Magdalena Salazar-Palma - Modern Characterization of Electromagnetic Systems and its Associated Metrology

1 Cover

2 Title Page

3 Copyright Page

4 Preface

5 Acknowledgments

6 Tribute to Tapan K. Sarkar by Magdalena Salazar Palma, Ming Da Zhu, and Heng Chen

7 1 Mathematical Principles Related to Modern System AnalysisSummary 1.1 Introduction 1.2 Reduced‐Rank Modelling: Bias Versus Variance Tradeoff 1.3 An Introduction to Singular Value Decomposition (SVD) and the Theory of Total Least Squares (TLS) 1.4 Conclusion References

8 2 Matrix Pencil Method (MPM)Summary 2.1 Introduction 2.2 Development of the Matrix Pencil Method for Noise Contaminated Data 2.3 Applications of the MPM for Evaluation of the Characteristic Impedance of a Transmission Line 2.4 Application of MPM for the Computation of the S‐Parameters Without any A Priori Knowledge of the Characteristic Impedance 2.5 Improving the Resolution of Network Analyzer Measurements Using MPM 2.6 Minimization of Multipath Effects Using MPM in Antenna Measurements Performed in Non‐Anechoic Environments 2.7 Application of the MPM for a Single Estimate of the SEM‐Poles When Utilizing Waveforms from Multiple Look Directions 2.8 Direction of Arrival (DOA) Estimation Along with Their Frequency of Operation Using MPM 2.9 Efficient Computation of the Oscillatory Functional Variation in the Tails of the Sommerfeld Integrals Using MPM 2.10 Identification of Multiple Objects Operating in Free Space Through Their SEM Pole Locations Using MPM 2.11 Other Miscellaneous Applications of MPM 2.12 Conclusion Appendix 2A Computer Codes for Implementing MPM References

9 3 The Cauchy MethodSummary 3.1 Introduction 3.2 Procedure for Interpolating or Extrapolating the System Response Using the Cauchy Method 3.3 Examples to Estimate the System Response Using the Cauchy Method 3.4 Illustration of Extrapolation by the Cauchy Method 3.5 Effect of Noise Contaminating the Data and Its Impact on the Performance of the Cauchy Method 3.6 Generating High Resolution Wideband Response from Sparse and Incomplete Amplitude‐Only Data 3.7 Generation of the Non‐minimum Phase Response from Amplitude‐Only Data Using the Cauchy Method 3.8 Development of an Adaptive Cauchy Method 3.9 Efficient Characterization of a Filter 3.10 Extraction of Resonant Frequencies of an Object from Frequency Domain Data 3.11 Conclusion Appendix 3A MATLAB Codes for the Cauchy Method References

10 4 Applications of the Hilbert Transform – A Nonparametric Method for Interpolation/Extrapolation of DataSummary 4.1 Introduction 4.2 Consequence of Causality and Its Relationship to the Hilbert Transform 4.3 Properties of the Hilbert Transform 4.4 Relationship Between the Hilbert and the Fourier Transforms for the Analog and the Discrete Cases 4.5 Methodology to Extrapolate/Interpolate Data in the Frequency Domain Using a Nonparametric Methodology 4.6 Interpolating Missing Data 4.7 Application of the Hilbert Transform for Efficient Computation of the Spectrum for Nonuniformly Spaced Data 4.8 Conclusion References

11 5 The Source Reconstruction MethodSummary 5.1 Introduction 5.2 An Overview of the Source Reconstruction Method (SRM) 5.3 Mathematical Formulation for the Integral Equations 5.4 Near‐Field to Far‐Field Transformation Using an Equivalent Magnetic Current Approach 5.5 Near‐Field to Near/Far‐Field Transformation for Arbitrary Near‐Field Geometry Utilizing an Equivalent Electric Current 5.6 Evaluating Near‐Field Radiation Patterns of Commercial Antennas 5.7 Conclusions References

