that is appropriate for the measurement technique used. If the reflection coefficients are not measured and a mismatch correction is not applied, the uncertainty in the gain results is estimated by evaluating the mismatch correction assuming typical values for the coefficients. If a correction is applied, the uncertainty is estimated by evaluating the mismatch correction using the measured values and values that reflect the estimated uncertainty in measuring the coefficients.

68




9.4.7 AUT alignment Rotational alignment errors rotate the pattern and may shift the boresight direction. Translational errors introduce a phase factor in the far field. The coordinate system for the AUT should be defined with accurately defined mechanical or optical references. The AUT is then aligned so that its coordinates are coincident with the reference measurement coordinates. The reference measurement system coordinates are defined using optical and mechanical instruments to locate the axes or planes defined by the mechanical scanners. The uncertainty in the boresight direction is due to AUT alignment and is determined by estimating the uncertainties in the mechanical and optical instruments and the procedures used to align the AUT coordinates with the reference coordinates. For instance, a laser tracker could be used to map the planarity of a planar scanner and the orientation of the best-fit plane transferred to a fixed reference mirror. If a mirror is also attached to the AUT and used to define its x- y plane, the alignment uncertainty would include the uncertainties of the laser tracker, the mathematical fitting process, the transfer to the reference mirror and its stability over time, the instrument used to measure the relative orientations of the two mirrors, and the alignment process.

9.4.8 Data point spacing This term will affect gain, directivity, side lobe level, cross polarization, and boresight direction, and the method for estimating uncertainties is similar for all three measurement geometries. For all three geometries, the near-field theory specifies required data point spacing to help avoid aliasing errors. For the planar case the spacing is generally slightly less than λ/2 and for the angular coordinates in cylindrical and spherical the spacing is defined by the wavelength and the radius of the minimum sphere centered at the origin that will enclose all of the radiating surfaces (See 6.3.1.7 and 7.2.1.2). To estimate the effect of a specific data point spacing, a complete measurement is performed with the spacing reduced to one half or less of the theoretical requirement. The far-field pattern is then computed using all of the data and compared to a pattern where only every other data point is used. An example of a typical result is shown in Figure 31 for a planar measurement. The ( ESS/S )dB curve is used to determine the uncertainty for a given side lobe level or angular region. The higher lobes in the ( ESS/S )dB curve in the region of 55° off axis are an indication of aliasing errors and these can be reduced by using a smaller spacing. If high accuracy is not needed beyond 40° off-axis or the −55 ( ESS/S )dB is acceptable, the λ/2 spacing can be used. Curves similar to Figure 31 are produced for all the self-comparison tests and the ( ESS/S )dB curve is used to estimate the ESS for side lobe and cross polarization. To estimate the uncertainties in gain, directivity, and boresight directions, these quantities are tabulated for each data set compared and the variations are used to derive uncertainty levels.

69




Data Point Spacing Test, Lambda/4 Data Compared with Lambda/2 Data Lambda/4

0

Lambda/2

ERR/SIG

-10 -10

-20 -20

-30 -30

B d n i e d-40 -40 u t i l p m A

-50 -50

-60 -60

-70 -70

-80 -80 -80

-60

-40

-20 0 20 Elevation Elevat ion Angle Angle in Degrees Degrees

40

60

80

Figure 31 —Results —Results of data point spacing test for planar measurements 9.4.9 Measurement area truncation The measurement surface will always be truncated in planar and cylindrical measurements and may be truncated in spherical measurements. The truncation has two effects on the far-field results as discussed in 5.3.1.6. To 5.3.1.6. To estimate the uncertainty due to truncation, a measurement is performed over the largest practical area available for the measurement system. The far-field is calculated using all the data and using subsets of the data where the amplitudes around the perimeter have been set to zero. Curves similar to Figure 31 and tabulations of gain, directivity, and beam pointing are generated. These can be used to estimate the uncertainty due to truncation. Another way to analyze truncation is to plot the variation in a far-field parameter of interest (such as pattern level) at a given angular location as a function of the truncation distance as shown in Figure in Figure 32 for the beam peak, the −35 dB side lobe at 12°, and the −38 dB side lobe at 45° of Figure Figure 31.

