Theory and Practice of Modern Antenna Range Measurements, Volume 1

Cover
Contents
Volume 2
About the authors
List of Abbreviations
Foreword to volumes 1 and 2
Preface to volumes 1 and 2
8 Spherical near-field antenna measurements
	8.1 Introduction
	8.2 Types of SNF ranges
	8.3 A solution to Maxwell’s equations in spherical coordinates
	8.4 Relating spherical mode coefficients to SNF data
	8.5 Sampling requirements and spherical mode truncation
	8.6 Development of the transmission formula
	8.7 Near-field probe correction
	8.8 Far-field expressions
	8.9 Practical acquisition schemes and examples
	8.10 Radial distance correction
	8.11 Summary
	References
9 Antenna field transformation from non-canonical surfaces
	9.1 Introduction
	9.2 Measurement configuration with non-canonical surfaces
	9.3 The reciprocity theorem
	9.4 Mathematical formulation of the Huygens principle and equivalence principles
	9.5 Forward transmission equation with probe correction
		9.5.1 Voltage-equivalent current formulation
		9.5.2 Spectral representation with propagating plane waves
		9.5.3 Gain normalised transmission equation
		9.5.4 Spatial and spectral probe representation
	9.6 Types and discretisation of equivalent sources for representing the AUT
		9.6.1 Surface current densities
		9.6.2 Surface current densities with Love condition
		9.6.3 Surface current densities with combined-source condition
		9.6.4 Sources in complex space
		9.6.5 Distributed spherical-wave or plane-wave expansion
	9.7 Equivalent source representations of the measurement probe
	9.8 Discretisation of the forward problem
		9.8.1 Discretisation of the transmission equations
		9.8.2 Discretisation of supplementary constraint equations
	9.9 Inversion of the discretised forward problem
	9.10 Rapid computation of the forward operator
		9.10.1 Single-level algorithm
		9.10.2 Multi-level algorithm
		9.10.3 Far-field translations
		9.10.4 Gaussian-beam translations
	9.11 Evaluation of constraint equations and adjoint operators
	9.12 Applications and evaluations
		9.12.1 Pyramidal horn antenna – synthetic measurement data
		9.12.2 Planar aperture antennas – synthetic measurement data
		9.12.3 Double-ridged waveguide antenna – spherical and multi-planar near-field measurements
		9.12.4 Parabolic reflector with defect – synthetic measurement data
		9.12.5 Satellite mock-up with Ku-band reflectors – synthetic measurement data
		9.12.6 Reflector antenna – irregular near-field measurements
	9.13 Antenna field transformations above ground
		9.13.1 Introduction
		9.13.2 Inverse equivalent source formulation above ground
		9.13.3 Post-processing of equivalent sources above different ground materials
		9.13.4 Field transformation results above ground – synthetic measurement data
	9.14 Summary
	References
10 Near-field range assessment
	10.1 Introduction
	10.2 A framework for measurement uncertainty
	10.3 The effects of unwanted signals on vector measurements
	10.4 The statistical nature of error signals
	10.5 Probe/illuminator-related errors
		10.5.1 Probe relative pattern
		10.5.2 Probe polarisation purity
		10.5.3 Probe alignment
	10.6 Mechanical/positioner-related errors
		10.6.1 AUT alignment
		10.6.2 PNF probe (x, y) position error
		10.6.3 PNF probe z-position (planarity) error
		10.6.4 CNF probe ρ-position error
		10.6.5 SNF (θ, ϕ, r) positioning uncertainty
		10.6.6 SNF axis non-orthogonality
		10.6.7 SNF axis (θ, ϕ) non-intersection error
	10.7 Absolute power level-related errors
		10.7.1 Gain standard uncertainty
		10.7.2 Normalisation constant
		10.7.3 Impedance mismatch
	10.8 Processing-related errors
		10.8.1 Aliasing
		10.8.2 Measurement area truncation
	10.9 RF sub-system related errors
		10.9.1 Receiver amplitude linearity
		10.9.2 Systematic phase
		10.9.3 Leakage
		10.9.4 Receiver dynamic range
	10.10 Environmental-related errors
		10.10.1 Probe structure reflection
		10.10.2 Chamber reflection
		10.10.3 Random errors
	10.11 Combining uncertainties
	10.12 Inter-range comparisons
	10.13 Summary
	References
11 Mobile and body-centric antenna measurements
	11.1 Introduction
	11.2 Indoor far-field antenna measurements
	11.3 Spherical near-field measurements
		11.3.1 Over-the-air measurements
	11.4 Low-gain antenna and S-parameter measurement methods
	11.5 Corruption by cables: the use of optical fibre links
	11.6 On-body measurements
	11.7 Efficiency measurement using Wheeler Cap
	11.8 UWB antenna measurements
		11.8.1 Return loss
		11.8.2 Radiation pattern
		11.8.3 UWB pseudo-time domain measurements
		11.8.4 Fidelity analysis
		11.8.5 True time domain measurements
		11.8.6 Mean gain
	11.9 Special facilities
		11.9.1 Over-the-air multipath environment simulation for MIMO testing
		11.9.2 Reverberation chamber measurements
	References
12 Advanced antenna measurement topics
	12.1 Introduction
	12.2 Common topics
