Principles of Planar Near-Field Antenna Measurements

Description

Cover Contents About the authors List of abbreviations Foreword Preface 1 Introduction 1.1 The phenomena of antenna coupling 1.2 Characterisation via the measurement process 1.2.1 Free space radiation pattern 1.2.2 Polarisation 1.2.3 Bandwidth 1.3 Assumed (suppressed) time dependency 1.4 The organisation of the book References 2 Maxwell’s equations and electromagnetic wave propagation 2.1 Electric charge 2.2 The electromagnetic field 2.3 Accelerated charges 2.4 Maxwell’s equations 2.5 The electric and magnetic potentials 2.5.1 Static potentials 2.5.2 Retarded potentials 2.6 The inapplicability of source excitation as a measurement methodology 2.7 Field equivalence principle 2.8 Characterising vector electromagnetic fields 2.9 Summary References 3 Introduction to near-field antenna measurements 3.1 Introduction 3.2 Antenna measurements 3.3 Forms of near-field antenna measurements 3.4 Plane rectilinear near-field antenna measurements 3.5 Chambers, screening and absorber 3.6 RF subsystem 3.7 Robotics positioner subsystem 3.8 Near-field probe 3.9 Generic antenna measurement process 3.10 Summary References 4 Plane-wave spectrum representation of electromagnetic waves 4.1 Introduction 4.2 Overview of the derivation of the plane-wave spectrum 4.3 Solution of the scalar Helmholtz equation in Cartesian co-ordinates 4.3.1 Introduction to integral transforms 4.3.2 Fourier transform solution of the scalar Helmholtz equation 4.4 On the choice of boundary conditions 4.5 Operator substitution (derivative of a Fourier transform) 4.6 Solution of the vector Helmholtz equation in Cartesian co-ordinates 4.7 Solution of the vector magnetic wave equation in Cartesian co-ordinates 4.8 The relationship between electric and magnetic spectral components 4.9 The free space propagation vector 4.10 Plane-wave impedance 4.11 Interpretation as an angular spectrum of plane waves 4.12 Far-field antenna radiation patterns: approximated by the angular spectrum 4.13 Stationary phase evaluation of a double integral 4.14 Co-ordinate free form of the near-field to angular spectrum transform 4.15 Reduction of the co-ordinate free form of the nearfield to far-field transform to Huygens’ principle 4.16 Far-fields from non-planar apertures 4.17 Microwave holographic metrology (plane-to-plane transform) 4.18 Far-field to near-field transform 4.19 Radiated power and the angular spectrum 4.20 Summary of conventional near-field to far-field transform References 5 Measurements – practicalities of planar near-field antenna measurements 5.1 Introduction 5.2 Sampling (interpolation theory) 5.3 Truncation, spectral leakage, and finite area scan errors 5.4 Antenna-to-antenna coupling (transmission) formula 5.4.1 Behaviour of evanescent plane wave mode coefficients 5.4.2 Simple scattering model of a near-field probe during a planar measurement 5.5 Effect of acquiring near-field data using an electric dipole probe 5.6 Rotationally symmetric, polarised, near-field probe 5.7 Evaluation of the conventional near-field to far-field transform 5.7.1 Standard techniques for the evaluation of a double Fourier integral 5.8 General antenna coupling formula: arbitrarily orientated antennas 5.9 Plane-polar and plane bi-polar near-field to far-field transform 5.9.1 Boundary values known in plane polar co-ordinates 5.9.2 Boundary values known in plane bi-polar co-ordinates 5.10 Regular azimuth over elevation & elevation over azimuth co-ordinate systems 5.11 Polarisation basis and antenna measurements 5.11.1 Cartesian polarisation basis – Ludwig I 5.11.2 Polar spherical polarisation basis 5.11.3 Azimuth over elevation basis – Ludwig II 5.11.4 Copolar and cross-polar polarisation basis – Ludwig III 5.11.5 Circular polarisation basis – RHCP and LHCP 5.12 Linear and circular polarisation bases – complex vector representations 5.13 Overview of antenna alignment corrections 5.13.1 Scalar rotation of far-field antenna patterns 5.13.2 Vector rotation of far-field antenna patterns 5.13.3 Rotation of copolar polarisation basis – generalised Ludwig III 5.13.4 Generalised compound vector rotation of far-field antenna patterns 5.14 Brief description of near-field co-ordinate systems 5.14.1 Range fixed system (RFS) 5.14.2 Antenna mechanical system 5.14.3 Antenna electrical system 5.14.4 Far-field azimuth and elevation co-ordinates 5.14.5 Ludwig III co-polar and cross-polar definition 5.14.6 Probe alignment definition (single port probe) 5.14.7 General vector rotation of antenna radiation patterns 5.15 Directivity & gain 5.15.1 Directivity 5.15.2 Calculating the power radiated in a direction-cosine coordinate system 5.15.3 Direct evaluation of directivity for a uniformly illuminated square aperture 5.15.4 Gain 5.15.5 Gain-transfer (gain-comparison) method 5.15.6 Approximation of the gain of a rectangular pyramidal horn 5.16 Calculating the peak of a pattern 5.16.1 Peak by series solution 5.16.2 Peak by polynomial fit 5.16.3 Peak by centroid 5.17 Estimating the position of a phase centre from far-field data 5.18 Summary References 6 Probe pattern characterisation 6.1 Introduction 6.2 Effect of the probe pattern on far-field data 6.3 Desirable characteristics of a near-field probe 6.3.1 Open-ended rectangular waveguide probes 6.3.2 Dual-polarised waveguide probes 6.3.3 Broadband probes 6.3.4 Other less commonly encountered types of near-field probes – dipoles 6.4 Acquisition of quasi