70




Scan Area Truncation Test, Far-Field Pattern Level Changes 0.05

EL = 0

EL = 12 Deg

EL = 45 Deg

0.04 0.03 0.02 B d n i 0.01 e g n a h C 0.00 e d u t i l -0.01 p m A

-0.02 -0.03 -0.04 -0.05 0.0

0.5 1.0 1.5 2.0 Scan length length truncated truncated from f rom each side, wav waveleng elengths ths

2.5

Figure 32 —Variation —Variation in far-field pattern levels due to planar area truncation. The original scan area is an 80 λ by 80 λ area. Removing a ring reduces the scan length by 1 λ in each dimension. 9.4.10 Probe-position errors To the extent that probe-position errors are known, error compensation is possible. For example, if the positions do not fall on the ideal grid points but the actual positions are known (e.g., by using a laser tracker), it is possible to perform compensation using k -correction -correction (Joy and Wilson Wilson [B69]) [B69]) or the NIST analytic method (Wittmann, Alpert, and Francis [B121], Francis [B121], [B122]). [B122]). It is also possible to use these methods to simulate position errors and to estimate the resulting uncertainties.

9.4.10.1 Transverse errors

9.4.10.1.1 Planar Equations have been derived for the planar measurements to estimate the uncertainties in far-field quantities due to x x- and y-position y-position errors. These errors are generally due to imperfections in the guide rails

71



IEEE Std 1720-2012 IEEE Recommended Practice for Near-Field Antenna Measurements Measurements

that the probe moves on. For the case where the main beam is approximately normal to the x- y y plane, the uncertainties in gain and side lobe are (Equations 53 and 55 in Newell [B93]) Newell [B93]),, for the main beam

8.7 ∆ xy ( RMS )

∆GdB ( K ) ≤

η L

g ( K ) ,

(66)

and for the side lobes

4.3 ∆ xy ( K )

∆GdB ( K ) ≤

L

g ( K ) ,

(67)

where

G L

is the antenna gain is the antenna major dimension η is the aperture efficiency is the ratio of the peak of the main beam to the side lobe (linear) g( K K ) ( RMS ) implies the root mean square value i s to be used. used. K ) is 100. K For instance, for a –40 dB side lobe, g( K

∆i ( K ) =

1 2

4π L x Ly

∫ ∆ (P )e

− iK • P

i

= k x xˆ + k y yˆ , ∆ xy ( K ) = ∆ x 2 ( K ) + ∆ y 2 ( K ) ,

d P , Δi (P) is the error in the x (or y or z) position, and P = xxˆ + yyˆ .

9.4.10.1.2 Cylindrical and spherical Computer simulation is generally used to estimate the effect of probe-position errors (chapter 6 in Hansen [B47]). [B47]). A script is used to modify measured data and impose specific types of position errors such as linear scale, random, periodic, etc. Typical mechanical misalignments such as non-intersection of axes, theta-zero errors and probe offsets in x or y can also be simulated. Plots similar to to Figure 31 and and Figure 32 are generated by comparing results for different simulated error levels. Mechanical and optical measurements on the scanner hardware are used to estimate the actual errors in a given system.

9.4.10.2 Probe radial or z -position -position errors

9.4.10.2.1 Planar The two equations for the effect of z errors on the main beam and side lobe region are (Equations 59 and 61 in Newell [B93]) Newell [B93]),, For the main beam,

∆GdB ( K ) ≤

43  δ z (rms) 

 η 

λ

2

2  cos θ B g ( K ) 

(68)

and for the side lobes

72




∆GdB K

13.5 δ z (K ) λ

cosθ B g K

(69)

where

δ z ( K ) =

1 2

4π L x Ly

∫∆

z

( P ) e− iK•P d P .

9.4.10.2.2 Cylindrical and spherical Computer simulation is generally used to estimate the effect of radial or z probe-position errors for these geometries as described for transverse position errors.