		12.2.1 Probes and probe selection
			12.2.1.1 Open-ended rectangular waveguide probes
			12.2.1.2 Dual polarised circular waveguide probes
			12.2.1.3 Broadband probes
			12.2.1.4 Far-field anechoic chamber measurements
			12.2.1.5 Probe calibration
		12.2.2 Channel-balance correction for antenna measurements
			12.2.2.1 Channel balance correction for measurements of linearly polarised antennas
			12.2.2.2 Channel balance correction for measurement of circularly polarised antennas
		12.2.3 Aperture diagnostics
			12.2.3.1 Holographic diagnosis for scattering suppression
		12.2.4 Amplitude and phase drift correction: tie-scan correction
		12.2.5 Alignment correction (in PNF, CNF, and SNF)
			12.2.5.1 Overview of antenna pattern rotation
			12.2.5.2 Alignment correction in planar antenna measurements
		12.2.6 Simple semi-empirical model of an open-ended rectangular waveguide probe
		12.2.7 Introduction to range reflection suppression
			12.2.7.1 Conventional methods for suppressing range reflections
			12.2.7.2 Advanced antenna pattern correction
			12.2.7.3 Introduction to mathematical absorber reflection suppression
	12.3 PNF topics
		12.3.1 Bias leakage error
		12.3.2 Compensation for probe translation effects in dual polarised planar near-field antenna measurements
		12.3.3 Introduction to phase-less near-field antenna measurements
		12.3.4 Planar mathematical absorber reflection suppression
	12.4 CNF topics
		12.4.1 Cylindrical mathematical absorber reflection suppression
		12.4.2 Application of C-MARS to far-field and CATR measurements – FF-MARS
	12.5 SNF topics
		12.5.1 Spherical near-field electrical alignment
		12.5.2 The radial distance to MRS ratio
		12.5.3 Spherical mathematical absorber reflection suppression
			12.5.3.1 MARS with a stationary AUT and an articulated mm-wave spherical antenna test system
			12.5.3.2 Generalised far-field MARS – matrix inversion method
		12.5.4 Rotary joint wow correction for LP antennas
	12.6 Power parameter definitions and their measurement
		12.6.1 Directivity
		12.6.2 Gain
			12.6.2.1 Gain measurement
			12.6.2.2 Three-antenna gain method
		12.6.3 Equivalent isotropically radiated power (EIRP)
		12.6.4 Saturating flux density (SFD)
	12.7 Summary
		12.7.1 Summary of MARS
	References
13 Electromagnetic modelling of antenna measurement ranges
	13.1 Introduction
	13.2 Simulation of a compact antenna test range
		13.2.1 Point source CATR
		13.2.2 Illumination of the CATR reflector
		13.2.3 Calculation of the reflected electric field
		13.2.4 Calculation of the local surface unit normal and elemental surface area
		13.2.5 Electromagnetic field propagation
			13.2.5.1 Vector-Huygens method (plane-wave spectrum method)
			13.2.5.2 Kirchhoff–Huygens method
			13.2.5.3 Current element method
			13.2.5.4 Geometric optics method
		13.2.6 Comparison of CATR CEM simulation methods with full-wave simulations
		13.2.7 Assessment of CATR QZ predictions
		13.2.8 Inclusion of feed spill-over in CATR quiet-zone
		13.2.9 End-to-end simulation of CATR measurement process
		13.2.10 Effect of amplitude taper, amplitude ripple and phase ripple on CATR measurements
			13.2.10.1 Amplitude taper
			13.2.10.2 Amplitude ripple
			13.2.10.3 Phase ripple
			13.2.10.4 Spatial frequency of QZ ripple
			13.2.10.5 Combined specification and effect of AUT position in CATR QZ
		13.2.11 Use of CATR EM model to verify post-processing and error correction techniques
			13.2.11.1 CEM verification of scattering suppression with mode filtering
			13.2.11.2 CEM verification of amplitude and phase ripple suppression with mode filtering
		13.2.12 CEM verification of scattering suppression and feed spill-over with mode filtering
			13.2.12.1 Summary
	13.3 Full-wave three-dimensional CEM simulations
		13.3.1 Full-wave simulation of a PNF measurement z-cut
		13.3.2 Full-wave simulation of a PNF measurement xy-scan
		13.3.3 Simulation of a pyramidal standard gain horn
		13.3.4 Full-wave simulation of a spherical test system
	13.4 Simulation of a cylindrical near-field antenna test system
		13.4.1 CEM verification of scattering suppression with mode filtering
		13.4.2 CEM verification of improvement in signal-to-noise ratio
		13.4.3 CEM verification of suppression of second-order truncation effect
	13.5 Simulation of a spherical near-field antenna test system
		13.5.1 Polar mode spherical acquisition simulation with arbitrary probe
		13.5.2 Equatorial mode spherical acquisition simulation with an arbitrary probe
	13.6 Summary
	References
Appendix A
	A.1 IEEE standard letter designations for radar-frequency bands (Table A.1)
	A.2 Standard rectangular waveguide bands and selected properties (Table A.3)
	A.3 Care and use of microwave coaxial connectors
	A.4 Reflection coefficient, return loss, transmission loss as a function of VSWR
Index
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