Principles of Planar Near-Field Antenna Measurements 介绍天线近场测量的基础知识 Contents Preface xi 1 Introduction 1 1.1 The phenomena of antenna coupling 1 1.2 Characterisation via the measurement process 4 1.2.1 Free space radiation pattern 6 1.2.2 Polarisation 7 1.2.3 Bandwidth 8 1.3 The organisation of the book 11 1.4 References 12 2 Maxwell’s equations and electromagnetic wave propagation 13 2.1 Electric charge 13 2.2 The EM field 14 2.3 Accelerated charges 16 2.4 Maxwell’s equations 18 2.5 The electric and magnetic potentials 24 2.5.1 Static potentials 24 2.5.2 Retarded potentials 24 2.6 The inapplicability of source excitation as a measurement methodology 28 2.7 Field equivalence principle 28 2.8 Characterising vector EM fields 30 2.9 Summary 33 2.10 References 33 3 Introduction to near-field antenna measurements 35 3.1 Introduction 35 3.2 Antenna measurements 35 3.3 Forms of near-field antenna measurements 40 3.4 Plane rectilinear near-field antenna measurements 43 3.5 Chambers, screening and absorber 44 3.6 RF subsystem 47 3.7 Robotics positioner subsystem 52 3.8 Near-field probe 56 3.9 Generic antenna measurement process 58 3.10 Summary 60 3.11 References 60 4 Plane wave spectrum representation of electromagnetic waves 63 4.1 Introduction 63 4.2 Overview of the derivation of the PWS 64 4.3 Solution of the scalar Helmholtz equation in Cartesian coordinates 65 4.3.1 Introduction to integral transforms 65 4.3.2 Fourier transform solution of the scalar Helmholtz equation 65 4.4 On the choice of boundary conditions 78 4.5 Operator substitution (derivative of a Fourier transform) 79 4.6 Solution of the vector Helmholtz equation in Cartesian coordinates 81 4.7 Solution of the vector magnetic wave equation in Cartesian coordinates 83 4.8 The relationship between electric and magnetic spectral components 84 4.9 The free-space propagation vector k 87 4.10 Plane wave impedance 88 4.11 Interpretation as an angular spectrum of plane waves 90 4.12 Far-field antenna radiation patterns: approximated by the angular spectrum 92 4.13 Stationary phase evaluation of a double integral 95 4.14 Coordinate free form of the near-field to angular spectrum transform 101 4.15 Reduction of the coordinate free form of the near-field to far-field transform to Huygens’ principle 104 4.16 Far-fields from non-planar apertures 106 4.17 Microwave holographic metrology (plane-to-plane transform) 107 4.18 Far-field to near-field transform 108 4.19 Radiated power and the angular spectrum 112 4.20 Summary of conventional near-field to far-field transform 115 4.21 References 117 5 Measurements – practicalities of planar near-field antenna measurements 119 5.1 Introduction 119 5.2 Sampling (interpolation theory) 120 5.3 Truncation, spectral leakage and finite area scan errors 121 5.4 Antenna-to-antenna coupling (transmission) formula 125 5.4.1 Attenuation of evanescent plane wave mode coefficients 136 5.4.2 Simple scattering model of a near-field probe during a planar measurement 137 5.5 Evaluation of the conventional near-field to far-field transform 138 5.5.1 Standard techniques for the evaluation of a double Fourier integral 139 5.6 General antenna coupling formula: arbitrarily orientated antennas 143 5.7 Plane-polar and plane-bipolar near-field to far-field transform 148 5.7.1 Boundary values known in plane-polar coordinates 150 5.7.2 Boundary values known in plane-bipolar coordinates 151 5.8 Regular azimuth over elevation and elevation over azimuth coordinate systems 156 5.9 Polarisation basis and antenna measurements 159 5.9.1 Cartesian polarisation basis – Ludwig I 159 5.9.2 Polar spherical polarisation basis 160 5.9.3 Azimuth over elevation basis – Ludwig II 161 5.9.4 Copolar and cross-polar polarisation basis – Ludwig III 163 5.9.5 Circular polarisation basis – RHCP and LHCP 165 5.10 Overview of antenna alignment corrections 169 5.10.1 Scalar rotation of far-field antenna patterns 169 5.10.2 Vector rotation of far-field antenna patterns 171 5.10.4 Rotation of copolar polarisation basis – generalized Ludwig III 173 5.10.5 Generalized compound vector rotation of far-field antenna patterns 174 5.11 Brief description of near-field coordinate systems 175 5.11.1 Range fixed system 176 5.11.2 Antenna mechanical system 177 5.11.3 Antenna electrical system 178 5.11.4 Far-field azimuth and elevation coordinates 178 5.11.5 Ludwig III copolar and cross-polar definition 178 5.11.6 Probe alignment definition (SPP) 178 5.11.7 General vector rotation of antenna radiation patterns 179 5.12 Directivity and gain 180 