9.4.11 Multiple reflections between the AUT and the probe The effects of multiple reflections are estimated by making repeat measurements where the only change is the separation distance between the AUT and probe. Four or five data sets are acquired with the z-spacing changed by λ/8 between each measurement. Each of the measurements is transformed to the far field and the complex patterns are averaged after correcting the far-field phase for each displacement. This averaging should reduce the effect of the multiple reflections and the average far field is then compared to the results from a single measurement. Graphs similar to Figure 31 and Figure 32 are also produced and the uncertainties are derived from these graphs. Figure 33 shows another way of displaying the effect of multiple reflections. Experience shows that the closer the AUT and probe are in gain, the greater the approximate relative error is due to multiple reflection. Thus, when the AUT is a standard gain horn, the effect of multiple reflections is greater than for higher gain antennas. The beam peak is distorted and the peak far field varies approximately with the probe-AUT separation distance. This illustrates why it is important to evaluate multiple reflection effects for both the AUT and gain standard measurements as discussed in 9.4.5.

73




Multiple Reflection Test, SGH on Planar Range Z distance changed from initial 2.6 wavelengths

0.0

0.0

0.125

0.250

0.375

-4

-2 0 2 Azimuth (deg)

4

0.500

-0.2 -0.4 -0.6 ) -0.8 i B d ( e d-1.0 u t i l p m A-1.2

-1.4 -1.6 -1.8 -2.0 -10

-8

-6

6

8

Figure 33 —Typical beam peak variations due to multiple reflections

9.4.12 Receiver amplitude linearity Amplitude nonlinearity arising from nonlinear electronics in the measurement system will cause errors primarily in gain and directivity. All modern microwave receivers are highly linear and it is difficult to devise a test that will truly measure nonlinearity. Repeat measurements can be made where the power level to the mixers and amplifiers is changed between measurements and the averaging is also changed to maintain a constant signal-to-noise ratio for each measurement. The far fields from these repeat measurements are then compared as discussed in previous sections. The differences are usually at the noise level or affected by instrument drift and it is difficult to identify nonlinear effects. Another technique has been developed (Newell and Newbold [B100]) that uses repeats of single centerline cuts where stop motion, bi-directional scanning and high averaging is used to reduce the effect of noise and drift. These cuts are repeated for different power levels and the resulting near-field data is compared. If the system is linear, the difference between two measurements with different power levels should be constant in both amplitude and phase. These tests have detected small, nonlinear effects that can be used to estimate the effects on far-field quantities.

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9.4.13 System phase errors

9.4.13.1 Planar The receiver phase error is evaluated with the tests for nonlinearity and the primary remaining sources of errors are the flexible cables and rotary joints that are used to translate or rotate the AUT or probe during the near-field measurements. These components can introduce a change in both amplitude and phase during the flexing or rotation that creates errors in the measured data. The cables and rotary joints are tested by temporarily replacing the AUT and probe with another transmission line that will have little or no variation as the mechanical scanning system is translated or rotated. For a planar system, the substitution transmission line, sometimes referred to as a loop back cable, is a long, semi-rigid cable that is supported at the AUT and probe locations using a service loop that will eliminate any strain on the connectors. The cable is configured in a long, gentle loop that will have a large bending radius and will not touch the floor when the probe is at the minimum height. The probe carriage is then moved over the full range of x- or ytravel and the amplitude and phase recorded as a function of position for each one-dimensional scan. A sample phase result is shown in Figure 34. The measured amplitude and phase variations for both x and y cables are then used to modify a complete set of two dimensional near-field data for the AUT being tested. Comparison of the far-field parameters with and without the cable variations is used to derive uncertainty estimates. Alternatively, cable variations can be estimated using Hess [B49].

Figure 34 —Variations of phase in the X cable on a planar range as measured with a loop back cable

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9.4.13.2 Spherical The tests and analysis for a spherical system are similar but an additional rotary joint is used instead of the loop back cable. The rotary joint and a ridged section of cable replaces the AUT/probe path and three separate measurements are made with either the rotary joint in series with either the φ , θ , or polarization rotary joints. Computer processing is then used to modify a regular data file and determine the resulting changes in the far-field parameters.

9.4.13.3 Cylindrical Cylindrical tests use a combination of the planar and spherical tests where the loop back cable is used for the linear motion of the probe and the rotary joint is used for the φ and polarization rotators.

