SPHERICAL NEAR-FIELD ANTENNA MEASUREMENTS

Transcription

1 SPHERICAL NEAR-FIELD ANTENNA MEASUREMENTS Edited by J.E.Hansen Peter Peregrinus Ltd. on behalf of the Institution of Electrical Engineers

2 Contents Contributing authors listed Preface v xiii 1 Introduction Background Introduction Brief outline of antenna testing Spherical near-field testing Organization of (this) book 4 References 6 2 Scattering matrix description of an antenna Introduction Spherical waves Introduction Power-normalized spherical waves The spherical waveguide Power flow The antenna scattering matrix Definitions Reciprocity The field from electric and magnetic dipoles Scattering matrices for electric and magnetic dipoles Remarks on the definition of antenna scattering matrices Antenna parameters expressed by spherical waves Far-field patterns Polarization Directivity and gain Maximum directivity 55 References 59 3 Scattering matrix description of antenna coupling Introduction The transmission formula Geometry Test antenna transmitting, probe receiving 63

3 w/7 Contents Test antenna receiving, probe transmitting Reciprocal and non-reciprocal test antennas Iterative scheme for probe calibration Special cases of the transmission formula Linearly polarized probe with u,= ± The Hertzian dipole as a probe Friis' transmission formula The transmission formula with multiple reflections included 82 References 87 Data reduction in spherical near-field mesaurements Introduction Measurement without probe correction Introduction General case Measurement of the radial field components Measurement of two tangential field components Wood's method Measurement with probe correction Introduction Analytical Solution of the transmission formula Discrete Solution of the transmission formula Field transformations and radiated fields Outline of a spherical near-field transformation algorithm Introduction Summary of the theory underlying a transformation algorithm On the number of sample points Block diagram of a transformation algorithm A simple example A test case Review of spherical near-field transformations 140 References 145 Measurements Introduction Probes for near-field scanning Introduction Rotationally Symmetrie probes Polarization correction Polarization calibration Pattern calibration Probe-corrected measurements Introduction The spherical near-field test ränge Basic measurement procedures Measurement examples Determination of gain Introduction Gain calibration of horns Gain determination by Substitution 210 References 214

4 Contents ix 6 Error analysis of spherical near-field measurements Introduction Near-field measurements Mechanical inaccuracies Receiver inaccuracies Probe correction Truncation Introduction Polar truncation Equatorial truncation Repetition and overlay of truncated fields Evaluation of measurements Conclusion 252 References Plane-wave synthesis Introduction Spherical near-field far-field transformation as a plane-wave synthesis method Basic concepts in generation of plane-wave fields Introduction Equivalence principle Relationship to a scattering problem Truncation and sampling of continuous sources of plane waves The Sheffield method Introduction Measurement without probe correction Measurement with probe correction Figures of merit for plane-wave deviation Introduction General figures of merit for plane-wave deviation Spherical test zone geometry Measurement error upper bounds Numerical optimization methods for plane-wave synthesis Introduction Arbitrary array and test zone geometry Ring sources and spherical test zones 291 References 310 Appendices AI Spherical wave functions, notation and properties 312 ALI Notation 312 AI. 1.1 The general spherical wave expansion 312 AI. 1.2 Single index Convention 313 AI.1.3 Representation of far fields 314 AI.2 Elementary functions 314 AI.2.1 Radial functions 314 AI.2.2 Angular functions 318 A1.3 Wave functions 325 AI.3.1 The spherical wave functions 325 AI.3.2 The far-field pattern functions 328

5 x Contents A1.4 Orthogonality of spherical wave function 330 AI.4.1 Product of radial components 330 AI.4.2 Products of tangential components 330 A Scalar product 331 AI.4.4 Vector product 331 A Reciprocity integral 331 AI.5 Calculation of spherical wave coefficients from current distributions 332 AI.5.1 General formulation 332 Al.5.2 Source symmetries 334 AI.5.3 The continuous x-polarized current ring 336 AI.5.4 The sampled x-polarized planar current ring 337 AI.5.5 Ring of currents tangential to a sphere 339 A1.6 The plane wave 341 AI.7 Relations between spherical and rectangular coordinates 341 A Coordinate transformations 341 A Scalar products of unit vectors 342 A Behaviour of certain vector distributions at 9 = 0 and 9 = n 342 References 342 A2 Rotation of spherical waves 343 A2.1 Euler angles 343 A2.2 Notation 343 A2.3 The rotation coefficient 345 A2.4 Thedeltas ' 347 A2.5 On the computation of rotation coefficients 350 A2.5.1 Stability of three-term recurrences 350 A2.5.2 Stability of delta recurrences 350 A2.6 Tables of low-order deltas 352 References 354 A3 Translation of spherical waves 355 A3.1 Notation 355 A3.2 The translation coefficient 356 References 360 A4 Data processing in antenna measurements 361 A4.1 Introduction 361 A4.2 The discrete Fourier transform 362 A4.2.1 Definitions 362 A4.2.2 Some discrete Fourier transform pairs 364 A4.3 Reconstruction of periodic functions 364 A4.3.1 Introduction 364 A4.3.2 Quasi-band-limited case 365 A4.3.3 Band-limited case with 2N -I-1 coefficients 367 A4.4 Special case of reconstruction 369 A4.4.1 Introduction 369 A4.4.2 Shifting of sample points 369 A4.4.3 Increased resolution 370 A4.4.4 Suppresion of noise 371 A4.4.5 Decreased resolution 371 A4.5 Numerical integration of periodic, band-limited functions 372

6 Contents xi A4.5.1 General case 372 A4.5.2 A special case 372 References 373 A5 List of principal Symbols and uses 374 Index 377