12 6 Planar Near‐Field to Far‐Field Transformation Using a Single Moving Probe and a Fixed Probe ArraysSummary 6.1 Introduction 6.2 Theory 6.3 Integral Equation Formulation 6.4 Formulation of the Matrix Equation 6.5 Use of an Magnetic Dipole Array as Equivalent Sources 6.6 Sample Numerical Results 6.7 Summary 6.8 Differences between Conventional Modal Expansion and the Equivalent Source Method for Planar Near‐Field to Far‐Field Transformation 6.9 A Direct Optimization Approach for Source Reconstruction and NF‐FF Transformation Using Amplitude‐Only Data 6.10 Use of Computational Electromagnetics to Enhance the Accuracy and Efficiency of Antenna Pattern Measurements Using an Array of Dipole Probes 6.11 A Fast and Efficient Method for Determining the Far Field Patterns Along the Principal Planes Using a Rectangular Probe Array 6.12 The Influence of the Size of Square Dipole Probe Array Measurement on the Accuracy of NF‐FF Pattern 6.13 Use of a Fixed Probe Array Measuring Amplitude‐Only Near‐Field Data for Calculating the Far‐Field 6.14 Probe Correction for Use with Electrically Large Probes 6.15 Conclusions References

13 7 Spherical Near‐Field to Far‐Field TransformationSummary 7.1 An Analytical Spherical Near‐Field to Far‐Field Transformation 7.2 Radial Field Retrieval in Spherical Scanning for Current Reconstruction and NF–FF Transformation 7.3 Conclusion Appendix 7A A Fortran Based Computer Program for Transforming Spherical Near‐Field to Far‐Field References

14 8 Deconvolving Measured Electromagnetic ResponsesSummary 8.1 Introduction 8.2 The Conjugate Gradient Method with Fast Fourier Transform for Computational Efficiency 8.3 Total Least Squares Approach Utilizing Singular Value Decomposition 8.4 Conclusion References

15 9 Performance of Different Functionals for Interpolation/Extrapolation of Near/Far‐Field DataSummary 9.1 Background 9.2 Approximating a Frequency Domain Response by Chebyshev Polynomials 9.3 The Cauchy Method Based on Gegenbauer Polynomials 9.4 Near‐Field to Far‐Field Transformation of a Zenith‐Directed Parabolic Reflector Using the Ordinary Cauchy Method 9.5 Near‐Field to Far‐Field Transformation of a Rotated Parabolic Reflector Using the Ordinary Cauchy Method 9.6 Near‐Field to Far‐Field Transformation of a Zenith‐Directed Parabolic Reflector Using the Matrix Pencil Method 9.7 Near‐Field to Far‐Field Transformation of a Rotated Parabolic Reflector Using the Matrix Pencil Method 9.8 Conclusion References

16 10 Retrieval of Free Space Radiation Patterns from Measured Data in a Non‐Anechoic EnvironmentSummary 10.1 Problem Background 10.2 Review of Pattern Reconstruction Methodologies 10.3 Deconvolution Method for Radiation Pattern Reconstruction 10.4 Effect of Different Types of Probe Antennas 10.5 Effect of Different Antenna Size 10.6 Effect of Using Different Sizes of PEC Plates 10.7 Extension of the Deconvolution Method to Three‐Dimensional Pattern Reconstruction 10.8 Conclusion Appendix A: Data Mapping Using the Conversion between the Spherical Coordinate System and the Cartesian Coordinate System Appendix B: Description of the 2D‐FFT during the Data Processing References

17 Index

18 End User License Agreement

1 Chapter 1 Table 1.1 List of all the singular values of the matrix A.

2 Chapter 2 Table 2.1 Percentage Errors occurring in the estimates using the MPM for nois... Table 2.2 Calculated Impulse Response of a Beatty standard terminated with 50... Table 2.3 Calculated Impulse Response of a Beatty standard terminated with a ... Table 2.4 The error levels obtained for the processed results using both tech... Table 2.5 Summary of the Signal Parameters Incident on the Antenna Array.Table 2.6 Actual vs. Estimated Target Coordinates (Two Spheres).Table 2.7 Actual vs. Estimated Target Coordinates (a Cone and a Wire).

3 Chapter 3Table 3.1 Computational Load Calculation.Table 3.2 E‐Plane Filter: Low‐Pass Polynomial Coefficients.Table 3.3 Microstrip Filter: Narrow‐Band Model Polynomial Coefficients.Table 3.4 Pole Library of the Six PEC Objects.

4 Chapter 5Table 5.1 Maximum emission levels for human exposure to EM fields, as regulat...

5 Chapter 6Table 6.1 Input impedance of the test antenna as a function of the number of ...

6 Chapter 7Table 7.1 Nominal Values of 2‐D EMC Distribution.