9.4.14 Noise and receiver dynamic range First a reference data set is obtained using the maximum available RF power that will not saturate the mixers (according to the manufacturer’s recommendations and the highest practical averaging to produce the highest signal-to-noise ratio). The number of averages is then reduced in steps to reduce the signal-tonoise ratio while maintaining the same RF power level to the mixers. Far fields are calculated for each condition and the changes are graphed and tabulated to provide an estimate of the uncertainty for a given signal-to-noise ratio that will be used in the final measurements. Parseval’s theorem states that the root sum square (RSS) noise in the near field is equal to the RSS noise in the far field. The noise level is the same in the near and far fields but the relative level of the peak of the far-field α is usually greater than that of the near-field β . This results in an improvement of the signal-tonoise ratio by a factor α/β .

9.4.15 Room scattering

9.4.15.1 Planar This test begins with the AUT and probe precisely aligned and the measurement system set for high accuracy measurement. A reference set of data is acquired and this data will include the effects of room scattering. The AUT and probe are then translated by the same x, y, and z increments to a new position in the room where the measurement is repeated. The translations should be on the order of a number of wavelengths and it is critical that the angular alignment of both the AUT and the probe is identical to the original condition and the new scan area is at the same location relative to the AUT. On a typical planar scanner, the probe can be moved in x, y, and z using the normal scanner controls without changing the probe’s angular orientation. Tr anslation of the AUT while maintaining its ali gnment is more difficult. If the AUT has alignment mirrors and/or alignment levels attached to the antenna, these can be used to realign the AUT in a new position. Centerline near-field cuts of amplitude and phase can be measured and compared to the same cuts from the reference measurement to fine tune the x, y, and z positions of the probe to the original origin relative to the AUT. They can also be used to verify or fine tune the angular alignment of the AUT by comparing the slopes of the near-field phase. In this new position, the room scattering will have a different effect on the near-field data and comparing far-field results from the two measurements will provide an estimate of the room scattering.

76




9.4.15.2 Spherical and cylindrical Translation of both the AUT and probe in x, y, and z is very difficult for these geometries. With a spherical system, translation in the z direction may be possible by moving a standoff from the AUT to the probe mount so that the separation between the AUT and probe remains the same. Alignment mirrors or levels will still be needed to verify the angular alignment of the AUT and probe after the standoff is moved. For a cylindrical system, it may also be feasible to translate the AUT in the axial direction and the probe can be re-centered using the linear probe transport. Room scattering can be partially mitigated by oversampling since room scattering frequently has contributions that vary more rapidly than λ. The effect of room scattering can also be estimated by using a post-processing technique that will reduce the effect of scattering within the measurement chamber and comparing the far field obtained from the original measured data with the far field obtained after the post-processing has been applied (Gregson, Newell, and Hindman [B43], Gregson et al. [B44], Gregson et al. [B45], Hess and McBride [B51], Hindman and Newell [B54], Hindman and Newell [B55]). These techniques can be applied to all three measurement geometries.

9.4.16 Crosstalk and leakage Crosstalk is the unwanted coupling between two ports of a measurement system or subsystem. Examples include signals traveling from the reference channel to the measurement channel of the receiver; signals traveling from the x polarization port to the y polarization port of a dual-port probe; and signals traveling from the local oscillator (LO) port to the RF port of a remote mixer. A good receiver will have 80 dB or better of isolation between the reference and measurement channels. Crosstalk problems are often due to poor isolation i n switches, mixers, isolators, or dual-port probes. The direct way to test for crosstalk is to insert a signal into one port and measure the output at the other port. Leakage is unwanted coupling due to imperfections in the signal sources, cables, connectors, and joints used to link the components of a measurement system. To estimate leakage, a reference measurement is acquired or one of the other reference files can be used if the AUT/probe and measurement conditions have not changed. The input transmission line is then removed from the AUT and terminated with a load. The load should be covered with conductive tape and then placed inside a small block of absorber since some loads are not completely shielded. Near-field measurements are then acquired with the same measurement parameters used for the reference data. Image plots of the amplitude data should be examined for any regions where the amplitude is above the noise level and appears to be coming from some leakage source. If regions of leakage do appear, the probe should be placed in these regions and the RF system examined to identify and eliminate the leakage. When the repairs have been made, the leakage scan should be repeated to verify correct performance. Another leakage scan is the made with the AUT transmitting and the output transmission line from the probe terminated. To estimate the effects of the residual leakage, the leakage data is transformed to produce far-field leakage patterns which are compared to the results of the reference measurement. In this comparison, the leakage far field is normalized to the far-field peak of the reference data.

