Principles of Planar Near-Field Antenna Measurements. Stuart Gregson, John McCormick and Clive Parini. The Institution of Engineering and Technology

Transcription

1 Principles of Planar Near-Field Antenna Measurements Stuart Gregson, John McCormick and Clive Parini The Institution of Engineering and Technology

2 Contents Preface xi 1 Introduction The phenomena of antenna coupling Characterisation via the measurement process Free space radiation pattern Polarisation Bandwidth The organisation of the book References 12 2 Maxwell's equations and electromagnetic wave propagation Electric charge The EM field Accelerated charges Maxwell's equations The electric and magnetic potentials Static potentials Retarded potentials The inapplicability of source excitation as a measurement methodology Field equivalence principle Characterising vector EM fields Summary References 33 3 Introduction to near-field antenna measurements Introduction Antenna measurements 35

3 vi Principles of planar near-field antenna measurements 3.3 Forms of near-field antenna measurements Plane rectilinear near-field antenna measurements Chambers, screening and absorber RF subsystem Robotics positioner subsystem Near-field probe Generic antenna measurement process Summary References 60 Plane wave spectrum representation of electromagnetic waves Introduction Overview of the derivation of the P WS Solution of the scalar Helmholtz equation in Cartesian coordinates Introduction to integral transforms Fourier transform solution of the scalar Helmholtz equation On the choice of boundary conditions Operator substitution (derivative of a Fourier transform) Solution of the vector Helmholtz equation in Cartesian coordinates Solution of the vector magnetic wave equation in Cartesian coordinates The relationship between electric and magnetic spectral components The free-space propagation vector k_ Plane wave impedance Interpretation as an angular spectrum of plane waves Far-field antenna radiation patterns: approximated by the angular spectrum Stationary phase evaluation of a double integral Coordinate free form of the near-field to angular spectrum transform Reduction of the coordinate free form of the near-field to far-field transform to Huygens' principle Far-fields from non-planar apertures Microwave holographic metrology (plane-to-plane transform) Far-field to near-field transform Radiated power and the angular spectrum Summary of conventional near-field to far-field transform References 117

4 List of contents vn Measurements - practicalities of planar near-field antenna measurements Introduction Sampling (interpolation theory) Truncation, spectral leakage and finite area scan errors Antenna-to-antenna coupling (transmission) formula Attenuation of evanescent plane wave mode coefficients Simple scattering model of a near-field probe during a planar measurement Evaluation of the conventional near-field to far-field transform Standard techniques for the evaluation of a double Fourier integral General antenna coupling formula: arbitrarily orientated antennas Plane-polar and plane-bipolar near-field to far-field transform Boundary values known in plane-polar coordinates Boundary values known in plane-bipolar coordinates Regular azimuth over elevation and elevation over azimuth coordinate systems Polarisation basis and antenna measurements Cartesian polarisation basis - Ludwig I Polar spherical polarisation basis Azimuth over elevation basis - Ludwig II Copolar and cross-polar polarisation basis - Ludwig III Circular polarisation basis - RHCP and LHCP Overview of antenna alignment corrections Scalar rotation of far-field antenna patterns Vector rotation of far-field antenna patterns Rotation of copolar polarisation basis - generalized Ludwig III Generalized compound vector rotation of far-field antenna patterns Brief description of near-field coordinate systems Range fixed system Antenna mechanical system Antenna electrical system Far-field azimuth and elevation coordinates Ludwig III copolar and cross-polar definition Probe alignment definition (SPP) General vector rotation of antenna radiation patterns 179

5 viii Principles of planar near-field antenna measurements 5.12 Directivity and gain Directivity Gain - by substitution method Gain-transfer (gain-comparison) method Calculating the peak of a pattern Peak by polynomial fit Peak by centroid Summary References 187 Probe pattern characterisation Introduction Effect of the probe pattern on far-field data Desirable characteristics of a near-field probe Acquisition of quasi far-field probe pattern Sampling scheme Electronic system drift (tie-scan correction) Channel-balance correction Assessment of chamber multiple reflections Correction for rotary errors Re-tabulation of probe vector pattern function Alternate interpolation formula True far-field probe pattern Finite element model of open-ended rectangular waveguide probe Probe displacement correction Channel-balance correction References 218 Computational electromagnetic model of a planar near-field measurement process Introduction Method of sub-apertures Aperture set in an infinite perfectly conducting ground plane Plane wave spectrum antenna-antenna coupling formula Vector Huygens'method Kirchhoff-Huygens' method Generalized technique for the simulation of near-field antenna measurements Mutual coupling and the reaction theorem Near-field measurement simulation Reaction theorem Lorentz reciprocity theorem (field reciprocity theorem) 240

6 List of contents ix Generalized reaction theorem Mutual impedance and the reaction theorem Summary References Antenna measurement analysis and assessment Introduction The establishment of the measure from the measurement results Measurement errors The sources of measurement ambiguity and error The examination of measurement result data to establish the measure Measurement error budgets Applicability of modelling error sources The empirical approach to error budgets Quantitative measures of correspondence between data sets The requirement for measures of correspondence Comparison techniques Examples of conventional data set comparison techniques Novel data comparison techniques Summary References Advanced planar near-field antenna measurements Introduction Active alignment correction Acquisition of alignment data in a planar near-field facility Acquisition of mechanical alignment data in a planar near-field facility Example of the application of active alignment correction Amplitude only planar near-field measurements PTP phase retrieval algorithm PTP phase retrieval algorithm - with aperture constraint Efficient position correction algorithms, in-plane and z plane corrections Taylor series expansion AT-correction method Partial scan techniques Auxiliary translation Rotations of the ATJT about the z-axis 319

7 x Principles of planar near-field antenna measurements Auxiliary rotation - bi-planar near-field antenna measurements Near-field to far-field transformation of probe corrected data Applicability of the poly-planar technique Complete poly-planar rotational technique Concluding remarks References 344 Appendix A: Other theories of interaction 347 A.l 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.l Antenna mechanical system (AMS) 357 C.2 Antenna electrical system (AES) 357 C.3 Far-field plotting systems 358 C.4 Direction cosine 358 С 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 CIO Transformation between coordinate systems 366 С11 Coordinate systems and elemental solid angles 367 С12 Relationship between coordinate systems 368 C.13 Azimuth, elevation and Roll angles 371 С14 Euler angles 373 С. 15 Quaternion 374 С. 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