Preface |
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1 Introduction |
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1.1 The phenomena of antenna coupling |
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1.2 Characterisation via the measurement process |
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1.2.1 Free space radiation pattern |
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1.3 The organisation of the book |
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2 Maxwell's equations and electromagnetic wave propagation |
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2.5 The electric and magnetic potentials |
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2.5.2 Retarded potentials |
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2.6 The inapplicability of source excitation as a measurement methodology |
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2.7 Field equivalence principle |
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2.8 Characterising vector EM fields |
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3 Introduction to near-field antenna measurements |
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3.3 Forms of near-field antenna measurements |
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3.4 Plane rectilinear near-field antenna measurements |
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3.5 Chambers, screening and absorber |
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3.7 Robotics positioner subsystem |
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3.9 Generic antenna measurement process |
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4 Plane wave spectrum representation of electromagnetic waves |
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4.2 Overview of the derivation of the PWS |
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4.3 Solution of the scalar Helmholtz equation in Cartesian coordinates |
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4.3.1 Introduction to integral transforms |
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4.3.2 Fourier transform solution of the scalar Helmholtz equation |
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4.4 On the choice of boundary conditions |
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4.5 Operator substitution (derivative of a Fourier transform) |
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4.6 Solution of the vector Helmholtz equation in Cartesian coordinates |
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4.7 Solution of the vector magnetic wave equation in Cartesian coordinates |
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4.8 The relationship between electric and magnetic spectral components |
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4.9 The free-space propagation vector k |
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4.10 Plane wave impedance |
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4.11 Interpretation as an angular spectrum of plane waves |
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4.12 Far-field antenna radiation patterns: approximated by the angular spectrum |
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4.13 Stationary phase evaluation of a double integral |
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4.14 Coordinate free fonn of the near-field to angular spectrum transform |
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4.15 Reduction of the coordinate free form of the near-field to far-field transform to Huygens' principle |
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4.16 Far-fields from non-planar apertures |
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4.17 Microwave holographic metrology (plane-to-plane transform) |
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4.18 Far-field to near-field transform |
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4.19 Radiated power and the angular spectrum |
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4.20 Summary of conventional near-field to far-field transform |
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5 Measurements – practicalities of planar near-field antenna measurements |
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5.2 Sampling (interpolation theory) |
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5.3 Truncation, spectral leakage and finite area scan errors |
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5.4 Antenna-to-antenna coupling (transmission) formula |
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5.4.1 Attenuation of evanescent plane wave mode coefficients |
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5.4.2 Simple scattering model of a near-field probe during a planar measurement |
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5.5 Evaluation of the conventional near-field to far-field transform |
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5.5.1 Standard techniques for the evaluation of a double Fourier integral |
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5.6 General antenna coupling formula: arbitrarily orientated antennas |
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5.7 Plane-polar and plane-bipolar near-field to far-field transform |
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5.7.1 Boundary values known in plane-polar coordinates |
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5.7.2 Boundary values known in plane-bipolar coordinates |
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5.8 Regular azimuth over elevation and elevation over azimuth coordinate systems |
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5.9 Polarisation basis and antenna measurements |
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5.9.1 Cartesian polarisation basis – Ludwig I |
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5.9.2 Polar spherical polarisation basis |
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5.9.3 Azimuth over elevation basis – Ludwig II |
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5.9.4 Copolar and cross-polar polarisation basis – Ludwig III |
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5.9.5 Circular polarisation basis – RHCP and LHCP |
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5.10 Overview of antenna alignment corrections |
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5.10.1 Scalar rotation of far-field antenna patterns |
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5.10.2 Vector rotation of far-field antenna patterns |
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5.10.4 Rotation of copolar polarisation basis – generalized Ludwig III |
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5.10.5 Generalized compound vector rotation of far-field antenna patterns |
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5.11 Brief description of near-field coordinate systems |
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5.11.1 Range fixed system |
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5.11.2 Antenna mechanical system |
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5.11.3 Antenna electrical system |
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5.11.4 Far-field azimuth and elevation coordinates |
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5.11.5 Ludwig III copolar and cross-polar definition |
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5.11.6 Probe alignment definition (SPP) |
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5.11.7 General vector rotation of antenna radiation patterns |
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5.12 Directivity and gain |
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5.12.2 Gain – by substitution method |
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5.12.3 Gain-transfer (gain-comparison) method |