9.4.17 Random errors Random errors arise from noise in the electrical and mechanical systems. The uncertainty due to random errors is estimated by repeating a measurement several times without making any changes in the AUT, probe, instrumentation, or measurement parameters. The far fields fr om these repeat measurements are then averaged and the average result used as the reference. This reference is then compared to a single measurement result and the uncertainty estimates derived from the comparison. For planar measurements, the effect of random errors on the far-field pattern can also be estimated by making a near-field measurement using a data point spacing that is less than one half wavelength and calculating the spectrum of the measured data without applying a probe correction or the cosine theta factor. The spectrum for

77




values of k much larger than ±2π/ λ will be due to random error since the evanescent modes in this region would be highly attenuated. The level of the spectrum in this region provides an estimate of the random error effect on the far-field pattern.

9.5 Combining uncertainties The results of an uncertainty analysis will be most useful if the individual estimates are tabulated. The individual estimates can then be combined to arrive at an estimate of the total uncertainty for each far-field parameter. Assuming that all the terms are independent and uncorrelated, the terms can be combined using a RSS procedure. The method of combination should be identified in reporting final estimates. Overall uncertainties include a coverage factor (ISO/IEC Guide 98-3:2008(E) [B56], p. 3). Most commonly a coverage factor of 2, which corresponds to 2σ for a normal distribution, is used . The uncertainties may be asymmetric.

10. Special topics

10.1 Effective isotropic radiated power There are two specific system power parameters associated with communication satellites that are obtainable from near-field measurements: a)

The effective isotropic radiated power (EIRP)

b)

The saturating flux density.

EIRP is defined as the product of the antenna gain Ga and the net input power to the antenna P i. One method of determining this is to determine the gain from near-field measurements and the input power using a power meter. However, often it is undesirable to break the connection between the transmitter and the AUT. If one measures the output power P o ( x0, y0 ) from the probe at a reference point x0, y0 of a planar near-field scan, then if the probe and AUT are polarization matched we can show that the EIRP in the direction k 0/k is given by (equation 32 in Newell, Ward, and McFarlane [B101])

2

EIRP ( k 0 ) =

1 − Γ  Γ p P0 ( x0 , y0 )

(1 − Γ ) (1 − Γ ) G (k ) 2

2

p



p

FF ,

(70)

0

where FF, the far-field maximum, is given by

δ xδ y

FF =

∑ B ′ ( x , y ) e 0

i

− i ( k0 x xi + k0 y yi )

2

i

i

λ 4

,

(71)

and Γℓ , Γ p are the reflection coefficients of the probe and load respectively. δ x , δ y are the sample spacings in x and y. G p is the probe gain; B0′ is the near field measured with respect to the near field at x0, y0; xi, yi are

78




the x and y coordinate of the ith measurement point; k 0 x and k 0 y are the x and y component of the propagation vector k 0, and λ is the wavelength. A comparison EIRP measurement can also be performed that does not require knowledge of the gain of the probe, normalization of the near-field data, or a power measurement at the probe output. In this approach, the AUT is installed on the near-field range and near-field data is obtained using the operating input power level. After measuring the AUT, a standard gain antenna (SGA) with a known gain GSGA is installed on the near-field range. Then the input power to the standard gain horn P SGA,in is adjusted so the probe output power at the reference point is the same as that measured when the AUT is in the system. P SGA,in needs to be determined (accounting for any mismatch). The EIRP is given by

EIRP ( k 0 ) =

FF AUT FF SGA

PSGA,inGSGA

(72)

The quantity FF needs to be determined for the both the AUT and the SGA systems.

