Principles and Applications of Vector Network Analyzer Calibration Techniques

Description

This book summarizes the work developed over more than two decades in the field of advanced calibration techniques for vector network analyzers, by the RF and Microwave Group at The Center for Scientific Research and Higher Education of Ensenada, Baja California, Mexico, which is led by Dr. J. Apolinar Reynoso-Hernández, author of this book. This book is written so that every electrical engineer, with knowledge of electrical circuits and linear algebra basics, can understand the principles of VNA calibration techniques. Vector network analyzers are normally used by engineers and researchers working in the RF and microwave field, which usually requires advanced and specialized courses at graduate level. The reader should be able to implement any VNA calibration technique, decide the most adequate calibration for a given measurement condition, and interpret the measurement results, as a seasoned RF metrology expert. Principles and Applications of Vector Network Analyzer Calibration Techniques is a useful book for beginners and professionals working on: Microwave de-embedding and test fixture characterizationCharacterization of uniform transmission linesLoad-pull measurements It is also: An ideal tutorial for professionals and postgraduate/research stu-dents taking courses in microwave calibration techniquesA useful textbook for practicing electronics engineering and researchers working in the RF microwave field: calibration techniques and load-pull measurements Cover Page Half Title page Series page Title Page Copyright Page Dedication Contents Foreword Preface Acknowledgements List of Figures List of Tables List of Abbreviations 1 Fundamentals 1.1 Introduction 1.2 Scattering Parameters 1.3 Wave-cascading Transmission Parameters 1.4 Voltage-Current Transmission Parameters 1.5 S-parameters Measurements 1.6 Large-signal Measurement Systems 2 Error Models for Vector Network Analyzers 2.1 Three-Terms Error Model 2.2 Twelve-Terms Error Model 2.3 Switching Errors 2.3.1 Forward measurement 2.3.2 Reverse measurement 2.3.3 Procedure I 2.3.4 Procedure II 2.3.5 Application examples 2.4 Eight-Terms Error Model 3 Microwave De-embedding 3.1 Introduction 3.2 The General De-embedding Method 3.2.1 The test fixture model 3.3 The Vector Network Analyzer Model 3.4 The Classical De-embedding Method 3.5 The Straightforward De-embedding Method [45], [70] 3.5.1 Coaxial devices (Lref = Lx = 0) 3.5.2 Devices mounted in test fixtures (Lref = 2Lx) 3.5.3 On-wafer calibration: calibration at the end of the probe's tip (Lx = 0; Lref ≠ 0 ) 3.6 Computation of a m c m , b m using the L-L Method (Two Uniform Lines) 3.7 Computation of am/cm and bm using the Line-Match (L-M) Method 3.7.1 Line measurement 3.7.2 Load measurements 3.8 Computation of am/cm and bm using the Thru-Attenuator (T-A) Method 3.9 Calculation of am 4 VNA Calibration Techniques 4.1 Introduction 4.2 ABCD-Parameters Representation of a Transmission Line 4.3 Measurement of Calibration Structures 4.3.1 Measurement of a transmission line Measurement of a thru: 4.3.2 Measurement of a pair of loads Measurement of a load at port 1: Measurement of a load at port 2: Measurement of a pair of reflecting loads: 4.4 The TRL Calibration Technique using Lines of Arbitrary Impedance 4.5 Generalized Theory of the TRM Calibration Technique 4.6 The TRRM Calibration Technique 4.7 The LZZ Calibration Technique 4.8 The LZZM Calibration Technique 4.9 The OSMT Calibration Technique 4.10 Sensitivity of Device Characterization Due to Uncertainty on Calibration Structures 5 Transmission Line Impedance Characterization Methods 5.1 The L-L Method to Calculate the Line's Characteristic Impedance of a Uniform Transmission Line [67] 5.2 Procedure I: Calculation of Characteristic Impedance Using Both the Partial Knowledge of T X Matrix and Line Propagation Constant γ 5.2.1 Calculation of A X ˜ C X ˜ , B X ˜ and the propagation constant γ [74] 5.3 Procedure II: Method to Calculate the Line's Characteristic Impedance [98], [99] 5.4 Method to Calculate the Line's Characteristic Impedance Using Calibration Comparison [67] 5.5 Method to Calculate the Line's Characteristic Impedance Using an Uncalibrated Vector Network Analyzer [75] 6 Load-pull Characterization of Power Transistors 6.1 Passive Load-pull Systems 6.2 Active Load-pull Systems 6.2.1 Open-loop load-pull systems 6.2.2 Feedforward load-pull systems 6.2.3 Closed-loop load-pull systems 6.3 Power-based Calibrated vs Vector-Receiver Load-pull Systems 6.4 Calibration of a VRLP System 6.4.1 Relative calibration 6.4.2 Power calibration 6.5 Implementation of a Vector-Receiver LP Measurement System 6.5.1 Load-pull contours of constant power, efficiency, and gain 6.5.2 Large-signal gain under optimal loading condition 6.6 Evaluation of the Impact of Calibration Techniques on the LP Characterization of Microwave Transistors 6.6.1 The impact of assuming the line/load used as calibration structures as a non-reflecting element 6.6.2 The impact of assuming the load used in the TRM calibration as a symmetrical element 6.6.3 The impact of knowing the impedance of the line used in the TRL on the LP characterization of power transistors A Diagonalization of the Matrix Representation of a Uniform Transmission Line A.1 Diagonalization of the ABCD-parameters Matrix Representation of a Uniform Transmission Line A.2 Diagonalization of the T-parameters Matrix of a Uniform Transmission Line Bibliography Index About the Authors