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5.13 Calculating the peak of a pattern |
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5.13.1 Peak by polynomial fit |
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6 Probe pattern characterisation |
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6.2 Effect of the probe pattern on far-field data |
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6.3 Desirable characteristics of a near-field probe |
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6.4 Acquisition of quasi far-field probe pattern |
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6.4.2 Electronic system drift (tie-scan correction) |
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6.4.3 Channel-balance correction |
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6.4.4 Assessment of chamber multiple reflections |
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6.4.5 Correction for rotary errors |
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6.4.6 Re-tabulation of probe vector pattern function |
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6.4.7 Alternate interpolation formula |
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6.4.8 True far-field probe pattern |
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6.5 Finite element model of open-ended rectangular waveguide probe |
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6.6 Probe displacement correction |
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6.7 Channel-balance correction |
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7 Computational electromagnetic model of a planar near-field measurement process |
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7.2 Method of sub-apertures |
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7.3 Aperture set in an infinite perfectly conducting ground plane |
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7.3.1 Plane wave spectrum antenna–antenna coupling formula |
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7.4 Vector Huygens' method |
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7.5 Kirchhoff–Huygens' method |
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7.6 Generalized technique for the simulation of near-field antenna measurements |
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7.6.1 Mutual coupling and the reaction theorem |
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7.7 Near-field measurement simulation |
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7.8.1 Lorentz reciprocity theorem (field reciprocity theorem) |
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7.8.2 Generalized reaction theorem |
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7.8.3 Mutual impedance and the reaction theorem |
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8 Antenna measurement analysis and assessment |
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8.2 The establishment of the measure from the measurement results |
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8.2.2 The sources of measurement ambiguity and error |
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8.2.3 The examination of measurement result data to establish the measure |
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8.3 Measurement error budgets |
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8.3.1 Applicability of modelling error sources |
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8.3.2 The empirical approach to error budgets |
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8.4 Quantitative measures of correspondence between data sets |
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8.4.1 The requirement for measures of correspondence |
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8.5 Comparison techniques |
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8.5.1 Examples of conventional data set comparison techniques |
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8.5.2 Novel data comparison techniques |
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9 Advanced planar near-field antenna measurements |
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9.2 Active alignment correction |
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9.2.1 Acquisition of alignment data in a planar near-field facility |
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9.2.2 Acquisition of mechanical alignment data in a planar near-field facility |
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9.2.3 Example of the application of active alignment correction |
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9.3 Amplitude only planar near-field measurements |
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9.3.1 PTP phase retrieval algorithm |
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9.3.2 PTP phase retrieval algorithm — with aperture constraint |
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9.4 Efficient position correction algorithms, in-plane and z—plane corrections |
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9.4.1 Taylor series expansion |
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9.4.2 K-correction method |
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9.5 Partial scan techniques |
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9.5.1 Auxiliary translation |
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9.5.2 Rotations of the AUT about the z-axis |
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9.5.3 Auxiliary rotation – bi-planar near-field antenna measurements |
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9.5.4 Near-field to far-field transformation of probe corrected data |
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9.5.5 Applicability of the poly-planar technique |
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9.5.6 Complete poly-planar rotational technique |
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Appendix A: Other theories of interaction |
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A.1 Examples of postulated mechanisms of interaction |
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Appendix B: Measurement definitions as used in the text |
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Appendix C: An overview of coordinate systems |
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C.1 Antenna mechanical system (AMS) |
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C.2 Antenna electrical system (AES) |
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C.3 Far-field plotting systems |
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C.5 Azimuth over elevation |
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C.6 Elevation over azimuth |
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C.8 Azimuth and elevation (true-view) |
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C.9 Range of spherical angles |
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C.10 Transformation between coordinate systems |
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C.11 Coordinate systems and elemental solid angles |
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C.12 Relationship between coordinate systems |
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C.13 Azimuth, elevation and Roll angles |
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C.16 Elemental solid angle for a true-view coordinate system |
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Appendix D: Trapezoidal discrete Fourier transform |
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Appendix E: Calculating the semi-major axis, semi-minor axis and tilt angle of a rotated ellipse |
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Index |
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