10.2 Saturating flux density In the far field, the flux density that is needed to saturate the system receiver S 0 is related to the net input to the source antenna P i and the gain of the source antenna G s by (Equation 33 in Newell, Ward, and McFarlane [B101])

S 0 =

PG i s 4π d 2

,

(73)

where d is the distance between the source antenna and the receive antenna. The development of a similar near-field equation is provided by (Newell, Ward, and McFarlane [B101]). The result is (Equation 39b in Newell, Ward, and McFarlane [B101])

   PG λ 2 i p ( k 0 )   S 0 =   4π     δ δ B ′ x , y e−i ( k  x y ∑ 0 ( i i ) i 

0 xx i + k 0 y

   . 2  y )   

(74)

i

10.3 Pulsed-mode measurement techniques Pulsed-mode testing in a near-field environment refers to a modulated continuous wave (CW) transmit signal being generated. Active antennas often need to be operated and tested in pulsed mode. For antennas operating in transmit mode, this is often based on power and temperature limitations. The average power can be controlled by adjusting the duty cycle where CW operation of the antenna is usually not possible.

79




From a measurement perspective, testing in pulsed mode places a synchronization requirement on the overall acquisition system and a bandwidth limitation on the receiver. Depending on the pulse width and pulse repetition frequency, a particular receiver bandwidth can be operated in CW or pulse synchronized modes as described in Swanstrom and Shoulders [B113]. In CW mode the receiver responds to the average received pulsed power level without any synchronization requirement. In cases where the receiver is synchronized with the pulsed RF signal, pulse profile detection is possible to within the resolution allowed by the receiver RF bandwidth (Fooshe [B33]).

10.4 Phase retrieval methods All near-field techniques require precise knowledge of amplitude and phase data at some specified distance and frequency on a prescribed surface; usually amplitude measurements are not critical when compared to the equivalent phase measurement. This is because, when dealing with higher frequencies, phase is prone to a higher degree of error. In some situations phase information is quite unreliable either because the equipment is not adequate to perform a high-frequency measurement (sometimes at a frequency above 100 GHz) or due to a complete lack of phase-measurement hardware. A conventional near-field range requires a stable source with the reference and signal path lengths to be as stable as possible. Problems also arise due to cable flexing (Tuovinen, Lehto, and Raisanen [B115]) at these high frequencies. Another major source of errors is probe-positioning errors. These errors will manifest themselves in the far-field radiation pattern in proportion to the size of error in the measured near-field region (Corey and Joy [B22]). While methods exist to correct for probe-position errors (Agrawal [B1], Joy [B63], Joy and Wilson [B69], Wittmann, Alpert, and Francis [B121], [B122]), the possibility of utilizing amplitude-only data is an appealing alternative. In general, phase retrieval addresses these problems by inferring phase information from amplitude data only. These methods become even more important when approaching higher frequencies (Anderson, Junkin, and McCormack [B2], Bucci et al. [B11]). Phase retrieval was first encountered in applied physics such as optics, astronomy, crystallography, and microscopy in the early 1970s (Gerchberg and Saxton [B41], Misell [B88]). Application of phase retrieval to radio frequency engineering problems commenced at the end of the 1980s with the measurement of millimeter-wave radio telescopes (Hills and Lasenby [B53], Morris et al. [B89]), where the aperture phase was inferred from the measurement of two amplitude patterns. In the mid-1980s, research was initiated to apply phase retrieval techniques to antenna measurement related problems based on work that was carried out previously in optical physics. Anderson and Sali [B3] proposed to apply existing iterative methods, which were at the time employed in optical physics, and compared them with a new algorithm named plane-to-plane (PTP) phase retrieval. This iterative procedure is described in detail in Anderson and Sali [B3] and Rizzo [B105].

10.5 Back projections The back projection or transform is simply a transformation from the far-field pattern toward the source (the transmitting antenna). It is useful in determining faults on large antenna apertures and radomes and providing amplitude and phase distribution diagnostics on phased-array antennas (MacReynolds et al. [B86]).