5.12.1 Directivity 180 5.12.2 Gain – by substitution method 181 5.12.3 Gain-transfer (gain-comparison) method 182 5.13 Calculating the peak of a pattern 183 5.13.1 Peak by polynomial fit 183 5.13.2 Peak by centroid 185 5.14 Summary 186 5.15 References 187 6Pr obe pattern characterisation 189 6.1 Introduction 189 6.2 Effect of the probe pattern on far-field data 189 6.3 Desirable characteristics of a near-field probe 191 6.4 Acquisition of quasi far-field probe pattern 193 6.4.1 Sampling scheme 194 6.4.2 Electronic system drift (tie-scan correction) 197 6.4.3 Channel-balance correction 198 6.4.4 Assessment of chamber multiple reflections 200 6.4.5 Correction for rotary errors 202 6.4.6 Re-tabulation of probe vector pattern function 205 6.4.7 Alternate interpolation formula 209 6.4.8 True far-field probe pattern 211 6.5 Finite element model of open-ended rectangular waveguide probe 213 6.6 Probe displacement correction 217 6.7 Channel-balance correction 217 6.8 References 218 7 Computational electromagnetic model of a planar near-field measurement process 219 7.1 Introduction 219 7.2 Method of sub-apertures 220 7.3 Aperture set in an infinite perfectly conducting ground plane 223 7.3.1 Plane wave spectrum antenna–antenna coupling formula 225 7.4 Vector Huygens’ method 227 7.5 Kirchhoff–Huygens’ method 229 7.6 Generalized technique for the simulation of near-field antenna measurements 233 7.6.1 Mutual coupling and the reaction theorem 234 7.7 Near-field measurement simulation 237 7.8 Reaction theorem 239 7.8.1 Lorentz reciprocity theorem (field reciprocity theorem) 240 7.8.2 Generalized reaction theorem 244 7.8.3 Mutual impedance and the reaction theorem 247 7.9 Summary 247 7.10 References 248 8 Antenna measurement analysis and assessment 249 8.1 Introduction 249 8.2 The establishment of the measure from the measurement results 249 8.2.1 Measurement errors 250 8.2.2 The sources of measurement ambiguity and error 253 8.2.3 The examination of measurement result data to establish the measure 256 8.3 Measurement error budgets 259 8.3.1 Applicability of modelling error sources 259 8.3.2 The empirical approach to error budgets 260 8.4 Quantitative measures of correspondence between data sets 261 8.4.1 The requirement for measures of correspondence 261 8.5 Comparison techniques 263 8.5.1 Examples of conventional data set comparison techniques 263 8.5.2 Novel data comparison techniques 267 8.6 Summary 282 8.7 References 283 9 Advanced planar near-field antenna measurements 285 9.1 Introduction 285 9.2 Active alignment correction 285 9.2.1 Acquisition of alignment data in a planar near-field facility 287 9.2.2 Acquisition of mechanical alignment data in a planar near-field facility 289 9.2.3 Example of the application of active alignment correction 291 9.3 Amplitude only planar near-field measurements 296 9.3.1 PTP phase retrieval algorithm 297 9.3.2 PTP phase retrieval algorithm – with aperture constraint 301 9.4 Efficient position correction algorithms, in-plane and z−plane corrections 303 9.4.1 Taylor series expansion 305 9.4.2 K-correction method 311 9.5 Partial scan techniques 315 9.5.1 Auxiliary translation 315 9.5.2 Rotations of the AUT about the z-axis 319 9.5.3 Auxiliary rotation – bi-planar near-field antenna measurements 320 9.5.4 Near-field to far-field transformation of probe corrected data 329 9.5.5 Applicability of the poly-planar technique 335 9.5.6 Complete poly-planar rotational technique 338 9.6 Concluding remarks 342 9.7 References 344 Appendix A: Other theories of interaction 347 A.1 Examples of postulated mechanisms of interaction 347 Appendix B: Measurement definitions as used in the text 354 Appendix C: An overview of coordinate systems 357 C.1 Antenna mechanical system (AMS) 357 C.2 Antenna electrical system (AES) 357 C.3 Far-field plotting systems 358 C.4 Direction cosine 358 C.5 Azimuth over elevation 360 C.6 Elevation over azimuth 361 C.7 Polar spherical 362 C.8 Azimuth and elevation (true-view) 364 C.9 Range of spherical angles 365 C.10 Transformation between coordinate systems 366 C.11 Coordinate systems and elemental solid angles 367 C.12 Relationship between coordinate systems 368 C.13 Azimuth, elevation and Roll angles 371 C.14 Euler angles 373 C.15 Quaternion 374 C.16 Elemental solid angle for a true-view coordinate system 377 Appendix D: Trapezoidal discrete Fourier transform 380 Appendix E: Calculating the semi-major axis, semi-minor axis and tilt angle of a rotated ellipse 384 Index 389

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