far-field probe pattern 6.4.1 Sampling scheme 6.4.2 Electronic system drift (Tie-scan correction) 6.4.3 Channel balance correction 6.4.4 Assessment of chamber multiple reflections 6.4.5 Correction for rotary errors Box 6.1. AAPC – circumscribing three non-linear points on a plane 6.4.6 Remote source antenna tilt-angle correction 6.4.7 Re-tabulation of probe vector pattern function 6.4.8 Alternate interpolation formula 6.4.9 Approximate unwrapping of two-dimensional phase functions 6.4.10 True far-field probe pattern 6.5 Finite element model of open ended rectangular waveguide probe 6.6 Probe displacement correction 6.7 Channel balance correction References 7 Computational electromagnetic model of a planar near-field measurement process 7.1 Introduction 7.2 Linear superposition of electric dipoles 7.3 Method of sub-apertures 7.4 Aperture set in an infinite perfectly conducting ground plane 7.4.1 Plane wave spectrum antenna–antenna coupling formula 7.5 Vector Huygens method 7.6 Kirchhoff–Huygens method 7.7 Current elements method 7.8 Equivalent currents method – near-field to far-field transform, antenna diagnostics, and range reflection suppression 7.9 Generalised technique for the simulation of near-field antenna measurements 7.9.1 Mutual coupling and the reaction theorem 7.10 Near-field measurement simulation 7.11 Reaction theorem 7.11.1 Lorentz reciprocity theorem (field reciprocity theorem) 7.11.2 Generalised Reaction theorem 7.11.3 Mutual impedance and the Reaction theorem 7.12 Full wave simulation of a planar near-field antenna measurement 7.13 Summary References 8 Antenna measurement analysis and assessment 8.1 Introduction 8.2 The establishment of the measure from the measurement results 8.2.1 Measurement errors 8.2.2 The sources of measurement ambiguity and error 8.2.3 The examination of measurement result data to establish the measure 8.3 Measurement error budgets 8.3.1 Applicability of modelling error sources 8.3.2 The empirical approach to error budgets 8.3.3 Applicability of the digital twin to assessing error budgets 8.3.4 Truncation 8.3.5 Numerical truncation and rounding error 8.3.6 Probe x,y (in-plane) position error 8.3.7 Aliasing (data point spacing) 8.3.8 Systematic phase, e.g. drift 8.3.9 Dynamic range 8.3.10 Summary 8.4 Illustration of the compilation of range assessment budgets 8.5 Quantitative measures of correspondence between data sets 8.5.1 The requirement for measures of correspondence 8.6 Comparison techniques 8.6.1 Examples of conventional data set comparison techniques 8.6.2 Novel data comparison techniques 8.7 Summary References 9 Advanced planar near-field antenna measurements 9.1 Introduction 9.2 Active alignment correction 9.2.1 Acquisition of alignment data in a planar near-field facility 9.2.2 Acquisition of mechanical alignment data in a planar near-field facility 9.2.3 Example of the application of active alignment correction 9.3 Amplitude only planar near-field measurements 9.3.1 Plane-to-plane phase retrieval algorithm 9.3.2 Plane-to-plane phase retrieval algorithm – with aperture constraint 9.4 Non-iterative phase retrieval technique 9.4.1 Current phase retrieval techniques 9.4.2 AUT phase and probe position reconstruction from four or more reference antenna phase measurements 9.4.3 Simulation of the measurement system 9.5 Traditional position correction algorithms, in plane and z plane corrections 9.5.1 Taylor-series expansion 9.5.2 K-Correction method 9.6 Non-canonical transforms, plane wave spectrumbased treatment 9.6.1 Matrix inversion method – solution of a system of equations 9.6.2 Non-uniform FFT-based algorithms 9.6.3 Non-canonical transform 9.7 Compressive sensing 9.7.1 Introduction to compressive sensing 9.7.2 Defective element detection using compressive sensing 9.7.3 Compressive sensing applied to a 2D array 9.7.4 Practical implementation 9.7.5 Compressive sensing using near-field scanning 9.7.6 Summary of compressing sensing technique 9.8 Three antenna extrapolated gain measurements 9.9 Partial scan techniques 9.9.1 Auxiliary translation 9.9.2 Rotations of the AUT about the z-axis 9.9.3 Auxiliary rotation – bi-planar near-field antenna measurements 9.9.4 Near-field to far-field transformation of probe-corrected data 9.9.5 Applicability of the poly-planar technique 9.9.6 Complete poly-planar rotational technique 9.10 Concluding remarks References Appendices A.1 Appendix A: Other theories of interaction A.1.1 Examples of postulated mechanisms of interaction A.2 Appendix B: Measurement definitions as used in the text A.3 Appendix C: An overview of co-ordinate systems A.3.1 Antenna mechanical system A.3.2 Antenna electrical system A.3.3 Far-field plotting systems A.3.4 Direction cosine A.3.5 Azimuth over elevation A.3.6 Elevation over azimuth A.3.7 Polar spherical A.3.8 Azimuth and elevation (true-view) A.3.9 Range of spherical angles A.3.10 Transformation between co-ordinate systems A.3.11 Co-ordinate systems and elemental solid angles A.3.12 Relationship between co-ordinate systems A.3.13 Azimuth, elevation and roll angles A.3.14 Euler angles A.3.15 Quaternion A.3.16 Elemental solid angle for a true-view co-ordinate system A.4 Appendix D: Trapezoidal discrete Fourier transform A.5 Appendix E: Calculating the semi-major axis, semiminor axis and tilt angle of a rotated ellipse A.6 Appendix F: Fast Fourier transform algorithm A.7 Appendix G: Asymptotic far-field form of the Kirchhoff–Huygens formula References Index Back Cover