10.5.1 Planar Evanescent modes, which may dominate in the region of interest, cannot be accurately determined at the measurement plane. These modes are exponentially attenuated away from the source so if the separation between the probe and AUT is more than 5 λ, these modes are usually below the noise floor. Therefore, when we transform back toward the source, we set the evanescent spectrum to zero. Thus, the backtransformed field is not the actual field, but it still contains useful information on scales greater than a wavelength. 80




10.5.2 Non-planar Methods for back transforms for spherical near field have been explored by Edward Joy and his students at the Georgia Institute of Technology [B46], [B64], [B66], [B70]. These techniques show promise for evaluating radome performance. In principle, back transformation is possible in the cylindrical geometry as well.

10.6 Probe-position correction Central to any near-to-far-field transformation is the ability to solve the linear system

Aξ = b ,

(75)

where ξ is a vector of N parameters that are required to accurately specify the radiated field of the test antenna. The Hermitian matrix A is known, as is the vector b that is determined from the measurements. The system of Equations (75) can be solved in O( N ³) operations using, say, Gaussian elimination; however 4 6 with problem sizes in the range 10 < N < 10 , computational efficiency is an important consideration. The traditional near-field-to-far-field transformation algorithms obtain better efficiencies by using data collected on regular grids on the measurement surfaces. Mechanical scanners capable of positioning a probe accurately enough (typically to within λ/50 or better) may become prohibitively costly as frequencies of operation increase. Unavoidable discrepancies between the actual and desired positions (probe-position errors) can result in significant uncertainties in measured test-antenna parameters. Instead of building ever more precise scanners, probe-position-correction algorithms can be applied whenever it is feasible to collect accurate actual probe-position data. Commercially available three-axis laser interferometers, built into near-field scanners, can determine actual measurement positions accurately; however, such interferometric systems are expensive and complicated. On the other hand, laser trackers, while not inexpensive, are portable and versatile devices that have many other uses both within and outside of the near-field laboratory. Perhaps the simplest and most widely used form of probe-position correction is termed k -correction (Agrawal [B1], Joy [B63], Joy and Wilson [B69]). This technique multiplies the data, point by point, by the phase factor

exp ( −ik 0 ⋅ δri ) ,

(76)

where k 0 is the direction of the main beam and δri is the position error at the ith measurement location. In general, k -correction gives “good” results; however, the method is approximate and it is difficult to characterize the associated uncertainty. Other approaches to probe-position correction (Corey [B21], Corey and Joy [B23], Muth [B90], Muth and Lewis [B91], Wittmann, Alpert, and Francis [B121], [B122]) solve the system of Equation (75) directly by iteratively refining an initial estimate for ξ. The conjugate gradient algorithm, an excellent choice, will always converge when A is nonsingular and will converge rapidly when A is well conditioned. (On the other hand, the convergence of certain perturbation techniques cannot be guaranteed.) Computational 3/2 complexities, per iteration, of O( N log N ) (planar) and O( N ) (spherical) have been demonstrated in 81




Wittmann, Alpert, and Francis [B121], [B122]. The number of iterations needed depends on the condition number of A, which is typically independent of N . Residual positioning uncertainties depend on the accuracy of the position-measuring device. The ability to account for the actual probe position can a)

extend the frequency range of existing scanners

b)

allow the use of light-weight, portable scanners for in situ measurements

c)

facilitate the processing of data collected on “nonstandard” grids (plane-polar, for example).

10.7 Truncation mitigation Scanning over a partial or truncated plane, sphere, or cylinder leads to two types of errors. The first is due to the fact that not all the energy has been intercepted, which results in portions of the far field for which there is no valid data. The second is due to the discontinuous nature of the data at the edge of the scan, which causes ringing in the near-to-far-field transform that may propagate into a region of interest. A number of methods have been explored to mitigate these errors (Bucci and Migliore [B19], Joy and Rose [B68], Rousseau [B106], Wittmann, Stubenrauch, and Francis [B124]. Joy and Rose [B68] and Rousseau [B106] smoothly extend the data to reduce the ringing effects. Wittmann, Stubenrauch, and Francis [B124] use an estimate of directivity to regularize the problem. Bucci and Migliore [B19] uses a priori information on the test antenna and reduced sampling outside of the truncated scan area. Although these methods have demonstrated some success, none has gained wide acceptance.

10.8 Time gating in near-field antenna measurements Gated time domain techniques have been in use for years in many RCS and far-field measurement installations. Time gating techniques can be extended to near-field antenna measurement systems, thereby offering the potential to improve measurement quality. Time gating can be implemented in either hardware or software. The AUT should support the bandwidth needed to implement the desired time gating. Time gating offers advantages in the mitigation of several terms in Newell’s 18-term error analysis [B93] including: probe-AUT multiple reflections, room scattering, and leakage. It is necessary to study the signal paths to determine the bandwidt h necessary to separate the desirabl e from undesirable signals ( Aubin et al. [B5], Winebrand and Aubin [B119], Winebrand, Soerens, and Aubin [B120]). Care needs to be taken so that desired signals are not excluded. For example, if the AUT is larger than the probe-AUT separation distance, probe-AUT multiple reflections cannot be separated from the desired signal.

11. Summary This document provides a description of the recommended practice for making near-field measurements. The document covers the three usual near-field geometries of planar, cylindrical, and spherical, a description of the calibration of near-field probes that are used as the reference antenna in the measurement, and a section discussing several special topics related to near-field measurements.

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Annex A (informative) Bibliography Bibliographical references are resources that provide additional or helpful material but do not need to be understood or used to implement this standard. Reference to these resources is made for informational use only. [B1] Agrawal, P. K., “A method to compensate for probe positioning errors in an antenna near field facility,” Proceedings of IEEE Antennas Propagation Society International Symposium , Albuquerque, NM, 5, 6 pp. 218–221, May 1982. [B2] Anderson, A. P., Junkin, G., and McCormack, J. E., “Phase retrieval enhancement of antenna metrology data,” Electronic Letters , vol. 24, no. 19, pp. 1243–1244, Sept. 1988. [B3] Anderson, A. P., and Sali, S., “New possibilities for phaseless microwave diagnostics. Part 1: Error reduction techniques,” IEE Proceedings, vol. 132, pt. H, no. 5, pp. 291–298, Aug. 1985. [B4] Appel-Hansen, J., “On cylindrical near-field scanning techniques,” IEEE Transactions on Antennas and Propagation, vol. AP-28, no. 2, pp. 231–234, Mar. 1980. [B5] Aubin, J., Winebrand, M., Soerens, R., and Vinogradov, V., “Accurate near-field measurements using time-gating,” Antenna Measurement Techniques Association Annual Symposium Proceedings, pp. 362– 365, Nov. 2007. [B6] Baird, R. C., Newell, A. C., and Stubenrauch, C. F., “A brief history of near-field measurements of antennas at the National Bureau of Standards,” IEEE Transactions on Antennas and Propagation, vol. AP36, pp. 727–733, June 1988. [B7] Balanis, C. A., Advanced Engineering Electromagnetrics. New York, NY: John Wiley & Sons, 1989. [B8] Bolomey, J. C., and Gardiol, F. E., Engineering Applications of the Modulated Scatterer Technique. Boston. MA: Artech House, 2001. [B9] Borgiotti, G. V., “Integral equation formulation for probe corrected far-field reconstruction from measurements on a cylinder,” IEEE Transactions on Antennas and Propagation, vol. AP-26, pp. 572–578, July 1978. [B10] Brown, J., and Jull, E. V., “The prediction of aerial radiation patterns from near-field measurements,” Proceedings of the IEE—Part B: Electronic and Communication Engineering, vol. 108, no. 42, pp. 635–644, Nov. 1961. [B11] Bucci, O. M., D’Elia, G., Leone, G., and Pierri, R., “Far-field pattern determination from the nearfield amplitude on two surfaces,” IEEE Transactions on Antennas and Propagation, vol. 38, no. 11, pp. 1772–1779, Nov. 1990. [B12] Bucci, O. M., and Franceschetti, G., “On the spatial bandwidth of scattered fields,” IEEE Transactions on Antennas and Propagation, vol. AP-35, pp. 1445–1455, Dec. 1987. [B13] Bucci, O. M., and Gennarelli, C., “Use of sampling expansions in near-field-far-field transformations: the cylindrical case,” IEEE Transactions on Antennas and Propagation, vol. AP-36, pp. 830–835, June 1988.

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